1,1,121,92,11.449364,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{c^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(405\,\cos\left(e+f\,x\right)+495\,\cos\left(3\,e+3\,f\,x\right)+85\,\cos\left(5\,e+5\,f\,x\right)-5\,\cos\left(7\,e+7\,f\,x\right)+1100\,\sin\left(2\,e+2\,f\,x\right)-16\,\sin\left(4\,e+4\,f\,x\right)-36\,\sin\left(6\,e+6\,f\,x\right)\right)}{960\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(405*cos(e + f*x) + 495*cos(3*e + 3*f*x) + 85*cos(5*e + 5*f*x) - 5*cos(7*e + 7*f*x) + 1100*sin(2*e + 2*f*x) - 16*sin(4*e + 4*f*x) - 36*sin(6*e + 6*f*x)))/(960*f*(cos(2*e + 2*f*x) + 1))","B"
2,1,110,92,10.452626,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(20\,\cos\left(e+f\,x\right)+25\,\cos\left(3\,e+3\,f\,x\right)+5\,\cos\left(5\,e+5\,f\,x\right)+75\,\sin\left(2\,e+2\,f\,x\right)+4\,\sin\left(4\,e+4\,f\,x\right)-\sin\left(6\,e+6\,f\,x\right)\right)}{80\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(20*cos(e + f*x) + 25*cos(3*e + 3*f*x) + 5*cos(5*e + 5*f*x) + 75*sin(2*e + 2*f*x) + 4*sin(4*e + 4*f*x) - sin(6*e + 6*f*x)))/(80*f*(cos(2*e + 2*f*x) + 1))","B"
3,1,97,92,1.714219,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2),x)","\frac{c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(12\,\cos\left(e+f\,x\right)+15\,\cos\left(3\,e+3\,f\,x\right)+3\,\cos\left(5\,e+5\,f\,x\right)+80\,\sin\left(2\,e+2\,f\,x\right)+8\,\sin\left(4\,e+4\,f\,x\right)\right)}{96\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(12*cos(e + f*x) + 15*cos(3*e + 3*f*x) + 3*cos(5*e + 5*f*x) + 80*sin(2*e + 2*f*x) + 8*sin(4*e + 4*f*x)))/(96*f*(cos(2*e + 2*f*x) + 1))","B"
4,1,64,92,0.895414,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2),x)","\frac{\left(10\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(4\,e+4\,f\,x\right)\right)\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}}{12\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"((10*sin(2*e + 2*f*x) + sin(4*e + 4*f*x))*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2))/(12*f*(cos(2*e + 2*f*x) + 1))","B"
5,1,73,45,8.959375,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(1/2),x)","-\frac{\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(\cos\left(e+f\,x\right)+\cos\left(3\,e+3\,f\,x\right)-4\,\sin\left(2\,e+2\,f\,x\right)\right)}{4\,c\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(cos(e + f*x) + cos(3*e + 3*f*x) - 4*sin(2*e + 2*f*x)))/(4*c*f*(cos(2*e + 2*f*x) + 1))","B"
6,0,-1,99,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
7,0,-1,97,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
8,0,-1,48,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
9,1,319,140,12.429258,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{{\mathrm{e}}^{-e\,7{}\mathrm{i}-f\,x\,7{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{5\,a\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{16\,f}+\frac{a\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{8\,f}+\frac{a\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{48\,f}+\frac{19\,a\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{96\,f}+\frac{a\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}-\frac{a\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{224\,f}+\frac{45\,a\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*7i - f*x*7i)*(c - c*sin(e + f*x))^(1/2)*((5*a*c^3*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(16*f) + (a*c^3*exp(e*7i + f*x*7i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(8*f) + (a*c^3*exp(e*7i + f*x*7i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(48*f) + (19*a*c^3*exp(e*7i + f*x*7i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(96*f) + (a*c^3*exp(e*7i + f*x*7i)*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2))/(160*f) - (a*c^3*exp(e*7i + f*x*7i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(224*f) + (45*a*c^3*exp(e*7i + f*x*7i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f)))/(2*cos(e + f*x))","B"
10,1,122,140,11.444192,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{a\,c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(75\,\cos\left(e+f\,x\right)+105\,\cos\left(3\,e+3\,f\,x\right)+35\,\cos\left(5\,e+5\,f\,x\right)+5\,\cos\left(7\,e+7\,f\,x\right)+700\,\sin\left(2\,e+2\,f\,x\right)+112\,\sin\left(4\,e+4\,f\,x\right)+12\,\sin\left(6\,e+6\,f\,x\right)\right)}{960\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(a*c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(75*cos(e + f*x) + 105*cos(3*e + 3*f*x) + 35*cos(5*e + 5*f*x) + 5*cos(7*e + 7*f*x) + 700*sin(2*e + 2*f*x) + 112*sin(4*e + 4*f*x) + 12*sin(6*e + 6*f*x)))/(960*f*(cos(2*e + 2*f*x) + 1))","B"
11,1,79,140,1.476568,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2),x)","\frac{a\,c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(175\,\sin\left(2\,e+2\,f\,x\right)+28\,\sin\left(4\,e+4\,f\,x\right)+3\,\sin\left(6\,e+6\,f\,x\right)\right)}{240\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(a*c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(175*sin(2*e + 2*f*x) + 28*sin(4*e + 4*f*x) + 3*sin(6*e + 6*f*x)))/(240*f*(cos(2*e + 2*f*x) + 1))","B"
12,1,97,92,9.812636,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(12\,\cos\left(e+f\,x\right)+15\,\cos\left(3\,e+3\,f\,x\right)+3\,\cos\left(5\,e+5\,f\,x\right)-80\,\sin\left(2\,e+2\,f\,x\right)-8\,\sin\left(4\,e+4\,f\,x\right)\right)}{96\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(12*cos(e + f*x) + 15*cos(3*e + 3*f*x) + 3*cos(5*e + 5*f*x) - 80*sin(2*e + 2*f*x) - 8*sin(4*e + 4*f*x)))/(96*f*(cos(2*e + 2*f*x) + 1))","B"
13,1,87,45,9.398127,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(1/2),x)","-\frac{a\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(6\,\cos\left(e+f\,x\right)+6\,\cos\left(3\,e+3\,f\,x\right)-14\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(4\,e+4\,f\,x\right)\right)}{12\,c\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(6*cos(e + f*x) + 6*cos(3*e + 3*f*x) - 14*sin(2*e + 2*f*x) + sin(4*e + 4*f*x)))/(12*c*f*(cos(2*e + 2*f*x) + 1))","B"
14,0,-1,147,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
15,0,-1,144,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
16,0,-1,147,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
17,0,-1,48,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
18,1,236,97,13.867156,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(11/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{40\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^6\,f}-\frac{8\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^6\,f}+\frac{32\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^6\,f}\right)}{84\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}-54\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)+2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)-96\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)+16\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((40*a*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^(1/2))/(3*c^6*f) - (8*a*exp(e*5i + f*x*5i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(c^6*f) + (32*a*exp(e*5i + f*x*5i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(3*c^6*f)))/(84*cos(e + f*x)*exp(e*5i + f*x*5i) - 54*exp(e*5i + f*x*5i)*cos(3*e + 3*f*x) + 2*exp(e*5i + f*x*5i)*cos(5*e + 5*f*x) - 96*exp(e*5i + f*x*5i)*sin(2*e + 2*f*x) + 16*exp(e*5i + f*x*5i)*sin(4*e + 4*f*x))","B"
19,1,376,188,12.623477,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{{\mathrm{e}}^{-e\,8{}\mathrm{i}-f\,x\,8{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{35\,a^2\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{7\,a^2\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}+\frac{7\,a^2\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{128\,f}+\frac{a^2\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}+\frac{a^2\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(8\,e+8\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{512\,f}+\frac{7\,a^2\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{7\,a^2\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{a^2\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{224\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*8i - f*x*8i)*(c - c*sin(e + f*x))^(1/2)*((35*a^2*c^3*exp(e*8i + f*x*8i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (7*a^2*c^3*exp(e*8i + f*x*8i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) + (7*a^2*c^3*exp(e*8i + f*x*8i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(128*f) + (a^2*c^3*exp(e*8i + f*x*8i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) + (a^2*c^3*exp(e*8i + f*x*8i)*cos(8*e + 8*f*x)*(a + a*sin(e + f*x))^(1/2))/(512*f) + (7*a^2*c^3*exp(e*8i + f*x*8i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (7*a^2*c^3*exp(e*8i + f*x*8i)*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2))/(160*f) + (a^2*c^3*exp(e*8i + f*x*8i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(224*f)))/(2*cos(e + f*x))","B"
20,1,179,188,11.802134,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{\frac{1225\,a^2\,c^2\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{32}+\frac{245\,a^2\,c^2\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{32}+\frac{49\,a^2\,c^2\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{32}+\frac{5\,a^2\,c^2\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{32}}{70\,f\,\cos\left(e+f\,x\right)}","Not used",1,"((1225*a^2*c^2*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/32 + (245*a^2*c^2*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/32 + (49*a^2*c^2*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/32 + (5*a^2*c^2*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/32)/(70*f*cos(e + f*x))","B"
21,1,122,140,11.516543,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2),x)","-\frac{a^2\,c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(75\,\cos\left(e+f\,x\right)+105\,\cos\left(3\,e+3\,f\,x\right)+35\,\cos\left(5\,e+5\,f\,x\right)+5\,\cos\left(7\,e+7\,f\,x\right)-700\,\sin\left(2\,e+2\,f\,x\right)-112\,\sin\left(4\,e+4\,f\,x\right)-12\,\sin\left(6\,e+6\,f\,x\right)\right)}{960\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^2*c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(75*cos(e + f*x) + 105*cos(3*e + 3*f*x) + 35*cos(5*e + 5*f*x) + 5*cos(7*e + 7*f*x) - 700*sin(2*e + 2*f*x) - 112*sin(4*e + 4*f*x) - 12*sin(6*e + 6*f*x)))/(960*f*(cos(2*e + 2*f*x) + 1))","B"
22,1,108,92,2.409591,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(20\,\cos\left(e+f\,x\right)+25\,\cos\left(3\,e+3\,f\,x\right)+5\,\cos\left(5\,e+5\,f\,x\right)-75\,\sin\left(2\,e+2\,f\,x\right)-4\,\sin\left(4\,e+4\,f\,x\right)+\sin\left(6\,e+6\,f\,x\right)\right)}{80\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(20*cos(e + f*x) + 25*cos(3*e + 3*f*x) + 5*cos(5*e + 5*f*x) - 75*sin(2*e + 2*f*x) - 4*sin(4*e + 4*f*x) + sin(6*e + 6*f*x)))/(80*f*(cos(2*e + 2*f*x) + 1))","B"
23,1,102,45,1.875261,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(1/2),x)","-\frac{a^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(28\,\cos\left(e+f\,x\right)+27\,\cos\left(3\,e+3\,f\,x\right)-\cos\left(5\,e+5\,f\,x\right)-48\,\sin\left(2\,e+2\,f\,x\right)+8\,\sin\left(4\,e+4\,f\,x\right)\right)}{32\,c\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(28*cos(e + f*x) + 27*cos(3*e + 3*f*x) - cos(5*e + 5*f*x) - 48*sin(2*e + 2*f*x) + 8*sin(4*e + 4*f*x)))/(32*c*f*(cos(2*e + 2*f*x) + 1))","B"
24,0,-1,193,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
25,0,-1,192,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
26,0,-1,195,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
27,0,-1,193,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
28,0,-1,48,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(11/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(11/2), x)","F"
29,1,317,97,14.860496,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(13/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,112{}\mathrm{i}}{5\,c^7\,f}+\frac{a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,56{}\mathrm{i}}{c^7\,f}-\frac{a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,16{}\mathrm{i}}{c^7\,f}-\frac{a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,8{}\mathrm{i}}{c^7\,f}\right)}{\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,264{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)\,220{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)\,20{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)\,330{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)\,88{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)\,2{}\mathrm{i}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((a^2*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2)*112i)/(5*c^7*f) + (a^2*exp(e*6i + f*x*6i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*56i)/(c^7*f) - (a^2*exp(e*6i + f*x*6i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2)*16i)/(c^7*f) - (a^2*exp(e*6i + f*x*6i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2)*8i)/(c^7*f)))/(cos(e + f*x)*exp(e*6i + f*x*6i)*264i - exp(e*6i + f*x*6i)*cos(3*e + 3*f*x)*220i + exp(e*6i + f*x*6i)*cos(5*e + 5*f*x)*20i - exp(e*6i + f*x*6i)*sin(2*e + 2*f*x)*330i + exp(e*6i + f*x*6i)*sin(4*e + 4*f*x)*88i - exp(e*6i + f*x*6i)*sin(6*e + 6*f*x)*2i)","B"
30,1,462,236,13.533369,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(9/2),x)","\frac{{\mathrm{e}}^{-e\,10{}\mathrm{i}-f\,x\,10{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{63\,a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}+\frac{21\,a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{256\,f}+\frac{3\,a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}+\frac{9\,a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{512\,f}+\frac{a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\cos\left(8\,e+8\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{256\,f}+\frac{a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\cos\left(10\,e+10\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{2560\,f}+\frac{7\,a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{9\,a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{9\,a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{896\,f}+\frac{a^3\,c^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sin\left(9\,e+9\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{1152\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*10i - f*x*10i)*(c - c*sin(e + f*x))^(1/2)*((63*a^3*c^4*exp(e*10i + f*x*10i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) + (21*a^3*c^4*exp(e*10i + f*x*10i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(256*f) + (3*a^3*c^4*exp(e*10i + f*x*10i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) + (9*a^3*c^4*exp(e*10i + f*x*10i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(512*f) + (a^3*c^4*exp(e*10i + f*x*10i)*cos(8*e + 8*f*x)*(a + a*sin(e + f*x))^(1/2))/(256*f) + (a^3*c^4*exp(e*10i + f*x*10i)*cos(10*e + 10*f*x)*(a + a*sin(e + f*x))^(1/2))/(2560*f) + (7*a^3*c^4*exp(e*10i + f*x*10i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (9*a^3*c^4*exp(e*10i + f*x*10i)*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2))/(160*f) + (9*a^3*c^4*exp(e*10i + f*x*10i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(896*f) + (a^3*c^4*exp(e*10i + f*x*10i)*sin(9*e + 9*f*x)*(a + a*sin(e + f*x))^(1/2))/(1152*f)))/(2*cos(e + f*x))","B"
31,1,247,236,12.115488,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{{\mathrm{e}}^{-e\,9{}\mathrm{i}-f\,x\,9{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{63\,a^3\,c^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}+\frac{7\,a^3\,c^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{9\,a^3\,c^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{9\,a^3\,c^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{896\,f}+\frac{a^3\,c^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(9\,e+9\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{1152\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*9i - f*x*9i)*(c - c*sin(e + f*x))^(1/2)*((63*a^3*c^3*exp(e*9i + f*x*9i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) + (7*a^3*c^3*exp(e*9i + f*x*9i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (9*a^3*c^3*exp(e*9i + f*x*9i)*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2))/(160*f) + (9*a^3*c^3*exp(e*9i + f*x*9i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(896*f) + (a^3*c^3*exp(e*9i + f*x*9i)*sin(9*e + 9*f*x)*(a + a*sin(e + f*x))^(1/2))/(1152*f)))/(2*cos(e + f*x))","B"
32,1,376,188,12.547985,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{{\mathrm{e}}^{-e\,8{}\mathrm{i}-f\,x\,8{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{35\,a^3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}-\frac{7\,a^3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}-\frac{7\,a^3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{128\,f}-\frac{a^3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}-\frac{a^3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(8\,e+8\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{512\,f}+\frac{7\,a^3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{7\,a^3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{a^3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{224\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*8i - f*x*8i)*(c - c*sin(e + f*x))^(1/2)*((35*a^3*c^2*exp(e*8i + f*x*8i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) - (7*a^3*c^2*exp(e*8i + f*x*8i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) - (7*a^3*c^2*exp(e*8i + f*x*8i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(128*f) - (a^3*c^2*exp(e*8i + f*x*8i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) - (a^3*c^2*exp(e*8i + f*x*8i)*cos(8*e + 8*f*x)*(a + a*sin(e + f*x))^(1/2))/(512*f) + (7*a^3*c^2*exp(e*8i + f*x*8i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (7*a^3*c^2*exp(e*8i + f*x*8i)*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2))/(160*f) + (a^3*c^2*exp(e*8i + f*x*8i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(224*f)))/(2*cos(e + f*x))","B"
33,1,319,140,12.143958,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(3/2),x)","-\frac{{\mathrm{e}}^{-e\,7{}\mathrm{i}-f\,x\,7{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{5\,a^3\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{16\,f}+\frac{a^3\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{8\,f}+\frac{a^3\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{48\,f}-\frac{19\,a^3\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{96\,f}-\frac{a^3\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{a^3\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{224\,f}-\frac{45\,a^3\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"-(exp(- e*7i - f*x*7i)*(c - c*sin(e + f*x))^(1/2)*((5*a^3*c*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(16*f) + (a^3*c*exp(e*7i + f*x*7i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(8*f) + (a^3*c*exp(e*7i + f*x*7i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(48*f) - (19*a^3*c*exp(e*7i + f*x*7i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(96*f) - (a^3*c*exp(e*7i + f*x*7i)*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2))/(160*f) + (a^3*c*exp(e*7i + f*x*7i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(224*f) - (45*a^3*c*exp(e*7i + f*x*7i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f)))/(2*cos(e + f*x))","B"
34,1,121,92,11.485233,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(405\,\cos\left(e+f\,x\right)+495\,\cos\left(3\,e+3\,f\,x\right)+85\,\cos\left(5\,e+5\,f\,x\right)-5\,\cos\left(7\,e+7\,f\,x\right)-1100\,\sin\left(2\,e+2\,f\,x\right)+16\,\sin\left(4\,e+4\,f\,x\right)+36\,\sin\left(6\,e+6\,f\,x\right)\right)}{960\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(405*cos(e + f*x) + 495*cos(3*e + 3*f*x) + 85*cos(5*e + 5*f*x) - 5*cos(7*e + 7*f*x) - 1100*sin(2*e + 2*f*x) + 16*sin(4*e + 4*f*x) + 36*sin(6*e + 6*f*x)))/(960*f*(cos(2*e + 2*f*x) + 1))","B"
35,1,113,45,10.689940,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(1/2),x)","-\frac{a^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(120\,\cos\left(e+f\,x\right)+110\,\cos\left(3\,e+3\,f\,x\right)-10\,\cos\left(5\,e+5\,f\,x\right)-165\,\sin\left(2\,e+2\,f\,x\right)+44\,\sin\left(4\,e+4\,f\,x\right)-\sin\left(6\,e+6\,f\,x\right)\right)}{80\,c\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(120*cos(e + f*x) + 110*cos(3*e + 3*f*x) - 10*cos(5*e + 5*f*x) - 165*sin(2*e + 2*f*x) + 44*sin(4*e + 4*f*x) - sin(6*e + 6*f*x)))/(80*c*f*(cos(2*e + 2*f*x) + 1))","B"
36,0,-1,241,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
37,0,-1,238,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
38,0,-1,239,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
39,0,-1,241,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
40,0,-1,243,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(11/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(11/2), x)","F"
41,0,-1,48,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(13/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{13/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(13/2), x)","F"
42,1,373,97,14.412805,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(15/2),x)","-\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{504\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{5\,c^8\,f}+\frac{576\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{5\,c^8\,f}-\frac{96\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^8\,f}+\frac{8\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^8\,f}-\frac{64\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^8\,f}\right)}{-858\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}+858\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)-130\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)+2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(7\,e+7\,f\,x\right)+1144\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)-416\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)+24\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)}","Not used",1,"-((c - c*sin(e + f*x))^(1/2)*((504*a^3*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^(1/2))/(5*c^8*f) + (576*a^3*exp(e*7i + f*x*7i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(5*c^8*f) - (96*a^3*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(c^8*f) + (8*a^3*exp(e*7i + f*x*7i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(c^8*f) - (64*a^3*exp(e*7i + f*x*7i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(3*c^8*f)))/(858*exp(e*7i + f*x*7i)*cos(3*e + 3*f*x) - 858*cos(e + f*x)*exp(e*7i + f*x*7i) - 130*exp(e*7i + f*x*7i)*cos(5*e + 5*f*x) + 2*exp(e*7i + f*x*7i)*cos(7*e + 7*f*x) + 1144*exp(e*7i + f*x*7i)*sin(2*e + 2*f*x) - 416*exp(e*7i + f*x*7i)*sin(4*e + 4*f*x) + 24*exp(e*7i + f*x*7i)*sin(6*e + 6*f*x))","B"
43,1,764,145,14.929383,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(17/2),x)","-\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{a^3\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,16{}\mathrm{i}}{3\,c^9\,f}+\frac{64\,a^3\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{3\,c^9\,f}-\frac{a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,1088{}\mathrm{i}}{15\,c^9\,f}-\frac{576\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,c^9\,f}+\frac{a^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,5472{}\mathrm{i}}{35\,c^9\,f}+\frac{576\,a^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,c^9\,f}-\frac{a^3\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,1088{}\mathrm{i}}{15\,c^9\,f}-\frac{64\,a^3\,{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{3\,c^9\,f}+\frac{a^3\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,16{}\mathrm{i}}{3\,c^9\,f}\right)}{1+910\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-2002\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}+2002\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}-910\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}+90\,{\mathrm{e}}^{e\,14{}\mathrm{i}+f\,x\,14{}\mathrm{i}}-{\mathrm{e}}^{e\,16{}\mathrm{i}+f\,x\,16{}\mathrm{i}}-90\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,14{}\mathrm{i}-{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,350{}\mathrm{i}+{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,1638{}\mathrm{i}-{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,1430{}\mathrm{i}-{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,1430{}\mathrm{i}+{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,1638{}\mathrm{i}-{\mathrm{e}}^{e\,13{}\mathrm{i}+f\,x\,13{}\mathrm{i}}\,350{}\mathrm{i}+{\mathrm{e}}^{e\,15{}\mathrm{i}+f\,x\,15{}\mathrm{i}}\,14{}\mathrm{i}}","Not used",1,"-((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((a^3*exp(e*4i + f*x*4i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*16i)/(3*c^9*f) + (64*a^3*exp(e*5i + f*x*5i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(3*c^9*f) - (a^3*exp(e*6i + f*x*6i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*1088i)/(15*c^9*f) - (576*a^3*exp(e*7i + f*x*7i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*c^9*f) + (a^3*exp(e*8i + f*x*8i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*5472i)/(35*c^9*f) + (576*a^3*exp(e*9i + f*x*9i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*c^9*f) - (a^3*exp(e*10i + f*x*10i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*1088i)/(15*c^9*f) - (64*a^3*exp(e*11i + f*x*11i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(3*c^9*f) + (a^3*exp(e*12i + f*x*12i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*16i)/(3*c^9*f)))/(exp(e*1i + f*x*1i)*14i - 90*exp(e*2i + f*x*2i) - exp(e*3i + f*x*3i)*350i + 910*exp(e*4i + f*x*4i) + exp(e*5i + f*x*5i)*1638i - 2002*exp(e*6i + f*x*6i) - exp(e*7i + f*x*7i)*1430i - exp(e*9i + f*x*9i)*1430i + 2002*exp(e*10i + f*x*10i) + exp(e*11i + f*x*11i)*1638i - 910*exp(e*12i + f*x*12i) - exp(e*13i + f*x*13i)*350i + 90*exp(e*14i + f*x*14i) + exp(e*15i + f*x*15i)*14i - exp(e*16i + f*x*16i) + 1)","B"
44,1,96,45,2.003057,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(1/2),x)","-\frac{c^2\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(28\,\cos\left(e+f\,x\right)+27\,\cos\left(3\,e+3\,f\,x\right)-\cos\left(5\,e+5\,f\,x\right)+48\,\sin\left(2\,e+2\,f\,x\right)-8\,\sin\left(4\,e+4\,f\,x\right)\right)}{64\,f\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-(c^2*(-c*(sin(e + f*x) - 1))^(1/2)*(28*cos(e + f*x) + 27*cos(3*e + 3*f*x) - cos(5*e + 5*f*x) + 48*sin(2*e + 2*f*x) - 8*sin(4*e + 4*f*x)))/(64*f*(a*(sin(e + f*x) + 1))^(1/2)*(sin(e + f*x) - 1))","B"
45,1,83,45,9.964434,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(1/2),x)","-\frac{c\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(6\,\cos\left(e+f\,x\right)+6\,\cos\left(3\,e+3\,f\,x\right)+14\,\sin\left(2\,e+2\,f\,x\right)-\sin\left(4\,e+4\,f\,x\right)\right)}{24\,f\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-(c*(-c*(sin(e + f*x) - 1))^(1/2)*(6*cos(e + f*x) + 6*cos(3*e + 3*f*x) + 14*sin(2*e + 2*f*x) - sin(4*e + 4*f*x)))/(24*f*(a*(sin(e + f*x) + 1))^(1/2)*(sin(e + f*x) - 1))","B"
46,1,67,45,0.931009,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(1/2),x)","-\frac{\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(\cos\left(e+f\,x\right)+\cos\left(3\,e+3\,f\,x\right)+4\,\sin\left(2\,e+2\,f\,x\right)\right)}{8\,f\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-((-c*(sin(e + f*x) - 1))^(1/2)*(cos(e + f*x) + cos(3*e + 3*f*x) + 4*sin(2*e + 2*f*x)))/(8*f*(a*(sin(e + f*x) + 1))^(1/2)*(sin(e + f*x) - 1))","B"
47,1,52,43,8.869003,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)),x)","-\frac{\sin\left(2\,e+2\,f\,x\right)\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}}{2\,c\,f\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-(sin(2*e + 2*f*x)*(-c*(sin(e + f*x) - 1))^(1/2))/(2*c*f*(a*(sin(e + f*x) + 1))^(1/2)*(sin(e + f*x) - 1))","B"
48,0,-1,54,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
49,1,88,42,9.770976,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2)),x)","-\frac{2\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\sin\left(2\,e+2\,f\,x\right)-2\right)}{c^3\,f\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(12\,{\sin\left(e+f\,x\right)}^2-15\,\sin\left(e+f\,x\right)+\sin\left(3\,e+3\,f\,x\right)+4\right)}","Not used",1,"-(2*(-c*(sin(e + f*x) - 1))^(1/2)*(sin(2*e + 2*f*x) + 4*sin(e/2 + (f*x)/2)^2 - 2))/(c^3*f*(a*(sin(e + f*x) + 1))^(1/2)*(sin(3*e + 3*f*x) - 15*sin(e + f*x) + 12*sin(e + f*x)^2 + 4))","B"
50,0,-1,239,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
51,0,-1,190,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
52,0,-1,145,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
53,0,-1,96,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
54,0,-1,51,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
55,0,-1,52,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
56,0,-1,104,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
57,0,-1,285,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
58,0,-1,237,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
59,0,-1,191,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
60,0,-1,143,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
61,0,-1,97,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
62,1,55,43,9.260625,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2)),x)","-\frac{2\,\cos\left(e+f\,x\right)\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}}{a^2\,c\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}}","Not used",1,"-(2*cos(e + f*x)*(-c*(sin(e + f*x) - 1))^(1/2))/(a^2*c*f*(cos(2*e + 2*f*x) + 1)*(a*(sin(e + f*x) + 1))^(1/2))","B"
63,0,-1,104,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
64,0,-1,152,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
65,0,-1,114,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n, x)","F"
66,0,-1,86,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3, x)","F"
67,0,-1,86,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^2,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^2, x)","F"
68,0,-1,84,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x)),x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(c-c\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x)), x)","F"
69,0,-1,81,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m, x)","F"
70,0,-1,77,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x)), x)","F"
71,0,-1,81,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^2,x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^2, x)","F"
72,0,-1,86,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^3,x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^3, x)","F"
73,1,1060,244,14.969740,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(5/2),x)","\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(-\frac{c^2\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m^3\,8{}\mathrm{i}+m^2\,60{}\mathrm{i}+m\,142{}\mathrm{i}+105{}\mathrm{i}\right)}{8\,f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{3\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(4\,m^2+48\,m+63\right)}{f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{3\,c^2\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m^2\,4{}\mathrm{i}+m\,48{}\mathrm{i}+63{}\mathrm{i}\right)}{f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}-\frac{c^2\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(8\,m^3+60\,m^2+142\,m+105\right)}{8\,f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{3\,c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(8\,m^3+92\,m^2+270\,m+225\right)}{8\,f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{3\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m^3\,8{}\mathrm{i}+m^2\,92{}\mathrm{i}+m\,270{}\mathrm{i}+225{}\mathrm{i}\right)}{8\,f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{3\,c^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(8\,m^3+108\,m^2+590\,m+2205\right)}{4\,f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{3\,c^2\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m^3\,8{}\mathrm{i}+m^2\,108{}\mathrm{i}+m\,590{}\mathrm{i}+2205{}\mathrm{i}\right)}{4\,f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{2\,c^2\,m\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(4\,m^2+48\,m+191\right)}{f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{2\,c^2\,m\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m^2\,4{}\mathrm{i}+m\,48{}\mathrm{i}+191{}\mathrm{i}\right)}{f\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}\right)}\right)}{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(16\,m^4+192\,m^3+824\,m^2+1488\,m+945\right)}{m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,824{}\mathrm{i}+m\,1488{}\mathrm{i}+945{}\mathrm{i}}}","Not used",1,"((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((3*c^2*exp(e*7i + f*x*7i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(48*m + 4*m^2 + 63))/(f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) - (c^2*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*142i + m^2*60i + m^3*8i + 105i))/(8*f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) + (3*c^2*exp(e*2i + f*x*2i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*48i + m^2*4i + 63i))/(f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) - (c^2*exp(e*9i + f*x*9i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(142*m + 60*m^2 + 8*m^3 + 105))/(8*f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) + (3*c^2*exp(e*1i + f*x*1i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(270*m + 92*m^2 + 8*m^3 + 225))/(8*f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) + (3*c^2*exp(e*8i + f*x*8i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*270i + m^2*92i + m^3*8i + 225i))/(8*f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) + (3*c^2*exp(e*5i + f*x*5i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(590*m + 108*m^2 + 8*m^3 + 2205))/(4*f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) + (3*c^2*exp(e*4i + f*x*4i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*590i + m^2*108i + m^3*8i + 2205i))/(4*f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) + (2*c^2*m*exp(e*3i + f*x*3i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(48*m + 4*m^2 + 191))/(f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i)) + (2*c^2*m*exp(e*6i + f*x*6i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*48i + m^2*4i + 191i))/(f*(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i))))/(exp(e*5i + f*x*5i) + (exp(e*4i + f*x*4i)*(1488*m + 824*m^2 + 192*m^3 + 16*m^4 + 945))/(m*1488i + m^2*824i + m^3*192i + m^4*16i + 945i))","B"
74,1,528,172,13.972539,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(3/2),x)","-\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{c\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,4{}\mathrm{i}+m\,16{}\mathrm{i}+15{}\mathrm{i}\right)}{4\,f\,\left(8\,m^3+60\,m^2+142\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+16\,m+15\right)}{4\,f\,\left(8\,m^3+60\,m^2+142\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+48\,m+63\right)}{4\,f\,\left(8\,m^3+60\,m^2+142\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(12\,m^2+80\,m-35\right)}{4\,f\,\left(8\,m^3+60\,m^2+142\,m+105\right)}+\frac{c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,4{}\mathrm{i}+m\,48{}\mathrm{i}+63{}\mathrm{i}\right)}{4\,f\,\left(8\,m^3+60\,m^2+142\,m+105\right)}+\frac{c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,12{}\mathrm{i}+m\,80{}\mathrm{i}-35{}\mathrm{i}\right)}{4\,f\,\left(8\,m^3+60\,m^2+142\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(12\,m^2+112\,m+525\right)}{4\,f\,\left(8\,m^3+60\,m^2+142\,m+105\right)}+\frac{c\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,12{}\mathrm{i}+m\,112{}\mathrm{i}+525{}\mathrm{i}\right)}{4\,f\,\left(8\,m^3+60\,m^2+142\,m+105\right)}\right)}{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(m^3\,8{}\mathrm{i}+m^2\,60{}\mathrm{i}+m\,142{}\mathrm{i}+105{}\mathrm{i}\right)}{8\,m^3+60\,m^2+142\,m+105}}","Not used",1,"-((c - c*sin(e + f*x))^(1/2)*((c*(a + a*sin(e + f*x))^m*(m*16i + m^2*4i + 15i))/(4*f*(142*m + 60*m^2 + 8*m^3 + 105)) - (c*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^m*(16*m + 4*m^2 + 15))/(4*f*(142*m + 60*m^2 + 8*m^3 + 105)) - (c*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^m*(48*m + 4*m^2 + 63))/(4*f*(142*m + 60*m^2 + 8*m^3 + 105)) - (c*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^m*(80*m + 12*m^2 - 35))/(4*f*(142*m + 60*m^2 + 8*m^3 + 105)) + (c*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^m*(m*48i + m^2*4i + 63i))/(4*f*(142*m + 60*m^2 + 8*m^3 + 105)) + (c*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^m*(m*80i + m^2*12i - 35i))/(4*f*(142*m + 60*m^2 + 8*m^3 + 105)) - (c*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^m*(112*m + 12*m^2 + 525))/(4*f*(142*m + 60*m^2 + 8*m^3 + 105)) + (c*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^m*(m*112i + m^2*12i + 525i))/(4*f*(142*m + 60*m^2 + 8*m^3 + 105))))/(exp(e*4i + f*x*4i) - (exp(e*3i + f*x*3i)*(m*142i + m^2*60i + m^3*8i + 105i))/(142*m + 60*m^2 + 8*m^3 + 105))","B"
75,1,104,107,1.719783,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1/2),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(25\,\cos\left(e+f\,x\right)+3\,\cos\left(3\,e+3\,f\,x\right)+8\,\sin\left(2\,e+2\,f\,x\right)+6\,m\,\cos\left(e+f\,x\right)+2\,m\,\cos\left(3\,e+3\,f\,x\right)\right)}{2\,f\,\left(\sin\left(e+f\,x\right)-1\right)\,\left(4\,m^2+16\,m+15\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^(1/2)*(25*cos(e + f*x) + 3*cos(3*e + 3*f*x) + 8*sin(2*e + 2*f*x) + 6*m*cos(e + f*x) + 2*m*cos(3*e + 3*f*x)))/(2*f*(sin(e + f*x) - 1)*(16*m + 4*m^2 + 15))","B"
76,1,68,50,0.898600,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(2\,\cos\left(e+f\,x\right)+\sin\left(2\,e+2\,f\,x\right)\right)}{c\,f\,\left(2\,m+3\right)\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^(1/2)*(2*cos(e + f*x) + sin(2*e + 2*f*x)))/(c*f*(2*m + 3)*(sin(e + f*x) - 1))","B"
77,0,-1,76,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(3/2), x)","F"
78,0,-1,79,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(5/2), x)","F"
79,1,68,50,0.002046,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(2\,\cos\left(e+f\,x\right)+\sin\left(2\,e+2\,f\,x\right)\right)}{c\,f\,\left(2\,m+3\right)\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^(1/2)*(2*cos(e + f*x) + sin(2*e + 2*f*x)))/(c*f*(2*m + 3)*(sin(e + f*x) - 1))","B"
80,1,68,50,9.110016,"\text{Not used}","int((cos(e + f*x)^2*(c + c*sin(e + f*x))^m)/(a - a*sin(e + f*x))^(1/2),x)","-\frac{\sqrt{-a\,\left(\sin\left(e+f\,x\right)-1\right)}\,{\left(c\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(2\,\cos\left(e+f\,x\right)+\sin\left(2\,e+2\,f\,x\right)\right)}{a\,f\,\left(2\,m+3\right)\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-((-a*(sin(e + f*x) - 1))^(1/2)*(c*(sin(e + f*x) + 1))^m*(2*cos(e + f*x) + sin(2*e + 2*f*x)))/(a*f*(2*m + 3)*(sin(e + f*x) - 1))","B"
81,1,334,182,15.747658,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 5),x)","\frac{\cos\left(e+f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(24\,m^2+120\,m+140\right)}{8\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+5}\,\left(8\,m^3+60\,m^2+142\,m+105\right)}-\frac{\cos\left(5\,e+5\,f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{8\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+5}\,\left(8\,m^3+60\,m^2+142\,m+105\right)}+\frac{\cos\left(3\,e+3\,f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(8\,m^2+40\,m+45\right)}{8\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+5}\,\left(8\,m^3+60\,m^2+142\,m+105\right)}+\frac{\sin\left(4\,e+4\,f\,x\right)\,\left(m\,4{}\mathrm{i}+10{}\mathrm{i}\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,1{}\mathrm{i}}{8\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+5}\,\left(8\,m^3+60\,m^2+142\,m+105\right)}+\frac{\sin\left(2\,e+2\,f\,x\right)\,\left(m\,8{}\mathrm{i}+20{}\mathrm{i}\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,1{}\mathrm{i}}{8\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+5}\,\left(8\,m^3+60\,m^2+142\,m+105\right)}","Not used",1,"(cos(e + f*x)*(a + a*sin(e + f*x))^m*(120*m + 24*m^2 + 140))/(8*f*(c - c*sin(e + f*x))^(m + 5)*(142*m + 60*m^2 + 8*m^3 + 105)) - (cos(5*e + 5*f*x)*(a + a*sin(e + f*x))^m)/(8*f*(c - c*sin(e + f*x))^(m + 5)*(142*m + 60*m^2 + 8*m^3 + 105)) + (sin(4*e + 4*f*x)*(m*4i + 10i)*(a + a*sin(e + f*x))^m*1i)/(8*f*(c - c*sin(e + f*x))^(m + 5)*(142*m + 60*m^2 + 8*m^3 + 105)) + (sin(2*e + 2*f*x)*(m*8i + 20i)*(a + a*sin(e + f*x))^m*1i)/(8*f*(c - c*sin(e + f*x))^(m + 5)*(142*m + 60*m^2 + 8*m^3 + 105)) + (cos(3*e + 3*f*x)*(a + a*sin(e + f*x))^m*(40*m + 8*m^2 + 45))/(8*f*(c - c*sin(e + f*x))^(m + 5)*(142*m + 60*m^2 + 8*m^3 + 105))","B"
82,1,177,114,10.598571,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 4),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(2\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(4\,e+4\,f\,x\right)+48\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+16\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2+12\,m\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)+4\,m\,\left(2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2-1\right)-32\right)}{c^4\,f\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(4\,m^2+16\,m+15\right)\,\left(56\,{\sin\left(e+f\,x\right)}^2-56\,\sin\left(e+f\,x\right)-2\,{\sin\left(2\,e+2\,f\,x\right)}^2+8\,\sin\left(3\,e+3\,f\,x\right)+8\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(2*sin(2*e + 2*f*x) + sin(4*e + 4*f*x) + 48*sin(e/2 + (f*x)/2)^2 + 16*sin((3*e)/2 + (3*f*x)/2)^2 + 12*m*(2*sin(e/2 + (f*x)/2)^2 - 1) + 4*m*(2*sin((3*e)/2 + (3*f*x)/2)^2 - 1) - 32))/(c^4*f*(-c*(sin(e + f*x) - 1))^m*(16*m + 4*m^2 + 15)*(8*sin(3*e + 3*f*x) - 56*sin(e + f*x) - 2*sin(2*e + 2*f*x)^2 + 56*sin(e + f*x)^2 + 8))","B"
83,1,101,54,1.042616,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 3),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(6\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2-4\right)}{c^3\,f\,\left(2\,m+3\right)\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(12\,{\sin\left(e+f\,x\right)}^2-15\,\sin\left(e+f\,x\right)+\sin\left(3\,e+3\,f\,x\right)+4\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(6*sin(e/2 + (f*x)/2)^2 + 2*sin((3*e)/2 + (3*f*x)/2)^2 - 4))/(c^3*f*(2*m + 3)*(-c*(sin(e + f*x) - 1))^m*(sin(3*e + 3*f*x) - 15*sin(e + f*x) + 12*sin(e + f*x)^2 + 4))","B"
84,0,-1,113,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+2}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 2), x)","F"
85,0,-1,114,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 1),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 1), x)","F"
86,0,-1,116,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^m,x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^m} \,d x","Not used",1,"int((cos(e + f*x)^2*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^m, x)","F"
87,0,-1,116,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1 - m),x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{1-m} \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1 - m), x)","F"
88,0,-1,343,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(7/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(7/2), x)","F"
89,0,-1,290,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2), x)","F"
90,0,-1,235,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2), x)","F"
91,0,-1,178,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2), x)","F"
92,0,-1,122,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(1/2), x)","F"
93,0,-1,123,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
94,0,-1,182,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
95,0,-1,237,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
96,0,-1,292,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
97,0,-1,352,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2), x)","F"
98,0,-1,295,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2), x)","F"
99,0,-1,235,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2), x)","F"
100,0,-1,180,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(1/2), x)","F"
101,0,-1,182,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
102,0,-1,186,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
103,0,-1,243,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
104,0,-1,300,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
105,0,-1,357,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(11/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(11/2), x)","F"
106,0,-1,406,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2), x)","F"
107,0,-1,352,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2), x)","F"
108,0,-1,290,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2), x)","F"
109,0,-1,234,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(1/2), x)","F"
110,0,-1,241,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
111,0,-1,243,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
112,0,-1,243,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
113,0,-1,300,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
114,0,-1,357,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(11/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(11/2), x)","F"
115,0,-1,414,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(13/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{13/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(13/2), x)","F"
116,0,-1,463,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(5/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(5/2), x)","F"
117,0,-1,409,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(3/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(3/2), x)","F"
118,0,-1,343,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(1/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(1/2), x)","F"
119,0,-1,288,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(1/2), x)","F"
120,0,-1,294,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
121,0,-1,298,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
122,0,-1,300,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
123,0,-1,300,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
124,0,-1,357,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(11/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(11/2), x)","F"
125,0,-1,414,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(13/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{13/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(13/2), x)","F"
126,0,-1,471,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(15/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{15/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(15/2), x)","F"
127,0,-1,234,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(1/2), x)","F"
128,0,-1,180,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(1/2), x)","F"
129,0,-1,122,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(1/2), x)","F"
130,0,-1,68,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
131,0,-1,121,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
132,0,-1,179,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
133,0,-1,233,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(7/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(7/2)), x)","F"
134,0,-1,294,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
135,0,-1,241,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
136,0,-1,182,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
137,0,-1,123,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
138,0,-1,121,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
139,0,-1,176,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
140,0,-1,237,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
141,0,-1,294,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2)), x)","F"
142,0,-1,357,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
143,0,-1,298,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
144,0,-1,243,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
145,0,-1,186,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
146,0,-1,182,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
147,0,-1,179,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
148,0,-1,237,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
149,0,-1,291,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
150,0,-1,350,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(7/2)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(7/2)), x)","F"
151,0,-1,119,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n, x)","F"
152,0,-1,93,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3, x)","F"
153,0,-1,93,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^2,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^2, x)","F"
154,0,-1,91,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x)),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(c-c\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x)), x)","F"
155,0,-1,88,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m, x)","F"
156,0,-1,84,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x)), x)","F"
157,0,-1,93,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^2,x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^2, x)","F"
158,0,-1,93,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^3,x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^3, x)","F"
159,0,-1,114,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(5/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(5/2), x)","F"
160,0,-1,112,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(3/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(3/2), x)","F"
161,0,-1,109,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1/2),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1/2), x)","F"
162,0,-1,106,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2), x)","F"
163,0,-1,106,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(3/2), x)","F"
164,0,-1,114,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(5/2), x)","F"
165,0,-1,106,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2), x)","F"
166,0,-1,106,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(c + c*sin(e + f*x))^m)/(a - a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+c\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{a-a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(c + c*sin(e + f*x))^m)/(a - a*sin(e + f*x))^(1/2), x)","F"
167,0,-1,123,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 3),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+3}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 3), x)","F"
168,0,-1,123,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+2}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 2), x)","F"
169,0,-1,120,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 1), x)","F"
170,0,-1,121,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^m,x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^m} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^m, x)","F"
171,0,-1,123,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1 - m),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{1-m} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1 - m), x)","F"
172,0,-1,123,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(2 - m),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{2-m} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(2 - m), x)","F"
173,0,-1,135,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((g*cos(e + f*x))^p*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n, x)","F"
174,0,-1,57,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1 - 2*m)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(m - 1),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^{1-2\,m}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m-1} \,d x","Not used",1,"int((g*cos(e + f*x))^(1 - 2*m)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(m - 1), x)","F"
175,1,1149,203,17.207479,"\text{Not used}","int((g*cos(e + f*x))^(5 - 2*m)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n\,\left(-\frac{{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{5-2\,m}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2-2\,m\,n-7\,m+n^2+7\,n+12\right)}{f\,\left(-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60\right)}-\frac{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{5-2\,m}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,1{}\mathrm{i}-m\,n\,2{}\mathrm{i}-m\,7{}\mathrm{i}+n^2\,1{}\mathrm{i}+n\,7{}\mathrm{i}+12{}\mathrm{i}\right)}{f\,\left(-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60\right)}+\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{5-2\,m}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(2\,m^2-4\,m\,n-22\,m+2\,n^2+22\,n+80\right)}{f\,\left(-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60\right)}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{5-2\,m}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(3\,m^2-6\,m\,n-29\,m+3\,n^2+29\,n+60\right)}{f\,\left(-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60\right)}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{5-2\,m}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,3{}\mathrm{i}-m\,n\,6{}\mathrm{i}-m\,29{}\mathrm{i}+n^2\,3{}\mathrm{i}+n\,29{}\mathrm{i}+60{}\mathrm{i}\right)}{f\,\left(-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60\right)}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{5-2\,m}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,2{}\mathrm{i}-m\,n\,4{}\mathrm{i}-m\,22{}\mathrm{i}+n^2\,2{}\mathrm{i}+n\,22{}\mathrm{i}+80{}\mathrm{i}\right)}{f\,\left(-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60\right)}\right)}{5\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-10\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}+{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}+\frac{-m^3\,1{}\mathrm{i}+m^2\,n\,3{}\mathrm{i}+m^2\,12{}\mathrm{i}-m\,n^2\,3{}\mathrm{i}-m\,n\,24{}\mathrm{i}-m\,47{}\mathrm{i}+n^3\,1{}\mathrm{i}+n^2\,12{}\mathrm{i}+n\,47{}\mathrm{i}+60{}\mathrm{i}}{-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60}-\frac{10\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(-m^3\,1{}\mathrm{i}+m^2\,n\,3{}\mathrm{i}+m^2\,12{}\mathrm{i}-m\,n^2\,3{}\mathrm{i}-m\,n\,24{}\mathrm{i}-m\,47{}\mathrm{i}+n^3\,1{}\mathrm{i}+n^2\,12{}\mathrm{i}+n\,47{}\mathrm{i}+60{}\mathrm{i}\right)}{-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60}+\frac{5\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(-m^3\,1{}\mathrm{i}+m^2\,n\,3{}\mathrm{i}+m^2\,12{}\mathrm{i}-m\,n^2\,3{}\mathrm{i}-m\,n\,24{}\mathrm{i}-m\,47{}\mathrm{i}+n^3\,1{}\mathrm{i}+n^2\,12{}\mathrm{i}+n\,47{}\mathrm{i}+60{}\mathrm{i}\right)}{-m^3+3\,m^2\,n+12\,m^2-3\,m\,n^2-24\,m\,n-47\,m+n^3+12\,n^2+47\,n+60}}","Not used",1,"((c - c*sin(e + f*x))^n*((exp(e*2i + f*x*2i)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(5 - 2*m)*(a + a*sin(e + f*x))^m*(22*n - 22*m - 4*m*n + 2*m^2 + 2*n^2 + 80))/(f*(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60)) - (exp(e*5i + f*x*5i)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(5 - 2*m)*(a + a*sin(e + f*x))^m*(n*7i - m*7i - m*n*2i + m^2*1i + n^2*1i + 12i))/(f*(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60)) - ((g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(5 - 2*m)*(a + a*sin(e + f*x))^m*(7*n - 7*m - 2*m*n + m^2 + n^2 + 12))/(f*(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60)) + (exp(e*4i + f*x*4i)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(5 - 2*m)*(a + a*sin(e + f*x))^m*(29*n - 29*m - 6*m*n + 3*m^2 + 3*n^2 + 60))/(f*(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60)) + (exp(e*1i + f*x*1i)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(5 - 2*m)*(a + a*sin(e + f*x))^m*(n*29i - m*29i - m*n*6i + m^2*3i + n^2*3i + 60i))/(f*(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60)) + (exp(e*3i + f*x*3i)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(5 - 2*m)*(a + a*sin(e + f*x))^m*(n*22i - m*22i - m*n*4i + m^2*2i + n^2*2i + 80i))/(f*(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60))))/(5*exp(e*1i + f*x*1i) - 10*exp(e*3i + f*x*3i) + exp(e*5i + f*x*5i) + (n*47i - m*47i - m*n*24i - m*n^2*3i + m^2*n*3i + m^2*12i - m^3*1i + n^2*12i + n^3*1i + 60i)/(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60) - (10*exp(e*2i + f*x*2i)*(n*47i - m*47i - m*n*24i - m*n^2*3i + m^2*n*3i + m^2*12i - m^3*1i + n^2*12i + n^3*1i + 60i))/(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60) + (5*exp(e*4i + f*x*4i)*(n*47i - m*47i - m*n*24i - m*n^2*3i + m^2*n*3i + m^2*12i - m^3*1i + n^2*12i + n^3*1i + 60i))/(47*n - 47*m - 24*m*n - 3*m*n^2 + 3*m^2*n + 12*m^2 - m^3 + 12*n^2 + n^3 + 60))","B"
176,1,476,127,18.127731,"\text{Not used}","int((g*cos(e + f*x))^(3 - 2*m)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","-\frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n\,\left(\frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3-2\,m}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(n-m+2\right)}{f\,\left(m^2-2\,m\,n-5\,m+n^2+5\,n+6\right)}-\frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3-2\,m}\,\left(\cos\left(3\,e+3\,f\,x\right)+\sin\left(3\,e+3\,f\,x\right)\,1{}\mathrm{i}\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(-m\,1{}\mathrm{i}+n\,1{}\mathrm{i}+2{}\mathrm{i}\right)}{f\,\left(m^2-2\,m\,n-5\,m+n^2+5\,n+6\right)}-\frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3-2\,m}\,\left(\cos\left(e+f\,x\right)+\sin\left(e+f\,x\right)\,1{}\mathrm{i}\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(-m\,1{}\mathrm{i}+n\,1{}\mathrm{i}+6{}\mathrm{i}\right)}{f\,\left(m^2-2\,m\,n-5\,m+n^2+5\,n+6\right)}+\frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3-2\,m}\,\left(\cos\left(2\,e+2\,f\,x\right)+\sin\left(2\,e+2\,f\,x\right)\,1{}\mathrm{i}\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(n-m+6\right)}{f\,\left(m^2-2\,m\,n-5\,m+n^2+5\,n+6\right)}\right)}{3\,\cos\left(e+f\,x\right)+\sin\left(e+f\,x\right)\,3{}\mathrm{i}-\cos\left(3\,e+3\,f\,x\right)-\sin\left(3\,e+3\,f\,x\right)\,1{}\mathrm{i}+\frac{m^2\,1{}\mathrm{i}-m\,n\,2{}\mathrm{i}-m\,5{}\mathrm{i}+n^2\,1{}\mathrm{i}+n\,5{}\mathrm{i}+6{}\mathrm{i}}{m^2-2\,m\,n-5\,m+n^2+5\,n+6}-\frac{3\,\left(\cos\left(2\,e+2\,f\,x\right)+\sin\left(2\,e+2\,f\,x\right)\,1{}\mathrm{i}\right)\,\left(m^2\,1{}\mathrm{i}-m\,n\,2{}\mathrm{i}-m\,5{}\mathrm{i}+n^2\,1{}\mathrm{i}+n\,5{}\mathrm{i}+6{}\mathrm{i}\right)}{m^2-2\,m\,n-5\,m+n^2+5\,n+6}}","Not used",1,"-((c - c*sin(e + f*x))^n*(((g*cos(e + f*x))^(3 - 2*m)*(a + a*sin(e + f*x))^m*(n - m + 2))/(f*(5*n - 5*m - 2*m*n + m^2 + n^2 + 6)) - ((g*cos(e + f*x))^(3 - 2*m)*(cos(3*e + 3*f*x) + sin(3*e + 3*f*x)*1i)*(a + a*sin(e + f*x))^m*(n*1i - m*1i + 2i))/(f*(5*n - 5*m - 2*m*n + m^2 + n^2 + 6)) - ((g*cos(e + f*x))^(3 - 2*m)*(cos(e + f*x) + sin(e + f*x)*1i)*(a + a*sin(e + f*x))^m*(n*1i - m*1i + 6i))/(f*(5*n - 5*m - 2*m*n + m^2 + n^2 + 6)) + ((g*cos(e + f*x))^(3 - 2*m)*(cos(2*e + 2*f*x) + sin(2*e + 2*f*x)*1i)*(a + a*sin(e + f*x))^m*(n - m + 6))/(f*(5*n - 5*m - 2*m*n + m^2 + n^2 + 6))))/(3*cos(e + f*x) + sin(e + f*x)*3i - cos(3*e + 3*f*x) - sin(3*e + 3*f*x)*1i + (n*5i - m*5i - m*n*2i + m^2*1i + n^2*1i + 6i)/(5*n - 5*m - 2*m*n + m^2 + n^2 + 6) - (3*(cos(2*e + 2*f*x) + sin(2*e + 2*f*x)*1i)*(n*5i - m*5i - m*n*2i + m^2*1i + n^2*1i + 6i))/(5*n - 5*m - 2*m*n + m^2 + n^2 + 6))","B"
177,1,74,58,9.417057,"\text{Not used}","int((g*cos(e + f*x))^(1 - 2*m)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","-\frac{g\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^n}{2\,f\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{2\,m}\,\left(\sin\left(e+f\,x\right)+1\right)\,\left(n-m+1\right)}","Not used",1,"-(g*(cos(2*e + 2*f*x) + 1)*(a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^n)/(2*f*(g*cos(e + f*x))^(2*m)*(sin(e + f*x) + 1)*(n - m + 1))","B"
178,0,-1,81,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n)/(g*cos(e + f*x))^(2*m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{2\,m+1}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n)/(g*cos(e + f*x))^(2*m + 1), x)","F"
179,0,-1,85,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n)/(g*cos(e + f*x))^(2*m + 3),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{2\,m+3}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n)/(g*cos(e + f*x))^(2*m + 3), x)","F"
180,0,-1,88,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n)/(g*cos(e + f*x))^(2*m + 5),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{2\,m+5}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n)/(g*cos(e + f*x))^(2*m + 5), x)","F"
181,0,-1,51,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^m)/(g*cos(e + f*x))^(2*m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^m}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{2\,m+1}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^m)/(g*cos(e + f*x))^(2*m + 1), x)","F"
182,0,-1,134,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n + 3))/(g*cos(e + f*x))^(m + n + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{n+3}}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{m+n+1}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n + 3))/(g*cos(e + f*x))^(m + n + 1), x)","F"
183,0,-1,134,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n + 2))/(g*cos(e + f*x))^(m + n + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{n+2}}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{m+n+1}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n + 2))/(g*cos(e + f*x))^(m + n + 1), x)","F"
184,0,-1,131,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n + 1))/(g*cos(e + f*x))^(m + n + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{n+1}}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{m+n+1}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n + 1))/(g*cos(e + f*x))^(m + n + 1), x)","F"
185,1,53,55,9.074269,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n)/(g*cos(e + f*x))^(m + n + 1),x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^n}{f\,g\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{m+n}\,\left(m-n\right)}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^n)/(f*g*(g*cos(e + f*x))^(m + n)*(m - n))","B"
186,1,128,125,10.157088,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n - 1))/(g*cos(e + f*x))^(m + n + 1),x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^n\,\left(2\,\cos\left(e+f\,x\right)-\sin\left(2\,e+2\,f\,x\right)+2\,m\,\cos\left(e+f\,x\right)-2\,n\,\cos\left(e+f\,x\right)\right)}{c\,f\,g\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{m+n}\,\left(2\,\cos\left(e+f\,x\right)-\sin\left(2\,e+2\,f\,x\right)\right)\,\left(m^2-2\,m\,n+2\,m+n^2-2\,n\right)}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^n*(2*cos(e + f*x) - sin(2*e + 2*f*x) + 2*m*cos(e + f*x) - 2*n*cos(e + f*x)))/(c*f*g*(g*cos(e + f*x))^(m + n)*(2*cos(e + f*x) - sin(2*e + 2*f*x))*(2*m - 2*n - 2*m*n + m^2 + n^2))","B"
187,1,887,204,15.647063,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n - 2))/(g*cos(e + f*x))^(m + n + 1),x)","-{\mathrm{e}}^{-e\,3{}\mathrm{i}-f\,x\,3{}\mathrm{i}}\,{\left(c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^{n-2}\,\left(\frac{{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m}{4\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^3-3\,m^2\,n+6\,m^2+3\,m\,n^2-12\,m\,n+8\,m-n^3+6\,n^2-8\,n\right)}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m}{4\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^3-3\,m^2\,n+6\,m^2+3\,m\,n^2-12\,m\,n+8\,m-n^3+6\,n^2-8\,n\right)}-\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(2\,m^2-4\,m\,n+8\,m+2\,n^2-8\,n+5\right)}{4\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^3-3\,m^2\,n+6\,m^2+3\,m\,n^2-12\,m\,n+8\,m-n^3+6\,n^2-8\,n\right)}-\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(2\,m^2-4\,m\,n+8\,m+2\,n^2-8\,n+5\right)}{4\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^3-3\,m^2\,n+6\,m^2+3\,m\,n^2-12\,m\,n+8\,m-n^3+6\,n^2-8\,n\right)}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m\,2{}\mathrm{i}-n\,2{}\mathrm{i}+4{}\mathrm{i}\right)}{4\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^3-3\,m^2\,n+6\,m^2+3\,m\,n^2-12\,m\,n+8\,m-n^3+6\,n^2-8\,n\right)}-\frac{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m\,2{}\mathrm{i}-n\,2{}\mathrm{i}+4{}\mathrm{i}\right)}{4\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^3-3\,m^2\,n+6\,m^2+3\,m\,n^2-12\,m\,n+8\,m-n^3+6\,n^2-8\,n\right)}\right)","Not used",1,"-exp(- e*3i - f*x*3i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(n - 2)*((a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m/(4*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(8*m - 8*n - 12*m*n + 3*m*n^2 - 3*m^2*n + 6*m^2 + m^3 + 6*n^2 - n^3)) + (exp(e*6i + f*x*6i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m)/(4*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(8*m - 8*n - 12*m*n + 3*m*n^2 - 3*m^2*n + 6*m^2 + m^3 + 6*n^2 - n^3)) - (exp(e*2i + f*x*2i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(8*m - 8*n - 4*m*n + 2*m^2 + 2*n^2 + 5))/(4*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(8*m - 8*n - 12*m*n + 3*m*n^2 - 3*m^2*n + 6*m^2 + m^3 + 6*n^2 - n^3)) - (exp(e*4i + f*x*4i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(8*m - 8*n - 4*m*n + 2*m^2 + 2*n^2 + 5))/(4*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(8*m - 8*n - 12*m*n + 3*m*n^2 - 3*m^2*n + 6*m^2 + m^3 + 6*n^2 - n^3)) + (exp(e*1i + f*x*1i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*2i - n*2i + 4i))/(4*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(8*m - 8*n - 12*m*n + 3*m*n^2 - 3*m^2*n + 6*m^2 + m^3 + 6*n^2 - n^3)) - (exp(e*5i + f*x*5i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*2i - n*2i + 4i))/(4*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(8*m - 8*n - 12*m*n + 3*m*n^2 - 3*m^2*n + 6*m^2 + m^3 + 6*n^2 - n^3)))","B"
188,1,1623,290,17.648535,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(n - 3))/(g*cos(e + f*x))^(m + n + 1),x)","-{\mathrm{e}}^{-e\,4{}\mathrm{i}-f\,x\,4{}\mathrm{i}}\,{\left(c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^{n-3}\,\left(\frac{3\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m}{8\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^4\,1{}\mathrm{i}-m^3\,n\,4{}\mathrm{i}+m^3\,12{}\mathrm{i}+m^2\,n^2\,6{}\mathrm{i}-m^2\,n\,36{}\mathrm{i}+m^2\,44{}\mathrm{i}-m\,n^3\,4{}\mathrm{i}+m\,n^2\,36{}\mathrm{i}-m\,n\,88{}\mathrm{i}+m\,48{}\mathrm{i}+n^4\,1{}\mathrm{i}-n^3\,12{}\mathrm{i}+n^2\,44{}\mathrm{i}-n\,48{}\mathrm{i}\right)}-\frac{3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m}{8\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^4\,1{}\mathrm{i}-m^3\,n\,4{}\mathrm{i}+m^3\,12{}\mathrm{i}+m^2\,n^2\,6{}\mathrm{i}-m^2\,n\,36{}\mathrm{i}+m^2\,44{}\mathrm{i}-m\,n^3\,4{}\mathrm{i}+m\,n^2\,36{}\mathrm{i}-m\,n\,88{}\mathrm{i}+m\,48{}\mathrm{i}+n^4\,1{}\mathrm{i}-n^3\,12{}\mathrm{i}+n^2\,44{}\mathrm{i}-n\,48{}\mathrm{i}\right)}-\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(6\,m^2-12\,m\,n+36\,m+6\,n^2-36\,n+42\right)}{8\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^4\,1{}\mathrm{i}-m^3\,n\,4{}\mathrm{i}+m^3\,12{}\mathrm{i}+m^2\,n^2\,6{}\mathrm{i}-m^2\,n\,36{}\mathrm{i}+m^2\,44{}\mathrm{i}-m\,n^3\,4{}\mathrm{i}+m\,n^2\,36{}\mathrm{i}-m\,n\,88{}\mathrm{i}+m\,48{}\mathrm{i}+n^4\,1{}\mathrm{i}-n^3\,12{}\mathrm{i}+n^2\,44{}\mathrm{i}-n\,48{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(6\,m^2-12\,m\,n+36\,m+6\,n^2-36\,n+42\right)}{8\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^4\,1{}\mathrm{i}-m^3\,n\,4{}\mathrm{i}+m^3\,12{}\mathrm{i}+m^2\,n^2\,6{}\mathrm{i}-m^2\,n\,36{}\mathrm{i}+m^2\,44{}\mathrm{i}-m\,n^3\,4{}\mathrm{i}+m\,n^2\,36{}\mathrm{i}-m\,n\,88{}\mathrm{i}+m\,48{}\mathrm{i}+n^4\,1{}\mathrm{i}-n^3\,12{}\mathrm{i}+n^2\,44{}\mathrm{i}-n\,48{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m\,6{}\mathrm{i}-n\,6{}\mathrm{i}+18{}\mathrm{i}\right)}{8\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^4\,1{}\mathrm{i}-m^3\,n\,4{}\mathrm{i}+m^3\,12{}\mathrm{i}+m^2\,n^2\,6{}\mathrm{i}-m^2\,n\,36{}\mathrm{i}+m^2\,44{}\mathrm{i}-m\,n^3\,4{}\mathrm{i}+m\,n^2\,36{}\mathrm{i}-m\,n\,88{}\mathrm{i}+m\,48{}\mathrm{i}+n^4\,1{}\mathrm{i}-n^3\,12{}\mathrm{i}+n^2\,44{}\mathrm{i}-n\,48{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m\,6{}\mathrm{i}-n\,6{}\mathrm{i}+18{}\mathrm{i}\right)}{8\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^4\,1{}\mathrm{i}-m^3\,n\,4{}\mathrm{i}+m^3\,12{}\mathrm{i}+m^2\,n^2\,6{}\mathrm{i}-m^2\,n\,36{}\mathrm{i}+m^2\,44{}\mathrm{i}-m\,n^3\,4{}\mathrm{i}+m\,n^2\,36{}\mathrm{i}-m\,n\,88{}\mathrm{i}+m\,48{}\mathrm{i}+n^4\,1{}\mathrm{i}-n^3\,12{}\mathrm{i}+n^2\,44{}\mathrm{i}-n\,48{}\mathrm{i}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m^3\,4{}\mathrm{i}-m^2\,n\,12{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,n^2\,12{}\mathrm{i}-m\,n\,72{}\mathrm{i}+m\,86{}\mathrm{i}-n^3\,4{}\mathrm{i}+n^2\,36{}\mathrm{i}-n\,86{}\mathrm{i}+42{}\mathrm{i}\right)}{8\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^4\,1{}\mathrm{i}-m^3\,n\,4{}\mathrm{i}+m^3\,12{}\mathrm{i}+m^2\,n^2\,6{}\mathrm{i}-m^2\,n\,36{}\mathrm{i}+m^2\,44{}\mathrm{i}-m\,n^3\,4{}\mathrm{i}+m\,n^2\,36{}\mathrm{i}-m\,n\,88{}\mathrm{i}+m\,48{}\mathrm{i}+n^4\,1{}\mathrm{i}-n^3\,12{}\mathrm{i}+n^2\,44{}\mathrm{i}-n\,48{}\mathrm{i}\right)}-\frac{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(m^3\,4{}\mathrm{i}-m^2\,n\,12{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,n^2\,12{}\mathrm{i}-m\,n\,72{}\mathrm{i}+m\,86{}\mathrm{i}-n^3\,4{}\mathrm{i}+n^2\,36{}\mathrm{i}-n\,86{}\mathrm{i}+42{}\mathrm{i}\right)}{8\,f\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^{m+n+1}\,\left(m^4\,1{}\mathrm{i}-m^3\,n\,4{}\mathrm{i}+m^3\,12{}\mathrm{i}+m^2\,n^2\,6{}\mathrm{i}-m^2\,n\,36{}\mathrm{i}+m^2\,44{}\mathrm{i}-m\,n^3\,4{}\mathrm{i}+m\,n^2\,36{}\mathrm{i}-m\,n\,88{}\mathrm{i}+m\,48{}\mathrm{i}+n^4\,1{}\mathrm{i}-n^3\,12{}\mathrm{i}+n^2\,44{}\mathrm{i}-n\,48{}\mathrm{i}\right)}\right)","Not used",1,"-exp(- e*4i - f*x*4i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(n - 3)*((3*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m)/(8*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(m*48i - n*48i - m*n*88i + m*n^2*36i - m^2*n*36i - m*n^3*4i - m^3*n*4i + m^2*44i + m^3*12i + m^4*1i + n^2*44i - n^3*12i + n^4*1i + m^2*n^2*6i)) - (3*exp(e*8i + f*x*8i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m)/(8*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(m*48i - n*48i - m*n*88i + m*n^2*36i - m^2*n*36i - m*n^3*4i - m^3*n*4i + m^2*44i + m^3*12i + m^4*1i + n^2*44i - n^3*12i + n^4*1i + m^2*n^2*6i)) - (exp(e*2i + f*x*2i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(36*m - 36*n - 12*m*n + 6*m^2 + 6*n^2 + 42))/(8*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(m*48i - n*48i - m*n*88i + m*n^2*36i - m^2*n*36i - m*n^3*4i - m^3*n*4i + m^2*44i + m^3*12i + m^4*1i + n^2*44i - n^3*12i + n^4*1i + m^2*n^2*6i)) + (exp(e*6i + f*x*6i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(36*m - 36*n - 12*m*n + 6*m^2 + 6*n^2 + 42))/(8*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(m*48i - n*48i - m*n*88i + m*n^2*36i - m^2*n*36i - m*n^3*4i - m^3*n*4i + m^2*44i + m^3*12i + m^4*1i + n^2*44i - n^3*12i + n^4*1i + m^2*n^2*6i)) + (exp(e*1i + f*x*1i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*6i - n*6i + 18i))/(8*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(m*48i - n*48i - m*n*88i + m*n^2*36i - m^2*n*36i - m*n^3*4i - m^3*n*4i + m^2*44i + m^3*12i + m^4*1i + n^2*44i - n^3*12i + n^4*1i + m^2*n^2*6i)) + (exp(e*7i + f*x*7i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*6i - n*6i + 18i))/(8*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(m*48i - n*48i - m*n*88i + m*n^2*36i - m^2*n*36i - m*n^3*4i - m^3*n*4i + m^2*44i + m^3*12i + m^4*1i + n^2*44i - n^3*12i + n^4*1i + m^2*n^2*6i)) - (exp(e*3i + f*x*3i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*86i - n*86i - m*n*72i + m*n^2*12i - m^2*n*12i + m^2*36i + m^3*4i + n^2*36i - n^3*4i + 42i))/(8*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(m*48i - n*48i - m*n*88i + m*n^2*36i - m^2*n*36i - m*n^3*4i - m^3*n*4i + m^2*44i + m^3*12i + m^4*1i + n^2*44i - n^3*12i + n^4*1i + m^2*n^2*6i)) - (exp(e*5i + f*x*5i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*(m*86i - n*86i - m*n*72i + m*n^2*12i - m^2*n*12i + m^2*36i + m^3*4i + n^2*36i - n^3*4i + 42i))/(8*f*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^(m + n + 1)*(m*48i - n*48i - m*n*88i + m*n^2*36i - m^2*n*36i - m*n^3*4i - m^3*n*4i + m^2*44i + m^3*12i + m^4*1i + n^2*44i - n^3*12i + n^4*1i + m^2*n^2*6i)))","B"
189,0,-1,138,0.000000,"\text{Not used}","int((g/cos(e + f*x))^p*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\int {\left(\frac{g}{\cos\left(e+f\,x\right)}\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((g/cos(e + f*x))^p*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n, x)","F"
190,1,24,33,0.051115,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^2*(a + a*sin(c + d*x)),x)","\frac{a\,{\sin\left(c+d\,x\right)}^3\,\left(3\,\sin\left(c+d\,x\right)+4\right)}{12\,d}","Not used",1,"(a*sin(c + d*x)^3*(3*sin(c + d*x) + 4))/(12*d)","B"
191,1,24,33,0.040053,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)*(a + a*sin(c + d*x)),x)","\frac{a\,{\sin\left(c+d\,x\right)}^2\,\left(2\,\sin\left(c+d\,x\right)+3\right)}{6\,d}","Not used",1,"(a*sin(c + d*x)^2*(2*sin(c + d*x) + 3))/(6*d)","B"
192,1,38,24,8.814448,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x)))/sin(c + d*x),x)","\frac{a\,\left(\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\sin\left(c+d\,x\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"(a*(log(tan(c/2 + (d*x)/2)) + sin(c + d*x) - log(tan(c/2 + (d*x)/2)^2 + 1)))/d","B"
193,1,55,25,8.580396,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x)))/sin(c + d*x)^2,x)","-\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+\frac{1}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,d}","Not used",1,"-(a*(tan(c/2 + (d*x)/2) - 2*log(tan(c/2 + (d*x)/2)) + 2*log(tan(c/2 + (d*x)/2)^2 + 1) + 1/tan(c/2 + (d*x)/2)))/(2*d)","B"
194,1,25,30,8.516541,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x)))/sin(c + d*x)^3,x)","-\frac{\frac{a}{2}+a\,\sin\left(c+d\,x\right)}{d\,{\sin\left(c+d\,x\right)}^2}","Not used",1,"-(a/2 + a*sin(c + d*x))/(d*sin(c + d*x)^2)","B"
195,1,39,33,8.601708,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x)))/sin(c + d*x)^4,x)","-\frac{\frac{5\,a\,\sin\left(c+d\,x\right)}{16}+\frac{a\,\left(\frac{3\,\sin\left(3\,c+3\,d\,x\right)}{16}+1\right)}{3}}{d\,{\sin\left(c+d\,x\right)}^3}","Not used",1,"-((5*a*sin(c + d*x))/16 + (a*((3*sin(3*c + 3*d*x))/16 + 1))/3)/(d*sin(c + d*x)^3)","B"
196,1,26,33,8.564535,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x)))/sin(c + d*x)^5,x)","-\frac{\frac{a}{4}+\frac{a\,\sin\left(c+d\,x\right)}{3}}{d\,{\sin\left(c+d\,x\right)}^4}","Not used",1,"-(a/4 + (a*sin(c + d*x))/3)/(d*sin(c + d*x)^4)","B"
197,1,36,55,8.492336,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^2*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,{\sin\left(c+d\,x\right)}^3\,\left(6\,{\sin\left(c+d\,x\right)}^2+15\,\sin\left(c+d\,x\right)+10\right)}{30\,d}","Not used",1,"(a^2*sin(c + d*x)^3*(15*sin(c + d*x) + 6*sin(c + d*x)^2 + 10))/(30*d)","B"
198,1,36,55,8.505212,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,{\sin\left(c+d\,x\right)}^2\,\left(3\,{\sin\left(c+d\,x\right)}^2+8\,\sin\left(c+d\,x\right)+6\right)}{12\,d}","Not used",1,"(a^2*sin(c + d*x)^2*(8*sin(c + d*x) + 3*sin(c + d*x)^2 + 6))/(12*d)","B"
199,1,119,47,8.987891,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (2*a^2*tan(c/2 + (d*x)/2)^2 + 4*a^2*tan(c/2 + (d*x)/2)^3 + 4*a^2*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
200,1,111,43,8.892233,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{2\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{2\,a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(2*a^2*log(tan(c/2 + (d*x)/2)))/d + (3*a^2*tan(c/2 + (d*x)/2)^2 - a^2)/(d*(2*tan(c/2 + (d*x)/2) + 2*tan(c/2 + (d*x)/2)^3)) - (a^2*tan(c/2 + (d*x)/2))/(2*d) - (2*a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
201,1,111,47,8.866153,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{8}+a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}-\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d - (a^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (cot(c/2 + (d*x)/2)^2*(a^2/8 + a^2*tan(c/2 + (d*x)/2)))/d - (a^2*tan(c/2 + (d*x)/2))/d - (a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
202,1,41,30,8.903284,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^2)/sin(c + d*x)^4,x)","-\frac{a^2\,{\sin\left(c+d\,x\right)}^2+a^2\,\sin\left(c+d\,x\right)+\frac{a^2}{3}}{d\,{\sin\left(c+d\,x\right)}^3}","Not used",1,"-(a^2*sin(c + d*x) + a^2/3 + a^2*sin(c + d*x)^2)/(d*sin(c + d*x)^3)","B"
203,1,43,55,8.852954,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^2)/sin(c + d*x)^5,x)","-\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{2\,a^2\,\sin\left(c+d\,x\right)}{3}+\frac{a^2}{4}}{d\,{\sin\left(c+d\,x\right)}^4}","Not used",1,"-((2*a^2*sin(c + d*x))/3 + a^2/4 + (a^2*sin(c + d*x)^2)/2)/(d*sin(c + d*x)^4)","B"
204,1,43,55,8.918362,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^2)/sin(c + d*x)^6,x)","-\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^2}{3}+\frac{a^2\,\sin\left(c+d\,x\right)}{2}+\frac{a^2}{5}}{d\,{\sin\left(c+d\,x\right)}^5}","Not used",1,"-((a^2*sin(c + d*x))/2 + a^2/5 + (a^2*sin(c + d*x)^2)/3)/(d*sin(c + d*x)^5)","B"
205,1,43,55,8.907113,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^2)/sin(c + d*x)^7,x)","-\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^2}{4}+\frac{2\,a^2\,\sin\left(c+d\,x\right)}{5}+\frac{a^2}{6}}{d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"-((2*a^2*sin(c + d*x))/5 + a^2/6 + (a^2*sin(c + d*x)^2)/4)/(d*sin(c + d*x)^6)","B"
206,1,57,73,0.065368,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^3*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a^3\,{\sin\left(c+d\,x\right)}^6}{2}+\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a^3\,{\sin\left(c+d\,x\right)}^4}{4}}{d}","Not used",1,"((a^3*sin(c + d*x)^4)/4 + (3*a^3*sin(c + d*x)^5)/5 + (a^3*sin(c + d*x)^6)/2 + (a^3*sin(c + d*x)^7)/7)/d","B"
207,1,57,73,0.062479,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^2*(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{3\,a^3\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{a^3\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"((a^3*sin(c + d*x)^3)/3 + (3*a^3*sin(c + d*x)^4)/4 + (3*a^3*sin(c + d*x)^5)/5 + (a^3*sin(c + d*x)^6)/6)/d","B"
208,1,56,45,0.060201,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^4}{4}+a^3\,{\sin\left(c+d\,x\right)}^3+\frac{a^3\,{\sin\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"((a^3*sin(c + d*x)^2)/2 + a^3*sin(c + d*x)^3 + (3*a^3*sin(c + d*x)^4)/4 + (a^3*sin(c + d*x)^5)/5)/d","B"
209,1,102,65,8.654957,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^3)/sin(c + d*x),x)","\frac{10\,a^3\,\sin\left(c+d\,x\right)}{3\,d}-\frac{a^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{3\,a^3\,{\cos\left(c+d\,x\right)}^2}{2\,d}-\frac{a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(10*a^3*sin(c + d*x))/(3*d) - (a^3*log(1/cos(c/2 + (d*x)/2)^2))/d + (a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (3*a^3*cos(c + d*x)^2)/(2*d) - (a^3*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
210,1,156,62,8.592913,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^3)/sin(c + d*x)^2,x)","\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{3\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)))/d + (10*a^3*tan(c/2 + (d*x)/2)^2 + 4*a^3*tan(c/2 + (d*x)/2)^3 + 11*a^3*tan(c/2 + (d*x)/2)^4 - a^3)/(d*(2*tan(c/2 + (d*x)/2) + 4*tan(c/2 + (d*x)/2)^3 + 2*tan(c/2 + (d*x)/2)^5)) - (a^3*tan(c/2 + (d*x)/2))/(2*d) - (3*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
211,1,163,61,8.573177,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^3)/sin(c + d*x)^3,x)","\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{3\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)))/d - ((a^3*tan(c/2 + (d*x)/2)^2)/2 - 2*a^3*tan(c/2 + (d*x)/2)^3 + a^3/2 + 6*a^3*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^4)) - (a^3*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*a^3*tan(c/2 + (d*x)/2))/(2*d) - (3*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
212,1,147,65,8.615829,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^3)/sin(c + d*x)^4,x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{3}\right)}{8\,d}-\frac{13\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d - (3*a^3*tan(c/2 + (d*x)/2)^2)/(8*d) - (a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (cot(c/2 + (d*x)/2)^3*(13*a^3*tan(c/2 + (d*x)/2)^2 + a^3/3 + 3*a^3*tan(c/2 + (d*x)/2)))/(8*d) - (13*a^3*tan(c/2 + (d*x)/2))/(8*d) - (a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
213,1,54,30,8.614034,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^3)/sin(c + d*x)^5,x)","-\frac{4\,a^3\,{\sin\left(c+d\,x\right)}^3+6\,a^3\,{\sin\left(c+d\,x\right)}^2+4\,a^3\,\sin\left(c+d\,x\right)+a^3}{4\,d\,{\sin\left(c+d\,x\right)}^4}","Not used",1,"-(4*a^3*sin(c + d*x) + a^3 + 6*a^3*sin(c + d*x)^2 + 4*a^3*sin(c + d*x)^3)/(4*d*sin(c + d*x)^4)","B"
214,1,56,61,8.603511,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^3)/sin(c + d*x)^6,x)","-\frac{10\,a^3\,{\sin\left(c+d\,x\right)}^3+20\,a^3\,{\sin\left(c+d\,x\right)}^2+15\,a^3\,\sin\left(c+d\,x\right)+4\,a^3}{20\,d\,{\sin\left(c+d\,x\right)}^5}","Not used",1,"-(15*a^3*sin(c + d*x) + 4*a^3 + 20*a^3*sin(c + d*x)^2 + 10*a^3*sin(c + d*x)^3)/(20*d*sin(c + d*x)^5)","B"
215,1,56,73,8.602854,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^3)/sin(c + d*x)^7,x)","-\frac{a^3\,\left(-20\,{\sin\left(c+d\,x\right)}^6+20\,{\sin\left(c+d\,x\right)}^3+45\,{\sin\left(c+d\,x\right)}^2+36\,\sin\left(c+d\,x\right)+10\right)}{60\,d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"-(a^3*(36*sin(c + d*x) + 45*sin(c + d*x)^2 + 20*sin(c + d*x)^3 - 20*sin(c + d*x)^6 + 10))/(60*d*sin(c + d*x)^6)","B"
216,1,56,73,8.664728,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^3)/sin(c + d*x)^8,x)","-\frac{35\,a^3\,{\sin\left(c+d\,x\right)}^3+84\,a^3\,{\sin\left(c+d\,x\right)}^2+70\,a^3\,\sin\left(c+d\,x\right)+20\,a^3}{140\,d\,{\sin\left(c+d\,x\right)}^7}","Not used",1,"-(70*a^3*sin(c + d*x) + 20*a^3 + 84*a^3*sin(c + d*x)^2 + 35*a^3*sin(c + d*x)^3)/(140*d*sin(c + d*x)^7)","B"
217,1,70,91,8.455472,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^4*(a + a*sin(c + d*x))^4,x)","\frac{\frac{a^4\,{\sin\left(c+d\,x\right)}^9}{9}+\frac{a^4\,{\sin\left(c+d\,x\right)}^8}{2}+\frac{6\,a^4\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{2\,a^4\,{\sin\left(c+d\,x\right)}^6}{3}+\frac{a^4\,{\sin\left(c+d\,x\right)}^5}{5}}{d}","Not used",1,"((a^4*sin(c + d*x)^5)/5 + (2*a^4*sin(c + d*x)^6)/3 + (6*a^4*sin(c + d*x)^7)/7 + (a^4*sin(c + d*x)^8)/2 + (a^4*sin(c + d*x)^9)/9)/d","B"
218,1,69,88,8.446022,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^3*(a + a*sin(c + d*x))^4,x)","\frac{\frac{a^4\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{4\,a^4\,{\sin\left(c+d\,x\right)}^7}{7}+a^4\,{\sin\left(c+d\,x\right)}^6+\frac{4\,a^4\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a^4\,{\sin\left(c+d\,x\right)}^4}{4}}{d}","Not used",1,"((a^4*sin(c + d*x)^4)/4 + (4*a^4*sin(c + d*x)^5)/5 + a^4*sin(c + d*x)^6 + (4*a^4*sin(c + d*x)^7)/7 + (a^4*sin(c + d*x)^8)/8)/d","B"
219,1,69,67,8.413663,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^2*(a + a*sin(c + d*x))^4,x)","\frac{\frac{a^4\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{2\,a^4\,{\sin\left(c+d\,x\right)}^6}{3}+\frac{6\,a^4\,{\sin\left(c+d\,x\right)}^5}{5}+a^4\,{\sin\left(c+d\,x\right)}^4+\frac{a^4\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"((a^4*sin(c + d*x)^3)/3 + a^4*sin(c + d*x)^4 + (6*a^4*sin(c + d*x)^5)/5 + (2*a^4*sin(c + d*x)^6)/3 + (a^4*sin(c + d*x)^7)/7)/d","B"
220,1,70,45,0.047964,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)*(a + a*sin(c + d*x))^4,x)","\frac{\frac{a^4\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{4\,a^4\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{3\,a^4\,{\sin\left(c+d\,x\right)}^4}{2}+\frac{4\,a^4\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a^4\,{\sin\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"((a^4*sin(c + d*x)^2)/2 + (4*a^4*sin(c + d*x)^3)/3 + (3*a^4*sin(c + d*x)^4)/2 + (4*a^4*sin(c + d*x)^5)/5 + (a^4*sin(c + d*x)^6)/6)/d","B"
221,1,118,81,8.620142,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^4)/sin(c + d*x),x)","\frac{16\,a^4\,\sin\left(c+d\,x\right)}{3\,d}-\frac{a^4\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a^4\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{7\,a^4\,{\cos\left(c+d\,x\right)}^2}{2\,d}+\frac{a^4\,{\cos\left(c+d\,x\right)}^4}{4\,d}-\frac{4\,a^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(16*a^4*sin(c + d*x))/(3*d) - (a^4*log(1/cos(c/2 + (d*x)/2)^2))/d + (a^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (7*a^4*cos(c + d*x)^2)/(2*d) + (a^4*cos(c + d*x)^4)/(4*d) - (4*a^4*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
222,1,235,78,8.646918,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^4)/sin(c + d*x)^2,x)","\frac{8\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d}-\frac{8\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}-\frac{4\,a^4\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{4\,a^4\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{28\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{16\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{8\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{23\,a^4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{a^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(8*a^4*cos(c/2 + (d*x)/2)^2)/d - (8*a^4*cos(c/2 + (d*x)/2)^4)/d - (4*a^4*log(1/cos(c/2 + (d*x)/2)^2))/d + (4*a^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (28*a^4*cos(c/2 + (d*x)/2)^3)/(3*d*sin(c/2 + (d*x)/2)) - (16*a^4*cos(c/2 + (d*x)/2)^5)/(3*d*sin(c/2 + (d*x)/2)) + (8*a^4*cos(c/2 + (d*x)/2)^7)/(3*d*sin(c/2 + (d*x)/2)) + (23*a^4*cos(c/2 + (d*x)/2))/(2*d*sin(c/2 + (d*x)/2)) - (a^4*sin(c/2 + (d*x)/2))/(2*d*cos(c/2 + (d*x)/2))","B"
223,1,207,80,8.618471,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^4)/sin(c + d*x)^3,x)","\frac{6\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{-24\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{15\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-16\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^4}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}-\frac{6\,a^4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(6*a^4*log(tan(c/2 + (d*x)/2)))/d - (a^4*tan(c/2 + (d*x)/2)^2)/(8*d) - (a^4*tan(c/2 + (d*x)/2)^2 - 16*a^4*tan(c/2 + (d*x)/2)^3 - (15*a^4*tan(c/2 + (d*x)/2)^4)/2 - 24*a^4*tan(c/2 + (d*x)/2)^5 + a^4/2 + 8*a^4*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 8*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6)) - (2*a^4*tan(c/2 + (d*x)/2))/d - (6*a^4*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
224,1,68,85,8.456038,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^4)/(a + a*sin(c + d*x)),x)","\frac{\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{a}-\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,"(log(sin(c + d*x) + 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*a))/d","B"
225,1,56,67,0.055517,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^3)/(a + a*sin(c + d*x)),x)","-\frac{\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{a}-\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}}{d}","Not used",1,"-(log(sin(c + d*x) + 1)/a - sin(c + d*x)/a + sin(c + d*x)^2/(2*a) - sin(c + d*x)^3/(3*a))/d","B"
226,1,35,49,0.047165,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^2)/(a + a*sin(c + d*x)),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)-\sin\left(c+d\,x\right)+\frac{{\sin\left(c+d\,x\right)}^2}{2}}{a\,d}","Not used",1,"(log(sin(c + d*x) + 1) - sin(c + d*x) + sin(c + d*x)^2/2)/(a*d)","B"
227,1,26,31,8.459475,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x))/(a + a*sin(c + d*x)),x)","-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)-\sin\left(c+d\,x\right)}{a\,d}","Not used",1,"-(log(sin(c + d*x) + 1) - sin(c + d*x))/(a*d)","B"
228,1,32,32,8.609263,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)) - 2*log(tan(c/2 + (d*x)/2) + 1))/(a*d)","B"
229,1,55,46,8.598703,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}}{2\,a\,d}","Not used",1,"-(2*log(tan(c/2 + (d*x)/2)) - 4*log(tan(c/2 + (d*x)/2) + 1) + tan(c/2 + (d*x)/2) + 1/tan(c/2 + (d*x)/2))/(2*a*d)","B"
230,1,106,63,8.823169,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}\right)}{4\,a\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) - (2*log(tan(c/2 + (d*x)/2) + 1))/(a*d) + tan(c/2 + (d*x)/2)/(2*a*d) + (cot(c/2 + (d*x)/2)^2*(2*tan(c/2 + (d*x)/2) - 1/2))/(4*a*d)","B"
231,1,139,82,8.590834,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a\,d}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{3}\right)}{8\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - tan(c/2 + (d*x)/2)^3/(24*a*d) - log(tan(c/2 + (d*x)/2))/(a*d) + (2*log(tan(c/2 + (d*x)/2) + 1))/(a*d) - (5*tan(c/2 + (d*x)/2))/(8*a*d) - (cot(c/2 + (d*x)/2)^3*(5*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2) + 1/3))/(8*a*d)","B"
232,1,72,87,0.054943,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^4)/(a + a*sin(c + d*x))^2,x)","-\frac{\frac{1}{a^2\,\sin\left(c+d\,x\right)+a^2}+\frac{4\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^2}-\frac{3\,\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)}^3}{3\,a^2}}{d}","Not used",1,"-(1/(a^2*sin(c + d*x) + a^2) + (4*log(sin(c + d*x) + 1))/a^2 - (3*sin(c + d*x))/a^2 + sin(c + d*x)^2/a^2 - sin(c + d*x)^3/(3*a^2))/d","B"
233,1,59,70,8.471418,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^3)/(a + a*sin(c + d*x))^2,x)","\frac{\frac{1}{a^2\,\sin\left(c+d\,x\right)+a^2}+\frac{3\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^2}-\frac{2\,\sin\left(c+d\,x\right)}{a^2}+\frac{{\sin\left(c+d\,x\right)}^2}{2\,a^2}}{d}","Not used",1,"(1/(a^2*sin(c + d*x) + a^2) + (3*log(sin(c + d*x) + 1))/a^2 - (2*sin(c + d*x))/a^2 + sin(c + d*x)^2/(2*a^2))/d","B"
234,1,45,52,0.082677,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^2)/(a + a*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^2-2}{a^2\,d\,\left(\sin\left(c+d\,x\right)+1\right)}-\frac{2\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^2\,d}","Not used",1,"(sin(c + d*x)^2 - 2)/(a^2*d*(sin(c + d*x) + 1)) - (2*log(sin(c + d*x) + 1))/(a^2*d)","B"
235,1,34,37,0.047873,"\text{Not used}","int((cos(c + d*x)*sin(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)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^2\,d}","Not used",1,"1/(a^2*d*(sin(c + d*x) + 1)) + log(sin(c + d*x) + 1)/(a^2*d)","B"
236,1,87,52,8.576359,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) - (2*log(tan(c/2 + (d*x)/2) + 1))/(a^2*d) - (2*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2 + 2*a^2*tan(c/2 + (d*x)/2)))","B"
237,1,136,68,8.608544,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^2\,d}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1}{d\,\left(2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}","Not used",1,"(4*log(tan(c/2 + (d*x)/2) + 1))/(a^2*d) - (2*log(tan(c/2 + (d*x)/2)))/(a^2*d) - (2*tan(c/2 + (d*x)/2) - 3*tan(c/2 + (d*x)/2)^2 + 1)/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 + 2*a^2*tan(c/2 + (d*x)/2)^3 + 2*a^2*tan(c/2 + (d*x)/2))) - tan(c/2 + (d*x)/2)/(2*a^2*d)","B"
238,1,168,85,8.613395,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{6\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^2\,d}+\frac{-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}}{d\,\left(4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}","Not used",1,"(3*log(tan(c/2 + (d*x)/2)))/(a^2*d) - tan(c/2 + (d*x)/2)^2/(8*a^2*d) - (6*log(tan(c/2 + (d*x)/2) + 1))/(a^2*d) + (3*tan(c/2 + (d*x)/2) + (15*tan(c/2 + (d*x)/2)^2)/2 - 4*tan(c/2 + (d*x)/2)^3 - 1/2)/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 + 8*a^2*tan(c/2 + (d*x)/2)^3 + 4*a^2*tan(c/2 + (d*x)/2)^4)) + tan(c/2 + (d*x)/2)/(a^2*d)","B"
239,1,202,101,8.627688,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{1}{3}}{d\,\left(8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^2\,d}-\frac{13\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(4*a^2*d) - tan(c/2 + (d*x)/2)^3/(24*a^2*d) - ((28*tan(c/2 + (d*x)/2)^2)/3 - (4*tan(c/2 + (d*x)/2))/3 + 24*tan(c/2 + (d*x)/2)^3 - 3*tan(c/2 + (d*x)/2)^4 + 1/3)/(d*(8*a^2*tan(c/2 + (d*x)/2)^3 + 16*a^2*tan(c/2 + (d*x)/2)^4 + 8*a^2*tan(c/2 + (d*x)/2)^5)) - (4*log(tan(c/2 + (d*x)/2)))/(a^2*d) + (8*log(tan(c/2 + (d*x)/2) + 1))/(a^2*d) - (13*tan(c/2 + (d*x)/2))/(8*a^2*d)","B"
240,1,108,111,0.128717,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^5)/(a + a*sin(c + d*x))^3,x)","\frac{6\,\sin\left(c+d\,x\right)}{a^3\,d}-\frac{5\,\sin\left(c+d\,x\right)+\frac{9}{2}}{d\,\left(a^3\,{\sin\left(c+d\,x\right)}^2+2\,a^3\,\sin\left(c+d\,x\right)+a^3\right)}-\frac{10\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^3\,d}-\frac{3\,{\sin\left(c+d\,x\right)}^2}{2\,a^3\,d}+\frac{{\sin\left(c+d\,x\right)}^3}{3\,a^3\,d}","Not used",1,"(6*sin(c + d*x))/(a^3*d) - (5*sin(c + d*x) + 9/2)/(d*(2*a^3*sin(c + d*x) + a^3 + a^3*sin(c + d*x)^2)) - (10*log(sin(c + d*x) + 1))/(a^3*d) - (3*sin(c + d*x)^2)/(2*a^3*d) + sin(c + d*x)^3/(3*a^3*d)","B"
241,1,91,93,8.489971,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^4)/(a + a*sin(c + d*x))^3,x)","\frac{6\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^3\,d}+\frac{4\,\sin\left(c+d\,x\right)+\frac{7}{2}}{d\,\left(a^3\,{\sin\left(c+d\,x\right)}^2+2\,a^3\,\sin\left(c+d\,x\right)+a^3\right)}-\frac{3\,\sin\left(c+d\,x\right)}{a^3\,d}+\frac{{\sin\left(c+d\,x\right)}^2}{2\,a^3\,d}","Not used",1,"(6*log(sin(c + d*x) + 1))/(a^3*d) + (4*sin(c + d*x) + 7/2)/(d*(2*a^3*sin(c + d*x) + a^3 + a^3*sin(c + d*x)^2)) - (3*sin(c + d*x))/(a^3*d) + sin(c + d*x)^2/(2*a^3*d)","B"
242,1,59,74,0.073921,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^3)/(a + a*sin(c + d*x))^3,x)","\frac{\sin\left(c+d\,x\right)}{a^3\,d}-\frac{3\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^3\,d}-\frac{3\,\sin\left(c+d\,x\right)+\frac{5}{2}}{a^3\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^2}","Not used",1,"sin(c + d*x)/(a^3*d) - (3*log(sin(c + d*x) + 1))/(a^3*d) - (3*sin(c + d*x) + 5/2)/(a^3*d*(sin(c + d*x) + 1)^2)","B"
243,1,44,60,0.056419,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^2)/(a + a*sin(c + d*x))^3,x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^3\,d}+\frac{2\,\sin\left(c+d\,x\right)+\frac{3}{2}}{a^3\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^2}","Not used",1,"log(sin(c + d*x) + 1)/(a^3*d) + (2*sin(c + d*x) + 3/2)/(a^3*d*(sin(c + d*x) + 1)^2)","B"
244,1,37,30,0.052657,"\text{Not used}","int((cos(c + d*x)*sin(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}-\frac{1}{a^3\,d\,\left(\sin\left(c+d\,x\right)+1\right)}","Not used",1,"1/(2*a^3*d*(sin(c + d*x) + 1)^2) - 1/(a^3*d*(sin(c + d*x) + 1))","B"
245,1,148,74,8.760753,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^3\right)}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) - (4*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^3)/(d*(6*a^3*tan(c/2 + (d*x)/2)^2 + 4*a^3*tan(c/2 + (d*x)/2)^3 + a^3*tan(c/2 + (d*x)/2)^4 + a^3 + 4*a^3*tan(c/2 + (d*x)/2))) - (2*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d)","B"
246,1,193,90,8.652379,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{6\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}","Not used",1,"(6*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) + 16*tan(c/2 + (d*x)/2)^3 + 11*tan(c/2 + (d*x)/2)^4 - 1)/(d*(8*a^3*tan(c/2 + (d*x)/2)^2 + 12*a^3*tan(c/2 + (d*x)/2)^3 + 8*a^3*tan(c/2 + (d*x)/2)^4 + 2*a^3*tan(c/2 + (d*x)/2)^5 + 2*a^3*tan(c/2 + (d*x)/2))) - (3*log(tan(c/2 + (d*x)/2)))/(a^3*d) + (6*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) - tan(c/2 + (d*x)/2)/(2*a^3*d)","B"
247,1,227,108,8.683560,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^3*(a + a*sin(c + d*x))^3),x)","\frac{6\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{-26\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{65\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+2\,{\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+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}}{d\,\left(4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+24\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+16\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{12\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}","Not used",1,"(6*log(tan(c/2 + (d*x)/2)))/(a^3*d) - tan(c/2 + (d*x)/2)^2/(8*a^3*d) + (4*tan(c/2 + (d*x)/2) + 21*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^3 - (65*tan(c/2 + (d*x)/2)^4)/2 - 26*tan(c/2 + (d*x)/2)^5 - 1/2)/(d*(4*a^3*tan(c/2 + (d*x)/2)^2 + 16*a^3*tan(c/2 + (d*x)/2)^3 + 24*a^3*tan(c/2 + (d*x)/2)^4 + 16*a^3*tan(c/2 + (d*x)/2)^5 + 4*a^3*tan(c/2 + (d*x)/2)^6)) - (12*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) + (3*tan(c/2 + (d*x)/2))/(2*a^3*d)","B"
248,1,260,126,8.676467,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^3\,d}-\frac{10\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{20\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}-\frac{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}-\frac{-55\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-47\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{175\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{250\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{1}{3}}{d\,\left(8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+48\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+32\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(3*tan(c/2 + (d*x)/2)^2)/(8*a^3*d) - tan(c/2 + (d*x)/2)^3/(24*a^3*d) - (10*log(tan(c/2 + (d*x)/2)))/(a^3*d) + (20*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) - (25*tan(c/2 + (d*x)/2))/(8*a^3*d) - (15*tan(c/2 + (d*x)/2)^2 - (5*tan(c/2 + (d*x)/2))/3 + (250*tan(c/2 + (d*x)/2)^3)/3 + (175*tan(c/2 + (d*x)/2)^4)/3 - 47*tan(c/2 + (d*x)/2)^5 - 55*tan(c/2 + (d*x)/2)^6 + 1/3)/(d*(8*a^3*tan(c/2 + (d*x)/2)^3 + 32*a^3*tan(c/2 + (d*x)/2)^4 + 48*a^3*tan(c/2 + (d*x)/2)^5 + 32*a^3*tan(c/2 + (d*x)/2)^6 + 8*a^3*tan(c/2 + (d*x)/2)^7))","B"
249,1,114,116,8.531870,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^5)/(a + a*sin(c + d*x))^4,x)","\frac{10\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^4\,d}-\frac{4\,\sin\left(c+d\,x\right)}{a^4\,d}+\frac{10\,{\sin\left(c+d\,x\right)}^2+\frac{35\,\sin\left(c+d\,x\right)}{2}+\frac{47}{6}}{d\,\left(a^4\,{\sin\left(c+d\,x\right)}^3+3\,a^4\,{\sin\left(c+d\,x\right)}^2+3\,a^4\,\sin\left(c+d\,x\right)+a^4\right)}+\frac{{\sin\left(c+d\,x\right)}^2}{2\,a^4\,d}","Not used",1,"(10*log(sin(c + d*x) + 1))/(a^4*d) - (4*sin(c + d*x))/(a^4*d) + ((35*sin(c + d*x))/2 + 10*sin(c + d*x)^2 + 47/6)/(d*(3*a^4*sin(c + d*x) + a^4 + 3*a^4*sin(c + d*x)^2 + a^4*sin(c + d*x)^3)) + sin(c + d*x)^2/(2*a^4*d)","B"
250,1,69,95,0.122958,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^4)/(a + a*sin(c + d*x))^4,x)","\frac{\sin\left(c+d\,x\right)}{a^4\,d}-\frac{4\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^4\,d}-\frac{6\,{\sin\left(c+d\,x\right)}^2+10\,\sin\left(c+d\,x\right)+\frac{13}{3}}{a^4\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^3}","Not used",1,"sin(c + d*x)/(a^4*d) - (4*log(sin(c + d*x) + 1))/(a^4*d) - (10*sin(c + d*x) + 6*sin(c + d*x)^2 + 13/3)/(a^4*d*(sin(c + d*x) + 1)^3)","B"
251,1,54,83,0.063029,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^3)/(a + a*sin(c + d*x))^4,x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^4\,d}+\frac{3\,{\sin\left(c+d\,x\right)}^2+\frac{9\,\sin\left(c+d\,x\right)}{2}+\frac{11}{6}}{a^4\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^3}","Not used",1,"log(sin(c + d*x) + 1)/(a^4*d) + ((9*sin(c + d*x))/2 + 3*sin(c + d*x)^2 + 11/6)/(a^4*d*(sin(c + d*x) + 1)^3)","B"
252,1,54,30,8.483473,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^2)/(a + a*sin(c + d*x))^4,x)","\frac{1}{a^4\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^2}-\frac{1}{a^4\,d\,\left(\sin\left(c+d\,x\right)+1\right)}-\frac{1}{3\,a^4\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^3}","Not used",1,"1/(a^4*d*(sin(c + d*x) + 1)^2) - 1/(a^4*d*(sin(c + d*x) + 1)) - 1/(3*a^4*d*(sin(c + d*x) + 1)^3)","B"
253,1,37,46,8.462331,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x))/(a + a*sin(c + d*x))^4,x)","\frac{1}{3\,a^4\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^3}-\frac{1}{2\,a^4\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^2}","Not used",1,"1/(3*a^4*d*(sin(c + d*x) + 1)^3) - 1/(2*a^4*d*(sin(c + d*x) + 1)^2)","B"
254,1,206,97,9.525625,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)*(a + a*sin(c + d*x))^4),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^4\,d}-\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+15\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+20\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+15\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^4\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^4*d) - (2*log(tan(c/2 + (d*x)/2) + 1))/(a^4*d) - (6*tan(c/2 + (d*x)/2) + 18*tan(c/2 + (d*x)/2)^2 + (80*tan(c/2 + (d*x)/2)^3)/3 + 18*tan(c/2 + (d*x)/2)^4 + 6*tan(c/2 + (d*x)/2)^5)/(d*(15*a^4*tan(c/2 + (d*x)/2)^2 + 20*a^4*tan(c/2 + (d*x)/2)^3 + 15*a^4*tan(c/2 + (d*x)/2)^4 + 6*a^4*tan(c/2 + (d*x)/2)^5 + a^4*tan(c/2 + (d*x)/2)^6 + a^4 + 6*a^4*tan(c/2 + (d*x)/2)))","B"
255,1,251,111,8.721511,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^2*(a + a*sin(c + d*x))^4),x)","\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+74\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{307\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+60\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1}{d\,\left(2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+40\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+30\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}+\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^4\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^4\,d}","Not used",1,"(9*tan(c/2 + (d*x)/2)^2 - 6*tan(c/2 + (d*x)/2) + 60*tan(c/2 + (d*x)/2)^3 + (307*tan(c/2 + (d*x)/2)^4)/3 + 74*tan(c/2 + (d*x)/2)^5 + 23*tan(c/2 + (d*x)/2)^6 - 1)/(d*(12*a^4*tan(c/2 + (d*x)/2)^2 + 30*a^4*tan(c/2 + (d*x)/2)^3 + 40*a^4*tan(c/2 + (d*x)/2)^4 + 30*a^4*tan(c/2 + (d*x)/2)^5 + 12*a^4*tan(c/2 + (d*x)/2)^6 + 2*a^4*tan(c/2 + (d*x)/2)^7 + 2*a^4*tan(c/2 + (d*x)/2))) - (4*log(tan(c/2 + (d*x)/2)))/(a^4*d) + (8*log(tan(c/2 + (d*x)/2) + 1))/(a^4*d) - tan(c/2 + (d*x)/2)/(2*a^4*d)","B"
256,1,286,131,8.690115,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^3*(a + a*sin(c + d*x))^4),x)","\frac{10\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^4\,d}-\frac{72\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{465\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{881\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{255\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-30\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{81\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{2}}{d\,\left(4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+60\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+80\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+60\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+24\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{20\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^4\,d}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4\,d}","Not used",1,"(10*log(tan(c/2 + (d*x)/2)))/(a^4*d) - tan(c/2 + (d*x)/2)^2/(8*a^4*d) - ((255*tan(c/2 + (d*x)/2)^4)/2 - (81*tan(c/2 + (d*x)/2)^2)/2 - 30*tan(c/2 + (d*x)/2)^3 - 5*tan(c/2 + (d*x)/2) + (881*tan(c/2 + (d*x)/2)^5)/3 + (465*tan(c/2 + (d*x)/2)^6)/2 + 72*tan(c/2 + (d*x)/2)^7 + 1/2)/(d*(4*a^4*tan(c/2 + (d*x)/2)^2 + 24*a^4*tan(c/2 + (d*x)/2)^3 + 60*a^4*tan(c/2 + (d*x)/2)^4 + 80*a^4*tan(c/2 + (d*x)/2)^5 + 60*a^4*tan(c/2 + (d*x)/2)^6 + 24*a^4*tan(c/2 + (d*x)/2)^7 + 4*a^4*tan(c/2 + (d*x)/2)^8)) - (20*log(tan(c/2 + (d*x)/2) + 1))/(a^4*d) + (2*tan(c/2 + (d*x)/2))/(a^4*d)","B"
257,1,43,51,8.729977,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x),x)","\frac{2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{d}-\frac{2\,\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\sqrt{a}}\right)}{d}","Not used",1,"(2*(a + a*sin(c + d*x))^(1/2))/d - (2*a^(1/2)*atanh((a + a*sin(c + d*x))^(1/2)/a^(1/2)))/d","B"
258,1,370,114,11.761660,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^n*(a + a*sin(c + d*x))^4,x)","\frac{a^4\,{\sin\left(c+d\,x\right)}^n\,\left(4888\,n+5040\,\sin\left(c+d\,x\right)-2880\,\cos\left(2\,c+2\,d\,x\right)+240\,\cos\left(4\,c+4\,d\,x\right)-1080\,\sin\left(3\,c+3\,d\,x\right)+24\,\sin\left(5\,c+5\,d\,x\right)+8580\,n\,\sin\left(c+d\,x\right)-5376\,n\,\cos\left(2\,c+2\,d\,x\right)+488\,n\,\cos\left(4\,c+4\,d\,x\right)-2122\,n\,\sin\left(3\,c+3\,d\,x\right)+50\,n\,\sin\left(5\,c+5\,d\,x\right)+5014\,n^2\,\sin\left(c+d\,x\right)+1188\,n^3\,\sin\left(c+d\,x\right)+98\,n^4\,\sin\left(c+d\,x\right)+2872\,n^2+680\,n^3+56\,n^4-3200\,n^2\,\cos\left(2\,c+2\,d\,x\right)-768\,n^3\,\cos\left(2\,c+2\,d\,x\right)-64\,n^4\,\cos\left(2\,c+2\,d\,x\right)+328\,n^2\,\cos\left(4\,c+4\,d\,x\right)+88\,n^3\,\cos\left(4\,c+4\,d\,x\right)+8\,n^4\,\cos\left(4\,c+4\,d\,x\right)-1351\,n^2\,\sin\left(3\,c+3\,d\,x\right)-338\,n^3\,\sin\left(3\,c+3\,d\,x\right)-29\,n^4\,\sin\left(3\,c+3\,d\,x\right)+35\,n^2\,\sin\left(5\,c+5\,d\,x\right)+10\,n^3\,\sin\left(5\,c+5\,d\,x\right)+n^4\,\sin\left(5\,c+5\,d\,x\right)+2640\right)}{16\,d\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}","Not used",1,"(a^4*sin(c + d*x)^n*(4888*n + 5040*sin(c + d*x) - 2880*cos(2*c + 2*d*x) + 240*cos(4*c + 4*d*x) - 1080*sin(3*c + 3*d*x) + 24*sin(5*c + 5*d*x) + 8580*n*sin(c + d*x) - 5376*n*cos(2*c + 2*d*x) + 488*n*cos(4*c + 4*d*x) - 2122*n*sin(3*c + 3*d*x) + 50*n*sin(5*c + 5*d*x) + 5014*n^2*sin(c + d*x) + 1188*n^3*sin(c + d*x) + 98*n^4*sin(c + d*x) + 2872*n^2 + 680*n^3 + 56*n^4 - 3200*n^2*cos(2*c + 2*d*x) - 768*n^3*cos(2*c + 2*d*x) - 64*n^4*cos(2*c + 2*d*x) + 328*n^2*cos(4*c + 4*d*x) + 88*n^3*cos(4*c + 4*d*x) + 8*n^4*cos(4*c + 4*d*x) - 1351*n^2*sin(3*c + 3*d*x) - 338*n^3*sin(3*c + 3*d*x) - 29*n^4*sin(3*c + 3*d*x) + 35*n^2*sin(5*c + 5*d*x) + 10*n^3*sin(5*c + 5*d*x) + n^4*sin(5*c + 5*d*x) + 2640))/(16*d*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))","B"
259,1,242,91,10.416348,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^n*(a + a*sin(c + d*x))^3,x)","\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\left(261\,n+336\,\sin\left(c+d\,x\right)-168\,\cos\left(2\,c+2\,d\,x\right)+6\,\cos\left(4\,c+4\,d\,x\right)-48\,\sin\left(3\,c+3\,d\,x\right)+460\,n\,\sin\left(c+d\,x\right)-272\,n\,\cos\left(2\,c+2\,d\,x\right)+11\,n\,\cos\left(4\,c+4\,d\,x\right)-84\,n\,\sin\left(3\,c+3\,d\,x\right)+198\,n^2\,\sin\left(c+d\,x\right)+26\,n^3\,\sin\left(c+d\,x\right)+114\,n^2+15\,n^3-120\,n^2\,\cos\left(2\,c+2\,d\,x\right)-16\,n^3\,\cos\left(2\,c+2\,d\,x\right)+6\,n^2\,\cos\left(4\,c+4\,d\,x\right)+n^3\,\cos\left(4\,c+4\,d\,x\right)-42\,n^2\,\sin\left(3\,c+3\,d\,x\right)-6\,n^3\,\sin\left(3\,c+3\,d\,x\right)+162\right)}{8\,d\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}","Not used",1,"(a^3*sin(c + d*x)^n*(261*n + 336*sin(c + d*x) - 168*cos(2*c + 2*d*x) + 6*cos(4*c + 4*d*x) - 48*sin(3*c + 3*d*x) + 460*n*sin(c + d*x) - 272*n*cos(2*c + 2*d*x) + 11*n*cos(4*c + 4*d*x) - 84*n*sin(3*c + 3*d*x) + 198*n^2*sin(c + d*x) + 26*n^3*sin(c + d*x) + 114*n^2 + 15*n^3 - 120*n^2*cos(2*c + 2*d*x) - 16*n^3*cos(2*c + 2*d*x) + 6*n^2*cos(4*c + 4*d*x) + n^3*cos(4*c + 4*d*x) - 42*n^2*sin(3*c + 3*d*x) - 6*n^3*sin(3*c + 3*d*x) + 162))/(8*d*(50*n + 35*n^2 + 10*n^3 + n^4 + 24))","B"
260,1,147,68,9.641197,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^n*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\left(16\,n+30\,\sin\left(c+d\,x\right)-2\,\sin\left(3\,c+3\,d\,x\right)+29\,n\,\sin\left(c+d\,x\right)+16\,n\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)-3\,n\,\sin\left(3\,c+3\,d\,x\right)+7\,n^2\,\sin\left(c+d\,x\right)+4\,n^2\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)+4\,n^2+24\,{\sin\left(c+d\,x\right)}^2-n^2\,\sin\left(3\,c+3\,d\,x\right)\right)}{4\,d\,\left(n^3+6\,n^2+11\,n+6\right)}","Not used",1,"(a^2*sin(c + d*x)^n*(16*n + 30*sin(c + d*x) - 2*sin(3*c + 3*d*x) + 29*n*sin(c + d*x) + 16*n*(2*sin(c + d*x)^2 - 1) - 3*n*sin(3*c + 3*d*x) + 7*n^2*sin(c + d*x) + 4*n^2*(2*sin(c + d*x)^2 - 1) + 4*n^2 + 24*sin(c + d*x)^2 - n^2*sin(3*c + 3*d*x)))/(4*d*(11*n + 6*n^2 + n^3 + 6))","B"
261,1,67,41,9.183887,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^n*(a + a*sin(c + d*x)),x)","\frac{a\,{\sin\left(c+d\,x\right)}^n\,\left(n+4\,\sin\left(c+d\,x\right)+2\,n\,\sin\left(c+d\,x\right)+n\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)+2\,{\sin\left(c+d\,x\right)}^2\right)}{2\,d\,\left(n^2+3\,n+2\right)}","Not used",1,"(a*sin(c + d*x)^n*(n + 4*sin(c + d*x) + 2*n*sin(c + d*x) + n*(2*sin(c + d*x)^2 - 1) + 2*sin(c + d*x)^2))/(2*d*(3*n + n^2 + 2))","B"
262,0,-1,38,0.000000,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^n)/(a + a*sin(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)*sin(c + d*x)^n)/(a + a*sin(c + d*x)), x)","F"
263,0,-1,38,0.000000,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^n)/(a + a*sin(c + d*x))^2,x)","\int \frac{\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)*sin(c + d*x)^n)/(a + a*sin(c + d*x))^2, x)","F"
264,0,-1,38,0.000000,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^n)/(a + a*sin(c + d*x))^3,x)","\int \frac{\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)*sin(c + d*x)^n)/(a + a*sin(c + d*x))^3, x)","F"
265,0,-1,38,0.000000,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^n)/(a + a*sin(c + d*x))^4,x)","\int \frac{\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)*sin(c + d*x)^n)/(a + a*sin(c + d*x))^4, x)","F"
266,1,226,105,12.130910,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{a\,x}{16}+\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\left(\frac{a\,\left(225\,c+225\,d\,x-960\right)}{240}-\frac{15\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{19\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\left(\frac{a\,\left(300\,c+300\,d\,x-640\right)}{240}-\frac{5\,a\,\left(c+d\,x\right)}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{19\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\left(\frac{a\,\left(90\,c+90\,d\,x-384\right)}{240}-\frac{3\,a\,\left(c+d\,x\right)}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{a\,\left(15\,c+15\,d\,x-64\right)}{240}-\frac{a\,\left(c+d\,x\right)}{16}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(a*x)/16 + ((a*(15*c + 15*d*x - 64))/240 - (a*tan(c/2 + (d*x)/2))/8 - (a*(c + d*x))/16 + tan(c/2 + (d*x)/2)^2*((a*(90*c + 90*d*x - 384))/240 - (3*a*(c + d*x))/8) + tan(c/2 + (d*x)/2)^6*((a*(300*c + 300*d*x - 640))/240 - (5*a*(c + d*x))/4) + tan(c/2 + (d*x)/2)^8*((a*(225*c + 225*d*x - 960))/240 - (15*a*(c + d*x))/16) - (17*a*tan(c/2 + (d*x)/2)^3)/24 + (19*a*tan(c/2 + (d*x)/2)^5)/4 - (19*a*tan(c/2 + (d*x)/2)^7)/4 + (17*a*tan(c/2 + (d*x)/2)^9)/24 + (a*tan(c/2 + (d*x)/2)^11)/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
267,1,198,81,11.972691,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^2*(a + a*sin(c + d*x)),x)","\frac{a\,x}{8}+\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+\left(\frac{a\,\left(150\,c+150\,d\,x-480\right)}{120}-\frac{5\,a\,\left(c+d\,x\right)}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{a\,\left(150\,c+150\,d\,x+160\right)}{120}-\frac{5\,a\,\left(c+d\,x\right)}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\left(\frac{a\,\left(75\,c+75\,d\,x-160\right)}{120}-\frac{5\,a\,\left(c+d\,x\right)}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{a\,\left(15\,c+15\,d\,x-32\right)}{120}-\frac{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,"(a*x)/8 + ((a*(15*c + 15*d*x - 32))/120 - (a*tan(c/2 + (d*x)/2))/4 - (a*(c + d*x))/8 + tan(c/2 + (d*x)/2)^2*((a*(75*c + 75*d*x - 160))/120 - (5*a*(c + d*x))/8) + tan(c/2 + (d*x)/2)^4*((a*(150*c + 150*d*x + 160))/120 - (5*a*(c + d*x))/4) + tan(c/2 + (d*x)/2)^6*((a*(150*c + 150*d*x - 480))/120 - (5*a*(c + d*x))/4) + (3*a*tan(c/2 + (d*x)/2)^3)/2 - (3*a*tan(c/2 + (d*x)/2)^7)/2 + (a*tan(c/2 + (d*x)/2)^9)/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
268,1,198,65,12.332273,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x)),x)","\frac{a\,x}{8}+\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\left(\frac{a\,\left(12\,c+12\,d\,x-48\right)}{24}-\frac{a\,\left(c+d\,x\right)}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\left(\frac{a\,\left(18\,c+18\,d\,x-48\right)}{24}-\frac{3\,a\,\left(c+d\,x\right)}{4}\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}{4}+\left(\frac{a\,\left(12\,c+12\,d\,x-16\right)}{24}-\frac{a\,\left(c+d\,x\right)}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{a\,\left(3\,c+3\,d\,x-16\right)}{24}-\frac{a\,\left(c+d\,x\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(a*x)/8 + ((a*(3*c + 3*d*x - 16))/24 - (a*tan(c/2 + (d*x)/2))/4 - (a*(c + d*x))/8 + tan(c/2 + (d*x)/2)^2*((a*(12*c + 12*d*x - 16))/24 - (a*(c + d*x))/2) + tan(c/2 + (d*x)/2)^6*((a*(12*c + 12*d*x - 48))/24 - (a*(c + d*x))/2) + tan(c/2 + (d*x)/2)^4*((a*(18*c + 18*d*x - 48))/24 - (3*a*(c + d*x))/4) + (7*a*tan(c/2 + (d*x)/2)^3)/4 - (7*a*tan(c/2 + (d*x)/2)^5)/4 + (a*tan(c/2 + (d*x)/2)^7)/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
269,1,160,51,8.717910,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x)))/sin(c + d*x),x)","\frac{-a\,{\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+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,a}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{a\,\mathrm{atan}\left(\frac{a^2}{2\,a^2-a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2-a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(2*a + a*tan(c/2 + (d*x)/2) + 2*a*tan(c/2 + (d*x)/2)^2 - a*tan(c/2 + (d*x)/2)^3)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) + (a*log(tan(c/2 + (d*x)/2)))/d + (a*atan(a^2/(2*a^2 - a^2*tan(c/2 + (d*x)/2)) + (2*a^2*tan(c/2 + (d*x)/2))/(2*a^2 - a^2*tan(c/2 + (d*x)/2))))/d","B"
270,1,108,41,8.799726,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{2\,a\,\mathrm{atan}\left(\frac{\sqrt{2}\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}\right)+a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\cos\left(c+d\,x\right)-\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\sin\left(c+d\,x\right)}","Not used",1,"(2*a*atan((2^(1/2)*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)))/(2*cos(c/2 - pi/4 + (d*x)/2))) + a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*cos(c + d*x) - (a*sin(2*c + 2*d*x))/2)/(d*sin(c + d*x))","B"
271,1,145,52,8.676007,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{a\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) - (a*cot(c/2 + (d*x)/2))/(2*d) - (2*a*atan((2*cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2) - 2*sin(c/2 + (d*x)/2))))/d - (a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(2*d) - (a*cot(c/2 + (d*x)/2)^2)/(8*d) + (a*tan(c/2 + (d*x)/2)^2)/(8*d)","B"
272,1,111,52,8.576527,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x)))/sin(c + d*x)^4,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{3}\right)}{8\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*tan(c/2 + (d*x)/2))/(8*d) + (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*log(tan(c/2 + (d*x)/2)))/(2*d) - (cot(c/2 + (d*x)/2)^3*(a/3 + a*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))/(8*d)","B"
273,1,112,74,8.593478,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x)))/sin(c + d*x)^5,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{a}{4}\right)}{16\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*tan(c/2 + (d*x)/2))/(8*d) + (a*tan(c/2 + (d*x)/2)^4)/(64*d) - (a*log(tan(c/2 + (d*x)/2)))/(8*d) - (cot(c/2 + (d*x)/2)^4*(a/4 + (2*a*tan(c/2 + (d*x)/2))/3 - 2*a*tan(c/2 + (d*x)/2)^3))/(16*d)","B"
274,1,143,90,8.648284,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x)))/sin(c + d*x)^6,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-2\,a\,{\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)}^2}{3}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}\right)}{32\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^3)/(96*d) - (a*tan(c/2 + (d*x)/2))/(16*d) + (a*tan(c/2 + (d*x)/2)^4)/(64*d) + (a*tan(c/2 + (d*x)/2)^5)/(160*d) - (a*log(tan(c/2 + (d*x)/2)))/(8*d) - (cot(c/2 + (d*x)/2)^5*(a/5 + (a*tan(c/2 + (d*x)/2))/2 + (a*tan(c/2 + (d*x)/2)^2)/3 - 2*a*tan(c/2 + (d*x)/2)^4))/(32*d)","B"
275,1,331,135,12.307528,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^3*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,x}{8}-\frac{\frac{a^2\,\left(c+d\,x\right)}{8}+\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{97\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{97\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}-\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}-\frac{a^2\,\left(105\,c+105\,d\,x-352\right)}{840}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{7\,a^2\,\left(c+d\,x\right)}{8}-\frac{a^2\,\left(735\,c+735\,d\,x-2464\right)}{840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{21\,a^2\,\left(c+d\,x\right)}{8}-\frac{a^2\,\left(2205\,c+2205\,d\,x-3360\right)}{840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{21\,a^2\,\left(c+d\,x\right)}{8}-\frac{a^2\,\left(2205\,c+2205\,d\,x-4032\right)}{840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{35\,a^2\,\left(c+d\,x\right)}{8}-\frac{a^2\,\left(3675\,c+3675\,d\,x+2240\right)}{840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{35\,a^2\,\left(c+d\,x\right)}{8}-\frac{a^2\,\left(3675\,c+3675\,d\,x-14560\right)}{840}\right)+\frac{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)}^7}","Not used",1,"(a^2*x)/8 - ((a^2*(c + d*x))/8 + (5*a^2*tan(c/2 + (d*x)/2)^3)/3 - (97*a^2*tan(c/2 + (d*x)/2)^5)/12 + (97*a^2*tan(c/2 + (d*x)/2)^9)/12 - (5*a^2*tan(c/2 + (d*x)/2)^11)/3 - (a^2*tan(c/2 + (d*x)/2)^13)/4 - (a^2*(105*c + 105*d*x - 352))/840 + tan(c/2 + (d*x)/2)^2*((7*a^2*(c + d*x))/8 - (a^2*(735*c + 735*d*x - 2464))/840) + tan(c/2 + (d*x)/2)^10*((21*a^2*(c + d*x))/8 - (a^2*(2205*c + 2205*d*x - 3360))/840) + tan(c/2 + (d*x)/2)^4*((21*a^2*(c + d*x))/8 - (a^2*(2205*c + 2205*d*x - 4032))/840) + tan(c/2 + (d*x)/2)^6*((35*a^2*(c + d*x))/8 - (a^2*(3675*c + 3675*d*x + 2240))/840) + tan(c/2 + (d*x)/2)^8*((35*a^2*(c + d*x))/8 - (a^2*(3675*c + 3675*d*x - 14560))/840) + (a^2*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
276,1,257,103,12.163298,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^2*(a + a*sin(c + d*x))^2,x)","\frac{3\,a^2\,x}{16}-\frac{\frac{3\,a^2\,\left(c+d\,x\right)}{16}-\frac{13\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}-\frac{25\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{25\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{13\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}-\frac{a^2\,\left(45\,c+45\,d\,x-128\right)}{240}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{9\,a^2\,\left(c+d\,x\right)}{8}-\frac{a^2\,\left(270\,c+270\,d\,x-768\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{15\,a^2\,\left(c+d\,x\right)}{4}-\frac{a^2\,\left(900\,c+900\,d\,x-1280\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{45\,a^2\,\left(c+d\,x\right)}{16}-\frac{a^2\,\left(675\,c+675\,d\,x-1920\right)}{240}\right)+\frac{3\,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,"(3*a^2*x)/16 - ((3*a^2*(c + d*x))/16 - (13*a^2*tan(c/2 + (d*x)/2)^3)/24 - (25*a^2*tan(c/2 + (d*x)/2)^5)/4 + (25*a^2*tan(c/2 + (d*x)/2)^7)/4 + (13*a^2*tan(c/2 + (d*x)/2)^9)/24 - (3*a^2*tan(c/2 + (d*x)/2)^11)/8 - (a^2*(45*c + 45*d*x - 128))/240 + tan(c/2 + (d*x)/2)^2*((9*a^2*(c + d*x))/8 - (a^2*(270*c + 270*d*x - 768))/240) + tan(c/2 + (d*x)/2)^6*((15*a^2*(c + d*x))/4 - (a^2*(900*c + 900*d*x - 1280))/240) + tan(c/2 + (d*x)/2)^8*((45*a^2*(c + d*x))/16 - (a^2*(675*c + 675*d*x - 1920))/240) + (3*a^2*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
277,1,262,91,12.132239,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,x}{4}-\frac{\frac{a^2\,\left(c+d\,x\right)}{4}-3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}-\frac{a^2\,\left(15\,c+15\,d\,x-56\right)}{60}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{5\,a^2\,\left(c+d\,x\right)}{4}-\frac{a^2\,\left(75\,c+75\,d\,x-120\right)}{60}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{5\,a^2\,\left(c+d\,x\right)}{4}-\frac{a^2\,\left(75\,c+75\,d\,x-160\right)}{60}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{5\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(150\,c+150\,d\,x-80\right)}{60}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{5\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(150\,c+150\,d\,x-480\right)}{60}\right)+\frac{a^2\,\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)}^2+1\right)}^5}","Not used",1,"(a^2*x)/4 - ((a^2*(c + d*x))/4 - 3*a^2*tan(c/2 + (d*x)/2)^3 + 3*a^2*tan(c/2 + (d*x)/2)^7 - (a^2*tan(c/2 + (d*x)/2)^9)/2 - (a^2*(15*c + 15*d*x - 56))/60 + tan(c/2 + (d*x)/2)^8*((5*a^2*(c + d*x))/4 - (a^2*(75*c + 75*d*x - 120))/60) + tan(c/2 + (d*x)/2)^2*((5*a^2*(c + d*x))/4 - (a^2*(75*c + 75*d*x - 160))/60) + tan(c/2 + (d*x)/2)^4*((5*a^2*(c + d*x))/2 - (a^2*(150*c + 150*d*x - 80))/60) + tan(c/2 + (d*x)/2)^6*((5*a^2*(c + d*x))/2 - (a^2*(150*c + 150*d*x - 480))/60) + (a^2*tan(c/2 + (d*x)/2))/2)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
278,1,188,71,9.043346,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{4\,a^2}{3}}{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\,a^2\,\mathrm{atan}\left(\frac{4\,a^4}{4\,a^4-4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^4-4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (4*a^2*tan(c/2 + (d*x)/2)^2 - 2*a^2*tan(c/2 + (d*x)/2)^5 + (4*a^2)/3 + 2*a^2*tan(c/2 + (d*x)/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*a^2*atan((4*a^4)/(4*a^4 - 4*a^4*tan(c/2 + (d*x)/2)) + (4*a^4*tan(c/2 + (d*x)/2))/(4*a^4 - 4*a^4*tan(c/2 + (d*x)/2))))/d","B"
279,1,201,74,8.811054,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{2\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{-3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a^2}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^4}{4\,a^4+a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^4+a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(2*a^2*log(tan(c/2 + (d*x)/2)))/d + (8*a^2*tan(c/2 + (d*x)/2)^3 - 3*a^2*tan(c/2 + (d*x)/2)^4 - a^2 + 8*a^2*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2) + 4*tan(c/2 + (d*x)/2)^3 + 2*tan(c/2 + (d*x)/2)^5)) + (a^2*atan(a^4/(4*a^4 + a^4*tan(c/2 + (d*x)/2)) - (4*a^4*tan(c/2 + (d*x)/2))/(4*a^4 + a^4*tan(c/2 + (d*x)/2))))/d + (a^2*tan(c/2 + (d*x)/2))/(2*d)","B"
280,1,213,73,8.776504,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{15\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}+\frac{4\,a^2\,\mathrm{atan}\left(\frac{16\,a^4}{4\,a^4+16\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^4+16\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (4*a^2*tan(c/2 + (d*x)/2)^3 - (15*a^2*tan(c/2 + (d*x)/2)^2)/2 + a^2/2 + 4*a^2*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^4)) + (a^2*log(tan(c/2 + (d*x)/2)))/(2*d) + (4*a^2*atan((16*a^4)/(4*a^4 + 16*a^4*tan(c/2 + (d*x)/2)) - (4*a^4*tan(c/2 + (d*x)/2))/(4*a^4 + 16*a^4*tan(c/2 + (d*x)/2))))/d + (a^2*tan(c/2 + (d*x)/2))/d","B"
281,1,193,73,8.937318,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^2)/sin(c + d*x)^4,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{2\,a^2\,\mathrm{atan}\left(\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{3\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(4*d) - (a^2*cot(c/2 + (d*x)/2)^3)/(24*d) - (a^2*cot(c/2 + (d*x)/2)^2)/(4*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (2*a^2*atan((cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))))/d - (a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (3*a^2*cot(c/2 + (d*x)/2))/(8*d) + (3*a^2*tan(c/2 + (d*x)/2))/(8*d)","B"
282,1,161,82,8.621872,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^2)/sin(c + d*x)^5,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{5\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{a^2}{4}\right)}{16\,d}-\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(12*d) + (a^2*tan(c/2 + (d*x)/2)^4)/(64*d) - (5*a^2*log(tan(c/2 + (d*x)/2)))/(8*d) - (cot(c/2 + (d*x)/2)^4*(2*a^2*tan(c/2 + (d*x)/2)^2 - 4*a^2*tan(c/2 + (d*x)/2)^3 + a^2/4 + (4*a^2*tan(c/2 + (d*x)/2))/3))/(16*d) - (a^2*tan(c/2 + (d*x)/2))/(4*d)","B"
283,1,160,100,8.629304,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^2)/sin(c + d*x)^6,x)","\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{5}\right)}{32\,d}-\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}","Not used",1,"(5*a^2*tan(c/2 + (d*x)/2)^3)/(96*d) + (a^2*tan(c/2 + (d*x)/2)^4)/(32*d) + (a^2*tan(c/2 + (d*x)/2)^5)/(160*d) - (a^2*log(tan(c/2 + (d*x)/2)))/(4*d) - (cot(c/2 + (d*x)/2)^5*((5*a^2*tan(c/2 + (d*x)/2)^2)/3 - 6*a^2*tan(c/2 + (d*x)/2)^4 + a^2/5 + a^2*tan(c/2 + (d*x)/2)))/(32*d) - (3*a^2*tan(c/2 + (d*x)/2))/(16*d)","B"
284,1,339,124,9.657656,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^2)/sin(c + d*x)^7,x)","-\frac{a^2\,\left(5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-24\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+360\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}{1920\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"-(a^2*(5*cos(c/2 + (d*x)/2)^12 - 5*sin(c/2 + (d*x)/2)^12 - 24*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 + 24*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 45*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 - 40*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 15*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 240*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 - 240*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 15*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 40*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 45*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 360*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6))/(1920*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
285,1,331,132,12.158530,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^2*(a + a*sin(c + d*x))^3,x)","\frac{5\,a^3\,x}{16}-\frac{\frac{5\,a^3\,\left(c+d\,x\right)}{16}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{119\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8}+\frac{119\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{2}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}-\frac{a^3\,\left(105\,c+105\,d\,x-320\right)}{336}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{35\,a^3\,\left(c+d\,x\right)}{16}-\frac{a^3\,\left(735\,c+735\,d\,x-2240\right)}{336}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{105\,a^3\,\left(c+d\,x\right)}{16}-\frac{a^3\,\left(2205\,c+2205\,d\,x-2688\right)}{336}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{175\,a^3\,\left(c+d\,x\right)}{16}-\frac{a^3\,\left(3675\,c+3675\,d\,x-896\right)}{336}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{105\,a^3\,\left(c+d\,x\right)}{16}-\frac{a^3\,\left(2205\,c+2205\,d\,x-4032\right)}{336}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{175\,a^3\,\left(c+d\,x\right)}{16}-\frac{a^3\,\left(3675\,c+3675\,d\,x-10304\right)}{336}\right)+\frac{5\,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,"(5*a^3*x)/16 - ((5*a^3*(c + d*x))/16 + (3*a^3*tan(c/2 + (d*x)/2)^3)/2 - (119*a^3*tan(c/2 + (d*x)/2)^5)/8 + (119*a^3*tan(c/2 + (d*x)/2)^9)/8 - (3*a^3*tan(c/2 + (d*x)/2)^11)/2 - (5*a^3*tan(c/2 + (d*x)/2)^13)/8 - (a^3*(105*c + 105*d*x - 320))/336 + tan(c/2 + (d*x)/2)^2*((35*a^3*(c + d*x))/16 - (a^3*(735*c + 735*d*x - 2240))/336) + tan(c/2 + (d*x)/2)^4*((105*a^3*(c + d*x))/16 - (a^3*(2205*c + 2205*d*x - 2688))/336) + tan(c/2 + (d*x)/2)^6*((175*a^3*(c + d*x))/16 - (a^3*(3675*c + 3675*d*x - 896))/336) + tan(c/2 + (d*x)/2)^10*((105*a^3*(c + d*x))/16 - (a^3*(2205*c + 2205*d*x - 4032))/336) + tan(c/2 + (d*x)/2)^8*((175*a^3*(c + d*x))/16 - (a^3*(3675*c + 3675*d*x - 10304))/336) + (5*a^3*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
286,1,349,117,10.717753,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))^3,x)","\frac{7\,a^3\,x}{16}-\frac{\frac{37\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}-\frac{37\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{73\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{73\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}-\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{a^3\,\left(105\,c+105\,d\,x\right)}{240}-\frac{a^3\,\left(105\,c+105\,d\,x-352\right)}{240}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{a^3\,\left(105\,c+105\,d\,x\right)}{40}-\frac{a^3\,\left(630\,c+630\,d\,x-480\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(105\,c+105\,d\,x\right)}{40}-\frac{a^3\,\left(630\,c+630\,d\,x-1632\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3\,\left(105\,c+105\,d\,x\right)}{16}-\frac{a^3\,\left(1575\,c+1575\,d\,x-960\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^3\,\left(105\,c+105\,d\,x\right)}{16}-\frac{a^3\,\left(1575\,c+1575\,d\,x-4320\right)}{240}\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(2100\,c+2100\,d\,x-3520\right)}{240}\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)}^6}","Not used",1,"(7*a^3*x)/16 - ((37*a^3*tan(c/2 + (d*x)/2)^7)/4 - (37*a^3*tan(c/2 + (d*x)/2)^5)/4 - (73*a^3*tan(c/2 + (d*x)/2)^3)/24 + (73*a^3*tan(c/2 + (d*x)/2)^9)/24 - (7*a^3*tan(c/2 + (d*x)/2)^11)/8 + (a^3*(105*c + 105*d*x))/240 - (a^3*(105*c + 105*d*x - 352))/240 + tan(c/2 + (d*x)/2)^10*((a^3*(105*c + 105*d*x))/40 - (a^3*(630*c + 630*d*x - 480))/240) + tan(c/2 + (d*x)/2)^2*((a^3*(105*c + 105*d*x))/40 - (a^3*(630*c + 630*d*x - 1632))/240) + tan(c/2 + (d*x)/2)^4*((a^3*(105*c + 105*d*x))/16 - (a^3*(1575*c + 1575*d*x - 960))/240) + tan(c/2 + (d*x)/2)^8*((a^3*(105*c + 105*d*x))/16 - (a^3*(1575*c + 1575*d*x - 4320))/240) + tan(c/2 + (d*x)/2)^6*((a^3*(105*c + 105*d*x))/12 - (a^3*(2100*c + 2100*d*x - 3520))/240) + (7*a^3*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
287,1,244,99,10.356942,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^3)/sin(c + d*x),x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{13\,a^3\,\mathrm{atan}\left(\frac{169\,a^6}{16\,\left(\frac{13\,a^6}{2}-\frac{169\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{13\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{13\,a^6}{2}-\frac{169\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}+\frac{-\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}-4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{19\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{19\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{11\,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)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d + (13*a^3*atan((169*a^6)/(16*((13*a^6)/2 - (169*a^6*tan(c/2 + (d*x)/2))/16)) + (13*a^6*tan(c/2 + (d*x)/2))/(2*((13*a^6)/2 - (169*a^6*tan(c/2 + (d*x)/2))/16))))/(4*d) + (4*a^3*tan(c/2 + (d*x)/2)^2 + (19*a^3*tan(c/2 + (d*x)/2)^3)/4 - (19*a^3*tan(c/2 + (d*x)/2)^5)/4 - 4*a^3*tan(c/2 + (d*x)/2)^6 - (11*a^3*tan(c/2 + (d*x)/2)^7)/4 + (11*a^3*tan(c/2 + (d*x)/2))/4)/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
288,1,264,92,8.766264,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^3)/sin(c + d*x)^2,x)","\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{a^3\,\mathrm{atan}\left(\frac{a^6}{6\,a^6-a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{6\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^6-a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{-7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+24\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{32\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-a^3}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)))/d + (a^3*atan(a^6/(6*a^6 - a^6*tan(c/2 + (d*x)/2)) + (6*a^6*tan(c/2 + (d*x)/2))/(6*a^6 - a^6*tan(c/2 + (d*x)/2))))/d + (a^3*tan(c/2 + (d*x)/2))/(2*d) + (3*a^3*tan(c/2 + (d*x)/2)^2 + 24*a^3*tan(c/2 + (d*x)/2)^3 - 3*a^3*tan(c/2 + (d*x)/2)^4 + 8*a^3*tan(c/2 + (d*x)/2)^5 - 7*a^3*tan(c/2 + (d*x)/2)^6 - a^3 + (32*a^3*tan(c/2 + (d*x)/2))/3)/(d*(2*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^3 + 6*tan(c/2 + (d*x)/2)^5 + 2*tan(c/2 + (d*x)/2)^7))","B"
289,1,259,98,8.680574,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^3)/sin(c + d*x)^3,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{5\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{47\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-23\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{5\,a^3\,\mathrm{atan}\left(\frac{25\,a^6}{25\,a^6+25\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{25\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{25\,a^6+25\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (5*a^3*log(tan(c/2 + (d*x)/2)))/(2*d) - (8*a^3*tan(c/2 + (d*x)/2)^3 - 23*a^3*tan(c/2 + (d*x)/2)^2 - (47*a^3*tan(c/2 + (d*x)/2)^4)/2 + 10*a^3*tan(c/2 + (d*x)/2)^5 + a^3/2 + 6*a^3*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 8*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6)) + (5*a^3*atan((25*a^6)/(25*a^6 + 25*a^6*tan(c/2 + (d*x)/2)) - (25*a^6*tan(c/2 + (d*x)/2))/(25*a^6 + 25*a^6*tan(c/2 + (d*x)/2))))/d + (3*a^3*tan(c/2 + (d*x)/2))/(2*d)","B"
290,1,249,91,8.675379,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^3)/sin(c + d*x)^4,x)","\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{6\,a^3\,\mathrm{atan}\left(\frac{36\,a^6}{6\,a^6-36\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{6\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^6-36\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{34\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{11\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(3*a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (a^3*log(tan(c/2 + (d*x)/2)))/(2*d) - (6*a^3*atan((36*a^6)/(6*a^6 - 36*a^6*tan(c/2 + (d*x)/2)) + (6*a^6*tan(c/2 + (d*x)/2))/(6*a^6 - 36*a^6*tan(c/2 + (d*x)/2))))/d - ((34*a^3*tan(c/2 + (d*x)/2)^2)/3 - 13*a^3*tan(c/2 + (d*x)/2)^3 + 11*a^3*tan(c/2 + (d*x)/2)^4 + a^3/3 + 3*a^3*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 8*tan(c/2 + (d*x)/2)^5)) + (11*a^3*tan(c/2 + (d*x)/2))/(8*d)","B"
291,1,237,100,8.893075,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^3)/sin(c + d*x)^5,x)","\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{2\,a^3\,\mathrm{atan}\left(\frac{8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+13\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{13\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{13\,a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8\,d}-\frac{a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(3*a^3*tan(c/2 + (d*x)/2)^2)/(8*d) - (a^3*cot(c/2 + (d*x)/2)^3)/(8*d) - (a^3*cot(c/2 + (d*x)/2)^4)/(64*d) - (3*a^3*cot(c/2 + (d*x)/2)^2)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^3)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^4)/(64*d) - (2*a^3*atan((8*cos(c/2 + (d*x)/2) + 13*sin(c/2 + (d*x)/2))/(13*cos(c/2 + (d*x)/2) - 8*sin(c/2 + (d*x)/2))))/d - (13*a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(8*d) - (a^3*cot(c/2 + (d*x)/2))/(8*d) + (a^3*tan(c/2 + (d*x)/2))/(8*d)","B"
292,1,291,100,9.304411,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^3)/sin(c + d*x)^6,x)","-\frac{a^3\,\left(6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-45\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-130\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+420\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-420\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+130\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}{960\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(a^3*(6*cos(c/2 + (d*x)/2)^10 - 6*sin(c/2 + (d*x)/2)^10 - 45*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 + 45*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - 130*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 - 120*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7 + 420*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 - 420*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 120*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3 + 130*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5))/(960*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)","B"
293,1,339,124,9.674730,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^3)/sin(c + d*x)^7,x)","-\frac{a^3\,\left(5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-36\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+36\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-140\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+600\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-600\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+140\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}{1920\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"-(a^3*(5*cos(c/2 + (d*x)/2)^12 - 5*sin(c/2 + (d*x)/2)^12 - 36*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 + 36*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 105*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 - 140*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 15*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 600*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 - 600*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 15*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 140*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 105*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6))/(1920*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
294,1,349,137,10.727790,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^4,x)","\frac{21\,a^4\,x}{16}-\frac{\frac{63\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}-\frac{63\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{235\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{235\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}-\frac{5\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{a^4\,\left(315\,c+315\,d\,x\right)}{240}-\frac{a^4\,\left(315\,c+315\,d\,x-896\right)}{240}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{a^4\,\left(315\,c+315\,d\,x\right)}{40}-\frac{a^4\,\left(1890\,c+1890\,d\,x-1920\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^4\,\left(315\,c+315\,d\,x\right)}{40}-\frac{a^4\,\left(1890\,c+1890\,d\,x-3456\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^4\,\left(315\,c+315\,d\,x\right)}{16}-\frac{a^4\,\left(4725\,c+4725\,d\,x-3840\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^4\,\left(315\,c+315\,d\,x\right)}{16}-\frac{a^4\,\left(4725\,c+4725\,d\,x-9600\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^4\,\left(315\,c+315\,d\,x\right)}{12}-\frac{a^4\,\left(6300\,c+6300\,d\,x-8960\right)}{240}\right)+\frac{5\,a^4\,\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,"(21*a^4*x)/16 - ((63*a^4*tan(c/2 + (d*x)/2)^7)/4 - (63*a^4*tan(c/2 + (d*x)/2)^5)/4 - (235*a^4*tan(c/2 + (d*x)/2)^3)/24 + (235*a^4*tan(c/2 + (d*x)/2)^9)/24 - (5*a^4*tan(c/2 + (d*x)/2)^11)/8 + (a^4*(315*c + 315*d*x))/240 - (a^4*(315*c + 315*d*x - 896))/240 + tan(c/2 + (d*x)/2)^10*((a^4*(315*c + 315*d*x))/40 - (a^4*(1890*c + 1890*d*x - 1920))/240) + tan(c/2 + (d*x)/2)^2*((a^4*(315*c + 315*d*x))/40 - (a^4*(1890*c + 1890*d*x - 3456))/240) + tan(c/2 + (d*x)/2)^4*((a^4*(315*c + 315*d*x))/16 - (a^4*(4725*c + 4725*d*x - 3840))/240) + tan(c/2 + (d*x)/2)^8*((a^4*(315*c + 315*d*x))/16 - (a^4*(4725*c + 4725*d*x - 9600))/240) + tan(c/2 + (d*x)/2)^6*((a^4*(315*c + 315*d*x))/12 - (a^4*(6300*c + 6300*d*x - 8960))/240) + (5*a^4*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
295,1,295,117,10.419481,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^4)/sin(c + d*x),x)","\frac{a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{5\,a^4\,\mathrm{atan}\left(\frac{25\,a^8}{10\,a^8-25\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{10\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{10\,a^8-25\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{3\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+10\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+14\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{8\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-14\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{34\,a^4}{15}}{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)}","Not used",1,"(a^4*log(tan(c/2 + (d*x)/2)))/d + (5*a^4*atan((25*a^8)/(10*a^8 - 25*a^8*tan(c/2 + (d*x)/2)) + (10*a^8*tan(c/2 + (d*x)/2))/(10*a^8 - 25*a^8*tan(c/2 + (d*x)/2))))/d - ((4*a^4*tan(c/2 + (d*x)/2)^2)/3 - 14*a^4*tan(c/2 + (d*x)/2)^3 + (8*a^4*tan(c/2 + (d*x)/2)^4)/3 + 20*a^4*tan(c/2 + (d*x)/2)^6 + 14*a^4*tan(c/2 + (d*x)/2)^7 + 10*a^4*tan(c/2 + (d*x)/2)^8 + 3*a^4*tan(c/2 + (d*x)/2)^9 + (34*a^4)/15 - 3*a^4*tan(c/2 + (d*x)/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))","B"
296,1,295,116,8.833792,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^4)/sin(c + d*x)^2,x)","\frac{4\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{17\,a^4\,\mathrm{atan}\left(\frac{289\,a^8}{16\,\left(34\,a^8-\frac{289\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{34\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{34\,a^8-\frac{289\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}}\right)}{4\,d}+\frac{-\frac{25\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}-\frac{39\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{19\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{128\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{15\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{32\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-a^4}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(4*a^4*log(tan(c/2 + (d*x)/2)))/d + (17*a^4*atan((289*a^8)/(16*(34*a^8 - (289*a^8*tan(c/2 + (d*x)/2))/16)) + (34*a^8*tan(c/2 + (d*x)/2))/(34*a^8 - (289*a^8*tan(c/2 + (d*x)/2))/16)))/(4*d) + ((15*a^4*tan(c/2 + (d*x)/2)^2)/2 + (128*a^4*tan(c/2 + (d*x)/2)^3)/3 + (19*a^4*tan(c/2 + (d*x)/2)^4)/2 + 32*a^4*tan(c/2 + (d*x)/2)^5 - (39*a^4*tan(c/2 + (d*x)/2)^6)/2 - (25*a^4*tan(c/2 + (d*x)/2)^8)/2 - a^4 + (32*a^4*tan(c/2 + (d*x)/2))/3)/(d*(2*tan(c/2 + (d*x)/2) + 8*tan(c/2 + (d*x)/2)^3 + 12*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^7 + 2*tan(c/2 + (d*x)/2)^9)) + (a^4*tan(c/2 + (d*x)/2))/(2*d)","B"
297,1,107,104,11.912514,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^4)/(a + a*sin(c + d*x)),x)","\frac{3\,x}{8\,a}+\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{16}{15}}{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) + ((16*tan(c/2 + (d*x)/2)^2)/3 - (3*tan(c/2 + (d*x)/2))/4 - (7*tan(c/2 + (d*x)/2)^3)/2 + (32*tan(c/2 + (d*x)/2)^4)/3 + (7*tan(c/2 + (d*x)/2)^7)/2 + (3*tan(c/2 + (d*x)/2)^9)/4 + 16/15)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
298,1,79,87,8.605058,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^3)/(a + a*sin(c + d*x)),x)","\frac{{\cos\left(c+d\,x\right)}^3}{3\,a\,d}-\frac{\cos\left(c+d\,x\right)}{a\,d}-\frac{3\,x}{8\,a}-\frac{{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,a\,d}+\frac{5\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,a\,d}","Not used",1,"cos(c + d*x)^3/(3*a*d) - cos(c + d*x)/(a*d) - (3*x)/(8*a) - (cos(c + d*x)^3*sin(c + d*x))/(4*a*d) + (5*cos(c + d*x)*sin(c + d*x))/(8*a*d)","B"
299,1,66,62,10.464204,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^2)/(a + a*sin(c + d*x)),x)","\frac{x}{2\,a}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{4}{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) + (4*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^5 + 4/3)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
300,1,33,45,8.686448,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x))/(a + a*sin(c + d*x)),x)","-\frac{x}{2\,a}-\frac{\cos\left(c+d\,x\right)-\frac{\sin\left(2\,c+2\,d\,x\right)}{4}}{a\,d}","Not used",1,"- x/(2*a) - (cos(c + d*x) - sin(2*c + 2*d*x)/4)/(a*d)","B"
301,1,79,22,8.769875,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}\right)}{a\,d}+\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}","Not used",1,"(2*atan((2^(1/2)*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)))/(2*cos(c/2 - pi/4 + (d*x)/2))))/(a*d) + log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(a*d)","B"
302,1,25,29,8.599205,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\mathrm{cot}\left(c+d\,x\right)}{a\,d}","Not used",1,"-(log(tan(c/2 + (d*x)/2)) + cot(c + d*x))/(a*d)","B"
303,1,87,53,8.652522,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}\right)}{4\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) + log(tan(c/2 + (d*x)/2))/(2*a*d) - tan(c/2 + (d*x)/2)/(2*a*d) + (cot(c/2 + (d*x)/2)^2*(2*tan(c/2 + (d*x)/2) - 1/2))/(4*a*d)","B"
304,1,119,72,8.621012,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{3}\right)}{8\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) - log(tan(c/2 + (d*x)/2))/(2*a*d) + (3*tan(c/2 + (d*x)/2))/(8*a*d) - (cot(c/2 + (d*x)/2)^3*(3*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2) + 1/3))/(8*a*d)","B"
305,1,151,95,8.675127,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{1}{4}\right)}{16\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - tan(c/2 + (d*x)/2)^3/(24*a*d) + tan(c/2 + (d*x)/2)^4/(64*a*d) + (3*log(tan(c/2 + (d*x)/2)))/(8*a*d) - (3*tan(c/2 + (d*x)/2))/(8*a*d) + (cot(c/2 + (d*x)/2)^4*((2*tan(c/2 + (d*x)/2))/3 - 2*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^3 - 1/4))/(16*a*d)","B"
306,1,291,114,9.250109,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^6*(a + a*sin(c + d*x))),x)","-\frac{6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-50\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-300\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+300\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+50\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+360\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{960\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(6*cos(c/2 + (d*x)/2)^10 - 6*sin(c/2 + (d*x)/2)^10 + 15*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 - 15*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - 50*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 + 120*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7 - 300*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + 300*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 - 120*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3 + 50*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 360*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/(960*a*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)","B"
307,1,147,111,12.339830,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^4)/(a + a*sin(c + d*x))^2,x)","-\frac{27\,x}{8\,a^2}-\frac{\frac{27\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4}+\frac{27\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{99\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{4}+\frac{99\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{157\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}+\frac{215\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{431\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{12}+\frac{47\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{12}+\frac{32}{3}}{a^2\,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)}^4}","Not used",1,"- (27*x)/(8*a^2) - ((47*tan(c/2 + (d*x)/2))/12 + (431*tan(c/2 + (d*x)/2)^2)/12 + (215*tan(c/2 + (d*x)/2)^3)/12 + (157*tan(c/2 + (d*x)/2)^4)/4 + (99*tan(c/2 + (d*x)/2)^5)/4 + (99*tan(c/2 + (d*x)/2)^6)/4 + (27*tan(c/2 + (d*x)/2)^7)/4 + (27*tan(c/2 + (d*x)/2)^8)/4 + 32/3)/(a^2*d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
308,1,120,83,12.377698,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^3)/(a + a*sin(c + d*x))^2,x)","\frac{3\,x}{a^2}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{10\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{28}{3}}{a^2\,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)}^3}","Not used",1,"(3*x)/a^2 + ((10*tan(c/2 + (d*x)/2))/3 + 22*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^3 + 16*tan(c/2 + (d*x)/2)^4 + 6*tan(c/2 + (d*x)/2)^5 + 6*tan(c/2 + (d*x)/2)^6 + 28/3)/(a^2*d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
309,1,95,69,10.792294,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^2)/(a + a*sin(c + d*x))^2,x)","-\frac{5\,x}{2\,a^2}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8}{a^2\,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)}^2}","Not used",1,"- (5*x)/(2*a^2) - (3*tan(c/2 + (d*x)/2) + 11*tan(c/2 + (d*x)/2)^2 + 5*tan(c/2 + (d*x)/2)^3 + 5*tan(c/2 + (d*x)/2)^4 + 8)/(a^2*d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
310,1,68,47,8.864669,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x))/(a + a*sin(c + d*x))^2,x)","\frac{2\,x}{a^2}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}{a^2\,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,"(2*x)/a^2 + (2*tan(c/2 + (d*x)/2) + 4*tan(c/2 + (d*x)/2)^2 + 6)/(a^2*d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1))","B"
311,1,39,40,8.675277,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{4}{a^2\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) + 4/(a^2*d*(tan(c/2 + (d*x)/2) + 1))","B"
312,1,87,54,8.685564,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1}{d\,\left(2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^2*d) - (9*tan(c/2 + (d*x)/2) + 1)/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 + 2*a^2*tan(c/2 + (d*x)/2))) - (2*log(tan(c/2 + (d*x)/2)))/(a^2*d)","B"
313,1,120,78,8.658394,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^2\,d}+\frac{20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{1}{2}}{d\,\left(4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) + (5*log(tan(c/2 + (d*x)/2)))/(2*a^2*d) + ((7*tan(c/2 + (d*x)/2))/2 + 20*tan(c/2 + (d*x)/2)^2 - 1/2)/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 + 4*a^2*tan(c/2 + (d*x)/2)^3)) - tan(c/2 + (d*x)/2)/(a^2*d)","B"
314,1,153,91,8.645317,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^2\,d}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{43\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{1}{3}}{d\,\left(8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^2*d) - tan(c/2 + (d*x)/2)^2/(4*a^2*d) - (3*log(tan(c/2 + (d*x)/2)))/(a^2*d) - (9*tan(c/2 + (d*x)/2)^2 - (5*tan(c/2 + (d*x)/2))/3 + 43*tan(c/2 + (d*x)/2)^3 + 1/3)/(d*(8*a^2*tan(c/2 + (d*x)/2)^3 + 8*a^2*tan(c/2 + (d*x)/2)^4)) + (11*tan(c/2 + (d*x)/2))/(8*a^2*d)","B"
315,1,121,97,12.071126,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^3)/(a + a*sin(c + d*x))^3,x)","-\frac{11\,x}{2\,a^3}-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+33\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{154\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{161\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+41\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{52}{3}}{a^3\,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)}^2}","Not used",1,"- (11*x)/(2*a^3) - (41*tan(c/2 + (d*x)/2) + (161*tan(c/2 + (d*x)/2)^2)/3 + 70*tan(c/2 + (d*x)/2)^3 + (154*tan(c/2 + (d*x)/2)^4)/3 + 33*tan(c/2 + (d*x)/2)^5 + 11*tan(c/2 + (d*x)/2)^6 + 52/3)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
316,1,94,76,11.322373,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^2)/(a + a*sin(c + d*x))^3,x)","\frac{3\,x}{a^3}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{58\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+22\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{28}{3}}{a^3\,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)}","Not used",1,"(3*x)/a^3 + (22*tan(c/2 + (d*x)/2) + (58*tan(c/2 + (d*x)/2)^2)/3 + 18*tan(c/2 + (d*x)/2)^3 + 6*tan(c/2 + (d*x)/2)^4 + 28/3)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^3*(tan(c/2 + (d*x)/2)^2 + 1))","B"
317,1,54,61,8.774167,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x))/(a + a*sin(c + d*x))^3,x)","-\frac{x}{a^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{10}{3}}{a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^3}","Not used",1,"- x/a^3 - (8*tan(c/2 + (d*x)/2) + 2*tan(c/2 + (d*x)/2)^2 + 10/3)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^3)","B"
318,1,64,68,8.900070,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{14}{3}}{a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^3}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) + (8*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^2 + 14/3)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^3)","B"
319,1,145,82,8.807220,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{61\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+1}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - ((61*tan(c/2 + (d*x)/2))/3 + 35*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^3 + 1)/(d*(6*a^3*tan(c/2 + (d*x)/2)^2 + 6*a^3*tan(c/2 + (d*x)/2)^3 + 2*a^3*tan(c/2 + (d*x)/2)^4 + 2*a^3*tan(c/2 + (d*x)/2))) - (3*log(tan(c/2 + (d*x)/2)))/(a^3*d)","B"
320,1,178,106,8.660154,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^3*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{11\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^3\,d}+\frac{62\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{227\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{403\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{6}+\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{1}{2}}{d\,\left(4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^3*d) + (11*log(tan(c/2 + (d*x)/2)))/(2*a^3*d) + ((9*tan(c/2 + (d*x)/2))/2 + (403*tan(c/2 + (d*x)/2)^2)/6 + (227*tan(c/2 + (d*x)/2)^3)/2 + 62*tan(c/2 + (d*x)/2)^4 - 1/2)/(d*(4*a^3*tan(c/2 + (d*x)/2)^2 + 12*a^3*tan(c/2 + (d*x)/2)^3 + 12*a^3*tan(c/2 + (d*x)/2)^4 + 4*a^3*tan(c/2 + (d*x)/2)^5)) - (3*tan(c/2 + (d*x)/2))/(2*a^3*d)","B"
321,1,207,144,9.055731,"\text{Not used}","int((cos(e + f*x)^2*sin(e + f*x))/(a + a*sin(e + f*x))^6,x)","-\frac{2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(11\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+99\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+81\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+609\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+441\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+945\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+315\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+315\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\right)}{315\,a^6\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^9}","Not used",1,"-(2*cos(e/2 + (f*x)/2)^2*(11*cos(e/2 + (f*x)/2)^7 + 315*sin(e/2 + (f*x)/2)^7 + 315*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^6 + 99*cos(e/2 + (f*x)/2)^6*sin(e/2 + (f*x)/2) + 945*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^5 + 441*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2)^4 + 609*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2)^3 + 81*cos(e/2 + (f*x)/2)^5*sin(e/2 + (f*x)/2)^2))/(315*a^6*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^9)","B"
322,0,-1,193,0.000000,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\sin\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)^2*sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2), x)","F"
323,0,-1,124,0.000000,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\sin\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*sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2), x)","F"
324,0,-1,92,0.000000,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2), x)","F"
325,0,-1,93,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\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))/sin(c + d*x), x)","F"
326,0,-1,89,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^2, x)","F"
327,0,-1,101,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^3, x)","F"
328,0,-1,137,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^4,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^4, x)","F"
329,0,-1,233,0.000000,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\sin\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)^2*sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2), x)","F"
330,0,-1,156,0.000000,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\sin\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*sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2), x)","F"
331,0,-1,124,0.000000,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))^(3/2), x)","F"
332,0,-1,123,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x), x)","F"
333,0,-1,121,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^2, x)","F"
334,0,-1,131,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^3, x)","F"
335,0,-1,139,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^4,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^4, x)","F"
336,0,-1,158,0.000000,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^3)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\sin\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)^2*sin(c + d*x)^3)/(a + a*sin(c + d*x))^(1/2), x)","F"
337,0,-1,92,0.000000,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\sin\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*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(1/2), x)","F"
338,0,-1,60,0.000000,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x))/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^2*sin(c + d*x))/(a + a*sin(c + d*x))^(1/2), x)","F"
339,0,-1,63,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^2/(sin(c + d*x)*(a + a*sin(c + d*x))^(1/2)), x)","F"
340,0,-1,62,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\sin\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/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2)), x)","F"
341,0,-1,100,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\sin\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)^2/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2)), x)","F"
342,0,-1,135,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\sin\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)^2/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(1/2)), x)","F"
343,0,-1,184,0.000000,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^3)/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\sin\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)^2*sin(c + d*x)^3)/(a + a*sin(c + d*x))^(3/2), x)","F"
344,0,-1,140,0.000000,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\sin\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*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(3/2), x)","F"
345,0,-1,108,0.000000,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x))/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*sin(c + d*x))/(a + a*sin(c + d*x))^(3/2), x)","F"
346,0,-1,85,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^2/(sin(c + d*x)*(a + a*sin(c + d*x))^(3/2)), x)","F"
347,0,-1,113,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\sin\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/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)), x)","F"
348,0,-1,153,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\sin\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)^2/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2)), x)","F"
349,0,-1,191,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\sin\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)^2/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(3/2)), x)","F"
350,1,49,65,0.065632,"\text{Not used}","int(cos(c + d*x)^3*sin(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^7}{7}-\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}{4}}{d}","Not used",1,"((a*sin(c + d*x)^4)/4 + (a*sin(c + d*x)^5)/5 - (a*sin(c + d*x)^6)/6 - (a*sin(c + d*x)^7)/7)/d","B"
351,1,49,65,0.061550,"\text{Not used}","int(cos(c + d*x)^3*sin(c + d*x)^2*(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}{4}+\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"((a*sin(c + d*x)^3)/3 + (a*sin(c + d*x)^4)/4 - (a*sin(c + d*x)^5)/5 - (a*sin(c + d*x)^6)/6)/d","B"
352,1,49,49,0.059314,"\text{Not used}","int(cos(c + d*x)^3*sin(c + d*x)*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^5}{5}-\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}}{d}","Not used",1,"((a*sin(c + d*x)^2)/2 + (a*sin(c + d*x)^3)/3 - (a*sin(c + d*x)^4)/4 - (a*sin(c + d*x)^5)/5)/d","B"
353,1,46,45,0.055079,"\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"
354,1,92,56,8.726793,"\text{Not used}","int((cos(c + d*x)^3*(a + a*sin(c + d*x)))/sin(c + d*x),x)","\frac{a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a\,{\cos\left(c+d\,x\right)}^2}{2\,d}+\frac{2\,a\,\sin\left(c+d\,x\right)}{3\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*log(1/cos(c/2 + (d*x)/2)^2))/d + (a*cos(c + d*x)^2)/(2*d) + (2*a*sin(c + d*x))/(3*d) + (a*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
355,1,140,53,8.695912,"\text{Not used}","int((cos(c + d*x)^3*(a + a*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)))/d - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a*tan(c/2 + (d*x)/2))/(2*d) - (a + 6*a*tan(c/2 + (d*x)/2)^2 + 4*a*tan(c/2 + (d*x)/2)^3 + 5*a*tan(c/2 + (d*x)/2)^4)/(d*(2*tan(c/2 + (d*x)/2) + 4*tan(c/2 + (d*x)/2)^3 + 2*tan(c/2 + (d*x)/2)^5))","B"
356,1,146,54,8.736926,"\text{Not used}","int((cos(c + d*x)^3*(a + a*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + 2*a*tan(c/2 + (d*x)/2) + (a*tan(c/2 + (d*x)/2)^2)/2 + 10*a*tan(c/2 + (d*x)/2)^3)/(d*(4*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^4)) - (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*log(tan(c/2 + (d*x)/2)))/d","B"
357,1,26,37,0.045232,"\text{Not used}","int((cos(c + d*x)^3*sin(c + d*x)^2)/(a + a*sin(c + d*x)),x)","-\frac{{\sin\left(c+d\,x\right)}^3\,\left(3\,\sin\left(c+d\,x\right)-4\right)}{12\,a\,d}","Not used",1,"-(sin(c + d*x)^3*(3*sin(c + d*x) - 4))/(12*a*d)","B"
358,1,26,37,8.536796,"\text{Not used}","int((cos(c + d*x)^3*sin(c + d*x))/(a + a*sin(c + d*x)),x)","-\frac{{\sin\left(c+d\,x\right)}^2\,\left(2\,\sin\left(c+d\,x\right)-3\right)}{6\,a\,d}","Not used",1,"-(sin(c + d*x)^2*(2*sin(c + d*x) - 3))/(6*a*d)","B"
359,1,22,32,0.040612,"\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"
360,1,71,29,8.762499,"\text{Not used}","int(cos(c + d*x)^3/(sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a*d) - (2*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d)","B"
361,1,59,30,8.696830,"\text{Not used}","int(cos(c + d*x)^3/(sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+\frac{1}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}}{a\,d}","Not used",1,"-(log(tan(c/2 + (d*x)/2)) + tan(c/2 + (d*x)/2)/2 - log(tan(c/2 + (d*x)/2)^2 + 1) + 1/(2*tan(c/2 + (d*x)/2)))/(a*d)","B"
362,1,23,32,8.626985,"\text{Not used}","int(cos(c + d*x)^3/(sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{\sin\left(c+d\,x\right)-\frac{1}{2}}{a\,d\,{\sin\left(c+d\,x\right)}^2}","Not used",1,"(sin(c + d*x) - 1/2)/(a*d*sin(c + d*x)^2)","B"
363,1,36,37,8.756726,"\text{Not used}","int(cos(c + d*x)^3/(sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{\frac{5\,\sin\left(c+d\,x\right)}{16}+\frac{\sin\left(3\,c+3\,d\,x\right)}{16}-\frac{1}{3}}{a\,d\,{\sin\left(c+d\,x\right)}^3}","Not used",1,"((5*sin(c + d*x))/16 + sin(3*c + 3*d*x)/16 - 1/3)/(a*d*sin(c + d*x)^3)","B"
364,1,25,37,8.644597,"\text{Not used}","int(cos(c + d*x)^3/(sin(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{\frac{\sin\left(c+d\,x\right)}{3}-\frac{1}{4}}{a\,d\,{\sin\left(c+d\,x\right)}^4}","Not used",1,"(sin(c + d*x)/3 - 1/4)/(a*d*sin(c + d*x)^4)","B"
365,1,353,143,12.342627,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^4*(a + a*sin(c + d*x)),x)","\frac{3\,a\,x}{128}+\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}+\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}-\frac{155\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\left(\frac{a\,\left(79380\,c+79380\,d\,x-430080\right)}{40320}-\frac{63\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\frac{169\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}+\left(\frac{a\,\left(119070\,c+119070\,d\,x+645120\right)}{40320}-\frac{189\,a\,\left(c+d\,x\right)}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(\frac{a\,\left(119070\,c+119070\,d\,x-903168\right)}{40320}-\frac{189\,a\,\left(c+d\,x\right)}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{169\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+\left(\frac{a\,\left(79380\,c+79380\,d\,x+258048\right)}{40320}-\frac{63\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{155\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}+\left(\frac{a\,\left(34020\,c+34020\,d\,x-73728\right)}{40320}-\frac{27\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}+\left(\frac{a\,\left(8505\,c+8505\,d\,x-18432\right)}{40320}-\frac{27\,a\,\left(c+d\,x\right)}{128}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{a\,\left(945\,c+945\,d\,x-2048\right)}{40320}-\frac{3\,a\,\left(c+d\,x\right)}{128}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(3*a*x)/128 + ((a*(945*c + 945*d*x - 2048))/40320 - (3*a*tan(c/2 + (d*x)/2))/64 - (3*a*(c + d*x))/128 + tan(c/2 + (d*x)/2)^2*((a*(8505*c + 8505*d*x - 18432))/40320 - (27*a*(c + d*x))/128) + tan(c/2 + (d*x)/2)^4*((a*(34020*c + 34020*d*x - 73728))/40320 - (27*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^6*((a*(79380*c + 79380*d*x + 258048))/40320 - (63*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^12*((a*(79380*c + 79380*d*x - 430080))/40320 - (63*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^10*((a*(119070*c + 119070*d*x + 645120))/40320 - (189*a*(c + d*x))/64) + tan(c/2 + (d*x)/2)^8*((a*(119070*c + 119070*d*x - 903168))/40320 - (189*a*(c + d*x))/64) - (13*a*tan(c/2 + (d*x)/2)^3)/32 + (155*a*tan(c/2 + (d*x)/2)^5)/32 - (169*a*tan(c/2 + (d*x)/2)^7)/32 + (169*a*tan(c/2 + (d*x)/2)^11)/32 - (155*a*tan(c/2 + (d*x)/2)^13)/32 + (13*a*tan(c/2 + (d*x)/2)^15)/32 + (3*a*tan(c/2 + (d*x)/2)^17)/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
366,1,320,127,12.475835,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{3\,a\,x}{128}+\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{23\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\left(\frac{a\,\left(2940\,c+2940\,d\,x-17920\right)}{4480}-\frac{21\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{333\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{671\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\left(\frac{a\,\left(7350\,c+7350\,d\,x-17920\right)}{4480}-\frac{105\,a\,\left(c+d\,x\right)}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{671\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{64}+\left(\frac{a\,\left(5880\,c+5880\,d\,x-28672\right)}{4480}-\frac{21\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{333\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64}+\left(\frac{a\,\left(2940\,c+2940\,d\,x+3584\right)}{4480}-\frac{21\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{23\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}+\left(\frac{a\,\left(840\,c+840\,d\,x-4096\right)}{4480}-\frac{3\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{a\,\left(105\,c+105\,d\,x-512\right)}{4480}-\frac{3\,a\,\left(c+d\,x\right)}{128}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"(3*a*x)/128 + ((a*(105*c + 105*d*x - 512))/4480 - (3*a*tan(c/2 + (d*x)/2))/64 - (3*a*(c + d*x))/128 + tan(c/2 + (d*x)/2)^2*((a*(840*c + 840*d*x - 4096))/4480 - (3*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^4*((a*(2940*c + 2940*d*x + 3584))/4480 - (21*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^12*((a*(2940*c + 2940*d*x - 17920))/4480 - (21*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^8*((a*(7350*c + 7350*d*x - 17920))/4480 - (105*a*(c + d*x))/64) + tan(c/2 + (d*x)/2)^6*((a*(5880*c + 5880*d*x - 28672))/4480 - (21*a*(c + d*x))/16) - (23*a*tan(c/2 + (d*x)/2)^3)/64 + (333*a*tan(c/2 + (d*x)/2)^5)/64 - (671*a*tan(c/2 + (d*x)/2)^7)/64 + (671*a*tan(c/2 + (d*x)/2)^9)/64 - (333*a*tan(c/2 + (d*x)/2)^11)/64 + (23*a*tan(c/2 + (d*x)/2)^13)/64 + (3*a*tan(c/2 + (d*x)/2)^15)/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
367,1,292,103,12.273642,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x)),x)","\frac{a\,x}{16}+\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{6}+\left(\frac{a\,\left(2205\,c+2205\,d\,x-6720\right)}{1680}-\frac{21\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{31\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\left(\frac{a\,\left(3675\,c+3675\,d\,x+6720\right)}{1680}-\frac{35\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(\frac{a\,\left(3675\,c+3675\,d\,x-13440\right)}{1680}-\frac{35\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{31\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{24}+\left(\frac{a\,\left(2205\,c+2205\,d\,x+2688\right)}{1680}-\frac{21\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\left(\frac{a\,\left(735\,c+735\,d\,x-1344\right)}{1680}-\frac{7\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{a\,\left(105\,c+105\,d\,x-192\right)}{1680}-\frac{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,"(a*x)/16 + ((a*(105*c + 105*d*x - 192))/1680 - (a*tan(c/2 + (d*x)/2))/8 - (a*(c + d*x))/16 + tan(c/2 + (d*x)/2)^2*((a*(735*c + 735*d*x - 1344))/1680 - (7*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^4*((a*(2205*c + 2205*d*x + 2688))/1680 - (21*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^10*((a*(2205*c + 2205*d*x - 6720))/1680 - (21*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^8*((a*(3675*c + 3675*d*x + 6720))/1680 - (35*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^6*((a*(3675*c + 3675*d*x - 13440))/1680 - (35*a*(c + d*x))/16) + (11*a*tan(c/2 + (d*x)/2)^3)/6 - (31*a*tan(c/2 + (d*x)/2)^5)/24 + (31*a*tan(c/2 + (d*x)/2)^9)/24 - (11*a*tan(c/2 + (d*x)/2)^11)/6 + (a*tan(c/2 + (d*x)/2)^13)/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
368,1,292,87,12.220424,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x)),x)","\frac{a\,x}{16}+\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\left(\frac{a\,\left(90\,c+90\,d\,x-480\right)}{240}-\frac{3\,a\,\left(c+d\,x\right)}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{47\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\left(\frac{a\,\left(225\,c+225\,d\,x-480\right)}{240}-\frac{15\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\left(\frac{a\,\left(300\,c+300\,d\,x-960\right)}{240}-\frac{5\,a\,\left(c+d\,x\right)}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\left(\frac{a\,\left(225\,c+225\,d\,x-960\right)}{240}-\frac{15\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{47\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\left(\frac{a\,\left(90\,c+90\,d\,x-96\right)}{240}-\frac{3\,a\,\left(c+d\,x\right)}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{a\,\left(15\,c+15\,d\,x-96\right)}{240}-\frac{a\,\left(c+d\,x\right)}{16}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(a*x)/16 + ((a*(15*c + 15*d*x - 96))/240 - (a*tan(c/2 + (d*x)/2))/8 - (a*(c + d*x))/16 + tan(c/2 + (d*x)/2)^2*((a*(90*c + 90*d*x - 96))/240 - (3*a*(c + d*x))/8) + tan(c/2 + (d*x)/2)^10*((a*(90*c + 90*d*x - 480))/240 - (3*a*(c + d*x))/8) + tan(c/2 + (d*x)/2)^8*((a*(225*c + 225*d*x - 480))/240 - (15*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^4*((a*(225*c + 225*d*x - 960))/240 - (15*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^6*((a*(300*c + 300*d*x - 960))/240 - (5*a*(c + d*x))/4) + (47*a*tan(c/2 + (d*x)/2)^3)/24 - (13*a*tan(c/2 + (d*x)/2)^5)/4 + (13*a*tan(c/2 + (d*x)/2)^7)/4 - (47*a*tan(c/2 + (d*x)/2)^9)/24 + (a*tan(c/2 + (d*x)/2)^11)/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
369,1,245,89,10.188789,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x),x)","\frac{-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{8\,a}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{3\,a\,\mathrm{atan}\left(\frac{9\,a^2}{16\,\left(\frac{3\,a^2}{2}-\frac{9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{3\,a^2}{2}-\frac{9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}","Not used",1,"((8*a)/3 + (5*a*tan(c/2 + (d*x)/2))/4 + (20*a*tan(c/2 + (d*x)/2)^2)/3 - (3*a*tan(c/2 + (d*x)/2)^3)/4 + 8*a*tan(c/2 + (d*x)/2)^4 + (3*a*tan(c/2 + (d*x)/2)^5)/4 + 4*a*tan(c/2 + (d*x)/2)^6 - (5*a*tan(c/2 + (d*x)/2)^7)/4)/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*log(tan(c/2 + (d*x)/2)))/d + (3*a*atan((9*a^2)/(16*((3*a^2)/2 - (9*a^2*tan(c/2 + (d*x)/2))/16)) + (3*a^2*tan(c/2 + (d*x)/2))/(2*((3*a^2)/2 - (9*a^2*tan(c/2 + (d*x)/2))/16))))/(4*d)","B"
370,1,244,83,8.766502,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a\,{\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+8\,a\,{\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+\frac{16\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-a}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{3\,a\,\mathrm{atan}\left(\frac{9\,a^2}{6\,a^2+9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{6\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^2+9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"((16*a*tan(c/2 + (d*x)/2))/3 - a - 5*a*tan(c/2 + (d*x)/2)^2 + 8*a*tan(c/2 + (d*x)/2)^3 - 3*a*tan(c/2 + (d*x)/2)^4 + 8*a*tan(c/2 + (d*x)/2)^5 + a*tan(c/2 + (d*x)/2)^6)/(d*(2*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^3 + 6*tan(c/2 + (d*x)/2)^5 + 2*tan(c/2 + (d*x)/2)^7)) + (a*tan(c/2 + (d*x)/2))/(2*d) + (a*log(tan(c/2 + (d*x)/2)))/d + (3*a*atan((9*a^2)/(6*a^2 + 9*a^2*tan(c/2 + (d*x)/2)) - (6*a^2*tan(c/2 + (d*x)/2))/(6*a^2 + 9*a^2*tan(c/2 + (d*x)/2))))/d","B"
371,1,239,94,8.707551,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{3\,a\,\mathrm{atan}\left(\frac{9\,a^2}{9\,a^2-9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,a^2-9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + 2*a*tan(c/2 + (d*x)/2) + 9*a*tan(c/2 + (d*x)/2)^2 + 8*a*tan(c/2 + (d*x)/2)^3 + (17*a*tan(c/2 + (d*x)/2)^4)/2 - 2*a*tan(c/2 + (d*x)/2)^5)/(d*(4*tan(c/2 + (d*x)/2)^2 + 8*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6)) + (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*a*log(tan(c/2 + (d*x)/2)))/(2*d) - (3*a*atan((9*a^2)/(9*a^2 - 9*a^2*tan(c/2 + (d*x)/2)) + (9*a^2*tan(c/2 + (d*x)/2))/(9*a^2 - 9*a^2*tan(c/2 + (d*x)/2))))/d","B"
372,1,228,82,8.698757,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x)^4,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{6\,a^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{6\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a/3 + a*tan(c/2 + (d*x)/2) - (14*a*tan(c/2 + (d*x)/2)^2)/3 + 17*a*tan(c/2 + (d*x)/2)^3 - 5*a*tan(c/2 + (d*x)/2)^4)/(d*(8*tan(c/2 + (d*x)/2)^3 + 8*tan(c/2 + (d*x)/2)^5)) - (5*a*tan(c/2 + (d*x)/2))/(8*d) + (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (3*a*log(tan(c/2 + (d*x)/2)))/(2*d) - (2*a*atan((4*a^2)/(6*a^2 + 4*a^2*tan(c/2 + (d*x)/2)) - (6*a^2*tan(c/2 + (d*x)/2))/(6*a^2 + 4*a^2*tan(c/2 + (d*x)/2))))/d","B"
373,1,217,88,8.923924,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x)^5,x)","\frac{2\,a\,\mathrm{atan}\left(\frac{8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8\,d}+\frac{5\,a\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}","Not used",1,"(2*a*atan((8*cos(c/2 + (d*x)/2) + 3*sin(c/2 + (d*x)/2))/(3*cos(c/2 + (d*x)/2) - 8*sin(c/2 + (d*x)/2))))/d + (3*a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(8*d) + (5*a*cot(c/2 + (d*x)/2))/(8*d) - (5*a*tan(c/2 + (d*x)/2))/(8*d) + (a*cot(c/2 + (d*x)/2)^2)/(8*d) - (a*cot(c/2 + (d*x)/2)^3)/(24*d) - (a*cot(c/2 + (d*x)/2)^4)/(64*d) - (a*tan(c/2 + (d*x)/2)^2)/(8*d) + (a*tan(c/2 + (d*x)/2)^3)/(24*d) + (a*tan(c/2 + (d*x)/2)^4)/(64*d)","B"
374,1,289,74,10.433907,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x)^6,x)","\frac{a\,\left(2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\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)}^8-40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-20\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}{320\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(a*(2*sin(c/2 + (d*x)/2)^10 - 2*cos(c/2 + (d*x)/2)^10 + 5*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 - 5*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - 10*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 - 40*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7 + 20*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 - 20*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 40*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3 + 10*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5))/(320*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)","B"
375,1,337,98,9.506397,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x)^7,x)","\frac{a\,\left(5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+12\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-12\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-60\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+60\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}{1920\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"(a*(5*sin(c/2 + (d*x)/2)^12 - 5*cos(c/2 + (d*x)/2)^12 + 12*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 - 12*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 15*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 - 60*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 - 15*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 120*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 - 120*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 + 15*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 60*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 15*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6))/(1920*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
376,1,385,114,9.946372,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x)^8,x)","\frac{a\,\left(15\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+35\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}{13440\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(a*(15*sin(c/2 + (d*x)/2)^14 - 15*cos(c/2 + (d*x)/2)^14 + 35*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 - 35*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) - 21*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 105*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 - 105*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 - 105*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 + 315*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 - 315*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 105*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 + 105*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 + 105*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 + 21*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7))/(13440*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)","B"
377,1,337,136,10.216928,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x)))/sin(c + d*x)^9,x)","\frac{a\,\left(35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+80\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-80\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-112\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-280\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+1680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-1680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+280\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+112\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+1680\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\right)}{71680\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}","Not used",1,"(a*(35*sin(c/2 + (d*x)/2)^16 - 35*cos(c/2 + (d*x)/2)^16 + 80*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^15 - 80*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2) - 112*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^13 - 280*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 - 560*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^11 + 1680*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^9 - 1680*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^7 + 560*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^5 + 280*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 + 112*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^3 + 1680*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8))/(71680*d*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8)","B"
378,1,469,185,12.210664,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^4*(a + a*sin(c + d*x))^2,x)","\frac{9\,a^2\,x}{256}-\frac{\frac{9\,a^2\,\left(c+d\,x\right)}{256}+\frac{87\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128}-\frac{553\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}-\frac{491\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+\frac{2555\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}-\frac{2555\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{491\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{553\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{160}-\frac{87\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{9\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}-\frac{a^2\,\left(2835\,c+2835\,d\,x-8192\right)}{80640}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{45\,a^2\,\left(c+d\,x\right)}{128}-\frac{a^2\,\left(28350\,c+28350\,d\,x-81920\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{405\,a^2\,\left(c+d\,x\right)}{256}-\frac{a^2\,\left(127575\,c+127575\,d\,x-368640\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{135\,a^2\,\left(c+d\,x\right)}{32}-\frac{a^2\,\left(340200\,c+340200\,d\,x+737280\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{945\,a^2\,\left(c+d\,x\right)}{128}-\frac{a^2\,\left(595350\,c+595350\,d\,x+860160\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{135\,a^2\,\left(c+d\,x\right)}{32}-\frac{a^2\,\left(340200\,c+340200\,d\,x-1720320\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{567\,a^2\,\left(c+d\,x\right)}{64}-\frac{a^2\,\left(714420\,c+714420\,d\,x-1032192\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{945\,a^2\,\left(c+d\,x\right)}{128}-\frac{a^2\,\left(595350\,c+595350\,d\,x-2580480\right)}{80640}\right)+\frac{9\,a^2\,\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,"(9*a^2*x)/256 - ((9*a^2*(c + d*x))/256 + (87*a^2*tan(c/2 + (d*x)/2)^3)/128 - (553*a^2*tan(c/2 + (d*x)/2)^5)/160 - (491*a^2*tan(c/2 + (d*x)/2)^7)/32 + (2555*a^2*tan(c/2 + (d*x)/2)^9)/64 - (2555*a^2*tan(c/2 + (d*x)/2)^11)/64 + (491*a^2*tan(c/2 + (d*x)/2)^13)/32 + (553*a^2*tan(c/2 + (d*x)/2)^15)/160 - (87*a^2*tan(c/2 + (d*x)/2)^17)/128 - (9*a^2*tan(c/2 + (d*x)/2)^19)/128 - (a^2*(2835*c + 2835*d*x - 8192))/80640 + tan(c/2 + (d*x)/2)^2*((45*a^2*(c + d*x))/128 - (a^2*(28350*c + 28350*d*x - 81920))/80640) + tan(c/2 + (d*x)/2)^4*((405*a^2*(c + d*x))/256 - (a^2*(127575*c + 127575*d*x - 368640))/80640) + tan(c/2 + (d*x)/2)^6*((135*a^2*(c + d*x))/32 - (a^2*(340200*c + 340200*d*x + 737280))/80640) + tan(c/2 + (d*x)/2)^12*((945*a^2*(c + d*x))/128 - (a^2*(595350*c + 595350*d*x + 860160))/80640) + tan(c/2 + (d*x)/2)^14*((135*a^2*(c + d*x))/32 - (a^2*(340200*c + 340200*d*x - 1720320))/80640) + tan(c/2 + (d*x)/2)^10*((567*a^2*(c + d*x))/64 - (a^2*(714420*c + 714420*d*x - 1032192))/80640) + tan(c/2 + (d*x)/2)^8*((945*a^2*(c + d*x))/128 - (a^2*(595350*c + 595350*d*x - 2580480))/80640) + (9*a^2*tan(c/2 + (d*x)/2))/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
379,1,437,159,12.153071,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^3*(a + a*sin(c + d*x))^2,x)","\frac{3\,a^2\,x}{64}-\frac{\frac{3\,a^2\,\left(c+d\,x\right)}{64}+\frac{13\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{16}-\frac{155\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{16}+\frac{169\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}-\frac{169\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{16}+\frac{155\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{16}-\frac{13\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{16}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{32}-\frac{a^2\,\left(945\,c+945\,d\,x-3328\right)}{20160}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{27\,a^2\,\left(c+d\,x\right)}{64}-\frac{a^2\,\left(8505\,c+8505\,d\,x-29952\right)}{20160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{27\,a^2\,\left(c+d\,x\right)}{16}-\frac{a^2\,\left(34020\,c+34020\,d\,x-39168\right)}{20160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{27\,a^2\,\left(c+d\,x\right)}{16}-\frac{a^2\,\left(34020\,c+34020\,d\,x-80640\right)}{20160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{63\,a^2\,\left(c+d\,x\right)}{16}-\frac{a^2\,\left(79380\,c+79380\,d\,x+16128\right)}{20160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{63\,a^2\,\left(c+d\,x\right)}{16}-\frac{a^2\,\left(79380\,c+79380\,d\,x-295680\right)}{20160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{189\,a^2\,\left(c+d\,x\right)}{32}-\frac{a^2\,\left(119070\,c+119070\,d\,x+241920\right)}{20160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{189\,a^2\,\left(c+d\,x\right)}{32}-\frac{a^2\,\left(119070\,c+119070\,d\,x-661248\right)}{20160}\right)+\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(3*a^2*x)/64 - ((3*a^2*(c + d*x))/64 + (13*a^2*tan(c/2 + (d*x)/2)^3)/16 - (155*a^2*tan(c/2 + (d*x)/2)^5)/16 + (169*a^2*tan(c/2 + (d*x)/2)^7)/16 - (169*a^2*tan(c/2 + (d*x)/2)^11)/16 + (155*a^2*tan(c/2 + (d*x)/2)^13)/16 - (13*a^2*tan(c/2 + (d*x)/2)^15)/16 - (3*a^2*tan(c/2 + (d*x)/2)^17)/32 - (a^2*(945*c + 945*d*x - 3328))/20160 + tan(c/2 + (d*x)/2)^2*((27*a^2*(c + d*x))/64 - (a^2*(8505*c + 8505*d*x - 29952))/20160) + tan(c/2 + (d*x)/2)^4*((27*a^2*(c + d*x))/16 - (a^2*(34020*c + 34020*d*x - 39168))/20160) + tan(c/2 + (d*x)/2)^14*((27*a^2*(c + d*x))/16 - (a^2*(34020*c + 34020*d*x - 80640))/20160) + tan(c/2 + (d*x)/2)^6*((63*a^2*(c + d*x))/16 - (a^2*(79380*c + 79380*d*x + 16128))/20160) + tan(c/2 + (d*x)/2)^12*((63*a^2*(c + d*x))/16 - (a^2*(79380*c + 79380*d*x - 295680))/20160) + tan(c/2 + (d*x)/2)^10*((189*a^2*(c + d*x))/32 - (a^2*(119070*c + 119070*d*x + 241920))/20160) + tan(c/2 + (d*x)/2)^8*((189*a^2*(c + d*x))/32 - (a^2*(119070*c + 119070*d*x - 661248))/20160) + (3*a^2*tan(c/2 + (d*x)/2))/32)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
380,1,363,141,12.350617,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^2,x)","\frac{11\,a^2\,x}{128}-\frac{\frac{11\,a^2\,\left(c+d\,x\right)}{128}-\frac{259\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}-\frac{1103\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}+\frac{2261\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{192}-\frac{2261\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{1103\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{192}+\frac{259\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}-\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}-\frac{a^2\,\left(1155\,c+1155\,d\,x-3072\right)}{13440}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{11\,a^2\,\left(c+d\,x\right)}{16}-\frac{a^2\,\left(9240\,c+9240\,d\,x-24576\right)}{13440}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{77\,a^2\,\left(c+d\,x\right)}{32}-\frac{a^2\,\left(32340\,c+32340\,d\,x+21504\right)}{13440}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{77\,a^2\,\left(c+d\,x\right)}{32}-\frac{a^2\,\left(32340\,c+32340\,d\,x-107520\right)}{13440}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{385\,a^2\,\left(c+d\,x\right)}{64}-\frac{a^2\,\left(80850\,c+80850\,d\,x-107520\right)}{13440}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{77\,a^2\,\left(c+d\,x\right)}{16}-\frac{a^2\,\left(64680\,c+64680\,d\,x-172032\right)}{13440}\right)+\frac{11\,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,"(11*a^2*x)/128 - ((11*a^2*(c + d*x))/128 - (259*a^2*tan(c/2 + (d*x)/2)^3)/192 - (1103*a^2*tan(c/2 + (d*x)/2)^5)/192 + (2261*a^2*tan(c/2 + (d*x)/2)^7)/192 - (2261*a^2*tan(c/2 + (d*x)/2)^9)/192 + (1103*a^2*tan(c/2 + (d*x)/2)^11)/192 + (259*a^2*tan(c/2 + (d*x)/2)^13)/192 - (11*a^2*tan(c/2 + (d*x)/2)^15)/64 - (a^2*(1155*c + 1155*d*x - 3072))/13440 + tan(c/2 + (d*x)/2)^2*((11*a^2*(c + d*x))/16 - (a^2*(9240*c + 9240*d*x - 24576))/13440) + tan(c/2 + (d*x)/2)^4*((77*a^2*(c + d*x))/32 - (a^2*(32340*c + 32340*d*x + 21504))/13440) + tan(c/2 + (d*x)/2)^12*((77*a^2*(c + d*x))/32 - (a^2*(32340*c + 32340*d*x - 107520))/13440) + tan(c/2 + (d*x)/2)^8*((385*a^2*(c + d*x))/64 - (a^2*(80850*c + 80850*d*x - 107520))/13440) + tan(c/2 + (d*x)/2)^6*((77*a^2*(c + d*x))/16 - (a^2*(64680*c + 64680*d*x - 172032))/13440) + (11*a^2*tan(c/2 + (d*x)/2))/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
381,1,388,129,10.747106,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,x}{8}-\frac{\frac{31\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}-\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{31\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}+\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+a^2\,\left(\frac{c}{8}+\frac{d\,x}{8}\right)-a^2\,\left(\frac{c}{8}+\frac{d\,x}{8}-\frac{18}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(7\,a^2\,\left(\frac{c}{8}+\frac{d\,x}{8}\right)-a^2\,\left(\frac{7\,c}{8}+\frac{7\,d\,x}{8}-2\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,a^2\,\left(\frac{c}{8}+\frac{d\,x}{8}\right)-a^2\,\left(\frac{7\,c}{8}+\frac{7\,d\,x}{8}-\frac{8}{5}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(21\,a^2\,\left(\frac{c}{8}+\frac{d\,x}{8}\right)-a^2\,\left(\frac{21\,c}{8}+\frac{21\,d\,x}{8}-8\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(21\,a^2\,\left(\frac{c}{8}+\frac{d\,x}{8}\right)-a^2\,\left(\frac{21\,c}{8}+\frac{21\,d\,x}{8}-\frac{14}{5}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(35\,a^2\,\left(\frac{c}{8}+\frac{d\,x}{8}\right)-a^2\,\left(\frac{35\,c}{8}+\frac{35\,d\,x}{8}-2\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(35\,a^2\,\left(\frac{c}{8}+\frac{d\,x}{8}\right)-a^2\,\left(\frac{35\,c}{8}+\frac{35\,d\,x}{8}-16\right)\right)+\frac{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)}^7}","Not used",1,"(a^2*x)/8 - ((31*a^2*tan(c/2 + (d*x)/2)^5)/12 - (11*a^2*tan(c/2 + (d*x)/2)^3)/3 - (31*a^2*tan(c/2 + (d*x)/2)^9)/12 + (11*a^2*tan(c/2 + (d*x)/2)^11)/3 - (a^2*tan(c/2 + (d*x)/2)^13)/4 + a^2*(c/8 + (d*x)/8) - a^2*(c/8 + (d*x)/8 - 18/35) + tan(c/2 + (d*x)/2)^12*(7*a^2*(c/8 + (d*x)/8) - a^2*((7*c)/8 + (7*d*x)/8 - 2)) + tan(c/2 + (d*x)/2)^2*(7*a^2*(c/8 + (d*x)/8) - a^2*((7*c)/8 + (7*d*x)/8 - 8/5)) + tan(c/2 + (d*x)/2)^10*(21*a^2*(c/8 + (d*x)/8) - a^2*((21*c)/8 + (21*d*x)/8 - 8)) + tan(c/2 + (d*x)/2)^4*(21*a^2*(c/8 + (d*x)/8) - a^2*((21*c)/8 + (21*d*x)/8 - 14/5)) + tan(c/2 + (d*x)/2)^8*(35*a^2*(c/8 + (d*x)/8) - a^2*((35*c)/8 + (35*d*x)/8 - 2)) + tan(c/2 + (d*x)/2)^6*(35*a^2*(c/8 + (d*x)/8) - a^2*((35*c)/8 + (35*d*x)/8 - 16)) + (a^2*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
382,1,293,119,10.215127,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{3\,a^2\,\mathrm{atan}\left(\frac{9\,a^4}{4\,\left(3\,a^4-\frac{9\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)}+\frac{3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,a^4-\frac{9\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}\right)}{2\,d}+\frac{-\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{32\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{28\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{34\,a^2}{15}}{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)}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (3*a^2*atan((9*a^4)/(4*(3*a^4 - (9*a^4*tan(c/2 + (d*x)/2))/4)) + (3*a^4*tan(c/2 + (d*x)/2))/(3*a^4 - (9*a^4*tan(c/2 + (d*x)/2))/4)))/(2*d) + ((28*a^2*tan(c/2 + (d*x)/2)^2)/3 + a^2*tan(c/2 + (d*x)/2)^3 + (32*a^2*tan(c/2 + (d*x)/2)^4)/3 + 12*a^2*tan(c/2 + (d*x)/2)^6 - a^2*tan(c/2 + (d*x)/2)^7 + 2*a^2*tan(c/2 + (d*x)/2)^8 - (5*a^2*tan(c/2 + (d*x)/2)^9)/2 + (34*a^2)/15 + (5*a^2*tan(c/2 + (d*x)/2))/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))","B"
383,1,310,116,8.827352,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{2\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{9\,a^2\,\mathrm{atan}\left(\frac{81\,a^4}{16\,\left(9\,a^4+\frac{81\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}-\frac{9\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,a^4+\frac{81\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}}\right)}{4\,d}-\frac{\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}-16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}-32\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{19\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-\frac{80\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+a^2}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(2*a^2*log(tan(c/2 + (d*x)/2)))/d + (9*a^2*atan((81*a^4)/(16*(9*a^4 + (81*a^4*tan(c/2 + (d*x)/2))/16)) - (9*a^4*tan(c/2 + (d*x)/2))/(9*a^4 + (81*a^4*tan(c/2 + (d*x)/2))/16)))/(4*d) - ((7*a^2*tan(c/2 + (d*x)/2)^2)/2 - (80*a^2*tan(c/2 + (d*x)/2)^3)/3 + (19*a^2*tan(c/2 + (d*x)/2)^4)/2 - 32*a^2*tan(c/2 + (d*x)/2)^5 + (a^2*tan(c/2 + (d*x)/2)^6)/2 - 16*a^2*tan(c/2 + (d*x)/2)^7 + (3*a^2*tan(c/2 + (d*x)/2)^8)/2 + a^2 - (32*a^2*tan(c/2 + (d*x)/2))/3)/(d*(2*tan(c/2 + (d*x)/2) + 8*tan(c/2 + (d*x)/2)^3 + 12*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^7 + 2*tan(c/2 + (d*x)/2)^9)) + (a^2*tan(c/2 + (d*x)/2))/(2*d)","B"
384,1,303,98,8.911247,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{6\,a^2\,\mathrm{atan}\left(\frac{36\,a^4}{6\,a^4-36\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{6\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^4-36\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{-4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{15\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{6}+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (a^2*log(tan(c/2 + (d*x)/2)))/(2*d) - (6*a^2*atan((36*a^4)/(6*a^4 - 36*a^4*tan(c/2 + (d*x)/2)) + (6*a^4*tan(c/2 + (d*x)/2))/(6*a^4 - 36*a^4*tan(c/2 + (d*x)/2))))/d - (20*a^2*tan(c/2 + (d*x)/2)^3 - (7*a^2*tan(c/2 + (d*x)/2)^2)/6 + (3*a^2*tan(c/2 + (d*x)/2)^4)/2 + 12*a^2*tan(c/2 + (d*x)/2)^5 - (15*a^2*tan(c/2 + (d*x)/2)^6)/2 - 4*a^2*tan(c/2 + (d*x)/2)^7 + a^2/2 + 4*a^2*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^4 + 12*tan(c/2 + (d*x)/2)^6 + 4*tan(c/2 + (d*x)/2)^8)) + (a^2*tan(c/2 + (d*x)/2))/d","B"
385,1,293,98,8.809667,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^4,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{3\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2\,\mathrm{atan}\left(\frac{a^4}{6\,a^4-a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{6\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^4-a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{-9\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+34\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{19\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+36\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(4*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (3*a^2*log(tan(c/2 + (d*x)/2)))/d - (a^2*atan(a^4/(6*a^4 - a^4*tan(c/2 + (d*x)/2)) + (6*a^4*tan(c/2 + (d*x)/2))/(6*a^4 - a^4*tan(c/2 + (d*x)/2))))/d - (36*a^2*tan(c/2 + (d*x)/2)^3 - (a^2*tan(c/2 + (d*x)/2)^2)/3 + (19*a^2*tan(c/2 + (d*x)/2)^4)/3 + 34*a^2*tan(c/2 + (d*x)/2)^5 - 9*a^2*tan(c/2 + (d*x)/2)^6 + a^2/3 + 2*a^2*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 16*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^7)) - (a^2*tan(c/2 + (d*x)/2))/(8*d)","B"
386,1,265,116,8.769989,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^5,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{9\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{4\,a^2\,\mathrm{atan}\left(\frac{16\,a^4}{9\,a^4+16\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{9\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,a^4+16\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}-\frac{-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+32\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{56\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}+\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{a^2}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^3)/(12*d) + (a^2*tan(c/2 + (d*x)/2)^4)/(64*d) - (9*a^2*log(tan(c/2 + (d*x)/2)))/(8*d) - (4*a^2*atan((16*a^4)/(9*a^4 + 16*a^4*tan(c/2 + (d*x)/2)) - (9*a^4*tan(c/2 + (d*x)/2))/(9*a^4 + 16*a^4*tan(c/2 + (d*x)/2))))/d - (5*a^2*tan(c/2 + (d*x)/2))/(4*d) - ((a^2*tan(c/2 + (d*x)/2)^2)/4 - (56*a^2*tan(c/2 + (d*x)/2)^3)/3 + 32*a^2*tan(c/2 + (d*x)/2)^4 - 20*a^2*tan(c/2 + (d*x)/2)^5 + a^2/4 + (4*a^2*tan(c/2 + (d*x)/2))/3)/(d*(16*tan(c/2 + (d*x)/2)^4 + 16*tan(c/2 + (d*x)/2)^6))","B"
387,1,275,118,9.158603,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^6,x)","\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{2\,a^2\,\mathrm{atan}\left(\frac{4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{9\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}","Not used",1,"(a^2*cot(c/2 + (d*x)/2)^2)/(4*d) - (a^2*cot(c/2 + (d*x)/2)^3)/(96*d) - (a^2*cot(c/2 + (d*x)/2)^4)/(32*d) - (a^2*cot(c/2 + (d*x)/2)^5)/(160*d) - (a^2*tan(c/2 + (d*x)/2)^2)/(4*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(96*d) + (a^2*tan(c/2 + (d*x)/2)^4)/(32*d) + (a^2*tan(c/2 + (d*x)/2)^5)/(160*d) + (2*a^2*atan((4*cos(c/2 + (d*x)/2) + 3*sin(c/2 + (d*x)/2))/(3*cos(c/2 + (d*x)/2) - 4*sin(c/2 + (d*x)/2))))/d + (3*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (9*a^2*cot(c/2 + (d*x)/2))/(16*d) - (9*a^2*tan(c/2 + (d*x)/2))/(16*d)","B"
388,1,339,132,9.754036,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^7,x)","\frac{a^2\,\left(5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+24\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-255\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+255\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}{1920\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"(a^2*(5*sin(c/2 + (d*x)/2)^12 - 5*cos(c/2 + (d*x)/2)^12 + 24*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 - 24*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) + 15*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 - 120*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 - 255*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 240*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 - 240*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 + 255*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 120*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 - 15*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6))/(1920*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
389,1,319,176,9.117096,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^9,x)","\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64\,d}+\frac{3\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{448\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64\,d}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{448\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}+\frac{11\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,d}-\frac{3\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,d}+\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,d}","Not used",1,"(a^2*cot(c/2 + (d*x)/2)^2)/(128*d) + (a^2*cot(c/2 + (d*x)/2)^3)/(64*d) + (3*a^2*cot(c/2 + (d*x)/2)^4)/(256*d) + (a^2*cot(c/2 + (d*x)/2)^5)/(320*d) - (a^2*cot(c/2 + (d*x)/2)^6)/(384*d) - (a^2*cot(c/2 + (d*x)/2)^7)/(448*d) - (a^2*cot(c/2 + (d*x)/2)^8)/(2048*d) - (a^2*tan(c/2 + (d*x)/2)^2)/(128*d) - (a^2*tan(c/2 + (d*x)/2)^3)/(64*d) - (3*a^2*tan(c/2 + (d*x)/2)^4)/(256*d) - (a^2*tan(c/2 + (d*x)/2)^5)/(320*d) + (a^2*tan(c/2 + (d*x)/2)^6)/(384*d) + (a^2*tan(c/2 + (d*x)/2)^7)/(448*d) + (a^2*tan(c/2 + (d*x)/2)^8)/(2048*d) + (11*a^2*log(tan(c/2 + (d*x)/2)))/(128*d) - (3*a^2*cot(c/2 + (d*x)/2))/(64*d) + (3*a^2*tan(c/2 + (d*x)/2))/(64*d)","B"
390,1,387,168,12.071272,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^10,x)","\frac{a^2\,\left(70\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-70\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+315\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+450\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-1008\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+11340\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-11340\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+1008\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-450\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+15120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\right)}{322560\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"(a^2*(70*sin(c/2 + (d*x)/2)^18 - 70*cos(c/2 + (d*x)/2)^18 + 315*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^17 - 315*cos(c/2 + (d*x)/2)^17*sin(c/2 + (d*x)/2) + 450*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^16 - 1008*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^14 - 2520*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^13 - 3360*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^12 + 11340*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^10 - 11340*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^8 + 3360*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^6 + 2520*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^5 + 1008*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^4 - 450*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^2 + 15120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^9))/(322560*d*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^9)","B"
391,1,395,218,9.523224,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^2)/sin(c + d*x)^11,x)","\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{3\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}+\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320\,d}+\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{1792\,d}-\frac{3\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2304\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{1792\,d}+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2304\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{9\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{256\,d}-\frac{3\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}+\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}","Not used",1,"(a^2*cot(c/2 + (d*x)/2)^3)/(192*d) - (a^2*cot(c/2 + (d*x)/2)^2)/(1024*d) + (3*a^2*cot(c/2 + (d*x)/2)^4)/(512*d) + (a^2*cot(c/2 + (d*x)/2)^5)/(320*d) + (a^2*cot(c/2 + (d*x)/2)^6)/(2048*d) - (a^2*cot(c/2 + (d*x)/2)^7)/(1792*d) - (3*a^2*cot(c/2 + (d*x)/2)^8)/(4096*d) - (a^2*cot(c/2 + (d*x)/2)^9)/(2304*d) - (a^2*cot(c/2 + (d*x)/2)^10)/(10240*d) + (a^2*tan(c/2 + (d*x)/2)^2)/(1024*d) - (a^2*tan(c/2 + (d*x)/2)^3)/(192*d) - (3*a^2*tan(c/2 + (d*x)/2)^4)/(512*d) - (a^2*tan(c/2 + (d*x)/2)^5)/(320*d) - (a^2*tan(c/2 + (d*x)/2)^6)/(2048*d) + (a^2*tan(c/2 + (d*x)/2)^7)/(1792*d) + (3*a^2*tan(c/2 + (d*x)/2)^8)/(4096*d) + (a^2*tan(c/2 + (d*x)/2)^9)/(2304*d) + (a^2*tan(c/2 + (d*x)/2)^10)/(10240*d) + (9*a^2*log(tan(c/2 + (d*x)/2)))/(256*d) - (3*a^2*cot(c/2 + (d*x)/2))/(128*d) + (3*a^2*tan(c/2 + (d*x)/2))/(128*d)","B"
392,1,506,203,11.719877,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^4*(a + a*sin(c + d*x))^3,x)","\frac{15\,a^3\,x}{256}-\frac{\frac{15\,a^3\,\left(c+d\,x\right)}{256}+\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}-\frac{231\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640}-\frac{242\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}+\frac{3987\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}-\frac{3987\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{242\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{5}+\frac{231\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{640}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{4}-\frac{15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{128}-\frac{a^3\,\left(17325\,c+17325\,d\,x-53248\right)}{295680}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{165\,a^3\,\left(c+d\,x\right)}{256}-\frac{a^3\,\left(190575\,c+190575\,d\,x-585728\right)}{295680}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{825\,a^3\,\left(c+d\,x\right)}{256}-\frac{a^3\,\left(952875\,c+952875\,d\,x-2928640\right)}{295680}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{2475\,a^3\,\left(c+d\,x\right)}{256}-\frac{a^3\,\left(2858625\,c+2858625\,d\,x+675840\right)}{295680}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{2475\,a^3\,\left(c+d\,x\right)}{128}-\frac{a^3\,\left(5717250\,c+5717250\,d\,x-3379200\right)}{295680}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{2475\,a^3\,\left(c+d\,x\right)}{256}-\frac{a^3\,\left(2858625\,c+2858625\,d\,x-9461760\right)}{295680}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{2475\,a^3\,\left(c+d\,x\right)}{128}-\frac{a^3\,\left(5717250\,c+5717250\,d\,x-14192640\right)}{295680}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{3465\,a^3\,\left(c+d\,x\right)}{128}-\frac{a^3\,\left(8004150\,c+8004150\,d\,x+16084992\right)}{295680}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{3465\,a^3\,\left(c+d\,x\right)}{128}-\frac{a^3\,\left(8004150\,c+8004150\,d\,x-40685568\right)}{295680}\right)+\frac{15\,a^3\,\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)}^{11}}","Not used",1,"(15*a^3*x)/256 - ((15*a^3*(c + d*x))/256 + (5*a^3*tan(c/2 + (d*x)/2)^3)/4 - (231*a^3*tan(c/2 + (d*x)/2)^5)/640 - (242*a^3*tan(c/2 + (d*x)/2)^7)/5 + (3987*a^3*tan(c/2 + (d*x)/2)^9)/64 - (3987*a^3*tan(c/2 + (d*x)/2)^13)/64 + (242*a^3*tan(c/2 + (d*x)/2)^15)/5 + (231*a^3*tan(c/2 + (d*x)/2)^17)/640 - (5*a^3*tan(c/2 + (d*x)/2)^19)/4 - (15*a^3*tan(c/2 + (d*x)/2)^21)/128 - (a^3*(17325*c + 17325*d*x - 53248))/295680 + tan(c/2 + (d*x)/2)^2*((165*a^3*(c + d*x))/256 - (a^3*(190575*c + 190575*d*x - 585728))/295680) + tan(c/2 + (d*x)/2)^4*((825*a^3*(c + d*x))/256 - (a^3*(952875*c + 952875*d*x - 2928640))/295680) + tan(c/2 + (d*x)/2)^6*((2475*a^3*(c + d*x))/256 - (a^3*(2858625*c + 2858625*d*x + 675840))/295680) + tan(c/2 + (d*x)/2)^8*((2475*a^3*(c + d*x))/128 - (a^3*(5717250*c + 5717250*d*x - 3379200))/295680) + tan(c/2 + (d*x)/2)^16*((2475*a^3*(c + d*x))/256 - (a^3*(2858625*c + 2858625*d*x - 9461760))/295680) + tan(c/2 + (d*x)/2)^14*((2475*a^3*(c + d*x))/128 - (a^3*(5717250*c + 5717250*d*x - 14192640))/295680) + tan(c/2 + (d*x)/2)^12*((3465*a^3*(c + d*x))/128 - (a^3*(8004150*c + 8004150*d*x + 16084992))/295680) + tan(c/2 + (d*x)/2)^10*((3465*a^3*(c + d*x))/128 - (a^3*(8004150*c + 8004150*d*x - 40685568))/295680) + (15*a^3*tan(c/2 + (d*x)/2))/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^11)","B"
393,1,572,182,10.812111,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^3*(a + a*sin(c + d*x))^3,x)","\frac{21\,a^3\,x}{256}-\frac{\frac{203\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128}-\frac{1973\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}-\frac{463\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+\frac{3231\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}-\frac{3231\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{463\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{1973\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{160}-\frac{203\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{21\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}+\frac{a^3\,\left(315\,c+315\,d\,x\right)}{3840}-\frac{a^3\,\left(315\,c+315\,d\,x-1024\right)}{3840}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(\frac{a^3\,\left(315\,c+315\,d\,x\right)}{384}-\frac{a^3\,\left(3150\,c+3150\,d\,x\right)}{3840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(315\,c+315\,d\,x\right)}{384}-\frac{a^3\,\left(3150\,c+3150\,d\,x-10240\right)}{3840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{3\,a^3\,\left(315\,c+315\,d\,x\right)}{256}-\frac{a^3\,\left(14175\,c+14175\,d\,x-15360\right)}{3840}\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)}{256}-\frac{a^3\,\left(14175\,c+14175\,d\,x-30720\right)}{3840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^3\,\left(315\,c+315\,d\,x\right)}{32}-\frac{a^3\,\left(37800\,c+37800\,d\,x+30720\right)}{3840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{7\,a^3\,\left(315\,c+315\,d\,x\right)}{128}-\frac{a^3\,\left(66150\,c+66150\,d\,x+30720\right)}{3840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{a^3\,\left(315\,c+315\,d\,x\right)}{32}-\frac{a^3\,\left(37800\,c+37800\,d\,x-153600\right)}{3840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{21\,a^3\,\left(315\,c+315\,d\,x\right)}{320}-\frac{a^3\,\left(79380\,c+79380\,d\,x-129024\right)}{3840}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{7\,a^3\,\left(315\,c+315\,d\,x\right)}{128}-\frac{a^3\,\left(66150\,c+66150\,d\,x-245760\right)}{3840}\right)+\frac{21\,a^3\,\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,"(21*a^3*x)/256 - ((203*a^3*tan(c/2 + (d*x)/2)^3)/128 - (1973*a^3*tan(c/2 + (d*x)/2)^5)/160 - (463*a^3*tan(c/2 + (d*x)/2)^7)/32 + (3231*a^3*tan(c/2 + (d*x)/2)^9)/64 - (3231*a^3*tan(c/2 + (d*x)/2)^11)/64 + (463*a^3*tan(c/2 + (d*x)/2)^13)/32 + (1973*a^3*tan(c/2 + (d*x)/2)^15)/160 - (203*a^3*tan(c/2 + (d*x)/2)^17)/128 - (21*a^3*tan(c/2 + (d*x)/2)^19)/128 + (a^3*(315*c + 315*d*x))/3840 - (a^3*(315*c + 315*d*x - 1024))/3840 + tan(c/2 + (d*x)/2)^18*((a^3*(315*c + 315*d*x))/384 - (a^3*(3150*c + 3150*d*x))/3840) + tan(c/2 + (d*x)/2)^2*((a^3*(315*c + 315*d*x))/384 - (a^3*(3150*c + 3150*d*x - 10240))/3840) + tan(c/2 + (d*x)/2)^16*((3*a^3*(315*c + 315*d*x))/256 - (a^3*(14175*c + 14175*d*x - 15360))/3840) + tan(c/2 + (d*x)/2)^4*((3*a^3*(315*c + 315*d*x))/256 - (a^3*(14175*c + 14175*d*x - 30720))/3840) + tan(c/2 + (d*x)/2)^6*((a^3*(315*c + 315*d*x))/32 - (a^3*(37800*c + 37800*d*x + 30720))/3840) + tan(c/2 + (d*x)/2)^12*((7*a^3*(315*c + 315*d*x))/128 - (a^3*(66150*c + 66150*d*x + 30720))/3840) + tan(c/2 + (d*x)/2)^14*((a^3*(315*c + 315*d*x))/32 - (a^3*(37800*c + 37800*d*x - 153600))/3840) + tan(c/2 + (d*x)/2)^10*((21*a^3*(315*c + 315*d*x))/320 - (a^3*(79380*c + 79380*d*x - 129024))/3840) + tan(c/2 + (d*x)/2)^8*((7*a^3*(315*c + 315*d*x))/128 - (a^3*(66150*c + 66150*d*x - 245760))/3840) + (21*a^3*tan(c/2 + (d*x)/2))/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
394,1,437,159,12.279738,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^3,x)","\frac{17\,a^3\,x}{128}-\frac{\frac{17\,a^3\,\left(c+d\,x\right)}{128}-\frac{35\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}-\frac{537\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}+\frac{531\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}-\frac{531\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}+\frac{537\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{35\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{96}-\frac{17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}-\frac{a^3\,\left(5355\,c+5355\,d\,x-15872\right)}{40320}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{153\,a^3\,\left(c+d\,x\right)}{128}-\frac{a^3\,\left(48195\,c+48195\,d\,x-142848\right)}{40320}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{153\,a^3\,\left(c+d\,x\right)}{32}-\frac{a^3\,\left(192780\,c+192780\,d\,x-87552\right)}{40320}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{153\,a^3\,\left(c+d\,x\right)}{32}-\frac{a^3\,\left(192780\,c+192780\,d\,x-483840\right)}{40320}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{357\,a^3\,\left(c+d\,x\right)}{32}-\frac{a^3\,\left(449820\,c+449820\,d\,x-419328\right)}{40320}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{1071\,a^3\,\left(c+d\,x\right)}{64}-\frac{a^3\,\left(674730\,c+674730\,d\,x+161280\right)}{40320}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{357\,a^3\,\left(c+d\,x\right)}{32}-\frac{a^3\,\left(449820\,c+449820\,d\,x-913920\right)}{40320}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{1071\,a^3\,\left(c+d\,x\right)}{64}-\frac{a^3\,\left(674730\,c+674730\,d\,x-2161152\right)}{40320}\right)+\frac{17\,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,"(17*a^3*x)/128 - ((17*a^3*(c + d*x))/128 - (35*a^3*tan(c/2 + (d*x)/2)^3)/96 - (537*a^3*tan(c/2 + (d*x)/2)^5)/32 + (531*a^3*tan(c/2 + (d*x)/2)^7)/32 - (531*a^3*tan(c/2 + (d*x)/2)^11)/32 + (537*a^3*tan(c/2 + (d*x)/2)^13)/32 + (35*a^3*tan(c/2 + (d*x)/2)^15)/96 - (17*a^3*tan(c/2 + (d*x)/2)^17)/64 - (a^3*(5355*c + 5355*d*x - 15872))/40320 + tan(c/2 + (d*x)/2)^2*((153*a^3*(c + d*x))/128 - (a^3*(48195*c + 48195*d*x - 142848))/40320) + tan(c/2 + (d*x)/2)^4*((153*a^3*(c + d*x))/32 - (a^3*(192780*c + 192780*d*x - 87552))/40320) + tan(c/2 + (d*x)/2)^14*((153*a^3*(c + d*x))/32 - (a^3*(192780*c + 192780*d*x - 483840))/40320) + tan(c/2 + (d*x)/2)^6*((357*a^3*(c + d*x))/32 - (a^3*(449820*c + 449820*d*x - 419328))/40320) + tan(c/2 + (d*x)/2)^10*((1071*a^3*(c + d*x))/64 - (a^3*(674730*c + 674730*d*x + 161280))/40320) + tan(c/2 + (d*x)/2)^12*((357*a^3*(c + d*x))/32 - (a^3*(449820*c + 449820*d*x - 913920))/40320) + tan(c/2 + (d*x)/2)^8*((1071*a^3*(c + d*x))/64 - (a^3*(674730*c + 674730*d*x - 2161152))/40320) + (17*a^3*tan(c/2 + (d*x)/2))/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
395,1,461,157,10.760806,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))^3,x)","\frac{27\,a^3\,x}{128}-\frac{\frac{919\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{64}-\frac{437\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64}-\frac{305\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}-\frac{919\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{437\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{305\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}-\frac{27\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{a^3\,\left(945\,c+945\,d\,x\right)}{4480}-\frac{a^3\,\left(945\,c+945\,d\,x-3328\right)}{4480}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{a^3\,\left(945\,c+945\,d\,x\right)}{560}-\frac{a^3\,\left(7560\,c+7560\,d\,x-8960\right)}{4480}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(945\,c+945\,d\,x\right)}{560}-\frac{a^3\,\left(7560\,c+7560\,d\,x-17664\right)}{4480}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3\,\left(945\,c+945\,d\,x\right)}{160}-\frac{a^3\,\left(26460\,c+26460\,d\,x-12544\right)}{4480}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{a^3\,\left(945\,c+945\,d\,x\right)}{160}-\frac{a^3\,\left(26460\,c+26460\,d\,x-80640\right)}{4480}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{a^3\,\left(945\,c+945\,d\,x\right)}{80}-\frac{a^3\,\left(52920\,c+52920\,d\,x-44800\right)}{4480}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^3\,\left(945\,c+945\,d\,x\right)}{80}-\frac{a^3\,\left(52920\,c+52920\,d\,x-141568\right)}{4480}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^3\,\left(945\,c+945\,d\,x\right)}{64}-\frac{a^3\,\left(66150\,c+66150\,d\,x-116480\right)}{4480}\right)+\frac{27\,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)}^8}","Not used",1,"(27*a^3*x)/128 - ((919*a^3*tan(c/2 + (d*x)/2)^7)/64 - (437*a^3*tan(c/2 + (d*x)/2)^5)/64 - (305*a^3*tan(c/2 + (d*x)/2)^3)/64 - (919*a^3*tan(c/2 + (d*x)/2)^9)/64 + (437*a^3*tan(c/2 + (d*x)/2)^11)/64 + (305*a^3*tan(c/2 + (d*x)/2)^13)/64 - (27*a^3*tan(c/2 + (d*x)/2)^15)/64 + (a^3*(945*c + 945*d*x))/4480 - (a^3*(945*c + 945*d*x - 3328))/4480 + tan(c/2 + (d*x)/2)^14*((a^3*(945*c + 945*d*x))/560 - (a^3*(7560*c + 7560*d*x - 8960))/4480) + tan(c/2 + (d*x)/2)^2*((a^3*(945*c + 945*d*x))/560 - (a^3*(7560*c + 7560*d*x - 17664))/4480) + tan(c/2 + (d*x)/2)^4*((a^3*(945*c + 945*d*x))/160 - (a^3*(26460*c + 26460*d*x - 12544))/4480) + tan(c/2 + (d*x)/2)^12*((a^3*(945*c + 945*d*x))/160 - (a^3*(26460*c + 26460*d*x - 80640))/4480) + tan(c/2 + (d*x)/2)^10*((a^3*(945*c + 945*d*x))/80 - (a^3*(52920*c + 52920*d*x - 44800))/4480) + tan(c/2 + (d*x)/2)^6*((a^3*(945*c + 945*d*x))/80 - (a^3*(52920*c + 52920*d*x - 141568))/4480) + tan(c/2 + (d*x)/2)^8*((a^3*(945*c + 945*d*x))/64 - (a^3*(66150*c + 66150*d*x - 116480))/4480) + (27*a^3*tan(c/2 + (d*x)/2))/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
396,1,355,143,10.510363,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x),x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{19\,a^3\,\mathrm{atan}\left(\frac{361\,a^6}{64\,\left(\frac{19\,a^6}{4}-\frac{361\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}+\frac{19\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{19\,a^6}{4}-\frac{361\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}\right)}{8\,d}+\frac{-\frac{29\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{173\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{44\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}-\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{173\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{54\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{29\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{22\,a^3}{15}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d + (19*a^3*atan((361*a^6)/(64*((19*a^6)/4 - (361*a^6*tan(c/2 + (d*x)/2))/64)) + (19*a^6*tan(c/2 + (d*x)/2))/(4*((19*a^6)/4 - (361*a^6*tan(c/2 + (d*x)/2))/64))))/(8*d) + ((54*a^3*tan(c/2 + (d*x)/2)^2)/5 + (173*a^3*tan(c/2 + (d*x)/2)^3)/24 + 12*a^3*tan(c/2 + (d*x)/2)^4 - (7*a^3*tan(c/2 + (d*x)/2)^5)/4 + (44*a^3*tan(c/2 + (d*x)/2)^6)/3 + (7*a^3*tan(c/2 + (d*x)/2)^7)/4 + 10*a^3*tan(c/2 + (d*x)/2)^8 - (173*a^3*tan(c/2 + (d*x)/2)^9)/24 - 2*a^3*tan(c/2 + (d*x)/2)^10 - (29*a^3*tan(c/2 + (d*x)/2)^11)/8 + (22*a^3)/15 + (29*a^3*tan(c/2 + (d*x)/2))/8)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
397,1,356,131,8.810870,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^2,x)","\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{-\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{2}+20\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+72\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+80\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+56\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{76\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}-a^3}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{3\,a^3\,\mathrm{atan}\left(\frac{9\,a^6}{16\,\left(\frac{9\,a^6}{2}+\frac{9\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}-\frac{9\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{9\,a^6}{2}+\frac{9\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)))/d + ((a^3*tan(c/2 + (d*x)/2)^2)/2 + 56*a^3*tan(c/2 + (d*x)/2)^3 - 11*a^3*tan(c/2 + (d*x)/2)^4 + 80*a^3*tan(c/2 + (d*x)/2)^5 - 10*a^3*tan(c/2 + (d*x)/2)^6 + 72*a^3*tan(c/2 + (d*x)/2)^7 - 4*a^3*tan(c/2 + (d*x)/2)^8 + 20*a^3*tan(c/2 + (d*x)/2)^9 - (13*a^3*tan(c/2 + (d*x)/2)^10)/2 - a^3 + (76*a^3*tan(c/2 + (d*x)/2))/5)/(d*(2*tan(c/2 + (d*x)/2) + 10*tan(c/2 + (d*x)/2)^3 + 20*tan(c/2 + (d*x)/2)^5 + 20*tan(c/2 + (d*x)/2)^7 + 10*tan(c/2 + (d*x)/2)^9 + 2*tan(c/2 + (d*x)/2)^11)) + (3*a^3*atan((9*a^6)/(16*((9*a^6)/2 + (9*a^6*tan(c/2 + (d*x)/2))/16)) - (9*a^6*tan(c/2 + (d*x)/2))/(2*((9*a^6)/2 + (9*a^6*tan(c/2 + (d*x)/2))/16))))/(4*d) + (a^3*tan(c/2 + (d*x)/2))/(2*d)","B"
398,1,347,137,8.808035,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^3,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}+\frac{33\,a^3\,\mathrm{atan}\left(\frac{1089\,a^6}{16\,\left(\frac{99\,a^6}{4}+\frac{1089\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}-\frac{99\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{99\,a^6}{4}+\frac{1089\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{79\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}-9\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+70\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-51\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+53\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-31\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+22\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a^3}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (3*a^3*log(tan(c/2 + (d*x)/2)))/(2*d) + (33*a^3*atan((1089*a^6)/(16*((99*a^6)/4 + (1089*a^6*tan(c/2 + (d*x)/2))/16)) - (99*a^6*tan(c/2 + (d*x)/2))/(4*((99*a^6)/4 + (1089*a^6*tan(c/2 + (d*x)/2))/16))))/(4*d) + (22*a^3*tan(c/2 + (d*x)/2)^2 - 31*a^3*tan(c/2 + (d*x)/2)^3 + 53*a^3*tan(c/2 + (d*x)/2)^4 - 51*a^3*tan(c/2 + (d*x)/2)^5 + 70*a^3*tan(c/2 + (d*x)/2)^6 - 9*a^3*tan(c/2 + (d*x)/2)^7 + (79*a^3*tan(c/2 + (d*x)/2)^8)/2 + a^3*tan(c/2 + (d*x)/2)^9 - a^3/2 - 6*a^3*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 16*tan(c/2 + (d*x)/2)^4 + 24*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8 + 4*tan(c/2 + (d*x)/2)^10)) + (3*a^3*tan(c/2 + (d*x)/2))/(2*d)","B"
399,1,339,134,8.781178,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^4,x)","\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{7\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{7\,a^3\,\mathrm{atan}\left(\frac{49\,a^6}{49\,a^6-49\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{49\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{49\,a^6-49\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{-17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+19\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{64\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+73\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+46\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{107\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(3*a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (7*a^3*log(tan(c/2 + (d*x)/2)))/(2*d) - (7*a^3*atan((49*a^6)/(49*a^6 - 49*a^6*tan(c/2 + (d*x)/2)) + (49*a^6*tan(c/2 + (d*x)/2))/(49*a^6 - 49*a^6*tan(c/2 + (d*x)/2))))/d + (7*a^3*tan(c/2 + (d*x)/2))/(8*d) - (8*a^3*tan(c/2 + (d*x)/2)^2 + (107*a^3*tan(c/2 + (d*x)/2)^3)/3 + 46*a^3*tan(c/2 + (d*x)/2)^4 + 73*a^3*tan(c/2 + (d*x)/2)^5 + (64*a^3*tan(c/2 + (d*x)/2)^6)/3 + 19*a^3*tan(c/2 + (d*x)/2)^7 - 17*a^3*tan(c/2 + (d*x)/2)^8 + a^3/3 + 3*a^3*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 24*tan(c/2 + (d*x)/2)^5 + 24*tan(c/2 + (d*x)/2)^7 + 8*tan(c/2 + (d*x)/2)^9))","B"
400,1,329,138,8.782336,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^5,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{33\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{3\,a^3\,\mathrm{atan}\left(\frac{9\,a^6}{\frac{99\,a^6}{4}+9\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{99\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{99\,a^6}{4}+9\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}-\frac{11\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{-38\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+100\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-26\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{417\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}-18\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{9\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(4*d) + (a^3*tan(c/2 + (d*x)/2)^3)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^4)/(64*d) - (33*a^3*log(tan(c/2 + (d*x)/2)))/(8*d) - (3*a^3*atan((9*a^6)/((99*a^6)/4 + 9*a^6*tan(c/2 + (d*x)/2)) - (99*a^6*tan(c/2 + (d*x)/2))/(4*((99*a^6)/4 + 9*a^6*tan(c/2 + (d*x)/2)))))/d - (11*a^3*tan(c/2 + (d*x)/2))/(8*d) - ((9*a^3*tan(c/2 + (d*x)/2)^2)/2 - 18*a^3*tan(c/2 + (d*x)/2)^3 + (417*a^3*tan(c/2 + (d*x)/2)^4)/4 - 26*a^3*tan(c/2 + (d*x)/2)^5 + 100*a^3*tan(c/2 + (d*x)/2)^6 - 38*a^3*tan(c/2 + (d*x)/2)^7 + a^3/4 + 2*a^3*tan(c/2 + (d*x)/2))/(d*(16*tan(c/2 + (d*x)/2)^4 + 32*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8))","B"
401,1,554,132,10.111344,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^6,x)","-\frac{a^3\,\left(2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+65\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+550\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+80\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-550\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-65\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+1920\,\mathrm{atan}\left(\frac{8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+1920\,\mathrm{atan}\left(\frac{8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}{320\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}","Not used",1,"-(a^3*(2*cos(c/2 + (d*x)/2)^12 - 2*sin(c/2 + (d*x)/2)^12 - 15*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 + 15*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 32*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 65*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 550*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 80*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 560*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 550*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 65*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 32*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 + 1920*atan((8*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2) + 8*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 1920*atan((8*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2) + 8*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5))/(320*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5*(cos(c/2 + (d*x)/2)^2 + sin(c/2 + (d*x)/2)^2))","B"
402,1,313,168,9.379845,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^7,x)","\frac{49\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{5\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{5\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{49\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{2\,a^3\,\mathrm{atan}\left(\frac{16\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+19\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{19\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{19\,a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{16\,d}+\frac{7\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{7\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}","Not used",1,"(49*a^3*cot(c/2 + (d*x)/2)^2)/(128*d) + (5*a^3*cot(c/2 + (d*x)/2)^3)/(96*d) - (5*a^3*cot(c/2 + (d*x)/2)^4)/(128*d) - (3*a^3*cot(c/2 + (d*x)/2)^5)/(160*d) - (a^3*cot(c/2 + (d*x)/2)^6)/(384*d) - (49*a^3*tan(c/2 + (d*x)/2)^2)/(128*d) - (5*a^3*tan(c/2 + (d*x)/2)^3)/(96*d) + (5*a^3*tan(c/2 + (d*x)/2)^4)/(128*d) + (3*a^3*tan(c/2 + (d*x)/2)^5)/(160*d) + (a^3*tan(c/2 + (d*x)/2)^6)/(384*d) + (2*a^3*atan((16*cos(c/2 + (d*x)/2) + 19*sin(c/2 + (d*x)/2))/(19*cos(c/2 + (d*x)/2) - 16*sin(c/2 + (d*x)/2))))/d + (19*a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(16*d) + (7*a^3*cot(c/2 + (d*x)/2))/(16*d) - (7*a^3*tan(c/2 + (d*x)/2))/(16*d)","B"
403,1,387,150,10.319993,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^8,x)","\frac{a^3\,\left(5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+35\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+77\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-455\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-665\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+945\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-945\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+665\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+455\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-77\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2520\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}{4480\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(a^3*(5*sin(c/2 + (d*x)/2)^14 - 5*cos(c/2 + (d*x)/2)^14 + 35*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 - 35*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) + 77*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 35*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 - 455*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 - 665*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 + 945*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 - 945*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 665*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 + 455*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 + 35*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 - 77*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 2520*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7))/(4480*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)","B"
404,1,319,176,9.220636,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^9,x)","\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{7\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}+\frac{7\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}-\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}+\frac{27\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,d}-\frac{17\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}+\frac{17\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}","Not used",1,"(3*a^3*cot(c/2 + (d*x)/2)^2)/(128*d) + (7*a^3*cot(c/2 + (d*x)/2)^3)/(128*d) + (7*a^3*cot(c/2 + (d*x)/2)^4)/(256*d) - (a^3*cot(c/2 + (d*x)/2)^5)/(640*d) - (a^3*cot(c/2 + (d*x)/2)^6)/(128*d) - (3*a^3*cot(c/2 + (d*x)/2)^7)/(896*d) - (a^3*cot(c/2 + (d*x)/2)^8)/(2048*d) - (3*a^3*tan(c/2 + (d*x)/2)^2)/(128*d) - (7*a^3*tan(c/2 + (d*x)/2)^3)/(128*d) - (7*a^3*tan(c/2 + (d*x)/2)^4)/(256*d) + (a^3*tan(c/2 + (d*x)/2)^5)/(640*d) + (a^3*tan(c/2 + (d*x)/2)^6)/(128*d) + (3*a^3*tan(c/2 + (d*x)/2)^7)/(896*d) + (a^3*tan(c/2 + (d*x)/2)^8)/(2048*d) + (27*a^3*log(tan(c/2 + (d*x)/2)))/(128*d) - (17*a^3*cot(c/2 + (d*x)/2))/(128*d) + (17*a^3*tan(c/2 + (d*x)/2))/(128*d)","B"
405,1,357,194,9.315295,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^10,x)","\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{5\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}+\frac{5\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{13\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}+\frac{17\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,d}-\frac{21\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}+\frac{21\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}","Not used",1,"(a^3*cot(c/2 + (d*x)/2)^2)/(128*d) + (5*a^3*cot(c/2 + (d*x)/2)^3)/(192*d) + (5*a^3*cot(c/2 + (d*x)/2)^4)/(256*d) + (a^3*cot(c/2 + (d*x)/2)^5)/(160*d) - (a^3*cot(c/2 + (d*x)/2)^6)/(384*d) - (13*a^3*cot(c/2 + (d*x)/2)^7)/(3584*d) - (3*a^3*cot(c/2 + (d*x)/2)^8)/(2048*d) - (a^3*cot(c/2 + (d*x)/2)^9)/(4608*d) - (a^3*tan(c/2 + (d*x)/2)^2)/(128*d) - (5*a^3*tan(c/2 + (d*x)/2)^3)/(192*d) - (5*a^3*tan(c/2 + (d*x)/2)^4)/(256*d) - (a^3*tan(c/2 + (d*x)/2)^5)/(160*d) + (a^3*tan(c/2 + (d*x)/2)^6)/(384*d) + (13*a^3*tan(c/2 + (d*x)/2)^7)/(3584*d) + (3*a^3*tan(c/2 + (d*x)/2)^8)/(2048*d) + (a^3*tan(c/2 + (d*x)/2)^9)/(4608*d) + (17*a^3*log(tan(c/2 + (d*x)/2)))/(128*d) - (21*a^3*cot(c/2 + (d*x)/2))/(256*d) + (21*a^3*tan(c/2 + (d*x)/2))/(256*d)","B"
406,1,395,216,9.552083,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^3)/sin(c + d*x)^11,x)","\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{7\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}+\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{512\,d}-\frac{7\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{1536\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64\,d}-\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{512\,d}+\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{1536\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{21\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{256\,d}-\frac{15\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}+\frac{15\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}","Not used",1,"(a^3*cot(c/2 + (d*x)/2)^3)/(64*d) - (a^3*cot(c/2 + (d*x)/2)^2)/(1024*d) + (7*a^3*cot(c/2 + (d*x)/2)^4)/(512*d) + (a^3*cot(c/2 + (d*x)/2)^5)/(160*d) + (a^3*cot(c/2 + (d*x)/2)^6)/(2048*d) - (a^3*cot(c/2 + (d*x)/2)^7)/(512*d) - (7*a^3*cot(c/2 + (d*x)/2)^8)/(4096*d) - (a^3*cot(c/2 + (d*x)/2)^9)/(1536*d) - (a^3*cot(c/2 + (d*x)/2)^10)/(10240*d) + (a^3*tan(c/2 + (d*x)/2)^2)/(1024*d) - (a^3*tan(c/2 + (d*x)/2)^3)/(64*d) - (7*a^3*tan(c/2 + (d*x)/2)^4)/(512*d) - (a^3*tan(c/2 + (d*x)/2)^5)/(160*d) - (a^3*tan(c/2 + (d*x)/2)^6)/(2048*d) + (a^3*tan(c/2 + (d*x)/2)^7)/(512*d) + (7*a^3*tan(c/2 + (d*x)/2)^8)/(4096*d) + (a^3*tan(c/2 + (d*x)/2)^9)/(1536*d) + (a^3*tan(c/2 + (d*x)/2)^10)/(10240*d) + (21*a^3*log(tan(c/2 + (d*x)/2)))/(256*d) - (15*a^3*cot(c/2 + (d*x)/2))/(256*d) + (15*a^3*tan(c/2 + (d*x)/2))/(256*d)","B"
407,1,572,187,10.836193,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^4,x)","\frac{55\,a^4\,x}{256}-\frac{\frac{571\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384}-\frac{14149\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{480}-\frac{469\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+\frac{4293\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}-\frac{4293\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{469\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{14149\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{480}-\frac{571\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{384}-\frac{55\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}+\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{80640}-\frac{a^4\,\left(17325\,c+17325\,d\,x-53248\right)}{80640}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{8064}-\frac{a^4\,\left(173250\,c+173250\,d\,x\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{8064}-\frac{a^4\,\left(173250\,c+173250\,d\,x-532480\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{1792}-\frac{a^4\,\left(779625\,c+779625\,d\,x-1105920\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{1792}-\frac{a^4\,\left(779625\,c+779625\,d\,x-1290240\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{672}-\frac{a^4\,\left(2079000\,c+2079000\,d\,x-368640\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{384}-\frac{a^4\,\left(3638250\,c+3638250\,d\,x-860160\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{672}-\frac{a^4\,\left(2079000\,c+2079000\,d\,x-6021120\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{320}-\frac{a^4\,\left(4365900\,c+4365900\,d\,x-6709248\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^4\,\left(17325\,c+17325\,d\,x\right)}{384}-\frac{a^4\,\left(3638250\,c+3638250\,d\,x-10321920\right)}{80640}\right)+\frac{55\,a^4\,\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,"(55*a^4*x)/256 - ((571*a^4*tan(c/2 + (d*x)/2)^3)/384 - (14149*a^4*tan(c/2 + (d*x)/2)^5)/480 - (469*a^4*tan(c/2 + (d*x)/2)^7)/32 + (4293*a^4*tan(c/2 + (d*x)/2)^9)/64 - (4293*a^4*tan(c/2 + (d*x)/2)^11)/64 + (469*a^4*tan(c/2 + (d*x)/2)^13)/32 + (14149*a^4*tan(c/2 + (d*x)/2)^15)/480 - (571*a^4*tan(c/2 + (d*x)/2)^17)/384 - (55*a^4*tan(c/2 + (d*x)/2)^19)/128 + (a^4*(17325*c + 17325*d*x))/80640 - (a^4*(17325*c + 17325*d*x - 53248))/80640 + tan(c/2 + (d*x)/2)^18*((a^4*(17325*c + 17325*d*x))/8064 - (a^4*(173250*c + 173250*d*x))/80640) + tan(c/2 + (d*x)/2)^2*((a^4*(17325*c + 17325*d*x))/8064 - (a^4*(173250*c + 173250*d*x - 532480))/80640) + tan(c/2 + (d*x)/2)^4*((a^4*(17325*c + 17325*d*x))/1792 - (a^4*(779625*c + 779625*d*x - 1105920))/80640) + tan(c/2 + (d*x)/2)^16*((a^4*(17325*c + 17325*d*x))/1792 - (a^4*(779625*c + 779625*d*x - 1290240))/80640) + tan(c/2 + (d*x)/2)^6*((a^4*(17325*c + 17325*d*x))/672 - (a^4*(2079000*c + 2079000*d*x - 368640))/80640) + tan(c/2 + (d*x)/2)^12*((a^4*(17325*c + 17325*d*x))/384 - (a^4*(3638250*c + 3638250*d*x - 860160))/80640) + tan(c/2 + (d*x)/2)^14*((a^4*(17325*c + 17325*d*x))/672 - (a^4*(2079000*c + 2079000*d*x - 6021120))/80640) + tan(c/2 + (d*x)/2)^10*((a^4*(17325*c + 17325*d*x))/320 - (a^4*(4365900*c + 4365900*d*x - 6709248))/80640) + tan(c/2 + (d*x)/2)^8*((a^4*(17325*c + 17325*d*x))/384 - (a^4*(3638250*c + 3638250*d*x - 10321920))/80640) + (55*a^4*tan(c/2 + (d*x)/2))/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
408,1,384,140,8.805389,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^4)/sin(c + d*x)^4,x)","\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d}+\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{2\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{61\,a^4\,\mathrm{atan}\left(\frac{3721\,a^8}{16\,\left(61\,a^8-\frac{3721\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{61\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{61\,a^8-\frac{3721\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}}\right)}{4\,d}+\frac{19\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{-19\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-60\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{67\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-48\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{508\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{8\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+116\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{16\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{61\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^4}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(a^4*tan(c/2 + (d*x)/2)^2)/(2*d) + (a^4*tan(c/2 + (d*x)/2)^3)/(24*d) - (2*a^4*log(tan(c/2 + (d*x)/2)))/d - (61*a^4*atan((3721*a^8)/(16*(61*a^8 - (3721*a^8*tan(c/2 + (d*x)/2))/16)) + (61*a^8*tan(c/2 + (d*x)/2))/(61*a^8 - (3721*a^8*tan(c/2 + (d*x)/2))/16)))/(4*d) + (19*a^4*tan(c/2 + (d*x)/2))/(8*d) - ((61*a^4*tan(c/2 + (d*x)/2)^2)/3 - (16*a^4*tan(c/2 + (d*x)/2)^3)/3 + 116*a^4*tan(c/2 + (d*x)/2)^4 + (8*a^4*tan(c/2 + (d*x)/2)^5)/3 + (508*a^4*tan(c/2 + (d*x)/2)^6)/3 - 48*a^4*tan(c/2 + (d*x)/2)^7 + (67*a^4*tan(c/2 + (d*x)/2)^8)/3 - 60*a^4*tan(c/2 + (d*x)/2)^9 - 19*a^4*tan(c/2 + (d*x)/2)^10 + a^4/3 + 4*a^4*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 32*tan(c/2 + (d*x)/2)^5 + 48*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9 + 8*tan(c/2 + (d*x)/2)^11))","B"
409,1,159,135,11.375231,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^4)/(a + a*sin(c + d*x)),x)","\frac{x}{16\,a}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{6}-\frac{97\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{97\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{24}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{16}{105}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"x/(16*a) + ((16*tan(c/2 + (d*x)/2)^2)/15 - tan(c/2 + (d*x)/2)/8 - (5*tan(c/2 + (d*x)/2)^3)/6 + (16*tan(c/2 + (d*x)/2)^4)/5 + (97*tan(c/2 + (d*x)/2)^5)/24 - (16*tan(c/2 + (d*x)/2)^6)/3 + (32*tan(c/2 + (d*x)/2)^8)/3 - (97*tan(c/2 + (d*x)/2)^9)/24 + (5*tan(c/2 + (d*x)/2)^11)/6 + tan(c/2 + (d*x)/2)^13/8 + 16/105)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
410,1,147,117,11.309257,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + a*sin(c + d*x)),x)","-\frac{x}{16\,a}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{17\,{\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{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{4}{15}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"- x/(16*a) - ((8*tan(c/2 + (d*x)/2)^2)/5 - tan(c/2 + (d*x)/2)/8 - (17*tan(c/2 + (d*x)/2)^3)/24 + (19*tan(c/2 + (d*x)/2)^5)/4 + (8*tan(c/2 + (d*x)/2)^6)/3 - (19*tan(c/2 + (d*x)/2)^7)/4 + 4*tan(c/2 + (d*x)/2)^8 + (17*tan(c/2 + (d*x)/2)^9)/24 + tan(c/2 + (d*x)/2)^11/8 + 4/15)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
411,1,120,91,12.008676,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x)),x)","\frac{x}{8\,a}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}-\frac{3\,{\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)}^6-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{4}{15}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"x/(8*a) + ((4*tan(c/2 + (d*x)/2)^2)/3 - tan(c/2 + (d*x)/2)/4 + (3*tan(c/2 + (d*x)/2)^3)/2 - (4*tan(c/2 + (d*x)/2)^4)/3 + 4*tan(c/2 + (d*x)/2)^6 - (3*tan(c/2 + (d*x)/2)^7)/2 + tan(c/2 + (d*x)/2)^9/4 + 4/15)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
412,1,43,73,8.797787,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x)),x)","-\frac{6\,\cos\left(c+d\,x\right)+2\,\cos\left(3\,c+3\,d\,x\right)-\frac{3\,\sin\left(4\,c+4\,d\,x\right)}{4}+3\,d\,x}{24\,a\,d}","Not used",1,"-(6*cos(c + d*x) + 2*cos(3*c + 3*d*x) - (3*sin(4*c + 4*d*x))/4 + 3*d*x)/(24*a*d)","B"
413,1,136,59,8.853153,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}+\frac{\mathrm{atan}\left(\frac{1}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2}\right)}{a\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a*d) + (2*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^3 + 2)/(d*(a + 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) + atan(1/(tan(c/2 + (d*x)/2) + 2) - (2*tan(c/2 + (d*x)/2))/(tan(c/2 + (d*x)/2) + 2))/(a*d)","B"
414,1,147,49,8.723104,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{2\,\mathrm{atan}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4}+\frac{4}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4}\right)}{a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1}{d\,\left(2\,a\,{\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)\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}","Not used",1,"(2*atan((4*tan(c/2 + (d*x)/2))/(4*tan(c/2 + (d*x)/2) - 4) + 4/(4*tan(c/2 + (d*x)/2) - 4)))/(a*d) - log(tan(c/2 + (d*x)/2))/(a*d) - (4*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2 + 1)/(d*(2*a*tan(c/2 + (d*x)/2) + 2*a*tan(c/2 + (d*x)/2)^3)) + tan(c/2 + (d*x)/2)/(2*a*d)","B"
415,1,159,58,8.748041,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{2\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,a\,d}+\frac{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - (2*atan((2*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2) + 2*sin(c/2 + (d*x)/2))))/(a*d) - cot(c/2 + (d*x)/2)^2/(8*a*d) - log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(2*a*d) + cot(c/2 + (d*x)/2)/(2*a*d) - tan(c/2 + (d*x)/2)/(2*a*d)","B"
416,1,115,58,8.669458,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{3}\right)}{8\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) + log(tan(c/2 + (d*x)/2))/(2*a*d) - tan(c/2 + (d*x)/2)/(8*a*d) + (cot(c/2 + (d*x)/2)^3*(tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2 - 1/3))/(8*a*d)","B"
417,1,119,82,8.682658,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{1}{4}\right)}{16\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a*d) - tan(c/2 + (d*x)/2)^3/(24*a*d) - log(tan(c/2 + (d*x)/2))/(8*a*d) + tan(c/2 + (d*x)/2)/(8*a*d) - (cot(c/2 + (d*x)/2)^4*(2*tan(c/2 + (d*x)/2)^3 - (2*tan(c/2 + (d*x)/2))/3 + 1/4))/(16*a*d)","B"
418,1,151,100,8.753507,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^6*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{1}{5}\right)}{32\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(96*a*d) - tan(c/2 + (d*x)/2)^4/(64*a*d) + tan(c/2 + (d*x)/2)^5/(160*a*d) + log(tan(c/2 + (d*x)/2))/(8*a*d) - tan(c/2 + (d*x)/2)/(16*a*d) + (cot(c/2 + (d*x)/2)^5*(tan(c/2 + (d*x)/2)/2 - tan(c/2 + (d*x)/2)^2/3 + 2*tan(c/2 + (d*x)/2)^4 - 1/5))/(32*a*d)","B"
419,1,339,124,9.679618,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^7*(a + a*sin(c + d*x))),x)","-\frac{5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+12\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-12\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+20\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-20\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1920\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"-(5*cos(c/2 + (d*x)/2)^12 - 5*sin(c/2 + (d*x)/2)^12 + 12*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 - 12*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 15*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 20*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 15*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 120*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 120*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 15*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 20*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 15*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/(1920*a*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
420,1,160,147,12.217113,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^5)/(a + a*sin(c + d*x))^2,x)","-\frac{5\,x}{8\,a^2}-\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}+\frac{283\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{176\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}-\frac{283\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{208\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{208\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{208}{105}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"- (5*x)/(8*a^2) - ((208*tan(c/2 + (d*x)/2)^2)/15 - (5*tan(c/2 + (d*x)/2))/4 - (25*tan(c/2 + (d*x)/2)^3)/3 + (208*tan(c/2 + (d*x)/2)^4)/5 - (283*tan(c/2 + (d*x)/2)^5)/12 + (176*tan(c/2 + (d*x)/2)^6)/3 + (32*tan(c/2 + (d*x)/2)^8)/3 + (283*tan(c/2 + (d*x)/2)^9)/12 + (25*tan(c/2 + (d*x)/2)^11)/3 + (5*tan(c/2 + (d*x)/2)^13)/4 + 208/105)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
421,1,146,129,11.242010,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^4)/(a + a*sin(c + d*x))^2,x)","\frac{11\,x}{16\,a^2}+\frac{\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{187\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{47\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}-\frac{47\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{187\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{32}{15}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(11*x)/(16*a^2) + ((64*tan(c/2 + (d*x)/2)^2)/5 - (11*tan(c/2 + (d*x)/2))/8 - (187*tan(c/2 + (d*x)/2)^3)/24 + 32*tan(c/2 + (d*x)/2)^4 - (47*tan(c/2 + (d*x)/2)^5)/4 + (64*tan(c/2 + (d*x)/2)^6)/3 + (47*tan(c/2 + (d*x)/2)^7)/4 + (187*tan(c/2 + (d*x)/2)^9)/24 + (11*tan(c/2 + (d*x)/2)^11)/8 + 32/15)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
422,1,89,102,8.718255,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + a*sin(c + d*x))^2,x)","\frac{3\,\cos\left(3\,c+3\,d\,x\right)}{16\,a^2\,d}-\frac{11\,\cos\left(c+d\,x\right)}{8\,a^2\,d}-\frac{3\,x}{4\,a^2}-\frac{\cos\left(5\,c+5\,d\,x\right)}{80\,a^2\,d}+\frac{\sin\left(2\,c+2\,d\,x\right)}{2\,a^2\,d}-\frac{\sin\left(4\,c+4\,d\,x\right)}{16\,a^2\,d}","Not used",1,"(3*cos(3*c + 3*d*x))/(16*a^2*d) - (11*cos(c + d*x))/(8*a^2*d) - (3*x)/(4*a^2) - cos(5*c + 5*d*x)/(80*a^2*d) + sin(2*c + 2*d*x)/(2*a^2*d) - sin(4*c + 4*d*x)/(16*a^2*d)","B"
423,1,79,87,8.661877,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x))^2,x)","\frac{7\,x}{8\,a^2}+\frac{2\,\cos\left(c+d\,x\right)}{a^2\,d}-\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{9\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,a^2\,d}","Not used",1,"(7*x)/(8*a^2) + (2*cos(c + d*x))/(a^2*d) - (2*cos(c + d*x)^3)/(3*a^2*d) + (cos(c + d*x)^3*sin(c + d*x))/(4*a^2*d) - (9*cos(c + d*x)*sin(c + d*x))/(8*a^2*d)","B"
424,1,55,70,8.637022,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x))^2,x)","\frac{\cos\left(3\,c+3\,d\,x\right)}{12\,a^2\,d}-\frac{7\,\cos\left(c+d\,x\right)}{4\,a^2\,d}-\frac{x}{a^2}+\frac{\sin\left(2\,c+2\,d\,x\right)}{2\,a^2\,d}","Not used",1,"cos(3*c + 3*d*x)/(12*a^2*d) - (7*cos(c + d*x))/(4*a^2*d) - x/a^2 + sin(2*c + 2*d*x)/(2*a^2*d)","B"
425,1,97,36,8.718472,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{4\,\mathrm{atan}\left(\frac{16}{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8}\right)}{a^2\,d}-\frac{2}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}","Not used",1,"(4*atan(16/(16*tan(c/2 + (d*x)/2) + 8) - (8*tan(c/2 + (d*x)/2))/(16*tan(c/2 + (d*x)/2) + 8)))/(a^2*d) - 2/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2)) + log(tan(c/2 + (d*x)/2))/(a^2*d)","B"
426,1,95,35,8.832061,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","-\frac{2\,\mathrm{atan}\left(\frac{\sqrt{5}\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{5\,\cos\left(\frac{c}{2}-\mathrm{atan}\left(\frac{1}{2}\right)+\frac{d\,x}{2}\right)}\right)}{a^2\,d}-\frac{\mathrm{cot}\left(c+d\,x\right)}{a^2\,d}-\frac{2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^2\,d}","Not used",1,"- (2*atan((5^(1/2)*(cos(c/2 + (d*x)/2) - 2*sin(c/2 + (d*x)/2)))/(5*cos(c/2 - atan(1/2) + (d*x)/2))))/(a^2*d) - cot(c + d*x)/(a^2*d) - (2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^2*d)","B"
427,1,84,54,8.688570,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{8}\right)}{a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) + (3*log(tan(c/2 + (d*x)/2)))/(2*a^2*d) - tan(c/2 + (d*x)/2)/(a^2*d) + (cot(c/2 + (d*x)/2)^2*(tan(c/2 + (d*x)/2) - 1/8))/(a^2*d)","B"
428,1,119,66,8.665406,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^2\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{3}\right)}{8\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^2*d) - tan(c/2 + (d*x)/2)^2/(4*a^2*d) - log(tan(c/2 + (d*x)/2))/(a^2*d) + (7*tan(c/2 + (d*x)/2))/(8*a^2*d) - (cot(c/2 + (d*x)/2)^3*(7*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) + 1/3))/(8*a^2*d)","B"
429,1,151,96,8.723327,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}+\frac{7\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a^2\,d}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^2\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{1}{4}\right)}{16\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(4*a^2*d) - tan(c/2 + (d*x)/2)^3/(12*a^2*d) + tan(c/2 + (d*x)/2)^4/(64*a^2*d) + (7*log(tan(c/2 + (d*x)/2)))/(8*a^2*d) - (3*tan(c/2 + (d*x)/2))/(4*a^2*d) + (cot(c/2 + (d*x)/2)^4*((4*tan(c/2 + (d*x)/2))/3 - 4*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^3 - 1/4))/(16*a^2*d)","B"
430,1,289,112,9.304100,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^6*(a + a*sin(c + d*x))^2),x)","-\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-110\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+110\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(cos(c/2 + (d*x)/2)^10 - sin(c/2 + (d*x)/2)^10 + 5*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 - 5*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - 15*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 + 40*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7 - 110*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + 110*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 - 40*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3 + 15*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/(160*a^2*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)","B"
431,1,339,138,9.738310,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^7*(a + a*sin(c + d*x))^2),x)","\frac{5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-24\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+75\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-200\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+465\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-1200\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+1200\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-465\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+200\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-75\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1320\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1920\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"(5*sin(c/2 + (d*x)/2)^12 - 5*cos(c/2 + (d*x)/2)^12 - 24*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 + 24*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) + 75*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 - 200*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 465*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 1200*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 1200*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 465*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 200*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 - 75*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 1320*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/(1920*a^2*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
432,1,146,109,12.345106,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + a*sin(c + d*x))^3,x)","\frac{51\,x}{8\,a^3}+\frac{\frac{51\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4}+\frac{51\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{187\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{4}+\frac{171\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{309\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}+\frac{133\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{269\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}+\frac{29\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+20}{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)}^4}","Not used",1,"(51*x)/(8*a^3) + ((29*tan(c/2 + (d*x)/2))/4 + (269*tan(c/2 + (d*x)/2)^2)/4 + (133*tan(c/2 + (d*x)/2)^3)/4 + (309*tan(c/2 + (d*x)/2)^4)/4 + (171*tan(c/2 + (d*x)/2)^5)/4 + (187*tan(c/2 + (d*x)/2)^6)/4 + (51*tan(c/2 + (d*x)/2)^7)/4 + (51*tan(c/2 + (d*x)/2)^8)/4 + 20)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
433,1,121,87,12.349179,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x))^3,x)","-\frac{11\,x}{2\,a^3}-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+41\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{19\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{52}{3}}{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)}^3}","Not used",1,"- (11*x)/(2*a^3) - ((19*tan(c/2 + (d*x)/2))/3 + 41*tan(c/2 + (d*x)/2)^2 + 20*tan(c/2 + (d*x)/2)^3 + 32*tan(c/2 + (d*x)/2)^4 + 11*tan(c/2 + (d*x)/2)^5 + 11*tan(c/2 + (d*x)/2)^6 + 52/3)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
434,1,94,80,10.795861,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x))^3,x)","\frac{9\,x}{2\,a^3}+\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\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+5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+14}{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)}^2}","Not used",1,"(9*x)/(2*a^3) + (5*tan(c/2 + (d*x)/2) + 21*tan(c/2 + (d*x)/2)^2 + 7*tan(c/2 + (d*x)/2)^3 + 9*tan(c/2 + (d*x)/2)^4 + 14)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
435,1,115,45,8.728758,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{8}{d\,\left(a^3+a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{2\,\mathrm{atan}\left(\frac{4\,a^3}{4\,a^3-4\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{4\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^3-4\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^3\,d}","Not used",1,"8/(d*(a^3 + a^3*tan(c/2 + (d*x)/2))) + log(tan(c/2 + (d*x)/2))/(a^3*d) + (2*atan((4*a^3)/(4*a^3 - 4*a^3*tan(c/2 + (d*x)/2)) + (4*a^3*tan(c/2 + (d*x)/2))/(4*a^3 - 4*a^3*tan(c/2 + (d*x)/2))))/(a^3*d)","B"
436,1,87,54,8.667818,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{17\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - (17*tan(c/2 + (d*x)/2) + 1)/(d*(2*a^3*tan(c/2 + (d*x)/2)^2 + 2*a^3*tan(c/2 + (d*x)/2))) - (3*log(tan(c/2 + (d*x)/2)))/(a^3*d)","B"
437,1,120,78,8.693225,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{9\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^3\,d}+\frac{38\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{1}{2}}{d\,\left(4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^3*d) + (9*log(tan(c/2 + (d*x)/2)))/(2*a^3*d) + ((11*tan(c/2 + (d*x)/2))/2 + 38*tan(c/2 + (d*x)/2)^2 - 1/2)/(d*(4*a^3*tan(c/2 + (d*x)/2)^2 + 4*a^3*tan(c/2 + (d*x)/2)^3)) - (3*tan(c/2 + (d*x)/2))/(2*a^3*d)","B"
438,1,153,96,8.689855,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^3\,d}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{11\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^3\,d}-\frac{83\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{1}{3}}{d\,\left(8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{19\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^3*d) - (3*tan(c/2 + (d*x)/2)^2)/(8*a^3*d) - (11*log(tan(c/2 + (d*x)/2)))/(2*a^3*d) - (16*tan(c/2 + (d*x)/2)^2 - (8*tan(c/2 + (d*x)/2))/3 + 83*tan(c/2 + (d*x)/2)^3 + 1/3)/(d*(8*a^3*tan(c/2 + (d*x)/2)^3 + 8*a^3*tan(c/2 + (d*x)/2)^4)) + (19*tan(c/2 + (d*x)/2))/(8*a^3*d)","B"
439,1,176,117,9.130583,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))^3),x)","\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^3\,d}+\frac{51\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a^3\,d}-\frac{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{89\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{8}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}-\frac{1}{64}\right)}{a^3\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"(5*tan(c/2 + (d*x)/2)^2)/(8*a^3*d) - tan(c/2 + (d*x)/2)^3/(8*a^3*d) + tan(c/2 + (d*x)/2)^4/(64*a^3*d) + (51*log(tan(c/2 + (d*x)/2)))/(8*a^3*d) - (25*tan(c/2 + (d*x)/2))/(8*a^3*d) + (cot(c/2 + (d*x)/2)^4*((7*tan(c/2 + (d*x)/2))/64 - tan(c/2 + (d*x)/2)^2/2 + (5*tan(c/2 + (d*x)/2)^3)/2 + (89*tan(c/2 + (d*x)/2)^4)/8 - 1/64))/(a^3*d*(tan(c/2 + (d*x)/2) + 1))","B"
440,1,157,58,8.892030,"\text{Not used}","int((cos(e + f*x)^4*sin(e + f*x))/(a + a*sin(e + f*x))^6,x)","-\frac{2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left({\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+7\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-14\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+70\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-35\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+35\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}{35\,a^6\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^7}","Not used",1,"-(2*cos(e/2 + (f*x)/2)^2*(cos(e/2 + (f*x)/2)^5 + 35*sin(e/2 + (f*x)/2)^5 - 35*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^4 + 7*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2) + 70*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^3 - 14*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2)^2))/(35*a^6*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^7)","B"
441,1,181,89,9.051308,"\text{Not used}","int((cos(e + f*x)^4*sin(e + f*x)^2)/(a + a*sin(e + f*x))^7,x)","-\frac{4\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left({\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+9\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+36\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-126\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+441\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-315\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+210\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\right)}{315\,a^7\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^9}","Not used",1,"-(4*cos(e/2 + (f*x)/2)^3*(cos(e/2 + (f*x)/2)^6 + 210*sin(e/2 + (f*x)/2)^6 - 315*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^5 + 9*cos(e/2 + (f*x)/2)^5*sin(e/2 + (f*x)/2) + 441*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^4 - 126*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2)^3 + 36*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2)^2))/(315*a^7*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^9)","B"
442,1,205,157,9.406542,"\text{Not used}","int((cos(e + f*x)^4*sin(e + f*x)^3)/(a + a*sin(e + f*x))^8,x)","-\frac{4\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left({\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+11\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+55\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+165\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-825\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2541\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-2079\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+1155\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\right)}{1155\,a^8\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^{11}}","Not used",1,"-(4*cos(e/2 + (f*x)/2)^4*(cos(e/2 + (f*x)/2)^7 + 1155*sin(e/2 + (f*x)/2)^7 - 2079*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^6 + 11*cos(e/2 + (f*x)/2)^6*sin(e/2 + (f*x)/2) + 2541*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^5 - 825*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2)^4 + 165*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2)^3 + 55*cos(e/2 + (f*x)/2)^5*sin(e/2 + (f*x)/2)^2))/(1155*a^8*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^11)","B"
443,0,-1,156,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2), x)","F"
444,0,-1,124,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2), x)","F"
445,0,-1,159,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\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))/sin(c + d*x), x)","F"
446,0,-1,148,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^2, x)","F"
447,0,-1,156,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^3, x)","F"
448,0,-1,163,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^4,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^4, x)","F"
449,0,-1,173,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^5,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^5, x)","F"
450,0,-1,209,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^6,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^6} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^6, x)","F"
451,0,-1,245,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^7,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^7} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^7, x)","F"
452,0,-1,281,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^8,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^8} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2))/sin(c + d*x)^8, x)","F"
453,0,-1,188,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2), x)","F"
454,0,-1,156,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))^(3/2), x)","F"
455,0,-1,199,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x), x)","F"
456,0,-1,178,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^2, x)","F"
457,0,-1,186,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^3, x)","F"
458,0,-1,197,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^4,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^4, x)","F"
459,0,-1,205,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^5,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^5, x)","F"
460,0,-1,215,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^6,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^6} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^6, x)","F"
461,0,-1,253,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^7,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^7} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^7, x)","F"
462,0,-1,291,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^8,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^8} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^8, x)","F"
463,0,-1,329,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^9,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^9} \,d x","Not used",1,"int((cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2))/sin(c + d*x)^9, x)","F"
464,0,-1,124,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(1/2), x)","F"
465,0,-1,92,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x))^(1/2), x)","F"
466,0,-1,130,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))^(1/2)), x)","F"
467,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2)), x)","F"
468,0,-1,125,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2)), x)","F"
469,0,-1,135,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(1/2)), x)","F"
470,0,-1,170,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))^(1/2)), x)","F"
471,0,-1,205,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^6*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^6*(a + a*sin(c + d*x))^(1/2)), x)","F"
472,0,-1,205,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^3)/(a + a*sin(c + d*x))^(3/2), x)","F"
473,0,-1,92,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(3/2), x)","F"
474,0,-1,60,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x))^(3/2), x)","F"
475,0,-1,98,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))^(3/2)), x)","F"
476,0,-1,94,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)), x)","F"
477,0,-1,106,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2)), x)","F"
478,0,-1,144,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(3/2)), x)","F"
479,0,-1,182,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))^(3/2)), x)","F"
480,0,-1,220,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^6*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^6*(a + a*sin(c + d*x))^(3/2)), x)","F"
481,0,-1,260,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^4)/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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*sin(c + d*x)^4)/(a + a*sin(c + d*x))^(5/2), x)","F"
482,0,-1,222,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^3)/(a + a*sin(c + d*x))^(5/2), x)","F"
483,0,-1,169,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2)/(a + a*sin(c + d*x))^(5/2), x)","F"
484,0,-1,137,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^4*sin(c + d*x))/(a + a*sin(c + d*x))^(5/2), x)","F"
485,0,-1,113,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(sin(c + d*x)*(a + a*sin(c + d*x))^(5/2)), x)","F"
486,0,-1,113,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(5/2)), x)","F"
487,0,-1,153,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(5/2)), x)","F"
488,0,-1,191,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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/(sin(c + d*x)^4*(a + a*sin(c + d*x))^(5/2)), x)","F"
489,0,-1,229,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\sin\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)^4/(sin(c + d*x)^5*(a + a*sin(c + d*x))^(5/2)), x)","F"
490,0,-1,200,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^n*(a + a*sin(c + d*x))^2,x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^n\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)^n*(a + a*sin(c + d*x))^2, x)","F"
491,0,-1,129,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^n*(a + a*sin(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^n\,\left(a+a\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)^n*(a + a*sin(c + d*x)), x)","F"
492,0,-1,134,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^n)/(a + a*sin(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^n}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^4*sin(c + d*x)^n)/(a + a*sin(c + d*x)), x)","F"
493,0,-1,173,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^n)/(a + a*sin(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^n}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^4*sin(c + d*x)^n)/(a + a*sin(c + d*x))^2, x)","F"
494,1,71,97,8.717823,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^5*(a + a*sin(c + d*x)),x)","\frac{\frac{a\,{\sin\left(c+d\,x\right)}^{11}}{11}+\frac{a\,{\sin\left(c+d\,x\right)}^{10}}{10}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^9}{9}-\frac{a\,{\sin\left(c+d\,x\right)}^8}{4}+\frac{a\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a\,{\sin\left(c+d\,x\right)}^6}{6}}{d}","Not used",1,"((a*sin(c + d*x)^6)/6 + (a*sin(c + d*x)^7)/7 - (a*sin(c + d*x)^8)/4 - (2*a*sin(c + d*x)^9)/9 + (a*sin(c + d*x)^10)/10 + (a*sin(c + d*x)^11)/11)/d","B"
495,1,71,97,8.699084,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^4*(a + a*sin(c + d*x)),x)","\frac{\frac{a\,{\sin\left(c+d\,x\right)}^{10}}{10}+\frac{a\,{\sin\left(c+d\,x\right)}^9}{9}-\frac{a\,{\sin\left(c+d\,x\right)}^8}{4}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{5}}{d}","Not used",1,"((a*sin(c + d*x)^5)/5 + (a*sin(c + d*x)^6)/6 - (2*a*sin(c + d*x)^7)/7 - (a*sin(c + d*x)^8)/4 + (a*sin(c + d*x)^9)/9 + (a*sin(c + d*x)^10)/10)/d","B"
496,1,71,81,0.054141,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{\frac{a\,{\sin\left(c+d\,x\right)}^9}{9}+\frac{a\,{\sin\left(c+d\,x\right)}^8}{8}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{3}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{4}}{d}","Not used",1,"((a*sin(c + d*x)^4)/4 + (a*sin(c + d*x)^5)/5 - (a*sin(c + d*x)^6)/3 - (2*a*sin(c + d*x)^7)/7 + (a*sin(c + d*x)^8)/8 + (a*sin(c + d*x)^9)/9)/d","B"
497,1,71,81,8.694358,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^2*(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}{3}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"((a*sin(c + d*x)^3)/3 + (a*sin(c + d*x)^4)/4 - (2*a*sin(c + d*x)^5)/5 - (a*sin(c + d*x)^6)/3 + (a*sin(c + d*x)^7)/7 + (a*sin(c + d*x)^8)/8)/d","B"
498,1,71,65,8.698884,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)*(a + a*sin(c + d*x)),x)","\frac{\frac{a\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a\,{\sin\left(c+d\,x\right)}^6}{6}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{a\,{\sin\left(c+d\,x\right)}^4}{2}+\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"((a*sin(c + d*x)^2)/2 + (a*sin(c + d*x)^3)/3 - (a*sin(c + d*x)^4)/2 - (2*a*sin(c + d*x)^5)/5 + (a*sin(c + d*x)^6)/6 + (a*sin(c + d*x)^7)/7)/d","B"
499,1,126,86,8.871455,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x),x)","\frac{a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a\,{\cos\left(c+d\,x\right)}^2}{2\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^4}{4\,d}+\frac{8\,a\,\sin\left(c+d\,x\right)}{15\,d}+\frac{4\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{15\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{5\,d}","Not used",1,"(a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*log(1/cos(c/2 + (d*x)/2)^2))/d + (a*cos(c + d*x)^2)/(2*d) + (a*cos(c + d*x)^4)/(4*d) + (8*a*sin(c + d*x))/(15*d) + (4*a*cos(c + d*x)^2*sin(c + d*x))/(15*d) + (a*cos(c + d*x)^4*sin(c + d*x))/(5*d)","B"
500,1,250,83,8.878207,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}-\frac{4\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d}+\frac{8\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}-\frac{8\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d}+\frac{4\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d}-\frac{9\,a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{20\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{16\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{8\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*log(1/cos(c/2 + (d*x)/2)^2))/d - (4*a*cos(c/2 + (d*x)/2)^2)/d + (8*a*cos(c/2 + (d*x)/2)^4)/d - (8*a*cos(c/2 + (d*x)/2)^6)/d + (4*a*cos(c/2 + (d*x)/2)^8)/d - (9*a*cos(c/2 + (d*x)/2))/(2*d*sin(c/2 + (d*x)/2)) - (a*sin(c/2 + (d*x)/2))/(2*d*cos(c/2 + (d*x)/2)) + (20*a*cos(c/2 + (d*x)/2)^3)/(3*d*sin(c/2 + (d*x)/2)) - (16*a*cos(c/2 + (d*x)/2)^5)/(3*d*sin(c/2 + (d*x)/2)) + (8*a*cos(c/2 + (d*x)/2)^7)/(3*d*sin(c/2 + (d*x)/2))","B"
501,1,229,86,8.861001,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{2\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{18\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{82\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+22\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{2\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(2*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a/2 + 2*a*tan(c/2 + (d*x)/2) + (3*a*tan(c/2 + (d*x)/2)^2)/2 + 22*a*tan(c/2 + (d*x)/2)^3 - (13*a*tan(c/2 + (d*x)/2)^4)/2 + (82*a*tan(c/2 + (d*x)/2)^5)/3 - (15*a*tan(c/2 + (d*x)/2)^6)/2 + 18*a*tan(c/2 + (d*x)/2)^7)/(d*(4*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^4 + 12*tan(c/2 + (d*x)/2)^6 + 4*tan(c/2 + (d*x)/2)^8)) - (a*tan(c/2 + (d*x)/2))/(2*d) - (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (2*a*log(tan(c/2 + (d*x)/2)))/d","B"
502,1,218,85,8.794015,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^4,x)","\frac{7\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{2\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{2\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{23\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{89\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{19\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(7*a*tan(c/2 + (d*x)/2))/(8*d) + (2*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (2*a*log(tan(c/2 + (d*x)/2)))/d + ((19*a*tan(c/2 + (d*x)/2)^2)/3 - a*tan(c/2 + (d*x)/2) - a/3 - 2*a*tan(c/2 + (d*x)/2)^3 + (89*a*tan(c/2 + (d*x)/2)^4)/3 + 15*a*tan(c/2 + (d*x)/2)^5 + 23*a*tan(c/2 + (d*x)/2)^6)/(d*(8*tan(c/2 + (d*x)/2)^3 + 16*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^7))","B"
503,1,207,81,9.032613,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^5,x)","\frac{7\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{46\,a\,{\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+\frac{40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{a}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(7*a*tan(c/2 + (d*x)/2))/(8*d) + ((11*a*tan(c/2 + (d*x)/2)^2)/4 - (2*a*tan(c/2 + (d*x)/2))/3 - a/4 + (40*a*tan(c/2 + (d*x)/2)^3)/3 + 3*a*tan(c/2 + (d*x)/2)^4 + 46*a*tan(c/2 + (d*x)/2)^5)/(d*(16*tan(c/2 + (d*x)/2)^4 + 16*tan(c/2 + (d*x)/2)^6)) - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d + (3*a*tan(c/2 + (d*x)/2)^2)/(16*d) - (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*tan(c/2 + (d*x)/2)^4)/(64*d) + (a*log(tan(c/2 + (d*x)/2)))/d","B"
504,1,193,86,8.898375,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^6,x)","\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}\right)}{32\,d}","Not used",1,"(3*a*tan(c/2 + (d*x)/2)^2)/(16*d) - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (5*a*tan(c/2 + (d*x)/2))/(16*d) + (5*a*tan(c/2 + (d*x)/2)^3)/(96*d) - (a*tan(c/2 + (d*x)/2)^4)/(64*d) - (a*tan(c/2 + (d*x)/2)^5)/(160*d) + (a*log(tan(c/2 + (d*x)/2)))/d - (cot(c/2 + (d*x)/2)^5*(a/5 + (a*tan(c/2 + (d*x)/2))/2 - (5*a*tan(c/2 + (d*x)/2)^2)/3 - 6*a*tan(c/2 + (d*x)/2)^3 + 10*a*tan(c/2 + (d*x)/2)^4))/(32*d)","B"
505,1,69,61,8.884019,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^7,x)","-\frac{a\,{\sin\left(c+d\,x\right)}^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}+\frac{a\,\sin\left(c+d\,x\right)}{5}+\frac{a}{6}}{d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"-(a/6 + (a*sin(c + d*x))/5 - (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)/(d*sin(c + d*x)^6)","B"
506,1,70,65,8.834357,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^8,x)","-\frac{105\,a\,{\sin\left(c+d\,x\right)}^5+70\,a\,{\sin\left(c+d\,x\right)}^4-105\,a\,{\sin\left(c+d\,x\right)}^3-84\,a\,{\sin\left(c+d\,x\right)}^2+35\,a\,\sin\left(c+d\,x\right)+30\,a}{210\,d\,{\sin\left(c+d\,x\right)}^7}","Not used",1,"-(30*a + 35*a*sin(c + d*x) - 84*a*sin(c + d*x)^2 - 105*a*sin(c + d*x)^3 + 70*a*sin(c + d*x)^4 + 105*a*sin(c + d*x)^5)/(210*d*sin(c + d*x)^7)","B"
507,1,70,81,8.844365,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^9,x)","-\frac{280\,a\,{\sin\left(c+d\,x\right)}^5+210\,a\,{\sin\left(c+d\,x\right)}^4-336\,a\,{\sin\left(c+d\,x\right)}^3-280\,a\,{\sin\left(c+d\,x\right)}^2+120\,a\,\sin\left(c+d\,x\right)+105\,a}{840\,d\,{\sin\left(c+d\,x\right)}^8}","Not used",1,"-(105*a + 120*a*sin(c + d*x) - 280*a*sin(c + d*x)^2 - 336*a*sin(c + d*x)^3 + 210*a*sin(c + d*x)^4 + 280*a*sin(c + d*x)^5)/(840*d*sin(c + d*x)^8)","B"
508,1,70,81,8.883998,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^10,x)","-\frac{\frac{a\,{\sin\left(c+d\,x\right)}^5}{4}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{5}-\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^2}{7}+\frac{a\,\sin\left(c+d\,x\right)}{8}+\frac{a}{9}}{d\,{\sin\left(c+d\,x\right)}^9}","Not used",1,"-(a/9 + (a*sin(c + d*x))/8 - (2*a*sin(c + d*x)^2)/7 - (a*sin(c + d*x)^3)/3 + (a*sin(c + d*x)^4)/5 + (a*sin(c + d*x)^5)/4)/(d*sin(c + d*x)^9)","B"
509,1,70,97,8.859015,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^11,x)","-\frac{252\,a\,{\sin\left(c+d\,x\right)}^5+210\,a\,{\sin\left(c+d\,x\right)}^4-360\,a\,{\sin\left(c+d\,x\right)}^3-315\,a\,{\sin\left(c+d\,x\right)}^2+140\,a\,\sin\left(c+d\,x\right)+126\,a}{1260\,d\,{\sin\left(c+d\,x\right)}^{10}}","Not used",1,"-(126*a + 140*a*sin(c + d*x) - 315*a*sin(c + d*x)^2 - 360*a*sin(c + d*x)^3 + 210*a*sin(c + d*x)^4 + 252*a*sin(c + d*x)^5)/(1260*d*sin(c + d*x)^10)","B"
510,1,70,97,8.975952,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x)))/sin(c + d*x)^12,x)","-\frac{\frac{a\,{\sin\left(c+d\,x\right)}^5}{6}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{7}-\frac{a\,{\sin\left(c+d\,x\right)}^3}{4}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^2}{9}+\frac{a\,\sin\left(c+d\,x\right)}{10}+\frac{a}{11}}{d\,{\sin\left(c+d\,x\right)}^{11}}","Not used",1,"-(a/11 + (a*sin(c + d*x))/10 - (2*a*sin(c + d*x)^2)/9 - (a*sin(c + d*x)^3)/4 + (a*sin(c + d*x)^4)/7 + (a*sin(c + d*x)^5)/6)/(d*sin(c + d*x)^11)","B"
511,1,96,127,8.737511,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^3*(a + a*sin(c + d*x))^2,x)","\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^{10}}{10}+\frac{2\,a^2\,{\sin\left(c+d\,x\right)}^9}{9}-\frac{a^2\,{\sin\left(c+d\,x\right)}^8}{8}-\frac{4\,a^2\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{a^2\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{2\,a^2\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a^2\,{\sin\left(c+d\,x\right)}^4}{4}}{d}","Not used",1,"((a^2*sin(c + d*x)^4)/4 + (2*a^2*sin(c + d*x)^5)/5 - (a^2*sin(c + d*x)^6)/6 - (4*a^2*sin(c + d*x)^7)/7 - (a^2*sin(c + d*x)^8)/8 + (2*a^2*sin(c + d*x)^9)/9 + (a^2*sin(c + d*x)^10)/10)/d","B"
512,1,96,109,8.762304,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^2*(a + a*sin(c + d*x))^2,x)","\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^9}{9}+\frac{a^2\,{\sin\left(c+d\,x\right)}^8}{4}-\frac{a^2\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{2\,a^2\,{\sin\left(c+d\,x\right)}^6}{3}-\frac{a^2\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a^2\,{\sin\left(c+d\,x\right)}^4}{2}+\frac{a^2\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"((a^2*sin(c + d*x)^3)/3 + (a^2*sin(c + d*x)^4)/2 - (a^2*sin(c + d*x)^5)/5 - (2*a^2*sin(c + d*x)^6)/3 - (a^2*sin(c + d*x)^7)/7 + (a^2*sin(c + d*x)^8)/4 + (a^2*sin(c + d*x)^9)/9)/d","B"
513,1,96,89,8.811549,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)*(a + a*sin(c + d*x))^2,x)","\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{2\,a^2\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{a^2\,{\sin\left(c+d\,x\right)}^6}{6}-\frac{4\,a^2\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{a^2\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{2\,a^2\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a^2\,{\sin\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"((a^2*sin(c + d*x)^2)/2 + (2*a^2*sin(c + d*x)^3)/3 - (a^2*sin(c + d*x)^4)/4 - (4*a^2*sin(c + d*x)^5)/5 - (a^2*sin(c + d*x)^6)/6 + (2*a^2*sin(c + d*x)^7)/7 + (a^2*sin(c + d*x)^8)/8)/d","B"
514,1,132,119,9.065720,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{5\,a^2\,\sin\left(c+d\,x\right)}{4\,d}-\frac{a^2\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{19\,a^2\,\cos\left(2\,c+2\,d\,x\right)}{64\,d}-\frac{a^2\,\cos\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{5\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{24\,d}+\frac{a^2\,\sin\left(5\,c+5\,d\,x\right)}{40\,d}","Not used",1,"(5*a^2*sin(c + d*x))/(4*d) - (a^2*log(1/cos(c/2 + (d*x)/2)^2))/d + (a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (19*a^2*cos(2*c + 2*d*x))/(64*d) - (a^2*cos(6*c + 6*d*x))/(192*d) + (5*a^2*sin(3*c + 3*d*x))/(24*d) + (a^2*sin(5*c + 5*d*x))/(40*d)","B"
515,1,333,114,8.946209,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{16\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}-\frac{8\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d}-\frac{16\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d}+\frac{8\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d}-\frac{2\,a^2\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{2\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{2\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{176\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{328\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{15\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{96\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{32\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{5\,a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(16*a^2*cos(c/2 + (d*x)/2)^4)/d - (8*a^2*cos(c/2 + (d*x)/2)^2)/d - (16*a^2*cos(c/2 + (d*x)/2)^6)/d + (8*a^2*cos(c/2 + (d*x)/2)^8)/d - (2*a^2*log(1/cos(c/2 + (d*x)/2)^2))/d + (2*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (2*a^2*cos(c/2 + (d*x)/2)^3)/(3*d*sin(c/2 + (d*x)/2)) + (176*a^2*cos(c/2 + (d*x)/2)^5)/(15*d*sin(c/2 + (d*x)/2)) - (328*a^2*cos(c/2 + (d*x)/2)^7)/(15*d*sin(c/2 + (d*x)/2)) + (96*a^2*cos(c/2 + (d*x)/2)^9)/(5*d*sin(c/2 + (d*x)/2)) - (32*a^2*cos(c/2 + (d*x)/2)^11)/(5*d*sin(c/2 + (d*x)/2)) - (5*a^2*cos(c/2 + (d*x)/2))/(2*d*sin(c/2 + (d*x)/2)) - (a^2*sin(c/2 + (d*x)/2))/(2*d*cos(c/2 + (d*x)/2))","B"
516,1,297,116,8.944333,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{36\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{17\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+\frac{272\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{296\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+48\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a^2*log(tan(c/2 + (d*x)/2)))/d - (2*a^2*tan(c/2 + (d*x)/2)^2 + 48*a^2*tan(c/2 + (d*x)/2)^3 + 11*a^2*tan(c/2 + (d*x)/2)^4 + (296*a^2*tan(c/2 + (d*x)/2)^5)/3 + 2*a^2*tan(c/2 + (d*x)/2)^6 + (272*a^2*tan(c/2 + (d*x)/2)^7)/3 + (17*a^2*tan(c/2 + (d*x)/2)^8)/2 + 36*a^2*tan(c/2 + (d*x)/2)^9 + a^2/2 + 4*a^2*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 16*tan(c/2 + (d*x)/2)^4 + 24*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8 + 4*tan(c/2 + (d*x)/2)^10)) - (a^2*tan(c/2 + (d*x)/2))/d - (a^2*tan(c/2 + (d*x)/2)^2)/(8*d)","B"
517,1,288,110,8.917648,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^2)/sin(c + d*x)^4,x)","\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{4\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{13\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-30\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-26\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{4\,a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(3*a^2*tan(c/2 + (d*x)/2))/(8*d) - (a^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (4*a^2*log(tan(c/2 + (d*x)/2)))/d - (a^2*tan(c/2 + (d*x)/2)^2)/(4*d) - (6*a^2*tan(c/2 + (d*x)/2)^3 - 2*a^2*tan(c/2 + (d*x)/2)^2 + 8*a^2*tan(c/2 + (d*x)/2)^4 - 26*a^2*tan(c/2 + (d*x)/2)^5 + 2*a^2*tan(c/2 + (d*x)/2)^6 - 30*a^2*tan(c/2 + (d*x)/2)^7 + 13*a^2*tan(c/2 + (d*x)/2)^8 + a^2/3 + 2*a^2*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 24*tan(c/2 + (d*x)/2)^5 + 24*tan(c/2 + (d*x)/2)^7 + 8*tan(c/2 + (d*x)/2)^9)) + (4*a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
518,1,276,116,8.796085,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^2)/sin(c + d*x)^5,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{7\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}+\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{92\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+33\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{356\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}+\frac{76\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{a^2}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(16*d) - (a^2*tan(c/2 + (d*x)/2)^3)/(12*d) - (a^2*tan(c/2 + (d*x)/2)^4)/(64*d) - (a^2*log(tan(c/2 + (d*x)/2)))/d + (7*a^2*tan(c/2 + (d*x)/2))/(4*d) + (a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d + ((a^2*tan(c/2 + (d*x)/2)^2)/2 + (76*a^2*tan(c/2 + (d*x)/2)^3)/3 + (7*a^2*tan(c/2 + (d*x)/2)^4)/4 + (356*a^2*tan(c/2 + (d*x)/2)^5)/3 + 33*a^2*tan(c/2 + (d*x)/2)^6 + 92*a^2*tan(c/2 + (d*x)/2)^7 - a^2/4 - (4*a^2*tan(c/2 + (d*x)/2))/3)/(d*(16*tan(c/2 + (d*x)/2)^4 + 32*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8))","B"
519,1,267,112,8.787830,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^2)/sin(c + d*x)^6,x)","\frac{82\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{55\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a^2}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{2\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{2\,a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"((2*a^2*tan(c/2 + (d*x)/2)^2)/15 + 11*a^2*tan(c/2 + (d*x)/2)^3 + (55*a^2*tan(c/2 + (d*x)/2)^4)/3 + 12*a^2*tan(c/2 + (d*x)/2)^5 + 82*a^2*tan(c/2 + (d*x)/2)^6 - a^2/5 - a^2*tan(c/2 + (d*x)/2))/(d*(32*tan(c/2 + (d*x)/2)^5 + 32*tan(c/2 + (d*x)/2)^7)) + (3*a^2*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(96*d) - (a^2*tan(c/2 + (d*x)/2)^4)/(32*d) - (a^2*tan(c/2 + (d*x)/2)^5)/(160*d) + (2*a^2*log(tan(c/2 + (d*x)/2)))/d + (9*a^2*tan(c/2 + (d*x)/2))/(16*d) - (2*a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
520,1,217,119,8.975454,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^2)/sin(c + d*x)^7,x)","\frac{19\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{48\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{80\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(40\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{19\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-\frac{20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{a^2}{6}\right)}{64\,d}-\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(19*a^2*tan(c/2 + (d*x)/2)^2)/(128*d) + (5*a^2*tan(c/2 + (d*x)/2)^3)/(48*d) - (a^2*tan(c/2 + (d*x)/2)^5)/(80*d) - (a^2*tan(c/2 + (d*x)/2)^6)/(384*d) + (a^2*log(tan(c/2 + (d*x)/2)))/d - (cot(c/2 + (d*x)/2)^6*(40*a^2*tan(c/2 + (d*x)/2)^5 - (19*a^2*tan(c/2 + (d*x)/2)^4)/2 - (20*a^2*tan(c/2 + (d*x)/2)^3)/3 + a^2/6 + (4*a^2*tan(c/2 + (d*x)/2))/5))/(64*d) - (5*a^2*tan(c/2 + (d*x)/2))/(8*d) - (a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
521,1,109,111,8.714792,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^2*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^{10}}{10}+\frac{a^3\,{\sin\left(c+d\,x\right)}^9}{3}+\frac{a^3\,{\sin\left(c+d\,x\right)}^8}{8}-\frac{5\,a^3\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{5\,a^3\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{a^3\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{a^3\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"((a^3*sin(c + d*x)^3)/3 + (3*a^3*sin(c + d*x)^4)/4 + (a^3*sin(c + d*x)^5)/5 - (5*a^3*sin(c + d*x)^6)/6 - (5*a^3*sin(c + d*x)^7)/7 + (a^3*sin(c + d*x)^8)/8 + (a^3*sin(c + d*x)^9)/3 + (a^3*sin(c + d*x)^10)/10)/d","B"
522,1,108,89,0.073294,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^9}{9}+\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{a^3\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{5\,a^3\,{\sin\left(c+d\,x\right)}^6}{6}-a^3\,{\sin\left(c+d\,x\right)}^5+\frac{a^3\,{\sin\left(c+d\,x\right)}^4}{4}+a^3\,{\sin\left(c+d\,x\right)}^3+\frac{a^3\,{\sin\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"((a^3*sin(c + d*x)^2)/2 + a^3*sin(c + d*x)^3 + (a^3*sin(c + d*x)^4)/4 - a^3*sin(c + d*x)^5 - (5*a^3*sin(c + d*x)^6)/6 + (a^3*sin(c + d*x)^7)/7 + (3*a^3*sin(c + d*x)^8)/8 + (a^3*sin(c + d*x)^9)/9)/d","B"
523,1,178,137,8.989054,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^3)/sin(c + d*x),x)","\frac{176\,a^3\,\sin\left(c+d\,x\right)}{105\,d}-\frac{a^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a^3\,{\cos\left(c+d\,x\right)}^2}{2\,d}+\frac{a^3\,{\cos\left(c+d\,x\right)}^4}{4\,d}-\frac{a^3\,{\cos\left(c+d\,x\right)}^6}{2\,d}+\frac{88\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{105\,d}+\frac{22\,a^3\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{35\,d}-\frac{a^3\,{\cos\left(c+d\,x\right)}^6\,\sin\left(c+d\,x\right)}{7\,d}","Not used",1,"(176*a^3*sin(c + d*x))/(105*d) - (a^3*log(1/cos(c/2 + (d*x)/2)^2))/d + (a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^3*cos(c + d*x)^2)/(2*d) + (a^3*cos(c + d*x)^4)/(4*d) - (a^3*cos(c + d*x)^6)/(2*d) + (88*a^3*cos(c + d*x)^2*sin(c + d*x))/(105*d) + (22*a^3*cos(c + d*x)^4*sin(c + d*x))/(35*d) - (a^3*cos(c + d*x)^6*sin(c + d*x))/(7*d)","B"
524,1,371,133,9.184835,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^3)/sin(c + d*x)^2,x)","\frac{14\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}-\frac{10\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d}+\frac{8\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3\,d}-\frac{28\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d}+\frac{32\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{d}-\frac{32\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3\,d}-\frac{3\,a^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{3\,a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{46\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{688\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{1064\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{15\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{288\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{96\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{3\,a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{a^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(14*a^3*cos(c/2 + (d*x)/2)^4)/d - (10*a^3*cos(c/2 + (d*x)/2)^2)/d + (8*a^3*cos(c/2 + (d*x)/2)^6)/(3*d) - (28*a^3*cos(c/2 + (d*x)/2)^8)/d + (32*a^3*cos(c/2 + (d*x)/2)^10)/d - (32*a^3*cos(c/2 + (d*x)/2)^12)/(3*d) - (3*a^3*log(1/cos(c/2 + (d*x)/2)^2))/d + (3*a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (46*a^3*cos(c/2 + (d*x)/2)^3)/(3*d*sin(c/2 + (d*x)/2)) + (688*a^3*cos(c/2 + (d*x)/2)^5)/(15*d*sin(c/2 + (d*x)/2)) - (1064*a^3*cos(c/2 + (d*x)/2)^7)/(15*d*sin(c/2 + (d*x)/2)) + (288*a^3*cos(c/2 + (d*x)/2)^9)/(5*d*sin(c/2 + (d*x)/2)) - (96*a^3*cos(c/2 + (d*x)/2)^11)/(5*d*sin(c/2 + (d*x)/2)) + (3*a^3*cos(c/2 + (d*x)/2))/(2*d*sin(c/2 + (d*x)/2)) - (a^3*sin(c/2 + (d*x)/2))/(2*d*cos(c/2 + (d*x)/2))","B"
525,1,342,133,9.013725,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^3)/sin(c + d*x)^3,x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{46\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\frac{81\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{2}+\frac{538\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3}+\frac{149\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+\frac{3796\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{15}+77\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{628\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+45\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+70\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d - (a^3*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*a^3*tan(c/2 + (d*x)/2))/(2*d) - ((5*a^3*tan(c/2 + (d*x)/2)^2)/2 + 70*a^3*tan(c/2 + (d*x)/2)^3 + 45*a^3*tan(c/2 + (d*x)/2)^4 + (628*a^3*tan(c/2 + (d*x)/2)^5)/3 + 77*a^3*tan(c/2 + (d*x)/2)^6 + (3796*a^3*tan(c/2 + (d*x)/2)^7)/15 + (149*a^3*tan(c/2 + (d*x)/2)^8)/2 + (538*a^3*tan(c/2 + (d*x)/2)^9)/3 + (81*a^3*tan(c/2 + (d*x)/2)^10)/2 + 46*a^3*tan(c/2 + (d*x)/2)^11 + a^3/2 + 6*a^3*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 20*tan(c/2 + (d*x)/2)^4 + 40*tan(c/2 + (d*x)/2)^6 + 40*tan(c/2 + (d*x)/2)^8 + 20*tan(c/2 + (d*x)/2)^10 + 4*tan(c/2 + (d*x)/2)^12)) - (a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
526,1,333,131,8.982472,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^3)/sin(c + d*x)^4,x)","\frac{5\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{5\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{5\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{85\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{589\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-52\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{622\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+102\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{19\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(5*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (5*a^3*log(tan(c/2 + (d*x)/2)))/d - (5*a^3*tan(c/2 + (d*x)/2))/(8*d) - (3*a^3*tan(c/2 + (d*x)/2)^2)/(8*d) - ((19*a^3*tan(c/2 + (d*x)/2)^2)/3 + 12*a^3*tan(c/2 + (d*x)/2)^3 + 102*a^3*tan(c/2 + (d*x)/2)^4 + 2*a^3*tan(c/2 + (d*x)/2)^5 + (622*a^3*tan(c/2 + (d*x)/2)^6)/3 - 52*a^3*tan(c/2 + (d*x)/2)^7 + (589*a^3*tan(c/2 + (d*x)/2)^8)/3 - 13*a^3*tan(c/2 + (d*x)/2)^9 + 85*a^3*tan(c/2 + (d*x)/2)^10 + a^3/3 + 3*a^3*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 32*tan(c/2 + (d*x)/2)^5 + 48*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9 + 8*tan(c/2 + (d*x)/2)^11))","B"
527,1,322,131,8.939506,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^3)/sin(c + d*x)^5,x)","\frac{66\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+93\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{620\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+\frac{347\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{4}+128\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{39\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}+28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a^3}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{5\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{17\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{5\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(28*a^3*tan(c/2 + (d*x)/2)^3 - (15*a^3*tan(c/2 + (d*x)/2)^2)/4 - (39*a^3*tan(c/2 + (d*x)/2)^4)/4 + 128*a^3*tan(c/2 + (d*x)/2)^5 + (347*a^3*tan(c/2 + (d*x)/2)^6)/4 + (620*a^3*tan(c/2 + (d*x)/2)^7)/3 + 93*a^3*tan(c/2 + (d*x)/2)^8 + 66*a^3*tan(c/2 + (d*x)/2)^9 - a^3/4 - 2*a^3*tan(c/2 + (d*x)/2))/(d*(16*tan(c/2 + (d*x)/2)^4 + 48*tan(c/2 + (d*x)/2)^6 + 48*tan(c/2 + (d*x)/2)^8 + 16*tan(c/2 + (d*x)/2)^10)) - (a^3*tan(c/2 + (d*x)/2)^3)/(8*d) - (a^3*tan(c/2 + (d*x)/2)^4)/(64*d) - (3*a^3*tan(c/2 + (d*x)/2)^2)/(16*d) - (5*a^3*log(tan(c/2 + (d*x)/2)))/d + (17*a^3*tan(c/2 + (d*x)/2))/(8*d) + (5*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
528,1,311,133,8.945971,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^3)/sin(c + d*x)^6,x)","\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{266\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+78\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{1013\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{53\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}+\frac{1037\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{41\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{a^3}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{37\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(7*a^3*tan(c/2 + (d*x)/2)^2)/(16*d) - (7*a^3*tan(c/2 + (d*x)/2)^3)/(96*d) - (3*a^3*tan(c/2 + (d*x)/2)^4)/(64*d) - (a^3*tan(c/2 + (d*x)/2)^5)/(160*d) + (a^3*log(tan(c/2 + (d*x)/2)))/d + (11*a^3*tan(c/2 + (d*x)/2)^3 - (41*a^3*tan(c/2 + (d*x)/2)^2)/15 + (1037*a^3*tan(c/2 + (d*x)/2)^4)/15 + (53*a^3*tan(c/2 + (d*x)/2)^5)/2 + (1013*a^3*tan(c/2 + (d*x)/2)^6)/3 + 78*a^3*tan(c/2 + (d*x)/2)^7 + 266*a^3*tan(c/2 + (d*x)/2)^8 - a^3/5 - (3*a^3*tan(c/2 + (d*x)/2))/2)/(d*(32*tan(c/2 + (d*x)/2)^5 + 64*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9)) + (37*a^3*tan(c/2 + (d*x)/2))/(16*d) - (a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
529,1,296,133,9.843154,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^3)/sin(c + d*x)^7,x)","\frac{67\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{a^3\,\left(5760\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-5760\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{1920\,d}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{31\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{67\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128}+\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{96}+\frac{63\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128}+\frac{23\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{240}-\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{384}-\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{160}-\frac{a^3}{384}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(67*a^3*tan(c/2 + (d*x)/2)^2)/(128*d) + (11*a^3*tan(c/2 + (d*x)/2)^3)/(96*d) - (a^3*tan(c/2 + (d*x)/2)^4)/(32*d) - (3*a^3*tan(c/2 + (d*x)/2)^5)/(160*d) - (a^3*tan(c/2 + (d*x)/2)^6)/(384*d) + (a^3*(5760*log(tan(c/2 + (d*x)/2)) - 5760*log(tan(c/2 + (d*x)/2)^2 + 1)))/(1920*d) - (a^3*tan(c/2 + (d*x)/2))/(16*d) + (cot(c/2 + (d*x)/2)^6*((23*a^3*tan(c/2 + (d*x)/2)^3)/240 - (13*a^3*tan(c/2 + (d*x)/2)^2)/384 + (63*a^3*tan(c/2 + (d*x)/2)^4)/128 + (5*a^3*tan(c/2 + (d*x)/2)^5)/96 + (67*a^3*tan(c/2 + (d*x)/2)^6)/128 + (31*a^3*tan(c/2 + (d*x)/2)^7)/16 - a^3/384 - (3*a^3*tan(c/2 + (d*x)/2))/160))/(d*(tan(c/2 + (d*x)/2)^2 + 1))","B"
530,1,378,145,8.970201,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^4)/sin(c + d*x)^4,x)","\frac{4\,a^4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{4\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{177\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+68\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+640\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+84\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{4549\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{5}+104\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+728\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+104\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{745\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+20\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{56\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^4}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{17\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d}","Not used",1,"(4*a^4*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a^4*tan(c/2 + (d*x)/2)^3)/(24*d) - (4*a^4*log(tan(c/2 + (d*x)/2)))/d - ((56*a^4*tan(c/2 + (d*x)/2)^2)/3 + 20*a^4*tan(c/2 + (d*x)/2)^3 + (745*a^4*tan(c/2 + (d*x)/2)^4)/3 + 104*a^4*tan(c/2 + (d*x)/2)^5 + 728*a^4*tan(c/2 + (d*x)/2)^6 + 104*a^4*tan(c/2 + (d*x)/2)^7 + (4549*a^4*tan(c/2 + (d*x)/2)^8)/5 + 84*a^4*tan(c/2 + (d*x)/2)^9 + 640*a^4*tan(c/2 + (d*x)/2)^10 + 68*a^4*tan(c/2 + (d*x)/2)^11 + 177*a^4*tan(c/2 + (d*x)/2)^12 + a^4/3 + 4*a^4*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 40*tan(c/2 + (d*x)/2)^5 + 80*tan(c/2 + (d*x)/2)^7 + 80*tan(c/2 + (d*x)/2)^9 + 40*tan(c/2 + (d*x)/2)^11 + 8*tan(c/2 + (d*x)/2)^13)) - (17*a^4*tan(c/2 + (d*x)/2))/(8*d) - (a^4*tan(c/2 + (d*x)/2)^2)/(2*d)","B"
531,1,368,148,9.073107,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^4)/sin(c + d*x)^5,x)","\frac{3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6\,d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{10\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{104\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-119\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+120\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-\frac{1135\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4}+80\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-73\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+48\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{75\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-\frac{40\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+10\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{8\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{a^4}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+96\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{9\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}+\frac{10\,a^4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(3*a^4*tan(c/2 + (d*x)/2))/(2*d) - (a^4*tan(c/2 + (d*x)/2)^3)/(6*d) - (a^4*tan(c/2 + (d*x)/2)^4)/(64*d) - (10*a^4*log(tan(c/2 + (d*x)/2)))/d - (10*a^4*tan(c/2 + (d*x)/2)^2 - (40*a^4*tan(c/2 + (d*x)/2)^3)/3 + (75*a^4*tan(c/2 + (d*x)/2)^4)/2 + 48*a^4*tan(c/2 + (d*x)/2)^5 - 73*a^4*tan(c/2 + (d*x)/2)^6 + 80*a^4*tan(c/2 + (d*x)/2)^7 - (1135*a^4*tan(c/2 + (d*x)/2)^8)/4 + 120*a^4*tan(c/2 + (d*x)/2)^9 - 119*a^4*tan(c/2 + (d*x)/2)^10 + 104*a^4*tan(c/2 + (d*x)/2)^11 + a^4/4 + (8*a^4*tan(c/2 + (d*x)/2))/3)/(d*(16*tan(c/2 + (d*x)/2)^4 + 64*tan(c/2 + (d*x)/2)^6 + 96*tan(c/2 + (d*x)/2)^8 + 64*tan(c/2 + (d*x)/2)^10 + 16*tan(c/2 + (d*x)/2)^12)) - (9*a^4*tan(c/2 + (d*x)/2)^2)/(16*d) + (10*a^4*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
532,1,357,146,9.085954,"\text{Not used}","int((cos(c + d*x)^5*(a + a*sin(c + d*x))^4)/sin(c + d*x)^6,x)","\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{19\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16\,d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{4\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{398\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+264\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+1017\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+278\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{3314\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+18\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{612\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{104\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a^4}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+96\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+96\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{71\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{4\,a^4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^4*tan(c/2 + (d*x)/2)^2)/(4*d) - (19*a^4*tan(c/2 + (d*x)/2)^3)/(96*d) - (a^4*tan(c/2 + (d*x)/2)^4)/(16*d) - (a^4*tan(c/2 + (d*x)/2)^5)/(160*d) - (4*a^4*log(tan(c/2 + (d*x)/2)))/d + (2*a^4*tan(c/2 + (d*x)/2)^3 - (104*a^4*tan(c/2 + (d*x)/2)^2)/15 + (612*a^4*tan(c/2 + (d*x)/2)^4)/5 + 18*a^4*tan(c/2 + (d*x)/2)^5 + (3314*a^4*tan(c/2 + (d*x)/2)^6)/5 + 278*a^4*tan(c/2 + (d*x)/2)^7 + 1017*a^4*tan(c/2 + (d*x)/2)^8 + 264*a^4*tan(c/2 + (d*x)/2)^9 + 398*a^4*tan(c/2 + (d*x)/2)^10 - a^4/5 - 2*a^4*tan(c/2 + (d*x)/2))/(d*(32*tan(c/2 + (d*x)/2)^5 + 96*tan(c/2 + (d*x)/2)^7 + 96*tan(c/2 + (d*x)/2)^9 + 32*tan(c/2 + (d*x)/2)^11)) + (71*a^4*tan(c/2 + (d*x)/2))/(16*d) + (4*a^4*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
533,1,57,73,0.068289,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^3)/(a + a*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^4}{4\,a}-\frac{{\sin\left(c+d\,x\right)}^5}{5\,a}-\frac{{\sin\left(c+d\,x\right)}^6}{6\,a}+\frac{{\sin\left(c+d\,x\right)}^7}{7\,a}}{d}","Not used",1,"(sin(c + d*x)^4/(4*a) - sin(c + d*x)^5/(5*a) - sin(c + d*x)^6/(6*a) + sin(c + d*x)^7/(7*a))/d","B"
534,1,57,73,0.063110,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^2)/(a + a*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^3}{3\,a}-\frac{{\sin\left(c+d\,x\right)}^4}{4\,a}-\frac{{\sin\left(c+d\,x\right)}^5}{5\,a}+\frac{{\sin\left(c+d\,x\right)}^6}{6\,a}}{d}","Not used",1,"(sin(c + d*x)^3/(3*a) - sin(c + d*x)^4/(4*a) - sin(c + d*x)^5/(5*a) + sin(c + d*x)^6/(6*a))/d","B"
535,1,57,55,0.062922,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x))/(a + a*sin(c + d*x)),x)","\frac{\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}+\frac{{\sin\left(c+d\,x\right)}^5}{5\,a}}{d}","Not used",1,"(sin(c + d*x)^2/(2*a) - sin(c + d*x)^3/(3*a) - sin(c + d*x)^4/(4*a) + sin(c + d*x)^5/(5*a))/d","B"
536,1,102,65,9.051334,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{a\,d}-\frac{2\,\sin\left(c+d\,x\right)}{3\,a\,d}+\frac{{\cos\left(c+d\,x\right)}^2}{2\,a\,d}-\frac{{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,a\,d}","Not used",1,"log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(a*d) - log(1/cos(c/2 + (d*x)/2)^2)/(a*d) - (2*sin(c + d*x))/(3*a*d) + cos(c + d*x)^2/(2*a*d) - (cos(c + d*x)^2*sin(c + d*x))/(3*a*d)","B"
537,1,146,62,8.800621,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1}{d\,\left(2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,{\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)\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}","Not used",1,"log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) - (6*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^3 + 5*tan(c/2 + (d*x)/2)^4 + 1)/(d*(2*a*tan(c/2 + (d*x)/2) + 4*a*tan(c/2 + (d*x)/2)^3 + 2*a*tan(c/2 + (d*x)/2)^5)) - tan(c/2 + (d*x)/2)/(2*a*d) - log(tan(c/2 + (d*x)/2))/(a*d)","B"
538,1,150,60,8.926875,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}}{d\,\left(4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"(2*tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2/2 + 10*tan(c/2 + (d*x)/2)^3 - 1/2)/(d*(4*a*tan(c/2 + (d*x)/2)^2 + 4*a*tan(c/2 + (d*x)/2)^4)) - log(tan(c/2 + (d*x)/2))/(a*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) + tan(c/2 + (d*x)/2)/(2*a*d) + log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d)","B"
539,1,138,64,8.947764,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{3}\right)}{8\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - tan(c/2 + (d*x)/2)^3/(24*a*d) + log(tan(c/2 + (d*x)/2))/(a*d) + (3*tan(c/2 + (d*x)/2))/(8*a*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) + (cot(c/2 + (d*x)/2)^3*(tan(c/2 + (d*x)/2) + 3*tan(c/2 + (d*x)/2)^2 - 1/3))/(8*a*d)","B"
540,1,45,51,8.932045,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{-{\sin\left(c+d\,x\right)}^3+\frac{{\sin\left(c+d\,x\right)}^2}{2}+\frac{\sin\left(c+d\,x\right)}{3}-\frac{1}{4}}{a\,d\,{\sin\left(c+d\,x\right)}^4}","Not used",1,"(sin(c + d*x)/3 + sin(c + d*x)^2/2 - sin(c + d*x)^3 - 1/4)/(a*d*sin(c + d*x)^4)","B"
541,1,46,55,8.958321,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^6*(a + a*sin(c + d*x))),x)","\frac{-30\,{\sin\left(c+d\,x\right)}^3+20\,{\sin\left(c+d\,x\right)}^2+15\,\sin\left(c+d\,x\right)-12}{60\,a\,d\,{\sin\left(c+d\,x\right)}^5}","Not used",1,"(15*sin(c + d*x) + 20*sin(c + d*x)^2 - 30*sin(c + d*x)^3 - 12)/(60*a*d*sin(c + d*x)^5)","B"
542,1,46,73,8.942130,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{-20\,{\sin\left(c+d\,x\right)}^3+15\,{\sin\left(c+d\,x\right)}^2+12\,\sin\left(c+d\,x\right)-10}{60\,a\,d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"(12*sin(c + d*x) + 15*sin(c + d*x)^2 - 20*sin(c + d*x)^3 - 10)/(60*a*d*sin(c + d*x)^6)","B"
543,1,46,73,8.962566,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^8*(a + a*sin(c + d*x))),x)","\frac{-105\,{\sin\left(c+d\,x\right)}^3+84\,{\sin\left(c+d\,x\right)}^2+70\,\sin\left(c+d\,x\right)-60}{420\,a\,d\,{\sin\left(c+d\,x\right)}^7}","Not used",1,"(70*sin(c + d*x) + 84*sin(c + d*x)^2 - 105*sin(c + d*x)^3 - 60)/(420*a*d*sin(c + d*x)^7)","B"
544,1,36,55,0.061000,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^3)/(a + a*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^4\,\left(10\,{\sin\left(c+d\,x\right)}^2-24\,\sin\left(c+d\,x\right)+15\right)}{60\,a^2\,d}","Not used",1,"(sin(c + d*x)^4*(10*sin(c + d*x)^2 - 24*sin(c + d*x) + 15))/(60*a^2*d)","B"
545,1,36,55,0.054245,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^2)/(a + a*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(6\,{\sin\left(c+d\,x\right)}^2-15\,\sin\left(c+d\,x\right)+10\right)}{30\,a^2\,d}","Not used",1,"(sin(c + d*x)^3*(6*sin(c + d*x)^2 - 15*sin(c + d*x) + 10))/(30*a^2*d)","B"
546,1,36,55,8.831792,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x))/(a + a*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^2\,\left(3\,{\sin\left(c+d\,x\right)}^2-8\,\sin\left(c+d\,x\right)+6\right)}{12\,a^2\,d}","Not used",1,"(sin(c + d*x)^2*(3*sin(c + d*x)^2 - 8*sin(c + d*x) + 6))/(12*a^2*d)","B"
547,1,120,47,9.108069,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) - (4*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^3)/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 + a^2*tan(c/2 + (d*x)/2)^4 + a^2))","B"
548,1,110,43,8.918559,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}{d\,\left(2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}+\frac{2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}","Not used",1,"(3*tan(c/2 + (d*x)/2)^2 - 1)/(d*(2*a^2*tan(c/2 + (d*x)/2)^3 + 2*a^2*tan(c/2 + (d*x)/2))) - (2*log(tan(c/2 + (d*x)/2)))/(a^2*d) - tan(c/2 + (d*x)/2)/(2*a^2*d) + (2*log(tan(c/2 + (d*x)/2)^2 + 1))/(a^2*d)","B"
549,1,104,47,8.887044,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{8}\right)}{a^2\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) - tan(c/2 + (d*x)/2)^2/(8*a^2*d) + tan(c/2 + (d*x)/2)/(a^2*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) + (cot(c/2 + (d*x)/2)^2*(tan(c/2 + (d*x)/2) - 1/8))/(a^2*d)","B"
550,1,34,31,8.930711,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","-\frac{{\sin\left(c+d\,x\right)}^2-\sin\left(c+d\,x\right)+\frac{1}{3}}{a^2\,d\,{\sin\left(c+d\,x\right)}^3}","Not used",1,"-(sin(c + d*x)^2 - sin(c + d*x) + 1/3)/(a^2*d*sin(c + d*x)^3)","B"
551,1,36,55,8.922827,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^5*(a + a*sin(c + d*x))^2),x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^2}{2}-\frac{2\,\sin\left(c+d\,x\right)}{3}+\frac{1}{4}}{a^2\,d\,{\sin\left(c+d\,x\right)}^4}","Not used",1,"-(sin(c + d*x)^2/2 - (2*sin(c + d*x))/3 + 1/4)/(a^2*d*sin(c + d*x)^4)","B"
552,1,36,55,8.940563,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^6*(a + a*sin(c + d*x))^2),x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^2}{3}-\frac{\sin\left(c+d\,x\right)}{2}+\frac{1}{5}}{a^2\,d\,{\sin\left(c+d\,x\right)}^5}","Not used",1,"-(sin(c + d*x)^2/3 - sin(c + d*x)/2 + 1/5)/(a^2*d*sin(c + d*x)^5)","B"
553,1,36,55,8.951006,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^7*(a + a*sin(c + d*x))^2),x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^2}{4}-\frac{2\,\sin\left(c+d\,x\right)}{5}+\frac{1}{6}}{a^2\,d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"-(sin(c + d*x)^2/4 - (2*sin(c + d*x))/5 + 1/6)/(a^2*d*sin(c + d*x)^6)","B"
554,1,83,102,0.063752,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^3)/(a + a*sin(c + d*x))^3,x)","-\frac{\frac{4\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^3}-\frac{4\,\sin\left(c+d\,x\right)}{a^3}+\frac{2\,{\sin\left(c+d\,x\right)}^2}{a^3}-\frac{4\,{\sin\left(c+d\,x\right)}^3}{3\,a^3}+\frac{3\,{\sin\left(c+d\,x\right)}^4}{4\,a^3}-\frac{{\sin\left(c+d\,x\right)}^5}{5\,a^3}}{d}","Not used",1,"-((4*log(sin(c + d*x) + 1))/a^3 - (4*sin(c + d*x))/a^3 + (2*sin(c + d*x)^2)/a^3 - (4*sin(c + d*x)^3)/(3*a^3) + (3*sin(c + d*x)^4)/(4*a^3) - sin(c + d*x)^5/(5*a^3))/d","B"
555,1,69,82,8.818791,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^2)/(a + a*sin(c + d*x))^3,x)","\frac{\frac{4\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^3}-\frac{4\,\sin\left(c+d\,x\right)}{a^3}+\frac{2\,{\sin\left(c+d\,x\right)}^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,"((4*log(sin(c + d*x) + 1))/a^3 - (4*sin(c + d*x))/a^3 + (2*sin(c + d*x)^2)/a^3 - sin(c + d*x)^3/a^3 + sin(c + d*x)^4/(4*a^3))/d","B"
556,1,57,68,0.054588,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x))/(a + a*sin(c + d*x))^3,x)","-\frac{\frac{4\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^3}-\frac{4\,\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}{3\,a^3}}{d}","Not used",1,"-((4*log(sin(c + d*x) + 1))/a^3 - (4*sin(c + d*x))/a^3 + (3*sin(c + d*x)^2)/(2*a^3) - sin(c + d*x)^3/(3*a^3))/d","B"
557,1,95,45,8.919269,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^3\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) - (8*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) + (2*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 + a^3)) + (3*log(tan(c/2 + (d*x)/2)^2 + 1))/(a^3*d)","B"
558,1,71,47,8.981644,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)+\frac{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^3\,d}","Not used",1,"-(3*log(tan(c/2 + (d*x)/2)) - 8*log(tan(c/2 + (d*x)/2) + 1) + cot(c/2 + (d*x)/2)/2 + tan(c/2 + (d*x)/2)/2 + log(tan(c/2 + (d*x)/2)^2 + 1))/(a^3*d)","B"
559,1,107,65,8.879202,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^3*(a + a*sin(c + d*x))^3),x)","\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}\right)}{4\,a^3\,d}","Not used",1,"(4*log(tan(c/2 + (d*x)/2)))/(a^3*d) - tan(c/2 + (d*x)/2)^2/(8*a^3*d) - (8*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) + (3*tan(c/2 + (d*x)/2))/(2*a^3*d) + (cot(c/2 + (d*x)/2)^2*(6*tan(c/2 + (d*x)/2) - 1/2))/(4*a^3*d)","B"
560,1,139,83,8.989514,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^3\,d}-\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}-\frac{17\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{3}\right)}{8\,a^3\,d}","Not used",1,"(3*tan(c/2 + (d*x)/2)^2)/(8*a^3*d) - tan(c/2 + (d*x)/2)^3/(24*a^3*d) - (4*log(tan(c/2 + (d*x)/2)))/(a^3*d) + (8*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) - (17*tan(c/2 + (d*x)/2))/(8*a^3*d) - (cot(c/2 + (d*x)/2)^3*(17*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2) + 1/3))/(8*a^3*d)","B"
561,1,171,96,8.876883,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^5*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^3\,d}-\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^3\,d}+\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}+\frac{19\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(38\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{4}\right)}{16\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(8*a^3*d) - (9*tan(c/2 + (d*x)/2)^2)/(16*a^3*d) - tan(c/2 + (d*x)/2)^4/(64*a^3*d) + (4*log(tan(c/2 + (d*x)/2)))/(a^3*d) - (8*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) + (19*tan(c/2 + (d*x)/2))/(8*a^3*d) + (cot(c/2 + (d*x)/2)^4*(2*tan(c/2 + (d*x)/2) - 9*tan(c/2 + (d*x)/2)^2 + 38*tan(c/2 + (d*x)/2)^3 - 1/4))/(16*a^3*d)","B"
562,1,203,117,8.960582,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^6*(a + a*sin(c + d*x))^3),x)","\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,a^3\,d}-\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,a^3\,d}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^3\,d}-\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}-\frac{41\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a^3\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(82\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{1}{5}\right)}{32\,a^3\,d}","Not used",1,"(11*tan(c/2 + (d*x)/2)^2)/(16*a^3*d) - (19*tan(c/2 + (d*x)/2)^3)/(96*a^3*d) + (3*tan(c/2 + (d*x)/2)^4)/(64*a^3*d) - tan(c/2 + (d*x)/2)^5/(160*a^3*d) - (4*log(tan(c/2 + (d*x)/2)))/(a^3*d) + (8*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) - (41*tan(c/2 + (d*x)/2))/(16*a^3*d) - (cot(c/2 + (d*x)/2)^5*((19*tan(c/2 + (d*x)/2)^2)/3 - (3*tan(c/2 + (d*x)/2))/2 - 22*tan(c/2 + (d*x)/2)^3 + 82*tan(c/2 + (d*x)/2)^4 + 1/5))/(32*a^3*d)","B"
563,1,233,120,8.885663,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^5*(a + a*sin(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6\,a^4\,d}-\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^4\,d}+\frac{16\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{32\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^4\,d}+\frac{-24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+191\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{218\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{143\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{12}+\frac{13\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6}-\frac{1}{4}}{d\,\left(16\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+16\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{13\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^4\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(6*a^4*d) - (17*tan(c/2 + (d*x)/2)^2)/(16*a^4*d) - tan(c/2 + (d*x)/2)^4/(64*a^4*d) + (16*log(tan(c/2 + (d*x)/2)))/(a^4*d) - (32*log(tan(c/2 + (d*x)/2) + 1))/(a^4*d) + ((13*tan(c/2 + (d*x)/2))/6 - (143*tan(c/2 + (d*x)/2)^2)/12 + (218*tan(c/2 + (d*x)/2)^3)/3 + 191*tan(c/2 + (d*x)/2)^4 - 24*tan(c/2 + (d*x)/2)^5 - 1/4)/(d*(16*a^4*tan(c/2 + (d*x)/2)^4 + 32*a^4*tan(c/2 + (d*x)/2)^5 + 16*a^4*tan(c/2 + (d*x)/2)^6)) + (13*tan(c/2 + (d*x)/2))/(2*a^4*d)","B"
564,1,266,135,8.906492,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^6*(a + a*sin(c + d*x))^4),x)","\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^4\,d}-\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^4\,d}-\frac{20\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{34\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+524\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{569\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{104\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{118\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{1}{5}}{d\,\left(32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+64\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{40\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^4\,d}-\frac{145\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a^4\,d}","Not used",1,"(7*tan(c/2 + (d*x)/2)^2)/(4*a^4*d) - (35*tan(c/2 + (d*x)/2)^3)/(96*a^4*d) + tan(c/2 + (d*x)/2)^4/(16*a^4*d) - tan(c/2 + (d*x)/2)^5/(160*a^4*d) - (20*log(tan(c/2 + (d*x)/2)))/(a^4*d) - ((118*tan(c/2 + (d*x)/2)^2)/15 - (8*tan(c/2 + (d*x)/2))/5 - (104*tan(c/2 + (d*x)/2)^3)/3 + (569*tan(c/2 + (d*x)/2)^4)/3 + 524*tan(c/2 + (d*x)/2)^5 + 34*tan(c/2 + (d*x)/2)^6 + 1/5)/(d*(32*a^4*tan(c/2 + (d*x)/2)^5 + 64*a^4*tan(c/2 + (d*x)/2)^6 + 32*a^4*tan(c/2 + (d*x)/2)^7)) + (40*log(tan(c/2 + (d*x)/2) + 1))/(a^4*d) - (145*tan(c/2 + (d*x)/2))/(16*a^4*d)","B"
565,1,923,181,15.448204,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^n*(a + a*sin(c + d*x))^3,x)","\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\left(27\,n^7+1028\,n^6+17366\,n^5+162200\,n^4+870443\,n^3+2585492\,n^2+3757604\,n+1896720\right)}{128\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}+\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(8\,c+8\,d\,x\right)\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}{128\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a^3\,\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(n^7\,17{}\mathrm{i}+n^6\,669{}\mathrm{i}+n^5\,11975{}\mathrm{i}+n^4\,118935{}\mathrm{i}+n^3\,675728{}\mathrm{i}+n^2\,2140836{}\mathrm{i}+n\,3467760{}\mathrm{i}+2217600{}\mathrm{i}\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(3\,n^7+86\,n^6+1010\,n^5+6260\,n^4+21947\,n^3+43094\,n^2+43280\,n+16800\right)}{32\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(7\,n^7+264\,n^6+3910\,n^5+29520\,n^4+122023\,n^3+273336\,n^2+303180\,n+126000\right)}{32\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(-3\,n^7-86\,n^6-498\,n^5+5260\,n^4+75333\,n^3+333226\,n^2+596208\,n+332640\right)}{32\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}+\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\sin\left(7\,c+7\,d\,x\right)\,\left(n^7\,1{}\mathrm{i}+n^6\,29{}\mathrm{i}+n^5\,343{}\mathrm{i}+n^4\,2135{}\mathrm{i}+n^3\,7504{}\mathrm{i}+n^2\,14756{}\mathrm{i}+n\,14832{}\mathrm{i}+5760{}\mathrm{i}\right)\,3{}\mathrm{i}}{64\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}+\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(-n^7\,1{}\mathrm{i}+n^6\,11{}\mathrm{i}+n^5\,617{}\mathrm{i}+n^4\,6785{}\mathrm{i}+n^3\,33296{}\mathrm{i}+n^2\,81404{}\mathrm{i}+n\,94608{}\mathrm{i}+40320{}\mathrm{i}\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(n^7\,21{}\mathrm{i}+n^6\,745{}\mathrm{i}+n^5\,10339{}\mathrm{i}+n^4\,72475{}\mathrm{i}+n^3\,275824{}\mathrm{i}+n^2\,567700{}\mathrm{i}+n\,583216{}\mathrm{i}+228480{}\mathrm{i}\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}","Not used",1,"(a^3*sin(c + d*x)^n*(3757604*n + 2585492*n^2 + 870443*n^3 + 162200*n^4 + 17366*n^5 + 1028*n^6 + 27*n^7 + 1896720))/(128*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) + (a^3*sin(c + d*x)^n*cos(8*c + 8*d*x)*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040))/(128*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a^3*sin(c + d*x)*sin(c + d*x)^n*(n*3467760i + n^2*2140836i + n^3*675728i + n^4*118935i + n^5*11975i + n^6*669i + n^7*17i + 2217600i)*1i)/(64*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a^3*sin(c + d*x)^n*cos(6*c + 6*d*x)*(43280*n + 43094*n^2 + 21947*n^3 + 6260*n^4 + 1010*n^5 + 86*n^6 + 3*n^7 + 16800))/(32*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a^3*sin(c + d*x)^n*cos(4*c + 4*d*x)*(303180*n + 273336*n^2 + 122023*n^3 + 29520*n^4 + 3910*n^5 + 264*n^6 + 7*n^7 + 126000))/(32*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a^3*sin(c + d*x)^n*cos(2*c + 2*d*x)*(596208*n + 333226*n^2 + 75333*n^3 + 5260*n^4 - 498*n^5 - 86*n^6 - 3*n^7 + 332640))/(32*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) + (a^3*sin(c + d*x)^n*sin(7*c + 7*d*x)*(n*14832i + n^2*14756i + n^3*7504i + n^4*2135i + n^5*343i + n^6*29i + n^7*1i + 5760i)*3i)/(64*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) + (a^3*sin(c + d*x)^n*sin(5*c + 5*d*x)*(n*94608i + n^2*81404i + n^3*33296i + n^4*6785i + n^5*617i + n^6*11i - n^7*1i + 40320i)*1i)/(64*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a^3*sin(c + d*x)^n*sin(3*c + 3*d*x)*(n*583216i + n^2*567700i + n^3*275824i + n^4*72475i + n^5*10339i + n^6*745i + n^7*21i + 228480i)*1i)/(64*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320))","B"
566,1,819,160,14.661479,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^n*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\left(n^6\,1{}\mathrm{i}+n^5\,30{}\mathrm{i}+n^4\,398{}\mathrm{i}+n^3\,2788{}\mathrm{i}+n^2\,10137{}\mathrm{i}+n\,16958{}\mathrm{i}+9240{}\mathrm{i}\right)}{8\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\sin\left(7\,c+7\,d\,x\right)\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)\,1{}\mathrm{i}}{64\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{a^2\,\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(11\,n^6+343\,n^5+4869\,n^4+36773\,n^3+148360\,n^2+296844\,n+226800\right)\,1{}\mathrm{i}}{64\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(n^6\,1{}\mathrm{i}+n^5\,22{}\mathrm{i}+n^4\,190{}\mathrm{i}+n^3\,820{}\mathrm{i}+n^2\,1849{}\mathrm{i}+n\,2038{}\mathrm{i}+840{}\mathrm{i}\right)}{16\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(n^6\,1{}\mathrm{i}+n^5\,30{}\mathrm{i}+n^4\,334{}\mathrm{i}+n^3\,1764{}\mathrm{i}+n^2\,4633{}\mathrm{i}+n\,5694{}\mathrm{i}+2520{}\mathrm{i}\right)}{8\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(-n^6\,1{}\mathrm{i}-n^5\,22{}\mathrm{i}-n^4\,62{}\mathrm{i}+n^3\,1228{}\mathrm{i}+n^2\,9159{}\mathrm{i}+n\,20490{}\mathrm{i}+12600{}\mathrm{i}\right)}{16\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(3\,n^6+55\,n^5+397\,n^4+1445\,n^3+2792\,n^2+2700\,n+1008\right)\,1{}\mathrm{i}}{64\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(15\,n^6+419\,n^5+4417\,n^4+22569\,n^3+58568\,n^2+71932\,n+31920\right)\,1{}\mathrm{i}}{64\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}","Not used",1,"(a^2*sin(c + d*x)^n*(n*16958i + n^2*10137i + n^3*2788i + n^4*398i + n^5*30i + n^6*1i + 9240i))/(8*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) - (a^2*sin(c + d*x)^n*sin(7*c + 7*d*x)*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)*1i)/(64*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) + (a^2*sin(c + d*x)*sin(c + d*x)^n*(296844*n + 148360*n^2 + 36773*n^3 + 4869*n^4 + 343*n^5 + 11*n^6 + 226800)*1i)/(64*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) - (a^2*sin(c + d*x)^n*cos(6*c + 6*d*x)*(n*2038i + n^2*1849i + n^3*820i + n^4*190i + n^5*22i + n^6*1i + 840i))/(16*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) - (a^2*sin(c + d*x)^n*cos(4*c + 4*d*x)*(n*5694i + n^2*4633i + n^3*1764i + n^4*334i + n^5*30i + n^6*1i + 2520i))/(8*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) - (a^2*sin(c + d*x)^n*cos(2*c + 2*d*x)*(n*20490i + n^2*9159i + n^3*1228i - n^4*62i - n^5*22i - n^6*1i + 12600i))/(16*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) + (a^2*sin(c + d*x)^n*sin(5*c + 5*d*x)*(2700*n + 2792*n^2 + 1445*n^3 + 397*n^4 + 55*n^5 + 3*n^6 + 1008)*1i)/(64*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) + (a^2*sin(c + d*x)^n*sin(3*c + 3*d*x)*(71932*n + 58568*n^2 + 22569*n^3 + 4417*n^4 + 419*n^5 + 15*n^6 + 31920)*1i)/(64*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i))","B"
567,1,550,123,13.560963,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^n*(a + a*sin(c + d*x)),x)","\frac{a\,{\sin\left(c+d\,x\right)}^n\,\left(n^5+23\,n^4+237\,n^3+1129\,n^2+2234\,n+1320\right)}{16\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{32\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(n^5+23\,n^4+173\,n^3+553\,n^2+762\,n+360\right)}{16\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(n^5\,1{}\mathrm{i}+n^4\,24{}\mathrm{i}+n^3\,263{}\mathrm{i}+n^2\,1476{}\mathrm{i}+n\,3876{}\mathrm{i}+3600{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(-n^5-15\,n^4+43\,n^3+927\,n^2+2670\,n+1800\right)}{32\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(n^5\,1{}\mathrm{i}+n^4\,16{}\mathrm{i}+n^3\,95{}\mathrm{i}+n^2\,260{}\mathrm{i}+n\,324{}\mathrm{i}+144{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(n^5\,3{}\mathrm{i}+n^4\,64{}\mathrm{i}+n^3\,493{}\mathrm{i}+n^2\,1676{}\mathrm{i}+n\,2444{}\mathrm{i}+1200{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}","Not used",1,"(a*sin(c + d*x)^n*(2234*n + 1129*n^2 + 237*n^3 + 23*n^4 + n^5 + 1320))/(16*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)^n*cos(6*c + 6*d*x)*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(32*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)^n*cos(4*c + 4*d*x)*(762*n + 553*n^2 + 173*n^3 + 23*n^4 + n^5 + 360))/(16*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)*sin(c + d*x)^n*(n*3876i + n^2*1476i + n^3*263i + n^4*24i + n^5*1i + 3600i)*1i)/(8*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)^n*cos(2*c + 2*d*x)*(2670*n + 927*n^2 + 43*n^3 - 15*n^4 - n^5 + 1800))/(32*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)^n*sin(5*c + 5*d*x)*(n*324i + n^2*260i + n^3*95i + n^4*16i + n^5*1i + 144i)*1i)/(16*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)^n*sin(3*c + 3*d*x)*(n*2444i + n^2*1676i + n^3*493i + n^4*64i + n^5*3i + 1200i)*1i)/(16*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))","B"
568,1,228,91,10.205031,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + a*sin(c + d*x)),x)","\frac{{\sin\left(c+d\,x\right)}^n\,\left(144\,\sin\left(c+d\,x\right)-43\,n+24\,\cos\left(2\,c+2\,d\,x\right)+6\,\cos\left(4\,c+4\,d\,x\right)+16\,\sin\left(3\,c+3\,d\,x\right)+124\,n\,\sin\left(c+d\,x\right)+32\,n\,\cos\left(2\,c+2\,d\,x\right)+11\,n\,\cos\left(4\,c+4\,d\,x\right)+28\,n\,\sin\left(3\,c+3\,d\,x\right)+30\,n^2\,\sin\left(c+d\,x\right)+2\,n^3\,\sin\left(c+d\,x\right)-14\,n^2-n^3+8\,n^2\,\cos\left(2\,c+2\,d\,x\right)+6\,n^2\,\cos\left(4\,c+4\,d\,x\right)+n^3\,\cos\left(4\,c+4\,d\,x\right)+14\,n^2\,\sin\left(3\,c+3\,d\,x\right)+2\,n^3\,\sin\left(3\,c+3\,d\,x\right)-30\right)}{8\,a\,d\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}","Not used",1,"(sin(c + d*x)^n*(144*sin(c + d*x) - 43*n + 24*cos(2*c + 2*d*x) + 6*cos(4*c + 4*d*x) + 16*sin(3*c + 3*d*x) + 124*n*sin(c + d*x) + 32*n*cos(2*c + 2*d*x) + 11*n*cos(4*c + 4*d*x) + 28*n*sin(3*c + 3*d*x) + 30*n^2*sin(c + d*x) + 2*n^3*sin(c + d*x) - 14*n^2 - n^3 + 8*n^2*cos(2*c + 2*d*x) + 6*n^2*cos(4*c + 4*d*x) + n^3*cos(4*c + 4*d*x) + 14*n^2*sin(3*c + 3*d*x) + 2*n^3*sin(3*c + 3*d*x) - 30))/(8*a*d*(50*n + 35*n^2 + 10*n^3 + n^4 + 24))","B"
569,1,146,68,9.540237,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + a*sin(c + d*x))^2,x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^n\,\left(24\,{\sin\left(c+d\,x\right)}^2-30\,\sin\left(c+d\,x\right)+2\,\sin\left(3\,c+3\,d\,x\right)\right)}{4}+\frac{n\,{\sin\left(c+d\,x\right)}^n\,\left(32\,{\sin\left(c+d\,x\right)}^2-29\,\sin\left(c+d\,x\right)+3\,\sin\left(3\,c+3\,d\,x\right)\right)}{4}+\frac{n^2\,{\sin\left(c+d\,x\right)}^n\,\left(8\,{\sin\left(c+d\,x\right)}^2-7\,\sin\left(c+d\,x\right)+\sin\left(3\,c+3\,d\,x\right)\right)}{4}}{a^2\,d\,\left(n^3+6\,n^2+11\,n+6\right)}","Not used",1,"-((sin(c + d*x)^n*(2*sin(3*c + 3*d*x) - 30*sin(c + d*x) + 24*sin(c + d*x)^2))/4 + (n*sin(c + d*x)^n*(3*sin(3*c + 3*d*x) - 29*sin(c + d*x) + 32*sin(c + d*x)^2))/4 + (n^2*sin(c + d*x)^n*(sin(3*c + 3*d*x) - 7*sin(c + d*x) + 8*sin(c + d*x)^2))/4)/(a^2*d*(11*n + 6*n^2 + n^3 + 6))","B"
570,0,-1,85,0.000000,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + a*sin(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^5\,{\sin\left(c+d\,x\right)}^n}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + a*sin(c + d*x))^3, x)","F"
571,0,-1,88,0.000000,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\cos\left(c+d\,x\right)}^5\,{\sin\left(c+d\,x\right)}^n}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + a*sin(c + d*x))^4, x)","F"
572,1,447,165,11.871999,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^4*(a + a*sin(c + d*x)),x)","\frac{3\,a\,x}{256}+\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{128}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{4}-\frac{3323\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{640}+\left(\frac{a\,\left(1715175\,c+1715175\,d\,x-9461760\right)}{887040}-\frac{495\,a\,\left(c+d\,x\right)}{256}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+\frac{54\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{5}+\left(\frac{a\,\left(3430350\,c+3430350\,d\,x+23654400\right)}{887040}-\frac{495\,a\,\left(c+d\,x\right)}{128}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-\frac{841\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\left(\frac{a\,\left(4802490\,c+4802490\,d\,x-52039680\right)}{887040}-\frac{693\,a\,\left(c+d\,x\right)}{128}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\left(\frac{a\,\left(4802490\,c+4802490\,d\,x+42577920\right)}{887040}-\frac{693\,a\,\left(c+d\,x\right)}{128}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{841\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\left(\frac{a\,\left(3430350\,c+3430350\,d\,x-30412800\right)}{887040}-\frac{495\,a\,\left(c+d\,x\right)}{128}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{54\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}+\left(\frac{a\,\left(1715175\,c+1715175\,d\,x+6082560\right)}{887040}-\frac{495\,a\,\left(c+d\,x\right)}{256}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{3323\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640}+\left(\frac{a\,\left(571725\,c+571725\,d\,x-1126400\right)}{887040}-\frac{165\,a\,\left(c+d\,x\right)}{256}\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}{4}+\left(\frac{a\,\left(114345\,c+114345\,d\,x-225280\right)}{887040}-\frac{33\,a\,\left(c+d\,x\right)}{256}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}+\frac{a\,\left(10395\,c+10395\,d\,x-20480\right)}{887040}-\frac{3\,a\,\left(c+d\,x\right)}{256}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{11}}","Not used",1,"(3*a*x)/256 + ((a*(10395*c + 10395*d*x - 20480))/887040 - (3*a*tan(c/2 + (d*x)/2))/128 - (3*a*(c + d*x))/256 + tan(c/2 + (d*x)/2)^2*((a*(114345*c + 114345*d*x - 225280))/887040 - (33*a*(c + d*x))/256) + tan(c/2 + (d*x)/2)^4*((a*(571725*c + 571725*d*x - 1126400))/887040 - (165*a*(c + d*x))/256) + tan(c/2 + (d*x)/2)^6*((a*(1715175*c + 1715175*d*x + 6082560))/887040 - (495*a*(c + d*x))/256) + tan(c/2 + (d*x)/2)^16*((a*(1715175*c + 1715175*d*x - 9461760))/887040 - (495*a*(c + d*x))/256) + tan(c/2 + (d*x)/2)^14*((a*(3430350*c + 3430350*d*x + 23654400))/887040 - (495*a*(c + d*x))/128) + tan(c/2 + (d*x)/2)^8*((a*(3430350*c + 3430350*d*x - 30412800))/887040 - (495*a*(c + d*x))/128) + tan(c/2 + (d*x)/2)^10*((a*(4802490*c + 4802490*d*x + 42577920))/887040 - (693*a*(c + d*x))/128) + tan(c/2 + (d*x)/2)^12*((a*(4802490*c + 4802490*d*x - 52039680))/887040 - (693*a*(c + d*x))/128) - (a*tan(c/2 + (d*x)/2)^3)/4 + (3323*a*tan(c/2 + (d*x)/2)^5)/640 - (54*a*tan(c/2 + (d*x)/2)^7)/5 + (841*a*tan(c/2 + (d*x)/2)^9)/64 - (841*a*tan(c/2 + (d*x)/2)^13)/64 + (54*a*tan(c/2 + (d*x)/2)^15)/5 - (3323*a*tan(c/2 + (d*x)/2)^17)/640 + (a*tan(c/2 + (d*x)/2)^19)/4 + (3*a*tan(c/2 + (d*x)/2)^21)/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^11)","B"
573,1,414,149,12.185550,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{3\,a\,x}{256}+\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}+\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}+\left(\frac{a\,\left(42525\,c+42525\,d\,x-322560\right)}{80640}-\frac{135\,a\,\left(c+d\,x\right)}{256}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-\frac{867\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{160}+\left(\frac{a\,\left(113400\,c+113400\,d\,x+215040\right)}{80640}-\frac{45\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\frac{519\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\left(\frac{a\,\left(198450\,c+198450\,d\,x-1075200\right)}{80640}-\frac{315\,a\,\left(c+d\,x\right)}{128}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{1879\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\left(\frac{a\,\left(238140\,c+238140\,d\,x-645120\right)}{80640}-\frac{189\,a\,\left(c+d\,x\right)}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{1879\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}-\frac{519\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+\left(\frac{a\,\left(113400\,c+113400\,d\,x-829440\right)}{80640}-\frac{45\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{867\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}+\left(\frac{a\,\left(42525\,c+42525\,d\,x+92160\right)}{80640}-\frac{135\,a\,\left(c+d\,x\right)}{256}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128}+\left(\frac{a\,\left(9450\,c+9450\,d\,x-51200\right)}{80640}-\frac{15\,a\,\left(c+d\,x\right)}{128}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}+\frac{a\,\left(945\,c+945\,d\,x-5120\right)}{80640}-\frac{3\,a\,\left(c+d\,x\right)}{256}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{10}}","Not used",1,"(3*a*x)/256 + ((a*(945*c + 945*d*x - 5120))/80640 - (3*a*tan(c/2 + (d*x)/2))/128 - (3*a*(c + d*x))/256 + tan(c/2 + (d*x)/2)^2*((a*(9450*c + 9450*d*x - 51200))/80640 - (15*a*(c + d*x))/128) + tan(c/2 + (d*x)/2)^4*((a*(42525*c + 42525*d*x + 92160))/80640 - (135*a*(c + d*x))/256) + tan(c/2 + (d*x)/2)^16*((a*(42525*c + 42525*d*x - 322560))/80640 - (135*a*(c + d*x))/256) + tan(c/2 + (d*x)/2)^14*((a*(113400*c + 113400*d*x + 215040))/80640 - (45*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^6*((a*(113400*c + 113400*d*x - 829440))/80640 - (45*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^10*((a*(238140*c + 238140*d*x - 645120))/80640 - (189*a*(c + d*x))/64) + tan(c/2 + (d*x)/2)^12*((a*(198450*c + 198450*d*x - 1075200))/80640 - (315*a*(c + d*x))/128) - (29*a*tan(c/2 + (d*x)/2)^3)/128 + (867*a*tan(c/2 + (d*x)/2)^5)/160 - (519*a*tan(c/2 + (d*x)/2)^7)/32 + (1879*a*tan(c/2 + (d*x)/2)^9)/64 - (1879*a*tan(c/2 + (d*x)/2)^11)/64 + (519*a*tan(c/2 + (d*x)/2)^13)/32 - (867*a*tan(c/2 + (d*x)/2)^15)/160 + (29*a*tan(c/2 + (d*x)/2)^17)/128 + (3*a*tan(c/2 + (d*x)/2)^19)/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
574,1,386,125,12.357237,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^2*(a + a*sin(c + d*x)),x)","\frac{5\,a\,x}{128}+\frac{\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}-\frac{191\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{96}+\left(\frac{a\,\left(11340\,c+11340\,d\,x-32256\right)}{8064}-\frac{45\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\frac{83\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\left(\frac{a\,\left(26460\,c+26460\,d\,x+53760\right)}{8064}-\frac{105\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{145\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}+\left(\frac{a\,\left(39690\,c+39690\,d\,x-161280\right)}{8064}-\frac{315\,a\,\left(c+d\,x\right)}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(\frac{a\,\left(39690\,c+39690\,d\,x+96768\right)}{8064}-\frac{315\,a\,\left(c+d\,x\right)}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{145\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+\left(\frac{a\,\left(26460\,c+26460\,d\,x-96768\right)}{8064}-\frac{105\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{83\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}+\left(\frac{a\,\left(11340\,c+11340\,d\,x+13824\right)}{8064}-\frac{45\,a\,\left(c+d\,x\right)}{32}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{191\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\left(\frac{a\,\left(2835\,c+2835\,d\,x-4608\right)}{8064}-\frac{45\,a\,\left(c+d\,x\right)}{128}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{a\,\left(315\,c+315\,d\,x-512\right)}{8064}-\frac{5\,a\,\left(c+d\,x\right)}{128}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(5*a*x)/128 + ((a*(315*c + 315*d*x - 512))/8064 - (5*a*tan(c/2 + (d*x)/2))/64 - (5*a*(c + d*x))/128 + tan(c/2 + (d*x)/2)^2*((a*(2835*c + 2835*d*x - 4608))/8064 - (45*a*(c + d*x))/128) + tan(c/2 + (d*x)/2)^4*((a*(11340*c + 11340*d*x + 13824))/8064 - (45*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^14*((a*(11340*c + 11340*d*x - 32256))/8064 - (45*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^12*((a*(26460*c + 26460*d*x + 53760))/8064 - (105*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^6*((a*(26460*c + 26460*d*x - 96768))/8064 - (105*a*(c + d*x))/32) + tan(c/2 + (d*x)/2)^8*((a*(39690*c + 39690*d*x + 96768))/8064 - (315*a*(c + d*x))/64) + tan(c/2 + (d*x)/2)^10*((a*(39690*c + 39690*d*x - 161280))/8064 - (315*a*(c + d*x))/64) + (191*a*tan(c/2 + (d*x)/2)^3)/96 - (83*a*tan(c/2 + (d*x)/2)^5)/32 + (145*a*tan(c/2 + (d*x)/2)^7)/32 - (145*a*tan(c/2 + (d*x)/2)^11)/32 + (83*a*tan(c/2 + (d*x)/2)^13)/32 - (191*a*tan(c/2 + (d*x)/2)^15)/96 + (5*a*tan(c/2 + (d*x)/2)^17)/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
575,1,96,109,9.391381,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)*(a + a*sin(c + d*x)),x)","-\frac{a\,\left(210\,\cos\left(c+d\,x\right)+126\,\cos\left(3\,c+3\,d\,x\right)+42\,\cos\left(5\,c+5\,d\,x\right)+6\,\cos\left(7\,c+7\,d\,x\right)-42\,\sin\left(2\,c+2\,d\,x\right)+21\,\sin\left(4\,c+4\,d\,x\right)+14\,\sin\left(6\,c+6\,d\,x\right)+\frac{21\,\sin\left(8\,c+8\,d\,x\right)}{8}-105\,d\,x\right)}{2688\,d}","Not used",1,"-(a*(210*cos(c + d*x) + 126*cos(3*c + 3*d*x) + 42*cos(5*c + 5*d*x) + 6*cos(7*c + 7*d*x) - 42*sin(2*c + 2*d*x) + 21*sin(4*c + 4*d*x) + 14*sin(6*c + 6*d*x) + (21*sin(8*c + 8*d*x))/8 - 105*d*x))/(2688*d)","B"
576,1,327,127,10.706505,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x),x)","\frac{-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+18\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{92\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{62\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{46\,a}{15}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{5\,a\,\mathrm{atan}\left(\frac{25\,a^2}{64\,\left(\frac{5\,a^2}{4}-\frac{25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}+\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{5\,a^2}{4}-\frac{25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}\right)}{8\,d}","Not used",1,"((46*a)/15 + (11*a*tan(c/2 + (d*x)/2))/8 + (62*a*tan(c/2 + (d*x)/2)^2)/5 - (5*a*tan(c/2 + (d*x)/2)^3)/24 + 28*a*tan(c/2 + (d*x)/2)^4 + (15*a*tan(c/2 + (d*x)/2)^5)/4 + (92*a*tan(c/2 + (d*x)/2)^6)/3 - (15*a*tan(c/2 + (d*x)/2)^7)/4 + 18*a*tan(c/2 + (d*x)/2)^8 + (5*a*tan(c/2 + (d*x)/2)^9)/24 + 6*a*tan(c/2 + (d*x)/2)^10 - (11*a*tan(c/2 + (d*x)/2)^11)/8)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a*log(tan(c/2 + (d*x)/2)))/d + (5*a*atan((25*a^2)/(64*((5*a^2)/4 - (25*a^2*tan(c/2 + (d*x)/2))/64)) + (5*a^2*tan(c/2 + (d*x)/2))/(4*((5*a^2)/4 - (25*a^2*tan(c/2 + (d*x)/2))/64))))/(8*d)","B"
577,1,313,121,8.922763,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{2}+12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,a\,{\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+\frac{112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{19\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{92\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}-a}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{15\,a\,\mathrm{atan}\left(\frac{225\,a^2}{16\,\left(\frac{15\,a^2}{2}+\frac{225\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}-\frac{15\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{15\,a^2}{2}+\frac{225\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}","Not used",1,"((92*a*tan(c/2 + (d*x)/2))/15 - a - (19*a*tan(c/2 + (d*x)/2)^2)/2 + (56*a*tan(c/2 + (d*x)/2)^3)/3 - 15*a*tan(c/2 + (d*x)/2)^4 + (112*a*tan(c/2 + (d*x)/2)^5)/3 - 10*a*tan(c/2 + (d*x)/2)^6 + 24*a*tan(c/2 + (d*x)/2)^7 + 12*a*tan(c/2 + (d*x)/2)^9 + (7*a*tan(c/2 + (d*x)/2)^10)/2)/(d*(2*tan(c/2 + (d*x)/2) + 10*tan(c/2 + (d*x)/2)^3 + 20*tan(c/2 + (d*x)/2)^5 + 20*tan(c/2 + (d*x)/2)^7 + 10*tan(c/2 + (d*x)/2)^9 + 2*tan(c/2 + (d*x)/2)^11)) + (a*tan(c/2 + (d*x)/2))/(2*d) + (a*log(tan(c/2 + (d*x)/2)))/d + (15*a*atan((225*a^2)/(16*((15*a^2)/2 + (225*a^2*tan(c/2 + (d*x)/2))/16)) - (15*a^2*tan(c/2 + (d*x)/2))/(2*((15*a^2)/2 + (225*a^2*tan(c/2 + (d*x)/2))/16))))/(4*d)","B"
578,1,321,134,8.857968,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{5\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{49\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+58\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{161\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{62\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{15\,a\,\mathrm{atan}\left(\frac{225\,a^2}{16\,\left(\frac{75\,a^2}{4}-\frac{225\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{75\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{75\,a^2}{4}-\frac{225\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) + (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (5*a*log(tan(c/2 + (d*x)/2)))/(2*d) - (a/2 + 2*a*tan(c/2 + (d*x)/2) + (62*a*tan(c/2 + (d*x)/2)^2)/3 + 17*a*tan(c/2 + (d*x)/2)^3 + (161*a*tan(c/2 + (d*x)/2)^4)/3 + 13*a*tan(c/2 + (d*x)/2)^5 + 58*a*tan(c/2 + (d*x)/2)^6 + 7*a*tan(c/2 + (d*x)/2)^7 + (49*a*tan(c/2 + (d*x)/2)^8)/2 - 7*a*tan(c/2 + (d*x)/2)^9)/(d*(4*tan(c/2 + (d*x)/2)^2 + 16*tan(c/2 + (d*x)/2)^4 + 24*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8 + 4*tan(c/2 + (d*x)/2)^10)) - (15*a*atan((225*a^2)/(16*((75*a^2)/4 - (225*a^2*tan(c/2 + (d*x)/2))/16)) + (75*a^2*tan(c/2 + (d*x)/2))/(4*((75*a^2)/4 - (225*a^2*tan(c/2 + (d*x)/2))/16))))/(4*d)","B"
579,1,310,130,8.969522,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^4,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+49\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{80\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+67\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-34\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{121\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{9\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{5\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{5\,a\,\mathrm{atan}\left(\frac{25\,a^2}{25\,a^2+25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{25\,a^2+25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a/3 + a*tan(c/2 + (d*x)/2) - 8*a*tan(c/2 + (d*x)/2)^2 + (121*a*tan(c/2 + (d*x)/2)^3)/3 - 34*a*tan(c/2 + (d*x)/2)^4 + 67*a*tan(c/2 + (d*x)/2)^5 - (80*a*tan(c/2 + (d*x)/2)^6)/3 + 49*a*tan(c/2 + (d*x)/2)^7 - a*tan(c/2 + (d*x)/2)^8)/(d*(8*tan(c/2 + (d*x)/2)^3 + 24*tan(c/2 + (d*x)/2)^5 + 24*tan(c/2 + (d*x)/2)^7 + 8*tan(c/2 + (d*x)/2)^9)) - (9*a*tan(c/2 + (d*x)/2))/(8*d) + (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (5*a*log(tan(c/2 + (d*x)/2)))/(2*d) - (5*a*atan((25*a^2)/(25*a^2 + 25*a^2*tan(c/2 + (d*x)/2)) - (25*a^2*tan(c/2 + (d*x)/2))/(25*a^2 + 25*a^2*tan(c/2 + (d*x)/2))))/d","B"
580,1,300,134,8.817095,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^5,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{9\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{15\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+36\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{154\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{159\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}+\frac{50\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{a}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{5\,a\,\mathrm{atan}\left(\frac{25\,a^2}{\frac{75\,a^2}{4}-25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{75\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{75\,a^2}{4}-25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*tan(c/2 + (d*x)/2)^2)/(4*d) - (9*a*tan(c/2 + (d*x)/2))/(8*d) + (a*tan(c/2 + (d*x)/2)^4)/(64*d) + (15*a*log(tan(c/2 + (d*x)/2)))/(8*d) + ((7*a*tan(c/2 + (d*x)/2)^2)/2 - (2*a*tan(c/2 + (d*x)/2))/3 - a/4 + (50*a*tan(c/2 + (d*x)/2)^3)/3 + (159*a*tan(c/2 + (d*x)/2)^4)/4 + (154*a*tan(c/2 + (d*x)/2)^5)/3 + 36*a*tan(c/2 + (d*x)/2)^6 + 2*a*tan(c/2 + (d*x)/2)^7)/(d*(16*tan(c/2 + (d*x)/2)^4 + 32*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8)) + (5*a*atan((25*a^2)/((75*a^2)/4 - 25*a^2*tan(c/2 + (d*x)/2)) + (75*a^2*tan(c/2 + (d*x)/2))/(4*((75*a^2)/4 - 25*a^2*tan(c/2 + (d*x)/2)))))/d","B"
581,1,291,122,8.866942,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^6,x)","\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{22\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-72\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{59\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{32\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{15\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}+\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{\frac{15\,a^2}{2}+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{15\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{15\,a^2}{2}+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}","Not used",1,"(11*a*tan(c/2 + (d*x)/2))/(16*d) - (a/5 + (a*tan(c/2 + (d*x)/2))/2 - (32*a*tan(c/2 + (d*x)/2)^2)/15 - (15*a*tan(c/2 + (d*x)/2)^3)/2 + (59*a*tan(c/2 + (d*x)/2)^4)/3 - 72*a*tan(c/2 + (d*x)/2)^5 + 22*a*tan(c/2 + (d*x)/2)^6)/(d*(32*tan(c/2 + (d*x)/2)^5 + 32*tan(c/2 + (d*x)/2)^7)) - (a*tan(c/2 + (d*x)/2)^2)/(4*d) - (7*a*tan(c/2 + (d*x)/2)^3)/(96*d) + (a*tan(c/2 + (d*x)/2)^4)/(64*d) + (a*tan(c/2 + (d*x)/2)^5)/(160*d) + (15*a*log(tan(c/2 + (d*x)/2)))/(8*d) + (2*a*atan((4*a^2)/((15*a^2)/2 + 4*a^2*tan(c/2 + (d*x)/2)) - (15*a^2*tan(c/2 + (d*x)/2))/(2*((15*a^2)/2 + 4*a^2*tan(c/2 + (d*x)/2)))))/d","B"
582,1,285,128,9.460119,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^7,x)","\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{5\,a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{16\,d}-\frac{11\,a\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{16\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{15\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{7\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{3\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}","Not used",1,"(11*a*tan(c/2 + (d*x)/2))/(16*d) - (5*a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(16*d) - (11*a*cot(c/2 + (d*x)/2))/(16*d) - (2*a*atan((16*cos(c/2 + (d*x)/2) + 5*sin(c/2 + (d*x)/2))/(5*cos(c/2 + (d*x)/2) - 16*sin(c/2 + (d*x)/2))))/d - (15*a*cot(c/2 + (d*x)/2)^2)/(128*d) + (7*a*cot(c/2 + (d*x)/2)^3)/(96*d) + (3*a*cot(c/2 + (d*x)/2)^4)/(128*d) - (a*cot(c/2 + (d*x)/2)^5)/(160*d) - (a*cot(c/2 + (d*x)/2)^6)/(384*d) + (15*a*tan(c/2 + (d*x)/2)^2)/(128*d) - (7*a*tan(c/2 + (d*x)/2)^3)/(96*d) - (3*a*tan(c/2 + (d*x)/2)^4)/(128*d) + (a*tan(c/2 + (d*x)/2)^5)/(160*d) + (a*tan(c/2 + (d*x)/2)^6)/(384*d)","B"
583,1,385,96,9.941692,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^8,x)","-\frac{a\,\left(3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+7\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}{2688\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(a*(3*cos(c/2 + (d*x)/2)^14 - 3*sin(c/2 + (d*x)/2)^14 - 7*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 + 7*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) + 21*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 + 63*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 - 63*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 - 315*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 + 105*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 - 105*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 315*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 + 63*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 - 63*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 - 21*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7))/(2688*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)","B"
584,1,285,122,9.154186,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^9,x)","\frac{5\,a\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{3\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{5\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,d}","Not used",1,"(5*a*cot(c/2 + (d*x)/2))/(128*d) - (5*a*tan(c/2 + (d*x)/2))/(128*d) - (a*cot(c/2 + (d*x)/2)^2)/(128*d) - (3*a*cot(c/2 + (d*x)/2)^3)/(128*d) - (a*cot(c/2 + (d*x)/2)^4)/(256*d) + (a*cot(c/2 + (d*x)/2)^5)/(128*d) + (a*cot(c/2 + (d*x)/2)^6)/(384*d) - (a*cot(c/2 + (d*x)/2)^7)/(896*d) - (a*cot(c/2 + (d*x)/2)^8)/(2048*d) + (a*tan(c/2 + (d*x)/2)^2)/(128*d) + (3*a*tan(c/2 + (d*x)/2)^3)/(128*d) + (a*tan(c/2 + (d*x)/2)^4)/(256*d) - (a*tan(c/2 + (d*x)/2)^5)/(128*d) - (a*tan(c/2 + (d*x)/2)^6)/(384*d) + (a*tan(c/2 + (d*x)/2)^7)/(896*d) + (a*tan(c/2 + (d*x)/2)^8)/(2048*d) - (5*a*log(tan(c/2 + (d*x)/2)))/(128*d)","B"
585,1,285,138,9.186499,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^10,x)","\frac{3\,a\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}-\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{3\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}-\frac{5\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,d}","Not used",1,"(3*a*cot(c/2 + (d*x)/2))/(256*d) - (3*a*tan(c/2 + (d*x)/2))/(256*d) - (a*cot(c/2 + (d*x)/2)^2)/(128*d) - (a*cot(c/2 + (d*x)/2)^3)/(192*d) - (a*cot(c/2 + (d*x)/2)^4)/(256*d) + (a*cot(c/2 + (d*x)/2)^6)/(384*d) + (3*a*cot(c/2 + (d*x)/2)^7)/(3584*d) - (a*cot(c/2 + (d*x)/2)^8)/(2048*d) - (a*cot(c/2 + (d*x)/2)^9)/(4608*d) + (a*tan(c/2 + (d*x)/2)^2)/(128*d) + (a*tan(c/2 + (d*x)/2)^3)/(192*d) + (a*tan(c/2 + (d*x)/2)^4)/(256*d) - (a*tan(c/2 + (d*x)/2)^6)/(384*d) - (3*a*tan(c/2 + (d*x)/2)^7)/(3584*d) + (a*tan(c/2 + (d*x)/2)^8)/(2048*d) + (a*tan(c/2 + (d*x)/2)^9)/(4608*d) - (5*a*log(tan(c/2 + (d*x)/2)))/(128*d)","B"
586,1,319,160,9.400312,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^11,x)","\frac{3\,a\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}-\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}+\frac{3\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{256\,d}","Not used",1,"(3*a*cot(c/2 + (d*x)/2))/(256*d) - (3*a*tan(c/2 + (d*x)/2))/(256*d) - (a*cot(c/2 + (d*x)/2)^2)/(1024*d) - (a*cot(c/2 + (d*x)/2)^3)/(192*d) - (a*cot(c/2 + (d*x)/2)^4)/(512*d) + (a*cot(c/2 + (d*x)/2)^6)/(2048*d) + (3*a*cot(c/2 + (d*x)/2)^7)/(3584*d) + (a*cot(c/2 + (d*x)/2)^8)/(4096*d) - (a*cot(c/2 + (d*x)/2)^9)/(4608*d) - (a*cot(c/2 + (d*x)/2)^10)/(10240*d) + (a*tan(c/2 + (d*x)/2)^2)/(1024*d) + (a*tan(c/2 + (d*x)/2)^3)/(192*d) + (a*tan(c/2 + (d*x)/2)^4)/(512*d) - (a*tan(c/2 + (d*x)/2)^6)/(2048*d) - (3*a*tan(c/2 + (d*x)/2)^7)/(3584*d) - (a*tan(c/2 + (d*x)/2)^8)/(4096*d) + (a*tan(c/2 + (d*x)/2)^9)/(4608*d) + (a*tan(c/2 + (d*x)/2)^10)/(10240*d) - (3*a*log(tan(c/2 + (d*x)/2)))/(256*d)","B"
587,1,387,176,9.979668,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x)))/sin(c + d*x)^12,x)","\frac{5\,a\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1024\,d}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1024\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}-\frac{5\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3072\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2048\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}+\frac{5\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14336\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{18432\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{22528\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3072\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2048\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14336\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{18432\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{22528\,d}-\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{256\,d}","Not used",1,"(5*a*cot(c/2 + (d*x)/2))/(1024*d) - (5*a*tan(c/2 + (d*x)/2))/(1024*d) - (a*cot(c/2 + (d*x)/2)^2)/(1024*d) - (5*a*cot(c/2 + (d*x)/2)^3)/(3072*d) - (a*cot(c/2 + (d*x)/2)^4)/(512*d) - (a*cot(c/2 + (d*x)/2)^5)/(2048*d) + (a*cot(c/2 + (d*x)/2)^6)/(2048*d) + (5*a*cot(c/2 + (d*x)/2)^7)/(14336*d) + (a*cot(c/2 + (d*x)/2)^8)/(4096*d) + (a*cot(c/2 + (d*x)/2)^9)/(18432*d) - (a*cot(c/2 + (d*x)/2)^10)/(10240*d) - (a*cot(c/2 + (d*x)/2)^11)/(22528*d) + (a*tan(c/2 + (d*x)/2)^2)/(1024*d) + (5*a*tan(c/2 + (d*x)/2)^3)/(3072*d) + (a*tan(c/2 + (d*x)/2)^4)/(512*d) + (a*tan(c/2 + (d*x)/2)^5)/(2048*d) - (a*tan(c/2 + (d*x)/2)^6)/(2048*d) - (5*a*tan(c/2 + (d*x)/2)^7)/(14336*d) - (a*tan(c/2 + (d*x)/2)^8)/(4096*d) - (a*tan(c/2 + (d*x)/2)^9)/(18432*d) + (a*tan(c/2 + (d*x)/2)^10)/(10240*d) + (a*tan(c/2 + (d*x)/2)^11)/(22528*d) - (3*a*log(tan(c/2 + (d*x)/2)))/(256*d)","B"
588,1,518,209,11.118007,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^4*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,\left(\frac{17\,c}{1024}-\frac{17\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512}-\frac{128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{231}-\frac{595\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{1536}-\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{21}+\frac{11097\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2560}+\frac{704\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{63}+\frac{27449\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2560}-\frac{384\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{7}-\frac{202307\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3840}+\frac{192\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{7}+\frac{28659\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{256}-\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}-\frac{28659\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{256}-64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\frac{202307\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{3840}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-\frac{27449\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{2560}-\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{3}-\frac{11097\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{2560}+\frac{595\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{1536}+\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{23}}{512}+\frac{17\,d\,x}{1024}+\frac{51\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(c+d\,x\right)}{256}+\frac{561\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(c+d\,x\right)}{512}+\frac{935\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(c+d\,x\right)}{256}+\frac{8415\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(c+d\,x\right)}{1024}+\frac{1683\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(c+d\,x\right)}{128}+\frac{3927\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(c+d\,x\right)}{256}+\frac{1683\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(c+d\,x\right)}{128}+\frac{8415\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(c+d\,x\right)}{1024}+\frac{935\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(c+d\,x\right)}{256}+\frac{561\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}\,\left(c+d\,x\right)}{512}+\frac{51\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}\,\left(c+d\,x\right)}{256}+\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{24}\,\left(c+d\,x\right)}{1024}-\frac{32}{693}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{12}}","Not used",1,"(a^2*((17*c)/1024 - (17*tan(c/2 + (d*x)/2))/512 - (128*tan(c/2 + (d*x)/2)^2)/231 - (595*tan(c/2 + (d*x)/2)^3)/1536 - (64*tan(c/2 + (d*x)/2)^4)/21 + (11097*tan(c/2 + (d*x)/2)^5)/2560 + (704*tan(c/2 + (d*x)/2)^6)/63 + (27449*tan(c/2 + (d*x)/2)^7)/2560 - (384*tan(c/2 + (d*x)/2)^8)/7 - (202307*tan(c/2 + (d*x)/2)^9)/3840 + (192*tan(c/2 + (d*x)/2)^10)/7 + (28659*tan(c/2 + (d*x)/2)^11)/256 - (64*tan(c/2 + (d*x)/2)^12)/3 - (28659*tan(c/2 + (d*x)/2)^13)/256 - 64*tan(c/2 + (d*x)/2)^14 + (202307*tan(c/2 + (d*x)/2)^15)/3840 + 32*tan(c/2 + (d*x)/2)^16 - (27449*tan(c/2 + (d*x)/2)^17)/2560 - (64*tan(c/2 + (d*x)/2)^18)/3 - (11097*tan(c/2 + (d*x)/2)^19)/2560 + (595*tan(c/2 + (d*x)/2)^21)/1536 + (17*tan(c/2 + (d*x)/2)^23)/512 + (17*d*x)/1024 + (51*tan(c/2 + (d*x)/2)^2*(c + d*x))/256 + (561*tan(c/2 + (d*x)/2)^4*(c + d*x))/512 + (935*tan(c/2 + (d*x)/2)^6*(c + d*x))/256 + (8415*tan(c/2 + (d*x)/2)^8*(c + d*x))/1024 + (1683*tan(c/2 + (d*x)/2)^10*(c + d*x))/128 + (3927*tan(c/2 + (d*x)/2)^12*(c + d*x))/256 + (1683*tan(c/2 + (d*x)/2)^14*(c + d*x))/128 + (8415*tan(c/2 + (d*x)/2)^16*(c + d*x))/1024 + (935*tan(c/2 + (d*x)/2)^18*(c + d*x))/256 + (561*tan(c/2 + (d*x)/2)^20*(c + d*x))/512 + (51*tan(c/2 + (d*x)/2)^22*(c + d*x))/256 + (17*tan(c/2 + (d*x)/2)^24*(c + d*x))/1024 - 32/693))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^12)","B"
589,1,543,183,12.054528,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^3*(a + a*sin(c + d*x))^2,x)","\frac{3\,a^2\,x}{128}-\frac{\frac{3\,a^2\,\left(c+d\,x\right)}{128}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{3323\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320}+\frac{108\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}-\frac{841\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{32}+\frac{841\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}-\frac{108\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{5}+\frac{3323\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{320}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{2}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{64}-a^2\,\left(\frac{3\,c}{128}+\frac{3\,d\,x}{128}-\frac{20}{231}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{33\,a^2\,\left(c+d\,x\right)}{128}-a^2\,\left(\frac{33\,c}{128}+\frac{33\,d\,x}{128}-\frac{20}{21}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(\frac{165\,a^2\,\left(c+d\,x\right)}{128}-a^2\,\left(\frac{165\,c}{128}+\frac{165\,d\,x}{128}-4\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{165\,a^2\,\left(c+d\,x\right)}{128}-a^2\,\left(\frac{165\,c}{128}+\frac{165\,d\,x}{128}-\frac{16}{21}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{495\,a^2\,\left(c+d\,x\right)}{64}-a^2\,\left(\frac{495\,c}{64}+\frac{495\,d\,x}{64}+16\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{495\,a^2\,\left(c+d\,x\right)}{128}-a^2\,\left(\frac{495\,c}{128}+\frac{495\,d\,x}{128}-12\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{495\,a^2\,\left(c+d\,x\right)}{128}-a^2\,\left(\frac{495\,c}{128}+\frac{495\,d\,x}{128}-\frac{16}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{495\,a^2\,\left(c+d\,x\right)}{64}-a^2\,\left(\frac{495\,c}{64}+\frac{495\,d\,x}{64}-\frac{312}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{693\,a^2\,\left(c+d\,x\right)}{64}-a^2\,\left(\frac{693\,c}{64}+\frac{693\,d\,x}{64}+40\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{693\,a^2\,\left(c+d\,x\right)}{64}-a^2\,\left(\frac{693\,c}{64}+\frac{693\,d\,x}{64}-80\right)\right)+\frac{3\,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)}^{11}}","Not used",1,"(3*a^2*x)/128 - ((3*a^2*(c + d*x))/128 + (a^2*tan(c/2 + (d*x)/2)^3)/2 - (3323*a^2*tan(c/2 + (d*x)/2)^5)/320 + (108*a^2*tan(c/2 + (d*x)/2)^7)/5 - (841*a^2*tan(c/2 + (d*x)/2)^9)/32 + (841*a^2*tan(c/2 + (d*x)/2)^13)/32 - (108*a^2*tan(c/2 + (d*x)/2)^15)/5 + (3323*a^2*tan(c/2 + (d*x)/2)^17)/320 - (a^2*tan(c/2 + (d*x)/2)^19)/2 - (3*a^2*tan(c/2 + (d*x)/2)^21)/64 - a^2*((3*c)/128 + (3*d*x)/128 - 20/231) + tan(c/2 + (d*x)/2)^2*((33*a^2*(c + d*x))/128 - a^2*((33*c)/128 + (33*d*x)/128 - 20/21)) + tan(c/2 + (d*x)/2)^18*((165*a^2*(c + d*x))/128 - a^2*((165*c)/128 + (165*d*x)/128 - 4)) + tan(c/2 + (d*x)/2)^4*((165*a^2*(c + d*x))/128 - a^2*((165*c)/128 + (165*d*x)/128 - 16/21)) + tan(c/2 + (d*x)/2)^14*((495*a^2*(c + d*x))/64 - a^2*((495*c)/64 + (495*d*x)/64 + 16)) + tan(c/2 + (d*x)/2)^16*((495*a^2*(c + d*x))/128 - a^2*((495*c)/128 + (495*d*x)/128 - 12)) + tan(c/2 + (d*x)/2)^6*((495*a^2*(c + d*x))/128 - a^2*((495*c)/128 + (495*d*x)/128 - 16/7)) + tan(c/2 + (d*x)/2)^8*((495*a^2*(c + d*x))/64 - a^2*((495*c)/64 + (495*d*x)/64 - 312/7)) + tan(c/2 + (d*x)/2)^10*((693*a^2*(c + d*x))/64 - a^2*((693*c)/64 + (693*d*x)/64 + 40)) + tan(c/2 + (d*x)/2)^12*((693*a^2*(c + d*x))/64 - a^2*((693*c)/64 + (693*d*x)/64 - 80)) + (3*a^2*tan(c/2 + (d*x)/2))/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^11)","B"
590,1,469,165,12.124688,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^2*(a + a*sin(c + d*x))^2,x)","\frac{13\,a^2\,x}{256}-\frac{\frac{13\,a^2\,\left(c+d\,x\right)}{256}-\frac{647\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384}-\frac{2311\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{480}+\frac{457\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}-\frac{2169\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{2169\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}-\frac{457\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{2311\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{480}+\frac{647\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{384}-\frac{13\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}-\frac{a^2\,\left(4095\,c+4095\,d\,x-10240\right)}{80640}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{65\,a^2\,\left(c+d\,x\right)}{128}-\frac{a^2\,\left(40950\,c+40950\,d\,x-102400\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{585\,a^2\,\left(c+d\,x\right)}{256}-\frac{a^2\,\left(184275\,c+184275\,d\,x+184320\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{585\,a^2\,\left(c+d\,x\right)}{256}-\frac{a^2\,\left(184275\,c+184275\,d\,x-645120\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{195\,a^2\,\left(c+d\,x\right)}{32}-\frac{a^2\,\left(491400\,c+491400\,d\,x+430080\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{195\,a^2\,\left(c+d\,x\right)}{32}-\frac{a^2\,\left(491400\,c+491400\,d\,x-1658880\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{819\,a^2\,\left(c+d\,x\right)}{64}-\frac{a^2\,\left(1031940\,c+1031940\,d\,x-1290240\right)}{80640}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{1365\,a^2\,\left(c+d\,x\right)}{128}-\frac{a^2\,\left(859950\,c+859950\,d\,x-2150400\right)}{80640}\right)+\frac{13\,a^2\,\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,"(13*a^2*x)/256 - ((13*a^2*(c + d*x))/256 - (647*a^2*tan(c/2 + (d*x)/2)^3)/384 - (2311*a^2*tan(c/2 + (d*x)/2)^5)/480 + (457*a^2*tan(c/2 + (d*x)/2)^7)/32 - (2169*a^2*tan(c/2 + (d*x)/2)^9)/64 + (2169*a^2*tan(c/2 + (d*x)/2)^11)/64 - (457*a^2*tan(c/2 + (d*x)/2)^13)/32 + (2311*a^2*tan(c/2 + (d*x)/2)^15)/480 + (647*a^2*tan(c/2 + (d*x)/2)^17)/384 - (13*a^2*tan(c/2 + (d*x)/2)^19)/128 - (a^2*(4095*c + 4095*d*x - 10240))/80640 + tan(c/2 + (d*x)/2)^2*((65*a^2*(c + d*x))/128 - (a^2*(40950*c + 40950*d*x - 102400))/80640) + tan(c/2 + (d*x)/2)^4*((585*a^2*(c + d*x))/256 - (a^2*(184275*c + 184275*d*x + 184320))/80640) + tan(c/2 + (d*x)/2)^16*((585*a^2*(c + d*x))/256 - (a^2*(184275*c + 184275*d*x - 645120))/80640) + tan(c/2 + (d*x)/2)^14*((195*a^2*(c + d*x))/32 - (a^2*(491400*c + 491400*d*x + 430080))/80640) + tan(c/2 + (d*x)/2)^6*((195*a^2*(c + d*x))/32 - (a^2*(491400*c + 491400*d*x - 1658880))/80640) + tan(c/2 + (d*x)/2)^10*((819*a^2*(c + d*x))/64 - (a^2*(1031940*c + 1031940*d*x - 1290240))/80640) + tan(c/2 + (d*x)/2)^12*((1365*a^2*(c + d*x))/128 - (a^2*(859950*c + 859950*d*x - 2150400))/80640) + (13*a^2*tan(c/2 + (d*x)/2))/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
591,1,501,153,10.852708,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)*(a + a*sin(c + d*x))^2,x)","\frac{5\,a^2\,x}{64}-\frac{\frac{83\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{16}-\frac{191\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{48}-\frac{145\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{145\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{16}-\frac{83\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{16}+\frac{191\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{48}-\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{32}+\frac{a^2\,\left(315\,c+315\,d\,x\right)}{4032}-\frac{a^2\,\left(315\,c+315\,d\,x-1408\right)}{4032}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{448}-\frac{a^2\,\left(2835\,c+2835\,d\,x-4608\right)}{4032}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{448}-\frac{a^2\,\left(2835\,c+2835\,d\,x-8064\right)}{4032}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{112}-\frac{a^2\,\left(11340\,c+11340\,d\,x-18432\right)}{4032}\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(11340\,c+11340\,d\,x-32256\right)}{4032}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{48}-\frac{a^2\,\left(26460\,c+26460\,d\,x-21504\right)}{4032}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{32}-\frac{a^2\,\left(39690\,c+39690\,d\,x-16128\right)}{4032}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{48}-\frac{a^2\,\left(26460\,c+26460\,d\,x-96768\right)}{4032}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{32}-\frac{a^2\,\left(39690\,c+39690\,d\,x-161280\right)}{4032}\right)+\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(5*a^2*x)/64 - ((83*a^2*tan(c/2 + (d*x)/2)^5)/16 - (191*a^2*tan(c/2 + (d*x)/2)^3)/48 - (145*a^2*tan(c/2 + (d*x)/2)^7)/16 + (145*a^2*tan(c/2 + (d*x)/2)^11)/16 - (83*a^2*tan(c/2 + (d*x)/2)^13)/16 + (191*a^2*tan(c/2 + (d*x)/2)^15)/48 - (5*a^2*tan(c/2 + (d*x)/2)^17)/32 + (a^2*(315*c + 315*d*x))/4032 - (a^2*(315*c + 315*d*x - 1408))/4032 + tan(c/2 + (d*x)/2)^2*((a^2*(315*c + 315*d*x))/448 - (a^2*(2835*c + 2835*d*x - 4608))/4032) + tan(c/2 + (d*x)/2)^16*((a^2*(315*c + 315*d*x))/448 - (a^2*(2835*c + 2835*d*x - 8064))/4032) + tan(c/2 + (d*x)/2)^4*((a^2*(315*c + 315*d*x))/112 - (a^2*(11340*c + 11340*d*x - 18432))/4032) + tan(c/2 + (d*x)/2)^14*((a^2*(315*c + 315*d*x))/112 - (a^2*(11340*c + 11340*d*x - 32256))/4032) + tan(c/2 + (d*x)/2)^12*((a^2*(315*c + 315*d*x))/48 - (a^2*(26460*c + 26460*d*x - 21504))/4032) + tan(c/2 + (d*x)/2)^8*((a^2*(315*c + 315*d*x))/32 - (a^2*(39690*c + 39690*d*x - 16128))/4032) + tan(c/2 + (d*x)/2)^6*((a^2*(315*c + 315*d*x))/48 - (a^2*(26460*c + 26460*d*x - 96768))/4032) + tan(c/2 + (d*x)/2)^10*((a^2*(315*c + 315*d*x))/32 - (a^2*(39690*c + 39690*d*x - 161280))/4032) + (5*a^2*tan(c/2 + (d*x)/2))/32)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
592,1,384,161,10.840151,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{5\,a^2\,\mathrm{atan}\left(\frac{25\,a^4}{16\,\left(\frac{5\,a^4}{2}-\frac{25\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{5\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{5\,a^4}{2}-\frac{25\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}+\frac{-\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}+24\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{85\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}+\frac{116\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{176\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{85\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{172\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{232\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{11\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{292\,a^2}{105}}{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,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (5*a^2*atan((25*a^4)/(16*((5*a^4)/2 - (25*a^4*tan(c/2 + (d*x)/2))/16)) + (5*a^4*tan(c/2 + (d*x)/2))/(2*((5*a^4)/2 - (25*a^4*tan(c/2 + (d*x)/2))/16))))/(4*d) + ((232*a^2*tan(c/2 + (d*x)/2)^2)/15 + (7*a^2*tan(c/2 + (d*x)/2)^3)/3 + (172*a^2*tan(c/2 + (d*x)/2)^4)/5 + (85*a^2*tan(c/2 + (d*x)/2)^5)/12 + (176*a^2*tan(c/2 + (d*x)/2)^6)/3 + (116*a^2*tan(c/2 + (d*x)/2)^8)/3 - (85*a^2*tan(c/2 + (d*x)/2)^9)/12 + 24*a^2*tan(c/2 + (d*x)/2)^10 - (7*a^2*tan(c/2 + (d*x)/2)^11)/3 + 4*a^2*tan(c/2 + (d*x)/2)^12 - (11*a^2*tan(c/2 + (d*x)/2)^13)/4 + (292*a^2)/105 + (11*a^2*tan(c/2 + (d*x)/2))/4)/(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"
593,1,401,158,8.972688,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{2\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{25\,a^2\,\mathrm{atan}\left(\frac{625\,a^4}{64\,\left(\frac{25\,a^4}{2}+\frac{625\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}-\frac{25\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{25\,a^4}{2}+\frac{625\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}\right)}{8\,d}+\frac{\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{4}+24\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\frac{47\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{12}+72\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-\frac{35\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+\frac{368\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{35\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+112\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{299\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{12}+\frac{248\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}-\frac{31\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}+\frac{184\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}-a^2}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+30\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+30\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(2*a^2*log(tan(c/2 + (d*x)/2)))/d + (25*a^2*atan((625*a^4)/(64*((25*a^4)/2 + (625*a^4*tan(c/2 + (d*x)/2))/64)) - (25*a^4*tan(c/2 + (d*x)/2))/(2*((25*a^4)/2 + (625*a^4*tan(c/2 + (d*x)/2))/64))))/(8*d) + ((248*a^2*tan(c/2 + (d*x)/2)^3)/5 - (31*a^2*tan(c/2 + (d*x)/2)^2)/4 - (299*a^2*tan(c/2 + (d*x)/2)^4)/12 + 112*a^2*tan(c/2 + (d*x)/2)^5 - (35*a^2*tan(c/2 + (d*x)/2)^6)/2 + (368*a^2*tan(c/2 + (d*x)/2)^7)/3 - (35*a^2*tan(c/2 + (d*x)/2)^8)/2 + 72*a^2*tan(c/2 + (d*x)/2)^9 + (47*a^2*tan(c/2 + (d*x)/2)^10)/12 + 24*a^2*tan(c/2 + (d*x)/2)^11 + (3*a^2*tan(c/2 + (d*x)/2)^12)/4 - a^2 + (184*a^2*tan(c/2 + (d*x)/2))/15)/(d*(2*tan(c/2 + (d*x)/2) + 12*tan(c/2 + (d*x)/2)^3 + 30*tan(c/2 + (d*x)/2)^5 + 40*tan(c/2 + (d*x)/2)^7 + 30*tan(c/2 + (d*x)/2)^9 + 12*tan(c/2 + (d*x)/2)^11 + 2*tan(c/2 + (d*x)/2)^13)) + (a^2*tan(c/2 + (d*x)/2))/(2*d)","B"
594,1,377,140,8.938852,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{15\,a^2\,\mathrm{atan}\left(\frac{225\,a^4}{4\,\left(\frac{45\,a^4}{2}-\frac{225\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)}+\frac{45\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{45\,a^4}{2}-\frac{225\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)}\right)}{2\,d}-\frac{-14\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{2}+\frac{69\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+40\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+37\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+60\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+37\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+38\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{89\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{10}+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*a^2*log(tan(c/2 + (d*x)/2)))/(2*d) - (15*a^2*atan((225*a^4)/(4*((45*a^4)/2 - (225*a^4*tan(c/2 + (d*x)/2))/4)) + (45*a^4*tan(c/2 + (d*x)/2))/(2*((45*a^4)/2 - (225*a^4*tan(c/2 + (d*x)/2))/4))))/(2*d) - ((89*a^2*tan(c/2 + (d*x)/2)^2)/10 + 38*a^2*tan(c/2 + (d*x)/2)^3 + 37*a^2*tan(c/2 + (d*x)/2)^4 + 60*a^2*tan(c/2 + (d*x)/2)^5 + 37*a^2*tan(c/2 + (d*x)/2)^6 + 40*a^2*tan(c/2 + (d*x)/2)^7 + (69*a^2*tan(c/2 + (d*x)/2)^8)/2 + (a^2*tan(c/2 + (d*x)/2)^10)/2 - 14*a^2*tan(c/2 + (d*x)/2)^11 + a^2/2 + 4*a^2*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 20*tan(c/2 + (d*x)/2)^4 + 40*tan(c/2 + (d*x)/2)^6 + 40*tan(c/2 + (d*x)/2)^8 + 20*tan(c/2 + (d*x)/2)^10 + 4*tan(c/2 + (d*x)/2)^12)) + (a^2*tan(c/2 + (d*x)/2))/d","B"
595,1,384,153,8.927445,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^4,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{5\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{5\,a^2\,\mathrm{atan}\left(\frac{25\,a^4}{16\,\left(\frac{25\,a^4}{2}+\frac{25\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}-\frac{25\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{25\,a^4}{2}+\frac{25\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}-\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{-15\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+98\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-\frac{41\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+232\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{104\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{644\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{248\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(4*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (5*a^2*log(tan(c/2 + (d*x)/2)))/d - (5*a^2*atan((25*a^4)/(16*((25*a^4)/2 + (25*a^4*tan(c/2 + (d*x)/2))/16)) - (25*a^4*tan(c/2 + (d*x)/2))/(2*((25*a^4)/2 + (25*a^4*tan(c/2 + (d*x)/2))/16))))/(4*d) - (5*a^2*tan(c/2 + (d*x)/2))/(8*d) - ((248*a^2*tan(c/2 + (d*x)/2)^3)/3 - (11*a^2*tan(c/2 + (d*x)/2)^2)/3 - 8*a^2*tan(c/2 + (d*x)/2)^4 + (644*a^2*tan(c/2 + (d*x)/2)^5)/3 - (104*a^2*tan(c/2 + (d*x)/2)^6)/3 + 232*a^2*tan(c/2 + (d*x)/2)^7 - (41*a^2*tan(c/2 + (d*x)/2)^8)/3 + 98*a^2*tan(c/2 + (d*x)/2)^9 - 15*a^2*tan(c/2 + (d*x)/2)^10 + a^2/3 + 2*a^2*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 32*tan(c/2 + (d*x)/2)^5 + 48*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9 + 8*tan(c/2 + (d*x)/2)^11))","B"
596,1,373,153,8.940114,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^5,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-62\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{320\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{233\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{4}+136\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{449\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{12}+32\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{a^2}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{5\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{10\,a^2\,\mathrm{atan}\left(\frac{100\,a^4}{\frac{25\,a^4}{2}+100\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{25\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{25\,a^4}{2}+100\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}-\frac{9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^3)/(12*d) - (a^2*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^2*tan(c/2 + (d*x)/2)^4)/(64*d) + ((5*a^2*tan(c/2 + (d*x)/2)^2)/4 + 32*a^2*tan(c/2 + (d*x)/2)^3 - (449*a^2*tan(c/2 + (d*x)/2)^4)/12 + 136*a^2*tan(c/2 + (d*x)/2)^5 - (233*a^2*tan(c/2 + (d*x)/2)^6)/4 + (320*a^2*tan(c/2 + (d*x)/2)^7)/3 - 62*a^2*tan(c/2 + (d*x)/2)^8 + 4*a^2*tan(c/2 + (d*x)/2)^9 - a^2/4 - (4*a^2*tan(c/2 + (d*x)/2))/3)/(d*(16*tan(c/2 + (d*x)/2)^4 + 48*tan(c/2 + (d*x)/2)^6 + 48*tan(c/2 + (d*x)/2)^8 + 16*tan(c/2 + (d*x)/2)^10)) - (5*a^2*log(tan(c/2 + (d*x)/2)))/(8*d) - (10*a^2*atan((100*a^4)/((25*a^4)/2 + 100*a^4*tan(c/2 + (d*x)/2)) - (25*a^4*tan(c/2 + (d*x)/2))/(2*((25*a^4)/2 + 100*a^4*tan(c/2 + (d*x)/2)))))/d - (9*a^2*tan(c/2 + (d*x)/2))/(4*d)","B"
597,1,363,139,8.898071,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^6,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{15\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}+\frac{-18\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+144\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+61\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+159\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{79\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+14\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a^2}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{3\,a^2\,\mathrm{atan}\left(\frac{9\,a^4}{\frac{45\,a^4}{2}-9\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{45\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{45\,a^4}{2}-9\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}-\frac{7\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^4)/(32*d) - (a^2*tan(c/2 + (d*x)/2)^3)/(32*d) - (a^2*tan(c/2 + (d*x)/2)^2)/(2*d) + (a^2*tan(c/2 + (d*x)/2)^5)/(160*d) + (15*a^2*log(tan(c/2 + (d*x)/2)))/(4*d) + ((3*a^2*tan(c/2 + (d*x)/2)^2)/5 + 14*a^2*tan(c/2 + (d*x)/2)^3 + (79*a^2*tan(c/2 + (d*x)/2)^4)/5 + 159*a^2*tan(c/2 + (d*x)/2)^5 + 61*a^2*tan(c/2 + (d*x)/2)^6 + 144*a^2*tan(c/2 + (d*x)/2)^7 - 18*a^2*tan(c/2 + (d*x)/2)^8 - a^2/5 - a^2*tan(c/2 + (d*x)/2))/(d*(32*tan(c/2 + (d*x)/2)^5 + 64*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9)) + (3*a^2*atan((9*a^4)/((45*a^4)/2 - 9*a^4*tan(c/2 + (d*x)/2)) + (45*a^4*tan(c/2 + (d*x)/2))/(2*((45*a^4)/2 - 9*a^4*tan(c/2 + (d*x)/2)))))/d - (7*a^2*tan(c/2 + (d*x)/2))/(16*d)","B"
598,1,657,157,11.009788,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^7,x)","\frac{5\,a^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-5\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+24\,a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-24\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-10\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-256\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-270\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+2360\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-255\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4095\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2360\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+270\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+256\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3000\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+3000\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+7680\,a^2\,\mathrm{atan}\left(\frac{32\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-25\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{25\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+32\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+7680\,a^2\,\mathrm{atan}\left(\frac{32\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-25\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{25\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+32\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1920\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}","Not used",1,"(5*a^2*sin(c/2 + (d*x)/2)^14 - 5*a^2*cos(c/2 + (d*x)/2)^14 + 24*a^2*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 - 24*a^2*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) - 10*a^2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 256*a^2*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 - 270*a^2*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 + 2360*a^2*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 - 255*a^2*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 4095*a^2*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 - 2360*a^2*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 + 270*a^2*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 + 256*a^2*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 + 10*a^2*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 3000*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 3000*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 7680*a^2*atan((32*cos(c/2 + (d*x)/2) - 25*sin(c/2 + (d*x)/2))/(25*cos(c/2 + (d*x)/2) + 32*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 7680*a^2*atan((32*cos(c/2 + (d*x)/2) - 25*sin(c/2 + (d*x)/2))/(25*cos(c/2 + (d*x)/2) + 32*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6)/(1920*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6*(cos(c/2 + (d*x)/2)^2 + sin(c/2 + (d*x)/2)^2))","B"
599,1,351,162,9.838906,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^8,x)","\frac{19\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}-\frac{15\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{3\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}+\frac{15\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}-\frac{19\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{2\,a^2\,\mathrm{atan}\left(\frac{8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{5\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8\,d}-\frac{83\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}+\frac{83\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}","Not used",1,"(19*a^2*cot(c/2 + (d*x)/2)^3)/(384*d) - (15*a^2*cot(c/2 + (d*x)/2)^2)/(64*d) + (3*a^2*cot(c/2 + (d*x)/2)^4)/(64*d) + (a^2*cot(c/2 + (d*x)/2)^5)/(640*d) - (a^2*cot(c/2 + (d*x)/2)^6)/(192*d) - (a^2*cot(c/2 + (d*x)/2)^7)/(896*d) + (15*a^2*tan(c/2 + (d*x)/2)^2)/(64*d) - (19*a^2*tan(c/2 + (d*x)/2)^3)/(384*d) - (3*a^2*tan(c/2 + (d*x)/2)^4)/(64*d) - (a^2*tan(c/2 + (d*x)/2)^5)/(640*d) + (a^2*tan(c/2 + (d*x)/2)^6)/(192*d) + (a^2*tan(c/2 + (d*x)/2)^7)/(896*d) - (2*a^2*atan((8*cos(c/2 + (d*x)/2) + 5*sin(c/2 + (d*x)/2))/(5*cos(c/2 + (d*x)/2) - 8*sin(c/2 + (d*x)/2))))/d - (5*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(8*d) - (83*a^2*cot(c/2 + (d*x)/2))/(128*d) + (83*a^2*tan(c/2 + (d*x)/2))/(128*d)","B"
600,1,387,182,11.163562,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^9,x)","-\frac{a^2\,\left(7\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-32\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+224\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+280\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-672\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-1792\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+1120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-1120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+1792\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+672\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-280\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-224\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5040\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\right)}{14336\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}","Not used",1,"-(a^2*(7*cos(c/2 + (d*x)/2)^16 - 7*sin(c/2 + (d*x)/2)^16 - 32*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^15 + 32*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2) + 224*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^13 + 280*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 - 672*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^11 - 1792*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 + 1120*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^9 - 1120*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^7 + 1792*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 + 672*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^5 - 280*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 - 224*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^3 + 5040*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8))/(14336*d*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8)","B"
601,1,357,152,9.406133,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^10,x)","\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}-\frac{11\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{1024\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{1024\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}-\frac{5\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,d}+\frac{13\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}-\frac{13\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}","Not used",1,"(a^2*cot(c/2 + (d*x)/2)^5)/(128*d) - (11*a^2*cot(c/2 + (d*x)/2)^3)/(384*d) - (a^2*cot(c/2 + (d*x)/2)^4)/(128*d) - (a^2*cot(c/2 + (d*x)/2)^2)/(64*d) + (a^2*cot(c/2 + (d*x)/2)^6)/(192*d) - (a^2*cot(c/2 + (d*x)/2)^7)/(3584*d) - (a^2*cot(c/2 + (d*x)/2)^8)/(1024*d) - (a^2*cot(c/2 + (d*x)/2)^9)/(4608*d) + (a^2*tan(c/2 + (d*x)/2)^2)/(64*d) + (11*a^2*tan(c/2 + (d*x)/2)^3)/(384*d) + (a^2*tan(c/2 + (d*x)/2)^4)/(128*d) - (a^2*tan(c/2 + (d*x)/2)^5)/(128*d) - (a^2*tan(c/2 + (d*x)/2)^6)/(192*d) + (a^2*tan(c/2 + (d*x)/2)^7)/(3584*d) + (a^2*tan(c/2 + (d*x)/2)^8)/(1024*d) + (a^2*tan(c/2 + (d*x)/2)^9)/(4608*d) - (5*a^2*log(tan(c/2 + (d*x)/2)))/(64*d) + (13*a^2*cot(c/2 + (d*x)/2))/(256*d) - (13*a^2*tan(c/2 + (d*x)/2))/(256*d)","B"
602,1,357,228,9.434585,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^11,x)","\frac{19\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{6144\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{3\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{9\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{3\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{1792\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2304\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{9\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{19\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{6144\,d}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{1792\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2304\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{13\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{256\,d}+\frac{3\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}-\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}","Not used",1,"(19*a^2*cot(c/2 + (d*x)/2)^6)/(6144*d) - (a^2*cot(c/2 + (d*x)/2)^3)/(96*d) - (3*a^2*cot(c/2 + (d*x)/2)^4)/(512*d) - (9*a^2*cot(c/2 + (d*x)/2)^2)/(1024*d) + (3*a^2*cot(c/2 + (d*x)/2)^7)/(1792*d) - (a^2*cot(c/2 + (d*x)/2)^8)/(4096*d) - (a^2*cot(c/2 + (d*x)/2)^9)/(2304*d) - (a^2*cot(c/2 + (d*x)/2)^10)/(10240*d) + (9*a^2*tan(c/2 + (d*x)/2)^2)/(1024*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(96*d) + (3*a^2*tan(c/2 + (d*x)/2)^4)/(512*d) - (19*a^2*tan(c/2 + (d*x)/2)^6)/(6144*d) - (3*a^2*tan(c/2 + (d*x)/2)^7)/(1792*d) + (a^2*tan(c/2 + (d*x)/2)^8)/(4096*d) + (a^2*tan(c/2 + (d*x)/2)^9)/(2304*d) + (a^2*tan(c/2 + (d*x)/2)^10)/(10240*d) - (13*a^2*log(tan(c/2 + (d*x)/2)))/(256*d) + (3*a^2*cot(c/2 + (d*x)/2))/(128*d) - (3*a^2*tan(c/2 + (d*x)/2))/(128*d)","B"
603,1,433,194,9.973992,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^12,x)","\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1024\,d}-\frac{7\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{1024\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2048\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{512\,d}+\frac{17\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14336\,d}+\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{6144\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{5120\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{22528\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{512\,d}+\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{1024\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2048\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1024\,d}-\frac{17\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14336\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{6144\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{5120\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{22528\,d}-\frac{3\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,d}+\frac{17\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1024\,d}-\frac{17\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1024\,d}","Not used",1,"(a^2*cot(c/2 + (d*x)/2)^6)/(1024*d) - (7*a^2*cot(c/2 + (d*x)/2)^3)/(1024*d) - (a^2*cot(c/2 + (d*x)/2)^4)/(256*d) - (a^2*cot(c/2 + (d*x)/2)^5)/(2048*d) - (a^2*cot(c/2 + (d*x)/2)^2)/(512*d) + (17*a^2*cot(c/2 + (d*x)/2)^7)/(14336*d) + (a^2*cot(c/2 + (d*x)/2)^8)/(2048*d) - (a^2*cot(c/2 + (d*x)/2)^9)/(6144*d) - (a^2*cot(c/2 + (d*x)/2)^10)/(5120*d) - (a^2*cot(c/2 + (d*x)/2)^11)/(22528*d) + (a^2*tan(c/2 + (d*x)/2)^2)/(512*d) + (7*a^2*tan(c/2 + (d*x)/2)^3)/(1024*d) + (a^2*tan(c/2 + (d*x)/2)^4)/(256*d) + (a^2*tan(c/2 + (d*x)/2)^5)/(2048*d) - (a^2*tan(c/2 + (d*x)/2)^6)/(1024*d) - (17*a^2*tan(c/2 + (d*x)/2)^7)/(14336*d) - (a^2*tan(c/2 + (d*x)/2)^8)/(2048*d) + (a^2*tan(c/2 + (d*x)/2)^9)/(6144*d) + (a^2*tan(c/2 + (d*x)/2)^10)/(5120*d) + (a^2*tan(c/2 + (d*x)/2)^11)/(22528*d) - (3*a^2*log(tan(c/2 + (d*x)/2)))/(128*d) + (17*a^2*cot(c/2 + (d*x)/2))/(1024*d) - (17*a^2*tan(c/2 + (d*x)/2))/(1024*d)","B"
604,1,471,270,10.358256,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^2)/sin(c + d*x)^13,x)","\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{5\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{1536\,d}-\frac{47\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16384\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{1024\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{5\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{7168\,d}+\frac{7\,a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16384\,d}+\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{9216\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{11264\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{49152\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{1536\,d}+\frac{47\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16384\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{1024\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{7168\,d}-\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16384\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{9216\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{11264\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{49152\,d}-\frac{17\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{1024\,d}+\frac{5\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,d}-\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,d}","Not used",1,"(a^2*cot(c/2 + (d*x)/2)^6)/(2048*d) - (5*a^2*cot(c/2 + (d*x)/2)^3)/(1536*d) - (47*a^2*cot(c/2 + (d*x)/2)^4)/(16384*d) - (a^2*cot(c/2 + (d*x)/2)^5)/(1024*d) - (a^2*cot(c/2 + (d*x)/2)^2)/(1024*d) + (5*a^2*cot(c/2 + (d*x)/2)^7)/(7168*d) + (7*a^2*cot(c/2 + (d*x)/2)^8)/(16384*d) + (a^2*cot(c/2 + (d*x)/2)^9)/(9216*d) - (a^2*cot(c/2 + (d*x)/2)^10)/(10240*d) - (a^2*cot(c/2 + (d*x)/2)^11)/(11264*d) - (a^2*cot(c/2 + (d*x)/2)^12)/(49152*d) + (a^2*tan(c/2 + (d*x)/2)^2)/(1024*d) + (5*a^2*tan(c/2 + (d*x)/2)^3)/(1536*d) + (47*a^2*tan(c/2 + (d*x)/2)^4)/(16384*d) + (a^2*tan(c/2 + (d*x)/2)^5)/(1024*d) - (a^2*tan(c/2 + (d*x)/2)^6)/(2048*d) - (5*a^2*tan(c/2 + (d*x)/2)^7)/(7168*d) - (7*a^2*tan(c/2 + (d*x)/2)^8)/(16384*d) - (a^2*tan(c/2 + (d*x)/2)^9)/(9216*d) + (a^2*tan(c/2 + (d*x)/2)^10)/(10240*d) + (a^2*tan(c/2 + (d*x)/2)^11)/(11264*d) + (a^2*tan(c/2 + (d*x)/2)^12)/(49152*d) - (17*a^2*log(tan(c/2 + (d*x)/2)))/(1024*d) + (5*a^2*cot(c/2 + (d*x)/2))/(512*d) - (5*a^2*tan(c/2 + (d*x)/2))/(512*d)","B"
605,1,612,224,12.192359,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^4*(a + a*sin(c + d*x))^3,x)","\frac{27\,a^3\,x}{1024}-\frac{\frac{27\,a^3\,\left(c+d\,x\right)}{1024}+\frac{171\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{256}-\frac{1603\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640}-\frac{59523\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{1280}+\frac{305539\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2560}-\frac{93973\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{640}+\frac{93973\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{640}-\frac{305539\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{2560}+\frac{59523\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{1280}+\frac{1603\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{640}-\frac{171\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{23}}{256}-\frac{27\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{25}}{512}-a^3\,\left(\frac{27\,c}{1024}+\frac{27\,d\,x}{1024}-\frac{80}{1001}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{351\,a^3\,\left(c+d\,x\right)}{1024}-a^3\,\left(\frac{351\,c}{1024}+\frac{351\,d\,x}{1024}-\frac{80}{77}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{1053\,a^3\,\left(c+d\,x\right)}{512}-a^3\,\left(\frac{1053\,c}{512}+\frac{1053\,d\,x}{512}-\frac{480}{77}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}\,\left(\frac{3861\,a^3\,\left(c+d\,x\right)}{512}-a^3\,\left(\frac{3861\,c}{512}+\frac{3861\,d\,x}{512}-32\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{3861\,a^3\,\left(c+d\,x\right)}{512}-a^3\,\left(\frac{3861\,c}{512}+\frac{3861\,d\,x}{512}+\frac{64}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{11583\,a^3\,\left(c+d\,x\right)}{256}-a^3\,\left(\frac{11583\,c}{256}+\frac{11583\,d\,x}{256}-320\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{11583\,a^3\,\left(c+d\,x\right)}{256}-a^3\,\left(\frac{11583\,c}{256}+\frac{11583\,d\,x}{256}+\frac{1280}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(\frac{19305\,a^3\,\left(c+d\,x\right)}{1024}-a^3\,\left(\frac{19305\,c}{1024}+\frac{19305\,d\,x}{1024}-16\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{19305\,a^3\,\left(c+d\,x\right)}{1024}-a^3\,\left(\frac{19305\,c}{1024}+\frac{19305\,d\,x}{1024}-\frac{288}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{34749\,a^3\,\left(c+d\,x\right)}{1024}-a^3\,\left(\frac{34749\,c}{1024}+\frac{34749\,d\,x}{1024}+48\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{34749\,a^3\,\left(c+d\,x\right)}{1024}-a^3\,\left(\frac{34749\,c}{1024}+\frac{34749\,d\,x}{1024}-\frac{1056}{7}\right)\right)+\frac{27\,a^3\,\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)}^{13}}","Not used",1,"(27*a^3*x)/1024 - ((27*a^3*(c + d*x))/1024 + (171*a^3*tan(c/2 + (d*x)/2)^3)/256 - (1603*a^3*tan(c/2 + (d*x)/2)^5)/640 - (59523*a^3*tan(c/2 + (d*x)/2)^7)/1280 + (305539*a^3*tan(c/2 + (d*x)/2)^9)/2560 - (93973*a^3*tan(c/2 + (d*x)/2)^11)/640 + (93973*a^3*tan(c/2 + (d*x)/2)^15)/640 - (305539*a^3*tan(c/2 + (d*x)/2)^17)/2560 + (59523*a^3*tan(c/2 + (d*x)/2)^19)/1280 + (1603*a^3*tan(c/2 + (d*x)/2)^21)/640 - (171*a^3*tan(c/2 + (d*x)/2)^23)/256 - (27*a^3*tan(c/2 + (d*x)/2)^25)/512 - a^3*((27*c)/1024 + (27*d*x)/1024 - 80/1001) + tan(c/2 + (d*x)/2)^2*((351*a^3*(c + d*x))/1024 - a^3*((351*c)/1024 + (351*d*x)/1024 - 80/77)) + tan(c/2 + (d*x)/2)^4*((1053*a^3*(c + d*x))/512 - a^3*((1053*c)/512 + (1053*d*x)/512 - 480/77)) + tan(c/2 + (d*x)/2)^20*((3861*a^3*(c + d*x))/512 - a^3*((3861*c)/512 + (3861*d*x)/512 - 32)) + tan(c/2 + (d*x)/2)^6*((3861*a^3*(c + d*x))/512 - a^3*((3861*c)/512 + (3861*d*x)/512 + 64/7)) + tan(c/2 + (d*x)/2)^14*((11583*a^3*(c + d*x))/256 - a^3*((11583*c)/256 + (11583*d*x)/256 - 320)) + tan(c/2 + (d*x)/2)^12*((11583*a^3*(c + d*x))/256 - a^3*((11583*c)/256 + (11583*d*x)/256 + 1280/7)) + tan(c/2 + (d*x)/2)^18*((19305*a^3*(c + d*x))/1024 - a^3*((19305*c)/1024 + (19305*d*x)/1024 - 16)) + tan(c/2 + (d*x)/2)^8*((19305*a^3*(c + d*x))/1024 - a^3*((19305*c)/1024 + (19305*d*x)/1024 - 288/7)) + tan(c/2 + (d*x)/2)^16*((34749*a^3*(c + d*x))/1024 - a^3*((34749*c)/1024 + (34749*d*x)/1024 + 48)) + tan(c/2 + (d*x)/2)^10*((34749*a^3*(c + d*x))/1024 - a^3*((34749*c)/1024 + (34749*d*x)/1024 - 1056/7)) + (27*a^3*tan(c/2 + (d*x)/2))/512)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^13)","B"
606,1,683,209,11.022680,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^3*(a + a*sin(c + d*x))^3,x)","\frac{41\,a^3\,x}{1024}-\frac{\frac{1435\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{1536}-\frac{36401\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2560}+\frac{1263\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2560}+\frac{184331\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3840}-\frac{35387\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{256}+\frac{35387\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{256}-\frac{184331\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{3840}-\frac{1263\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{2560}+\frac{36401\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{2560}-\frac{1435\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{1536}-\frac{41\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{23}}{512}+a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}-\frac{92}{693}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}\,\left(a^3\,\left(\frac{123\,c}{256}+\frac{123\,d\,x}{256}\right)-12\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^3\,\left(\frac{123\,c}{256}+\frac{123\,d\,x}{256}-\frac{368}{231}\right)-12\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}\,\left(66\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{1353\,c}{512}+\frac{1353\,d\,x}{512}-4\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(66\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{1353\,c}{512}+\frac{1353\,d\,x}{512}-\frac{100}{21}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(220\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{2255\,c}{256}+\frac{2255\,d\,x}{256}-\frac{112}{3}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(220\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{2255\,c}{256}+\frac{2255\,d\,x}{256}+\frac{512}{63}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(792\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{4059\,c}{128}+\frac{4059\,d\,x}{128}-128\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(792\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{4059\,c}{128}+\frac{4059\,d\,x}{128}+\frac{160}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(924\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{9471\,c}{256}+\frac{9471\,d\,x}{256}-\frac{184}{3}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(495\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{20295\,c}{1024}+\frac{20295\,d\,x}{1024}+36\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(495\,a^3\,\left(\frac{41\,c}{1024}+\frac{41\,d\,x}{1024}\right)-a^3\,\left(\frac{20295\,c}{1024}+\frac{20295\,d\,x}{1024}-\frac{712}{7}\right)\right)+\frac{41\,a^3\,\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,"(41*a^3*x)/1024 - ((1435*a^3*tan(c/2 + (d*x)/2)^3)/1536 - (36401*a^3*tan(c/2 + (d*x)/2)^5)/2560 + (1263*a^3*tan(c/2 + (d*x)/2)^7)/2560 + (184331*a^3*tan(c/2 + (d*x)/2)^9)/3840 - (35387*a^3*tan(c/2 + (d*x)/2)^11)/256 + (35387*a^3*tan(c/2 + (d*x)/2)^13)/256 - (184331*a^3*tan(c/2 + (d*x)/2)^15)/3840 - (1263*a^3*tan(c/2 + (d*x)/2)^17)/2560 + (36401*a^3*tan(c/2 + (d*x)/2)^19)/2560 - (1435*a^3*tan(c/2 + (d*x)/2)^21)/1536 - (41*a^3*tan(c/2 + (d*x)/2)^23)/512 + a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((41*c)/1024 + (41*d*x)/1024 - 92/693) - tan(c/2 + (d*x)/2)^22*(a^3*((123*c)/256 + (123*d*x)/256) - 12*a^3*((41*c)/1024 + (41*d*x)/1024)) - tan(c/2 + (d*x)/2)^2*(a^3*((123*c)/256 + (123*d*x)/256 - 368/231) - 12*a^3*((41*c)/1024 + (41*d*x)/1024)) + tan(c/2 + (d*x)/2)^20*(66*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((1353*c)/512 + (1353*d*x)/512 - 4)) + tan(c/2 + (d*x)/2)^4*(66*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((1353*c)/512 + (1353*d*x)/512 - 100/21)) + tan(c/2 + (d*x)/2)^18*(220*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((2255*c)/256 + (2255*d*x)/256 - 112/3)) + tan(c/2 + (d*x)/2)^6*(220*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((2255*c)/256 + (2255*d*x)/256 + 512/63)) + tan(c/2 + (d*x)/2)^14*(792*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((4059*c)/128 + (4059*d*x)/128 - 128)) + tan(c/2 + (d*x)/2)^10*(792*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((4059*c)/128 + (4059*d*x)/128 + 160/7)) + tan(c/2 + (d*x)/2)^12*(924*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((9471*c)/256 + (9471*d*x)/256 - 184/3)) + tan(c/2 + (d*x)/2)^16*(495*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((20295*c)/1024 + (20295*d*x)/1024 + 36)) + tan(c/2 + (d*x)/2)^8*(495*a^3*((41*c)/1024 + (41*d*x)/1024) - a^3*((20295*c)/1024 + (20295*d*x)/1024 - 712/7)) + (41*a^3*tan(c/2 + (d*x)/2))/512)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^12)","B"
607,1,543,183,12.122518,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^2*(a + a*sin(c + d*x))^3,x)","\frac{19\,a^3\,x}{256}-\frac{\frac{19\,a^3\,\left(c+d\,x\right)}{256}-\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}-\frac{32417\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{1920}+\frac{466\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{15}-\frac{2937\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{2937\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}-\frac{466\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{15}+\frac{32417\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{1920}+\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{12}-\frac{19\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{128}-a^3\,\left(\frac{19\,c}{256}+\frac{19\,d\,x}{256}-\frac{148}{693}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{209\,a^3\,\left(c+d\,x\right)}{256}-a^3\,\left(\frac{209\,c}{256}+\frac{209\,d\,x}{256}-\frac{148}{63}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(\frac{1045\,a^3\,\left(c+d\,x\right)}{256}-a^3\,\left(\frac{1045\,c}{256}+\frac{1045\,d\,x}{256}-12\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{1045\,a^3\,\left(c+d\,x\right)}{256}-a^3\,\left(\frac{1045\,c}{256}+\frac{1045\,d\,x}{256}+\frac{16}{63}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{3135\,a^3\,\left(c+d\,x\right)}{128}-a^3\,\left(\frac{3135\,c}{128}+\frac{3135\,d\,x}{128}-\frac{16}{3}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{3135\,a^3\,\left(c+d\,x\right)}{256}-a^3\,\left(\frac{3135\,c}{256}+\frac{3135\,d\,x}{256}-\frac{44}{3}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{3135\,a^3\,\left(c+d\,x\right)}{128}-a^3\,\left(\frac{3135\,c}{128}+\frac{3135\,d\,x}{128}-\frac{456}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{3135\,a^3\,\left(c+d\,x\right)}{256}-a^3\,\left(\frac{3135\,c}{256}+\frac{3135\,d\,x}{256}-\frac{144}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{4389\,a^3\,\left(c+d\,x\right)}{128}-a^3\,\left(\frac{4389\,c}{128}+\frac{4389\,d\,x}{128}+24\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{4389\,a^3\,\left(c+d\,x\right)}{128}-a^3\,\left(\frac{4389\,c}{128}+\frac{4389\,d\,x}{128}-\frac{368}{3}\right)\right)+\frac{19\,a^3\,\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)}^{11}}","Not used",1,"(19*a^3*x)/256 - ((19*a^3*(c + d*x))/256 - (13*a^3*tan(c/2 + (d*x)/2)^3)/12 - (32417*a^3*tan(c/2 + (d*x)/2)^5)/1920 + (466*a^3*tan(c/2 + (d*x)/2)^7)/15 - (2937*a^3*tan(c/2 + (d*x)/2)^9)/64 + (2937*a^3*tan(c/2 + (d*x)/2)^13)/64 - (466*a^3*tan(c/2 + (d*x)/2)^15)/15 + (32417*a^3*tan(c/2 + (d*x)/2)^17)/1920 + (13*a^3*tan(c/2 + (d*x)/2)^19)/12 - (19*a^3*tan(c/2 + (d*x)/2)^21)/128 - a^3*((19*c)/256 + (19*d*x)/256 - 148/693) + tan(c/2 + (d*x)/2)^2*((209*a^3*(c + d*x))/256 - a^3*((209*c)/256 + (209*d*x)/256 - 148/63)) + tan(c/2 + (d*x)/2)^18*((1045*a^3*(c + d*x))/256 - a^3*((1045*c)/256 + (1045*d*x)/256 - 12)) + tan(c/2 + (d*x)/2)^4*((1045*a^3*(c + d*x))/256 - a^3*((1045*c)/256 + (1045*d*x)/256 + 16/63)) + tan(c/2 + (d*x)/2)^14*((3135*a^3*(c + d*x))/128 - a^3*((3135*c)/128 + (3135*d*x)/128 - 16/3)) + tan(c/2 + (d*x)/2)^16*((3135*a^3*(c + d*x))/256 - a^3*((3135*c)/256 + (3135*d*x)/256 - 44/3)) + tan(c/2 + (d*x)/2)^8*((3135*a^3*(c + d*x))/128 - a^3*((3135*c)/128 + (3135*d*x)/128 - 456/7)) + tan(c/2 + (d*x)/2)^6*((3135*a^3*(c + d*x))/256 - a^3*((3135*c)/256 + (3135*d*x)/256 - 144/7)) + tan(c/2 + (d*x)/2)^10*((4389*a^3*(c + d*x))/128 - a^3*((4389*c)/128 + (4389*d*x)/128 + 24)) + tan(c/2 + (d*x)/2)^12*((4389*a^3*(c + d*x))/128 - a^3*((4389*c)/128 + (4389*d*x)/128 - 368/3)) + (19*a^3*tan(c/2 + (d*x)/2))/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^11)","B"
608,1,572,181,10.962917,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)*(a + a*sin(c + d*x))^3,x)","\frac{33\,a^3\,x}{256}-\frac{\frac{333\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}-\frac{577\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}-\frac{705\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128}-\frac{2749\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{2749\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}-\frac{333\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{577\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{160}+\frac{705\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{33\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}+a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}-\frac{10}{21}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(10\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{165\,c}{128}+\frac{165\,d\,x}{128}-2\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(10\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{165\,c}{128}+\frac{165\,d\,x}{128}-\frac{58}{21}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(120\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{495\,c}{32}+\frac{495\,d\,x}{32}-8\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(120\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{495\,c}{32}+\frac{495\,d\,x}{32}-\frac{344}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(45\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{1485\,c}{256}+\frac{1485\,d\,x}{256}-18\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(45\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{1485\,c}{256}+\frac{1485\,d\,x}{256}-\frac{24}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(252\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{2079\,c}{64}+\frac{2079\,d\,x}{64}-60\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(210\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{3465\,c}{128}+\frac{3465\,d\,x}{128}-28\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(210\,a^3\,\left(\frac{33\,c}{256}+\frac{33\,d\,x}{256}\right)-a^3\,\left(\frac{3465\,c}{128}+\frac{3465\,d\,x}{128}-72\right)\right)+\frac{33\,a^3\,\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,"(33*a^3*x)/256 - ((333*a^3*tan(c/2 + (d*x)/2)^7)/32 - (577*a^3*tan(c/2 + (d*x)/2)^5)/160 - (705*a^3*tan(c/2 + (d*x)/2)^3)/128 - (2749*a^3*tan(c/2 + (d*x)/2)^9)/64 + (2749*a^3*tan(c/2 + (d*x)/2)^11)/64 - (333*a^3*tan(c/2 + (d*x)/2)^13)/32 + (577*a^3*tan(c/2 + (d*x)/2)^15)/160 + (705*a^3*tan(c/2 + (d*x)/2)^17)/128 - (33*a^3*tan(c/2 + (d*x)/2)^19)/128 + a^3*((33*c)/256 + (33*d*x)/256) - a^3*((33*c)/256 + (33*d*x)/256 - 10/21) + tan(c/2 + (d*x)/2)^18*(10*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((165*c)/128 + (165*d*x)/128 - 2)) + tan(c/2 + (d*x)/2)^2*(10*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((165*c)/128 + (165*d*x)/128 - 58/21)) + tan(c/2 + (d*x)/2)^14*(120*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((495*c)/32 + (495*d*x)/32 - 8)) + tan(c/2 + (d*x)/2)^6*(120*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((495*c)/32 + (495*d*x)/32 - 344/7)) + tan(c/2 + (d*x)/2)^16*(45*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((1485*c)/256 + (1485*d*x)/256 - 18)) + tan(c/2 + (d*x)/2)^4*(45*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((1485*c)/256 + (1485*d*x)/256 - 24/7)) + tan(c/2 + (d*x)/2)^10*(252*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((2079*c)/64 + (2079*d*x)/64 - 60)) + tan(c/2 + (d*x)/2)^8*(210*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((3465*c)/128 + (3465*d*x)/128 - 28)) + tan(c/2 + (d*x)/2)^12*(210*a^3*((33*c)/256 + (33*d*x)/256) - a^3*((3465*c)/128 + (3465*d*x)/128 - 72)) + (33*a^3*tan(c/2 + (d*x)/2))/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
609,1,429,185,10.853720,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x),x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{125\,a^3\,\mathrm{atan}\left(\frac{15625\,a^6}{4096\,\left(\frac{125\,a^6}{32}-\frac{15625\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4096}\right)}+\frac{125\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32\,\left(\frac{125\,a^6}{32}-\frac{15625\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4096}\right)}\right)}{64\,d}+\frac{-\frac{259\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}-\frac{1861\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}+24\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{1817\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{192}+\frac{128\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}-\frac{3805\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{232\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{3805\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{192}+\frac{1216\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}+\frac{1817\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}+\frac{568\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+\frac{1861\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{1856\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{105}+\frac{259\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{232\,a^3}{105}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d + (125*a^3*atan((15625*a^6)/(4096*((125*a^6)/32 - (15625*a^6*tan(c/2 + (d*x)/2))/4096)) + (125*a^6*tan(c/2 + (d*x)/2))/(32*((125*a^6)/32 - (15625*a^6*tan(c/2 + (d*x)/2))/4096))))/(64*d) + ((1856*a^3*tan(c/2 + (d*x)/2)^2)/105 + (1861*a^3*tan(c/2 + (d*x)/2)^3)/192 + (568*a^3*tan(c/2 + (d*x)/2)^4)/15 + (1817*a^3*tan(c/2 + (d*x)/2)^5)/192 + (1216*a^3*tan(c/2 + (d*x)/2)^6)/15 + (3805*a^3*tan(c/2 + (d*x)/2)^7)/192 + (232*a^3*tan(c/2 + (d*x)/2)^8)/3 - (3805*a^3*tan(c/2 + (d*x)/2)^9)/192 + (128*a^3*tan(c/2 + (d*x)/2)^10)/3 - (1817*a^3*tan(c/2 + (d*x)/2)^11)/192 + 24*a^3*tan(c/2 + (d*x)/2)^12 - (1861*a^3*tan(c/2 + (d*x)/2)^13)/192 - (259*a^3*tan(c/2 + (d*x)/2)^15)/64 + (232*a^3)/105 + (259*a^3*tan(c/2 + (d*x)/2))/64)/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1))","B"
610,1,429,173,9.377725,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^2,x)","\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{15\,a^3\,\mathrm{atan}\left(\frac{225\,a^6}{64\,\left(\frac{45\,a^6}{4}+\frac{225\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}-\frac{45\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{45\,a^6}{4}+\frac{225\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}\right)}{8\,d}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{\frac{19\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{4}-32\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-144\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\frac{111\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{4}-272\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+35\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-352\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{113\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{4}-\frac{1152\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{464\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}+\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{624\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}+a^3}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+42\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+42\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)))/d + (15*a^3*atan((225*a^6)/(64*((45*a^6)/4 + (225*a^6*tan(c/2 + (d*x)/2))/64)) - (45*a^6*tan(c/2 + (d*x)/2))/(4*((45*a^6)/4 + (225*a^6*tan(c/2 + (d*x)/2))/64))))/(8*d) + (a^3*tan(c/2 + (d*x)/2))/(2*d) - ((13*a^3*tan(c/2 + (d*x)/2)^2)/4 - (464*a^3*tan(c/2 + (d*x)/2)^3)/5 + 28*a^3*tan(c/2 + (d*x)/2)^4 - (1152*a^3*tan(c/2 + (d*x)/2)^5)/5 + (113*a^3*tan(c/2 + (d*x)/2)^6)/4 - 352*a^3*tan(c/2 + (d*x)/2)^7 + 35*a^3*tan(c/2 + (d*x)/2)^8 - 272*a^3*tan(c/2 + (d*x)/2)^9 + (111*a^3*tan(c/2 + (d*x)/2)^10)/4 - 144*a^3*tan(c/2 + (d*x)/2)^11 - 32*a^3*tan(c/2 + (d*x)/2)^13 + (19*a^3*tan(c/2 + (d*x)/2)^14)/4 + a^3 - (624*a^3*tan(c/2 + (d*x)/2))/35)/(d*(2*tan(c/2 + (d*x)/2) + 14*tan(c/2 + (d*x)/2)^3 + 42*tan(c/2 + (d*x)/2)^5 + 70*tan(c/2 + (d*x)/2)^7 + 70*tan(c/2 + (d*x)/2)^9 + 42*tan(c/2 + (d*x)/2)^11 + 14*tan(c/2 + (d*x)/2)^13 + 2*tan(c/2 + (d*x)/2)^15))","B"
611,1,438,181,8.916076,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^3,x)","\frac{\frac{31\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{2}+\frac{95\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{2}+\frac{131\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{6}+109\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-75\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{1043\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{6}-135\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+150\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{887\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{6}+\frac{533\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{10}-\frac{115\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{227\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a^3}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+60\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+60\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}+\frac{85\,a^3\,\mathrm{atan}\left(\frac{7225\,a^6}{64\,\left(\frac{85\,a^6}{8}+\frac{7225\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}-\frac{85\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{85\,a^6}{8}+\frac{7225\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}\right)}{8\,d}+\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"((227*a^3*tan(c/2 + (d*x)/2)^2)/15 - (115*a^3*tan(c/2 + (d*x)/2)^3)/2 + (533*a^3*tan(c/2 + (d*x)/2)^4)/10 - (887*a^3*tan(c/2 + (d*x)/2)^5)/6 + 150*a^3*tan(c/2 + (d*x)/2)^6 - 135*a^3*tan(c/2 + (d*x)/2)^7 + (1043*a^3*tan(c/2 + (d*x)/2)^8)/6 - 75*a^3*tan(c/2 + (d*x)/2)^9 + 109*a^3*tan(c/2 + (d*x)/2)^10 + (131*a^3*tan(c/2 + (d*x)/2)^11)/6 + (95*a^3*tan(c/2 + (d*x)/2)^12)/2 + (31*a^3*tan(c/2 + (d*x)/2)^13)/2 - a^3/2 - 6*a^3*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 24*tan(c/2 + (d*x)/2)^4 + 60*tan(c/2 + (d*x)/2)^6 + 80*tan(c/2 + (d*x)/2)^8 + 60*tan(c/2 + (d*x)/2)^10 + 24*tan(c/2 + (d*x)/2)^12 + 4*tan(c/2 + (d*x)/2)^14)) + (a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^3*log(tan(c/2 + (d*x)/2)))/(2*d) + (85*a^3*atan((7225*a^6)/(64*((85*a^6)/8 + (7225*a^6*tan(c/2 + (d*x)/2))/64)) - (85*a^6*tan(c/2 + (d*x)/2))/(8*((85*a^6)/8 + (7225*a^6*tan(c/2 + (d*x)/2))/64))))/(8*d) + (3*a^3*tan(c/2 + (d*x)/2))/(2*d)","B"
612,1,429,176,8.993923,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^4,x)","\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{13\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{-43\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+99\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-\frac{86\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}+399\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{95\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{1562\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+\frac{232\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{1114\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{193\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{1537\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{15}+\frac{14\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{25\,a^3\,\mathrm{atan}\left(\frac{625\,a^6}{16\,\left(\frac{325\,a^6}{4}-\frac{625\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{325\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{325\,a^6}{4}-\frac{625\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}+\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(3*a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (13*a^3*log(tan(c/2 + (d*x)/2)))/(2*d) - ((14*a^3*tan(c/2 + (d*x)/2)^2)/3 + (1537*a^3*tan(c/2 + (d*x)/2)^3)/15 + (193*a^3*tan(c/2 + (d*x)/2)^4)/3 + (1114*a^3*tan(c/2 + (d*x)/2)^5)/3 + (232*a^3*tan(c/2 + (d*x)/2)^6)/3 + (1562*a^3*tan(c/2 + (d*x)/2)^7)/3 + (95*a^3*tan(c/2 + (d*x)/2)^8)/3 + 399*a^3*tan(c/2 + (d*x)/2)^9 - (86*a^3*tan(c/2 + (d*x)/2)^10)/3 + 99*a^3*tan(c/2 + (d*x)/2)^11 - 43*a^3*tan(c/2 + (d*x)/2)^12 + a^3/3 + 3*a^3*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 40*tan(c/2 + (d*x)/2)^5 + 80*tan(c/2 + (d*x)/2)^7 + 80*tan(c/2 + (d*x)/2)^9 + 40*tan(c/2 + (d*x)/2)^11 + 8*tan(c/2 + (d*x)/2)^13)) - (25*a^3*atan((625*a^6)/(16*((325*a^6)/4 - (625*a^6*tan(c/2 + (d*x)/2))/16)) + (325*a^6*tan(c/2 + (d*x)/2))/(4*((325*a^6)/4 - (625*a^6*tan(c/2 + (d*x)/2))/16))))/(4*d) + (3*a^3*tan(c/2 + (d*x)/2))/(8*d)","B"
613,1,419,178,8.956227,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^5,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{45\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{-34\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+258\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-138\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{2337\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4}-312\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+525\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-184\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{403\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-38\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+96\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{45\,a^3\,\mathrm{atan}\left(\frac{2025\,a^6}{16\,\left(\frac{2025\,a^6}{16}+\frac{2025\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}-\frac{2025\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,\left(\frac{2025\,a^6}{16}+\frac{2025\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}-\frac{23\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^3)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^4)/(64*d) - (45*a^3*log(tan(c/2 + (d*x)/2)))/(8*d) - (3*a^3*tan(c/2 + (d*x)/2)^2 - 38*a^3*tan(c/2 + (d*x)/2)^3 + (403*a^3*tan(c/2 + (d*x)/2)^4)/2 - 184*a^3*tan(c/2 + (d*x)/2)^5 + 525*a^3*tan(c/2 + (d*x)/2)^6 - 312*a^3*tan(c/2 + (d*x)/2)^7 + (2337*a^3*tan(c/2 + (d*x)/2)^8)/4 - 138*a^3*tan(c/2 + (d*x)/2)^9 + 258*a^3*tan(c/2 + (d*x)/2)^10 - 34*a^3*tan(c/2 + (d*x)/2)^11 + a^3/4 + 2*a^3*tan(c/2 + (d*x)/2))/(d*(16*tan(c/2 + (d*x)/2)^4 + 64*tan(c/2 + (d*x)/2)^6 + 96*tan(c/2 + (d*x)/2)^8 + 64*tan(c/2 + (d*x)/2)^10 + 16*tan(c/2 + (d*x)/2)^12)) - (45*a^3*atan((2025*a^6)/(16*((2025*a^6)/16 + (2025*a^6*tan(c/2 + (d*x)/2))/16)) - (2025*a^6*tan(c/2 + (d*x)/2))/(16*((2025*a^6)/16 + (2025*a^6*tan(c/2 + (d*x)/2))/16))))/(4*d) - (23*a^3*tan(c/2 + (d*x)/2))/(8*d)","B"
614,1,408,175,8.924446,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^6,x)","\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{25\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}+\frac{13\,a^3\,\mathrm{atan}\left(\frac{169\,a^6}{\frac{325\,a^6}{4}-169\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{325\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{325\,a^6}{4}-169\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}+\frac{-10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+20\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{769\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{373\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+\frac{1744\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{589\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{6}+\frac{402\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{31\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{34\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{a^3}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+96\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+96\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{43\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}","Not used",1,"(5*a^3*tan(c/2 + (d*x)/2)^3)/(96*d) - (5*a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (3*a^3*tan(c/2 + (d*x)/2)^4)/(64*d) + (a^3*tan(c/2 + (d*x)/2)^5)/(160*d) + (25*a^3*log(tan(c/2 + (d*x)/2)))/(8*d) + (13*a^3*atan((169*a^6)/((325*a^6)/4 - 169*a^6*tan(c/2 + (d*x)/2)) + (325*a^6*tan(c/2 + (d*x)/2))/(4*((325*a^6)/4 - 169*a^6*tan(c/2 + (d*x)/2)))))/d + ((31*a^3*tan(c/2 + (d*x)/2)^3)/2 - (34*a^3*tan(c/2 + (d*x)/2)^2)/15 + (402*a^3*tan(c/2 + (d*x)/2)^4)/5 + (589*a^3*tan(c/2 + (d*x)/2)^5)/6 + (1744*a^3*tan(c/2 + (d*x)/2)^6)/5 + (373*a^3*tan(c/2 + (d*x)/2)^7)/2 + (769*a^3*tan(c/2 + (d*x)/2)^8)/3 + 20*a^3*tan(c/2 + (d*x)/2)^9 - 10*a^3*tan(c/2 + (d*x)/2)^10 - a^3/5 - (3*a^3*tan(c/2 + (d*x)/2))/2)/(d*(32*tan(c/2 + (d*x)/2)^5 + 96*tan(c/2 + (d*x)/2)^7 + 96*tan(c/2 + (d*x)/2)^9 + 32*tan(c/2 + (d*x)/2)^11)) - (43*a^3*tan(c/2 + (d*x)/2))/(16*d)","B"
615,1,396,182,8.940238,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^7,x)","\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}-\frac{17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{81\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{85\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{16\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{a^6}{\frac{85\,a^6}{8}+a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{85\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{85\,a^6}{8}+a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}-\frac{124\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-\frac{849\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+\frac{134\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{927\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{578\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}-\frac{112\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{134\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{15}+\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{6}+\frac{6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{a^3}{6}}{d\,\left(64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}+\frac{15\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}","Not used",1,"(3*a^3*tan(c/2 + (d*x)/2)^4)/(128*d) - (17*a^3*tan(c/2 + (d*x)/2)^3)/(96*d) - (81*a^3*tan(c/2 + (d*x)/2)^2)/(128*d) + (3*a^3*tan(c/2 + (d*x)/2)^5)/(160*d) + (a^3*tan(c/2 + (d*x)/2)^6)/(384*d) + (85*a^3*log(tan(c/2 + (d*x)/2)))/(16*d) + (a^3*atan(a^6/((85*a^6)/8 + a^6*tan(c/2 + (d*x)/2)) - (85*a^6*tan(c/2 + (d*x)/2))/(8*((85*a^6)/8 + a^6*tan(c/2 + (d*x)/2)))))/d - ((11*a^3*tan(c/2 + (d*x)/2)^2)/6 - (134*a^3*tan(c/2 + (d*x)/2)^3)/15 - (112*a^3*tan(c/2 + (d*x)/2)^4)/3 + (578*a^3*tan(c/2 + (d*x)/2)^5)/15 - (927*a^3*tan(c/2 + (d*x)/2)^6)/2 + (134*a^3*tan(c/2 + (d*x)/2)^7)/3 - (849*a^3*tan(c/2 + (d*x)/2)^8)/2 + 124*a^3*tan(c/2 + (d*x)/2)^9 + a^3/6 + (6*a^3*tan(c/2 + (d*x)/2))/5)/(d*(64*tan(c/2 + (d*x)/2)^6 + 128*tan(c/2 + (d*x)/2)^8 + 64*tan(c/2 + (d*x)/2)^10)) + (15*a^3*tan(c/2 + (d*x)/2))/(16*d)","B"
616,1,388,172,9.044037,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^8,x)","\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{25\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}-\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}+\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}+\frac{15\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{16\,d}+\frac{6\,a^3\,\mathrm{atan}\left(\frac{36\,a^6}{\frac{45\,a^6}{4}+36\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{45\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{45\,a^6}{4}+36\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}-\frac{259\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-243\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+234\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{118\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{54\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{7}}{d\,\left(128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}+\frac{259\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}","Not used",1,"(13*a^3*tan(c/2 + (d*x)/2)^2)/(128*d) - (25*a^3*tan(c/2 + (d*x)/2)^3)/(128*d) - (7*a^3*tan(c/2 + (d*x)/2)^4)/(128*d) + (7*a^3*tan(c/2 + (d*x)/2)^5)/(640*d) + (a^3*tan(c/2 + (d*x)/2)^6)/(128*d) + (a^3*tan(c/2 + (d*x)/2)^7)/(896*d) + (15*a^3*log(tan(c/2 + (d*x)/2)))/(16*d) + (6*a^3*atan((36*a^6)/((45*a^6)/4 + 36*a^6*tan(c/2 + (d*x)/2)) - (45*a^6*tan(c/2 + (d*x)/2))/(4*((45*a^6)/4 + 36*a^6*tan(c/2 + (d*x)/2)))))/d - ((54*a^3*tan(c/2 + (d*x)/2)^2)/35 - 6*a^3*tan(c/2 + (d*x)/2)^3 - (118*a^3*tan(c/2 + (d*x)/2)^4)/5 + 6*a^3*tan(c/2 + (d*x)/2)^5 + 234*a^3*tan(c/2 + (d*x)/2)^6 - 243*a^3*tan(c/2 + (d*x)/2)^7 + 259*a^3*tan(c/2 + (d*x)/2)^8 + a^3/7 + a^3*tan(c/2 + (d*x)/2))/(d*(128*tan(c/2 + (d*x)/2)^7 + 128*tan(c/2 + (d*x)/2)^9)) + (259*a^3*tan(c/2 + (d*x)/2))/(128*d)","B"
617,1,389,238,10.301879,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^9,x)","\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}-\frac{23\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{17\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{11\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}+\frac{23\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}-\frac{17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{2\,a^3\,\mathrm{atan}\left(\frac{128\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+125\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{125\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-128\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{125\,a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{128\,d}-\frac{73\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}+\frac{73\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}","Not used",1,"(a^3*cot(c/2 + (d*x)/2)^3)/(384*d) - (23*a^3*cot(c/2 + (d*x)/2)^2)/(64*d) + (17*a^3*cot(c/2 + (d*x)/2)^4)/(256*d) + (11*a^3*cot(c/2 + (d*x)/2)^5)/(640*d) - (a^3*cot(c/2 + (d*x)/2)^6)/(192*d) - (3*a^3*cot(c/2 + (d*x)/2)^7)/(896*d) - (a^3*cot(c/2 + (d*x)/2)^8)/(2048*d) + (23*a^3*tan(c/2 + (d*x)/2)^2)/(64*d) - (a^3*tan(c/2 + (d*x)/2)^3)/(384*d) - (17*a^3*tan(c/2 + (d*x)/2)^4)/(256*d) - (11*a^3*tan(c/2 + (d*x)/2)^5)/(640*d) + (a^3*tan(c/2 + (d*x)/2)^6)/(192*d) + (3*a^3*tan(c/2 + (d*x)/2)^7)/(896*d) + (a^3*tan(c/2 + (d*x)/2)^8)/(2048*d) - (2*a^3*atan((128*cos(c/2 + (d*x)/2) + 125*sin(c/2 + (d*x)/2))/(125*cos(c/2 + (d*x)/2) - 128*sin(c/2 + (d*x)/2))))/d - (125*a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(128*d) - (73*a^3*cot(c/2 + (d*x)/2))/(128*d) + (73*a^3*tan(c/2 + (d*x)/2))/(128*d)","B"
618,1,357,200,9.404218,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^10,x)","\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{29\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}-\frac{9\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}+\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}-\frac{9\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}+\frac{9\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{29\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}+\frac{9\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}-\frac{55\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,d}+\frac{33\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}-\frac{33\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}","Not used",1,"(3*a^3*cot(c/2 + (d*x)/2)^4)/(256*d) - (29*a^3*cot(c/2 + (d*x)/2)^3)/(384*d) - (9*a^3*cot(c/2 + (d*x)/2)^2)/(64*d) + (3*a^3*cot(c/2 + (d*x)/2)^5)/(128*d) + (a^3*cot(c/2 + (d*x)/2)^6)/(192*d) - (9*a^3*cot(c/2 + (d*x)/2)^7)/(3584*d) - (3*a^3*cot(c/2 + (d*x)/2)^8)/(2048*d) - (a^3*cot(c/2 + (d*x)/2)^9)/(4608*d) + (9*a^3*tan(c/2 + (d*x)/2)^2)/(64*d) + (29*a^3*tan(c/2 + (d*x)/2)^3)/(384*d) - (3*a^3*tan(c/2 + (d*x)/2)^4)/(256*d) - (3*a^3*tan(c/2 + (d*x)/2)^5)/(128*d) - (a^3*tan(c/2 + (d*x)/2)^6)/(192*d) + (9*a^3*tan(c/2 + (d*x)/2)^7)/(3584*d) + (3*a^3*tan(c/2 + (d*x)/2)^8)/(2048*d) + (a^3*tan(c/2 + (d*x)/2)^9)/(4608*d) - (55*a^3*log(tan(c/2 + (d*x)/2)))/(128*d) + (33*a^3*cot(c/2 + (d*x)/2))/(256*d) - (33*a^3*tan(c/2 + (d*x)/2))/(256*d)","B"
619,1,395,228,9.646784,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^11,x)","\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}-\frac{5\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}-\frac{7\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{25\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{17\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}+\frac{5\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}-\frac{5\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{1536\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{25\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}+\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}-\frac{17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3584\,d}+\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{1536\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{33\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{256\,d}+\frac{19\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}-\frac{19\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,d}","Not used",1,"(a^3*cot(c/2 + (d*x)/2)^5)/(128*d) - (5*a^3*cot(c/2 + (d*x)/2)^3)/(128*d) - (7*a^3*cot(c/2 + (d*x)/2)^4)/(512*d) - (25*a^3*cot(c/2 + (d*x)/2)^2)/(1024*d) + (17*a^3*cot(c/2 + (d*x)/2)^6)/(2048*d) + (5*a^3*cot(c/2 + (d*x)/2)^7)/(3584*d) - (5*a^3*cot(c/2 + (d*x)/2)^8)/(4096*d) - (a^3*cot(c/2 + (d*x)/2)^9)/(1536*d) - (a^3*cot(c/2 + (d*x)/2)^10)/(10240*d) + (25*a^3*tan(c/2 + (d*x)/2)^2)/(1024*d) + (5*a^3*tan(c/2 + (d*x)/2)^3)/(128*d) + (7*a^3*tan(c/2 + (d*x)/2)^4)/(512*d) - (a^3*tan(c/2 + (d*x)/2)^5)/(128*d) - (17*a^3*tan(c/2 + (d*x)/2)^6)/(2048*d) - (5*a^3*tan(c/2 + (d*x)/2)^7)/(3584*d) + (5*a^3*tan(c/2 + (d*x)/2)^8)/(4096*d) + (a^3*tan(c/2 + (d*x)/2)^9)/(1536*d) + (a^3*tan(c/2 + (d*x)/2)^10)/(10240*d) - (33*a^3*log(tan(c/2 + (d*x)/2)))/(256*d) + (19*a^3*cot(c/2 + (d*x)/2))/(256*d) - (19*a^3*tan(c/2 + (d*x)/2))/(256*d)","B"
620,1,433,246,9.975807,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^12,x)","\frac{25\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{6144\,d}-\frac{53\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3072\,d}-\frac{5\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2048\,d}-\frac{11\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{41\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14336\,d}+\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}-\frac{11\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{18432\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{22528\,d}+\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{53\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3072\,d}+\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2048\,d}-\frac{25\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{6144\,d}-\frac{41\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14336\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4096\,d}+\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{18432\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{22528\,d}-\frac{19\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{256\,d}+\frac{41\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1024\,d}-\frac{41\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1024\,d}","Not used",1,"(25*a^3*cot(c/2 + (d*x)/2)^6)/(6144*d) - (53*a^3*cot(c/2 + (d*x)/2)^3)/(3072*d) - (5*a^3*cot(c/2 + (d*x)/2)^4)/(512*d) - (a^3*cot(c/2 + (d*x)/2)^5)/(2048*d) - (11*a^3*cot(c/2 + (d*x)/2)^2)/(1024*d) + (41*a^3*cot(c/2 + (d*x)/2)^7)/(14336*d) + (a^3*cot(c/2 + (d*x)/2)^8)/(4096*d) - (11*a^3*cot(c/2 + (d*x)/2)^9)/(18432*d) - (3*a^3*cot(c/2 + (d*x)/2)^10)/(10240*d) - (a^3*cot(c/2 + (d*x)/2)^11)/(22528*d) + (11*a^3*tan(c/2 + (d*x)/2)^2)/(1024*d) + (53*a^3*tan(c/2 + (d*x)/2)^3)/(3072*d) + (5*a^3*tan(c/2 + (d*x)/2)^4)/(512*d) + (a^3*tan(c/2 + (d*x)/2)^5)/(2048*d) - (25*a^3*tan(c/2 + (d*x)/2)^6)/(6144*d) - (41*a^3*tan(c/2 + (d*x)/2)^7)/(14336*d) - (a^3*tan(c/2 + (d*x)/2)^8)/(4096*d) + (11*a^3*tan(c/2 + (d*x)/2)^9)/(18432*d) + (3*a^3*tan(c/2 + (d*x)/2)^10)/(10240*d) + (a^3*tan(c/2 + (d*x)/2)^11)/(22528*d) - (19*a^3*log(tan(c/2 + (d*x)/2)))/(256*d) + (41*a^3*cot(c/2 + (d*x)/2))/(1024*d) - (41*a^3*tan(c/2 + (d*x)/2))/(1024*d)","B"
621,1,471,270,10.395288,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^13,x)","\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{31\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3072\,d}-\frac{111\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16384\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2048\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{27\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14336\,d}+\frac{15\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16384\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{18432\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{3\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{22528\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{49152\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{31\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3072\,d}+\frac{111\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16384\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2048\,d}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{27\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14336\,d}-\frac{15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16384\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{18432\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{22528\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{49152\,d}-\frac{41\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{1024\,d}+\frac{27\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1024\,d}-\frac{27\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1024\,d}","Not used",1,"(3*a^3*cot(c/2 + (d*x)/2)^6)/(2048*d) - (31*a^3*cot(c/2 + (d*x)/2)^3)/(3072*d) - (111*a^3*cot(c/2 + (d*x)/2)^4)/(16384*d) - (3*a^3*cot(c/2 + (d*x)/2)^5)/(2048*d) - (3*a^3*cot(c/2 + (d*x)/2)^2)/(1024*d) + (27*a^3*cot(c/2 + (d*x)/2)^7)/(14336*d) + (15*a^3*cot(c/2 + (d*x)/2)^8)/(16384*d) - (a^3*cot(c/2 + (d*x)/2)^9)/(18432*d) - (3*a^3*cot(c/2 + (d*x)/2)^10)/(10240*d) - (3*a^3*cot(c/2 + (d*x)/2)^11)/(22528*d) - (a^3*cot(c/2 + (d*x)/2)^12)/(49152*d) + (3*a^3*tan(c/2 + (d*x)/2)^2)/(1024*d) + (31*a^3*tan(c/2 + (d*x)/2)^3)/(3072*d) + (111*a^3*tan(c/2 + (d*x)/2)^4)/(16384*d) + (3*a^3*tan(c/2 + (d*x)/2)^5)/(2048*d) - (3*a^3*tan(c/2 + (d*x)/2)^6)/(2048*d) - (27*a^3*tan(c/2 + (d*x)/2)^7)/(14336*d) - (15*a^3*tan(c/2 + (d*x)/2)^8)/(16384*d) + (a^3*tan(c/2 + (d*x)/2)^9)/(18432*d) + (3*a^3*tan(c/2 + (d*x)/2)^10)/(10240*d) + (3*a^3*tan(c/2 + (d*x)/2)^11)/(22528*d) + (a^3*tan(c/2 + (d*x)/2)^12)/(49152*d) - (41*a^3*log(tan(c/2 + (d*x)/2)))/(1024*d) + (27*a^3*cot(c/2 + (d*x)/2))/(1024*d) - (27*a^3*tan(c/2 + (d*x)/2))/(1024*d)","B"
622,1,509,286,10.900146,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^3)/sin(c + d*x)^14,x)","\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{45\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8192\,d}-\frac{77\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16384\,d}-\frac{15\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8192\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{33\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{28672\,d}+\frac{13\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16384\,d}+\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4096\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{13\,a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{90112\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{16384\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{106496\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{1024\,d}+\frac{45\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8192\,d}+\frac{77\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16384\,d}+\frac{15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8192\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2048\,d}-\frac{33\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{28672\,d}-\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16384\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4096\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}+\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{90112\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{16384\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{106496\,d}-\frac{27\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{1024\,d}+\frac{35\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2048\,d}-\frac{35\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2048\,d}","Not used",1,"(a^3*cot(c/2 + (d*x)/2)^6)/(2048*d) - (45*a^3*cot(c/2 + (d*x)/2)^3)/(8192*d) - (77*a^3*cot(c/2 + (d*x)/2)^4)/(16384*d) - (15*a^3*cot(c/2 + (d*x)/2)^5)/(8192*d) - (a^3*cot(c/2 + (d*x)/2)^2)/(1024*d) + (33*a^3*cot(c/2 + (d*x)/2)^7)/(28672*d) + (13*a^3*cot(c/2 + (d*x)/2)^8)/(16384*d) + (a^3*cot(c/2 + (d*x)/2)^9)/(4096*d) - (a^3*cot(c/2 + (d*x)/2)^10)/(10240*d) - (13*a^3*cot(c/2 + (d*x)/2)^11)/(90112*d) - (a^3*cot(c/2 + (d*x)/2)^12)/(16384*d) - (a^3*cot(c/2 + (d*x)/2)^13)/(106496*d) + (a^3*tan(c/2 + (d*x)/2)^2)/(1024*d) + (45*a^3*tan(c/2 + (d*x)/2)^3)/(8192*d) + (77*a^3*tan(c/2 + (d*x)/2)^4)/(16384*d) + (15*a^3*tan(c/2 + (d*x)/2)^5)/(8192*d) - (a^3*tan(c/2 + (d*x)/2)^6)/(2048*d) - (33*a^3*tan(c/2 + (d*x)/2)^7)/(28672*d) - (13*a^3*tan(c/2 + (d*x)/2)^8)/(16384*d) - (a^3*tan(c/2 + (d*x)/2)^9)/(4096*d) + (a^3*tan(c/2 + (d*x)/2)^10)/(10240*d) + (13*a^3*tan(c/2 + (d*x)/2)^11)/(90112*d) + (a^3*tan(c/2 + (d*x)/2)^12)/(16384*d) + (a^3*tan(c/2 + (d*x)/2)^13)/(106496*d) - (27*a^3*log(tan(c/2 + (d*x)/2)))/(1024*d) + (35*a^3*cot(c/2 + (d*x)/2))/(2048*d) - (35*a^3*tan(c/2 + (d*x)/2))/(2048*d)","B"
623,1,474,178,8.979041,"\text{Not used}","int((cos(c + d*x)^6*(a + a*sin(c + d*x))^4)/sin(c + d*x)^4,x)","\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d}+\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{6\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{135\,a^4\,\mathrm{atan}\left(\frac{18225\,a^8}{64\,\left(\frac{405\,a^8}{2}-\frac{18225\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}+\frac{405\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{405\,a^8}{2}-\frac{18225\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}\right)}\right)}{8\,d}-\frac{-74\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-\frac{346\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}+280\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+153\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+572\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+379\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+592\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{1312\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{1836\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+184\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{376\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}+17\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^4}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+160\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{15\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(a^4*tan(c/2 + (d*x)/2)^2)/(2*d) + (a^4*tan(c/2 + (d*x)/2)^3)/(24*d) - (6*a^4*log(tan(c/2 + (d*x)/2)))/d - (135*a^4*atan((18225*a^8)/(64*((405*a^8)/2 - (18225*a^8*tan(c/2 + (d*x)/2))/64)) + (405*a^8*tan(c/2 + (d*x)/2))/(2*((405*a^8)/2 - (18225*a^8*tan(c/2 + (d*x)/2))/64))))/(8*d) - (17*a^4*tan(c/2 + (d*x)/2)^2 + (376*a^4*tan(c/2 + (d*x)/2)^3)/5 + 184*a^4*tan(c/2 + (d*x)/2)^4 + (1836*a^4*tan(c/2 + (d*x)/2)^5)/5 + (1312*a^4*tan(c/2 + (d*x)/2)^6)/3 + 592*a^4*tan(c/2 + (d*x)/2)^7 + 379*a^4*tan(c/2 + (d*x)/2)^8 + 572*a^4*tan(c/2 + (d*x)/2)^9 + 153*a^4*tan(c/2 + (d*x)/2)^10 + 280*a^4*tan(c/2 + (d*x)/2)^11 - (346*a^4*tan(c/2 + (d*x)/2)^12)/3 + 4*a^4*tan(c/2 + (d*x)/2)^13 - 74*a^4*tan(c/2 + (d*x)/2)^14 + a^4/3 + 4*a^4*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 48*tan(c/2 + (d*x)/2)^5 + 120*tan(c/2 + (d*x)/2)^7 + 160*tan(c/2 + (d*x)/2)^9 + 120*tan(c/2 + (d*x)/2)^11 + 48*tan(c/2 + (d*x)/2)^13 + 8*tan(c/2 + (d*x)/2)^15)) + (15*a^4*tan(c/2 + (d*x)/2))/(8*d)","B"
624,1,211,159,11.406775,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^4)/(a + a*sin(c + d*x)),x)","\frac{3\,x}{128\,a}+\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}-\frac{155\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}+\frac{169\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}-16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{112\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{5}-\frac{169\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}-\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{155\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}-\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{16}{315}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(3*x)/(128*a) + ((16*tan(c/2 + (d*x)/2)^2)/35 - (3*tan(c/2 + (d*x)/2))/64 - (13*tan(c/2 + (d*x)/2)^3)/32 + (64*tan(c/2 + (d*x)/2)^4)/35 + (155*tan(c/2 + (d*x)/2)^5)/32 - (32*tan(c/2 + (d*x)/2)^6)/5 - (169*tan(c/2 + (d*x)/2)^7)/32 + (112*tan(c/2 + (d*x)/2)^8)/5 - 16*tan(c/2 + (d*x)/2)^10 + (169*tan(c/2 + (d*x)/2)^11)/32 + (32*tan(c/2 + (d*x)/2)^12)/3 - (155*tan(c/2 + (d*x)/2)^13)/32 + (13*tan(c/2 + (d*x)/2)^15)/32 + (3*tan(c/2 + (d*x)/2)^17)/64 + 16/315)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
625,1,199,141,11.619465,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^3)/(a + a*sin(c + d*x)),x)","-\frac{3\,x}{128\,a}-\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{333\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{671\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{671\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{64}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{333\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{4}{35}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"- (3*x)/(128*a) - ((32*tan(c/2 + (d*x)/2)^2)/35 - (3*tan(c/2 + (d*x)/2))/64 - (23*tan(c/2 + (d*x)/2)^3)/64 - (4*tan(c/2 + (d*x)/2)^4)/5 + (333*tan(c/2 + (d*x)/2)^5)/64 + (32*tan(c/2 + (d*x)/2)^6)/5 - (671*tan(c/2 + (d*x)/2)^7)/64 + 4*tan(c/2 + (d*x)/2)^8 + (671*tan(c/2 + (d*x)/2)^9)/64 - (333*tan(c/2 + (d*x)/2)^11)/64 + 4*tan(c/2 + (d*x)/2)^12 + (23*tan(c/2 + (d*x)/2)^13)/64 + (3*tan(c/2 + (d*x)/2)^15)/64 + 4/35)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
626,1,172,115,12.749350,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^2)/(a + a*sin(c + d*x)),x)","\frac{x}{16\,a}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{6}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{31\,{\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+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{31\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{24}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{4}{35}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"x/(16*a) + ((4*tan(c/2 + (d*x)/2)^2)/5 - tan(c/2 + (d*x)/2)/8 + (11*tan(c/2 + (d*x)/2)^3)/6 - (8*tan(c/2 + (d*x)/2)^4)/5 - (31*tan(c/2 + (d*x)/2)^5)/24 + 8*tan(c/2 + (d*x)/2)^6 - 4*tan(c/2 + (d*x)/2)^8 + (31*tan(c/2 + (d*x)/2)^9)/24 + 4*tan(c/2 + (d*x)/2)^10 - (11*tan(c/2 + (d*x)/2)^11)/6 + tan(c/2 + (d*x)/2)^13/8 + 4/35)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
627,1,173,97,12.485971,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x))/(a + a*sin(c + d*x)),x)","-\frac{x}{16\,a}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{47\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{47\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{2}{5}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"- x/(16*a) - ((2*tan(c/2 + (d*x)/2)^2)/5 - tan(c/2 + (d*x)/2)/8 + (47*tan(c/2 + (d*x)/2)^3)/24 + 4*tan(c/2 + (d*x)/2)^4 - (13*tan(c/2 + (d*x)/2)^5)/4 + 4*tan(c/2 + (d*x)/2)^6 + (13*tan(c/2 + (d*x)/2)^7)/4 + 2*tan(c/2 + (d*x)/2)^8 - (47*tan(c/2 + (d*x)/2)^9)/24 + 2*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^11/8 + 2/5)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
628,1,225,101,10.434475,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{3\,\mathrm{atan}\left(\frac{9}{16\,\left(\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{3}{2}\right)}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{3}{2}\right)}\right)}{4\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{3\,{\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{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{8}{3}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(3*atan(9/(16*((9*tan(c/2 + (d*x)/2))/16 + 3/2)) - (3*tan(c/2 + (d*x)/2))/(2*((9*tan(c/2 + (d*x)/2))/16 + 3/2))))/(4*a*d) + log(tan(c/2 + (d*x)/2))/(a*d) + ((20*tan(c/2 + (d*x)/2)^2)/3 - (5*tan(c/2 + (d*x)/2))/4 + (3*tan(c/2 + (d*x)/2)^3)/4 + 8*tan(c/2 + (d*x)/2)^4 - (3*tan(c/2 + (d*x)/2)^5)/4 + 4*tan(c/2 + (d*x)/2)^6 + (5*tan(c/2 + (d*x)/2)^7)/4 + 8/3)/(d*(a + 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 + 4*a*tan(c/2 + (d*x)/2)^6 + a*tan(c/2 + (d*x)/2)^8))","B"
629,1,229,95,9.026477,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{3\,\mathrm{atan}\left(\frac{6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6}+\frac{9}{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6}\right)}{a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+1}{d\,\left(2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,a\,{\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)\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}","Not used",1,"(3*atan((6*tan(c/2 + (d*x)/2))/(9*tan(c/2 + (d*x)/2) - 6) + 9/(9*tan(c/2 + (d*x)/2) - 6)))/(a*d) - log(tan(c/2 + (d*x)/2))/(a*d) - ((16*tan(c/2 + (d*x)/2))/3 + 5*tan(c/2 + (d*x)/2)^2 + 8*tan(c/2 + (d*x)/2)^3 + 3*tan(c/2 + (d*x)/2)^4 + 8*tan(c/2 + (d*x)/2)^5 - tan(c/2 + (d*x)/2)^6 + 1)/(d*(2*a*tan(c/2 + (d*x)/2) + 6*a*tan(c/2 + (d*x)/2)^3 + 6*a*tan(c/2 + (d*x)/2)^5 + 2*a*tan(c/2 + (d*x)/2)^7)) + tan(c/2 + (d*x)/2)/(2*a*d)","B"
630,1,223,106,8.976438,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{3\,\mathrm{atan}\left(\frac{9}{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+9}-\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+9}\right)}{a\,d}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{2}}{d\,\left(4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - (3*atan(9/(9*tan(c/2 + (d*x)/2) + 9) - (9*tan(c/2 + (d*x)/2))/(9*tan(c/2 + (d*x)/2) + 9)))/(a*d) - (3*log(tan(c/2 + (d*x)/2)))/(2*a*d) - (9*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) - 8*tan(c/2 + (d*x)/2)^3 + (17*tan(c/2 + (d*x)/2)^4)/2 + 2*tan(c/2 + (d*x)/2)^5 + 1/2)/(d*(4*a*tan(c/2 + (d*x)/2)^2 + 8*a*tan(c/2 + (d*x)/2)^4 + 4*a*tan(c/2 + (d*x)/2)^6)) - tan(c/2 + (d*x)/2)/(2*a*d)","B"
631,1,212,94,8.972518,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{2\,\mathrm{atan}\left(\frac{6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6}+\frac{4}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6}\right)}{a\,d}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{3}}{d\,\left(8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) - (2*atan((6*tan(c/2 + (d*x)/2))/(4*tan(c/2 + (d*x)/2) - 6) + 4/(4*tan(c/2 + (d*x)/2) - 6)))/(a*d) + (3*log(tan(c/2 + (d*x)/2)))/(2*a*d) + (tan(c/2 + (d*x)/2) + (14*tan(c/2 + (d*x)/2)^2)/3 + 17*tan(c/2 + (d*x)/2)^3 + 5*tan(c/2 + (d*x)/2)^4 - 1/3)/(d*(8*a*tan(c/2 + (d*x)/2)^3 + 8*a*tan(c/2 + (d*x)/2)^5)) - (5*tan(c/2 + (d*x)/2))/(8*a*d)","B"
632,1,317,102,9.419121,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+384\,\mathrm{atan}\left(\frac{8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+72\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{192\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}","Not used",1,"(3*sin(c/2 + (d*x)/2)^8 - 3*cos(c/2 + (d*x)/2)^8 - 8*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^7 + 8*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2) - 24*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^6 + 120*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^5 - 120*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^3 + 24*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2 + 384*atan((8*cos(c/2 + (d*x)/2) - 3*sin(c/2 + (d*x)/2))/(3*cos(c/2 + (d*x)/2) + 8*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4 + 72*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4)/(192*a*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4)","B"
633,1,183,82,9.043665,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^6*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{1}{5}\right)}{32\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - tan(c/2 + (d*x)/2)^3/(32*a*d) - tan(c/2 + (d*x)/2)^4/(64*a*d) + tan(c/2 + (d*x)/2)^5/(160*a*d) - (3*log(tan(c/2 + (d*x)/2)))/(8*a*d) + tan(c/2 + (d*x)/2)/(16*a*d) - (cot(c/2 + (d*x)/2)^5*(4*tan(c/2 + (d*x)/2)^3 - tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)/2 + 2*tan(c/2 + (d*x)/2)^4 + 1/5))/(32*a*d)","B"
634,1,173,135,12.660545,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^3)/(a + a*sin(c + d*x))^2,x)","-\frac{x}{8\,a^2}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{97\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}+\frac{52\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{97\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{44\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{44}{105}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"- x/(8*a^2) - ((44*tan(c/2 + (d*x)/2)^2)/15 - tan(c/2 + (d*x)/2)/4 - (5*tan(c/2 + (d*x)/2)^3)/3 + (24*tan(c/2 + (d*x)/2)^4)/5 + (97*tan(c/2 + (d*x)/2)^5)/12 - (8*tan(c/2 + (d*x)/2)^6)/3 + (52*tan(c/2 + (d*x)/2)^8)/3 - (97*tan(c/2 + (d*x)/2)^9)/12 + 4*tan(c/2 + (d*x)/2)^10 + (5*tan(c/2 + (d*x)/2)^11)/3 + tan(c/2 + (d*x)/2)^13/4 + 44/105)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
635,1,146,104,11.703377,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^2)/(a + a*sin(c + d*x))^2,x)","\frac{3\,x}{16\,a^2}+\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}-\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{8}{15}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(3*x)/(16*a^2) + ((16*tan(c/2 + (d*x)/2)^2)/5 - (3*tan(c/2 + (d*x)/2))/8 + (13*tan(c/2 + (d*x)/2)^3)/24 + (25*tan(c/2 + (d*x)/2)^5)/4 + (16*tan(c/2 + (d*x)/2)^6)/3 - (25*tan(c/2 + (d*x)/2)^7)/4 + 8*tan(c/2 + (d*x)/2)^8 - (13*tan(c/2 + (d*x)/2)^9)/24 + (3*tan(c/2 + (d*x)/2)^11)/8 + 8/15)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
636,1,81,100,8.998627,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x))/(a + a*sin(c + d*x))^2,x)","\frac{{\cos\left(c+d\,x\right)}^5}{5\,a^2\,d}-\frac{2\,{\cos\left(c+d\,x\right)}^3}{3\,a^2\,d}-\frac{x}{4\,a^2}+\frac{{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{2\,a^2\,d}-\frac{\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{4\,a^2\,d}","Not used",1,"cos(c + d*x)^5/(5*a^2*d) - (2*cos(c + d*x)^3)/(3*a^2*d) - x/(4*a^2) + (cos(c + d*x)^3*sin(c + d*x))/(2*a^2*d) - (cos(c + d*x)*sin(c + d*x))/(4*a^2*d)","B"
637,1,167,73,9.468720,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{2\,\mathrm{atan}\left(\frac{4}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4}\right)}{a^2\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{4}{3}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}","Not used",1,"(2*atan(4/(4*tan(c/2 + (d*x)/2) + 4) - (4*tan(c/2 + (d*x)/2))/(4*tan(c/2 + (d*x)/2) + 4)))/(a^2*d) + log(tan(c/2 + (d*x)/2))/(a^2*d) + (4*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) + 2*tan(c/2 + (d*x)/2)^5 + 4/3)/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2))","B"
638,1,175,74,9.063469,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1}{d\,\left(2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{\mathrm{atan}\left(\frac{1}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4}\right)}{a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^2*d) - (8*tan(c/2 + (d*x)/2) + 8*tan(c/2 + (d*x)/2)^3 + 3*tan(c/2 + (d*x)/2)^4 + 1)/(d*(4*a^2*tan(c/2 + (d*x)/2)^3 + 2*a^2*tan(c/2 + (d*x)/2)^5 + 2*a^2*tan(c/2 + (d*x)/2))) - (2*log(tan(c/2 + (d*x)/2)))/(a^2*d) + atan(1/(tan(c/2 + (d*x)/2) - 4) + (4*tan(c/2 + (d*x)/2))/(tan(c/2 + (d*x)/2) - 4))/(a^2*d)","B"
639,1,186,73,9.104341,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{4\,\mathrm{atan}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4}+\frac{16}{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4}\right)}{a^2\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^2\,d}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}}{d\,\left(4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) - (4*atan((4*tan(c/2 + (d*x)/2))/(16*tan(c/2 + (d*x)/2) - 4) + 16/(16*tan(c/2 + (d*x)/2) - 4)))/(a^2*d) + log(tan(c/2 + (d*x)/2))/(2*a^2*d) + (4*tan(c/2 + (d*x)/2) + (15*tan(c/2 + (d*x)/2)^2)/2 + 4*tan(c/2 + (d*x)/2)^3 - 1/2)/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 + 4*a^2*tan(c/2 + (d*x)/2)^4)) - tan(c/2 + (d*x)/2)/(a^2*d)","B"
640,1,261,73,9.296736,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+9\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-9\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+48\,\mathrm{atan}\left(\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+24\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"(sin(c/2 + (d*x)/2)^6 - cos(c/2 + (d*x)/2)^6 - 6*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^5 + 6*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2) + 9*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 9*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 48*atan((cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^3 + 24*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^3)/(24*a^2*d*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^3)","B"
641,1,151,82,9.027359,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^5*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}-\frac{5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^2\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{1}{4}\right)}{16\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) - tan(c/2 + (d*x)/2)^3/(12*a^2*d) + tan(c/2 + (d*x)/2)^4/(64*a^2*d) - (5*log(tan(c/2 + (d*x)/2)))/(8*a^2*d) + tan(c/2 + (d*x)/2)/(4*a^2*d) - (cot(c/2 + (d*x)/2)^4*(2*tan(c/2 + (d*x)/2)^2 - (4*tan(c/2 + (d*x)/2))/3 + 4*tan(c/2 + (d*x)/2)^3 + 1/4))/(16*a^2*d)","B"
642,1,149,100,9.023562,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^6*(a + a*sin(c + d*x))^2),x)","\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^2\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a^2\,d}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a^2\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{5}\right)}{32\,a^2\,d}","Not used",1,"(5*tan(c/2 + (d*x)/2)^3)/(96*a^2*d) - tan(c/2 + (d*x)/2)^4/(32*a^2*d) + tan(c/2 + (d*x)/2)^5/(160*a^2*d) + log(tan(c/2 + (d*x)/2))/(4*a^2*d) - (3*tan(c/2 + (d*x)/2))/(16*a^2*d) + (cot(c/2 + (d*x)/2)^5*(tan(c/2 + (d*x)/2) - (5*tan(c/2 + (d*x)/2)^2)/3 + 6*tan(c/2 + (d*x)/2)^4 - 1/5))/(32*a^2*d)","B"
643,1,339,124,10.110079,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^7*(a + a*sin(c + d*x))^2),x)","-\frac{5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+24\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+360\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1920\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"-(5*cos(c/2 + (d*x)/2)^12 - 5*sin(c/2 + (d*x)/2)^12 + 24*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 - 24*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 45*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 40*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 15*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 240*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 240*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 15*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 40*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 45*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 360*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/(1920*a^2*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
644,1,160,129,11.555896,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^3)/(a + a*sin(c + d*x))^3,x)","-\frac{23\,x}{16\,a^3}-\frac{\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{391\,{\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{75\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{136\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}-\frac{75\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{391\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{136\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{23\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{68}{15}}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"- (23*x)/(16*a^3) - ((136*tan(c/2 + (d*x)/2)^2)/5 - (23*tan(c/2 + (d*x)/2))/8 - (391*tan(c/2 + (d*x)/2)^3)/24 + 64*tan(c/2 + (d*x)/2)^4 - (75*tan(c/2 + (d*x)/2)^5)/4 + (136*tan(c/2 + (d*x)/2)^6)/3 + (75*tan(c/2 + (d*x)/2)^7)/4 + 4*tan(c/2 + (d*x)/2)^8 + (391*tan(c/2 + (d*x)/2)^9)/24 + (23*tan(c/2 + (d*x)/2)^11)/8 + 68/15)/(a^3*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
645,1,95,105,9.034425,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^2)/(a + a*sin(c + d*x))^3,x)","\frac{13\,x}{8\,a^3}+\frac{4\,\cos\left(c+d\,x\right)}{a^3\,d}-\frac{5\,{\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{19\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,a^3\,d}","Not used",1,"(13*x)/(8*a^3) + (4*cos(c + d*x))/(a^3*d) - (5*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) - (19*cos(c + d*x)*sin(c + d*x))/(8*a^3*d)","B"
646,1,78,84,9.004036,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x))/(a + a*sin(c + d*x))^3,x)","\frac{{\cos\left(c+d\,x\right)}^3}{a^3\,d}-\frac{4\,\cos\left(c+d\,x\right)}{a^3\,d}-\frac{15\,x}{8\,a^3}-\frac{{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,a^3\,d}+\frac{17\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,a^3\,d}","Not used",1,"cos(c + d*x)^3/(a^3*d) - (4*cos(c + d*x))/(a^3*d) - (15*x)/(8*a^3) - (cos(c + d*x)^3*sin(c + d*x))/(4*a^3*d) + (17*cos(c + d*x)*sin(c + d*x))/(8*a^3*d)","B"
647,1,150,60,9.436534,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{7\,\mathrm{atan}\left(\frac{49}{49\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+14}-\frac{14\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{49\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+14}\right)}{a^3\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}","Not used",1,"(7*atan(49/(49*tan(c/2 + (d*x)/2) + 14) - (14*tan(c/2 + (d*x)/2))/(49*tan(c/2 + (d*x)/2) + 14)))/(a^3*d) + log(tan(c/2 + (d*x)/2))/(a^3*d) - (6*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^3 + 6)/(d*(2*a^3*tan(c/2 + (d*x)/2)^2 + a^3*tan(c/2 + (d*x)/2)^4 + a^3))","B"
648,1,151,49,9.478683,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{6\,\mathrm{atan}\left(\frac{36}{36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+36}-\frac{36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+36}\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - (3*log(tan(c/2 + (d*x)/2)))/(a^3*d) - (6*atan(36/(36*tan(c/2 + (d*x)/2) + 36) - (36*tan(c/2 + (d*x)/2))/(36*tan(c/2 + (d*x)/2) + 36)))/(a^3*d) - (tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) + 1)/(d*(2*a^3*tan(c/2 + (d*x)/2)^3 + 2*a^3*tan(c/2 + (d*x)/2)))","B"
649,1,161,60,9.347145,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^3*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{2\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^3\,d}+\frac{7\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,a^3\,d}+\frac{3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^3*d) - cot(c/2 + (d*x)/2)^2/(8*a^3*d) + (2*atan((2*cos(c/2 + (d*x)/2) - 7*sin(c/2 + (d*x)/2))/(7*cos(c/2 + (d*x)/2) + 2*sin(c/2 + (d*x)/2))))/(a^3*d) + (7*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(2*a^3*d) + (3*cot(c/2 + (d*x)/2))/(2*a^3*d) - (3*tan(c/2 + (d*x)/2))/(2*a^3*d)","B"
650,1,119,72,9.246163,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^3\,d}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^3\,d}+\frac{15\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{3}\right)}{8\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^3*d) - (3*tan(c/2 + (d*x)/2)^2)/(8*a^3*d) - (5*log(tan(c/2 + (d*x)/2)))/(2*a^3*d) + (15*tan(c/2 + (d*x)/2))/(8*a^3*d) - (cot(c/2 + (d*x)/2)^3*(15*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2) + 1/3))/(8*a^3*d)","B"
651,1,151,93,9.289818,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^5*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^3\,d}+\frac{15\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a^3\,d}-\frac{13\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(26\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{4}\right)}{16\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(2*a^3*d) - tan(c/2 + (d*x)/2)^3/(8*a^3*d) + tan(c/2 + (d*x)/2)^4/(64*a^3*d) + (15*log(tan(c/2 + (d*x)/2)))/(8*a^3*d) - (13*tan(c/2 + (d*x)/2))/(8*a^3*d) + (cot(c/2 + (d*x)/2)^4*(2*tan(c/2 + (d*x)/2) - 8*tan(c/2 + (d*x)/2)^2 + 26*tan(c/2 + (d*x)/2)^3 - 1/4))/(16*a^3*d)","B"
652,1,291,114,9.846771,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^6*(a + a*sin(c + d*x))^3),x)","-\frac{6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+45\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-170\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+480\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-1380\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+1380\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-480\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+170\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1560\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{960\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(6*cos(c/2 + (d*x)/2)^10 - 6*sin(c/2 + (d*x)/2)^10 + 45*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 - 45*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - 170*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 + 480*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7 - 1380*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + 1380*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 - 480*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3 + 170*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 1560*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/(960*a^3*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)","B"
653,0,-1,267,0.000000,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^n*(a + a*sin(c + d*x))^3,x)","\int {\cos\left(c+d\,x\right)}^6\,{\sin\left(c+d\,x\right)}^n\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int(cos(c + d*x)^6*sin(c + d*x)^n*(a + a*sin(c + d*x))^3, x)","F"
654,0,-1,200,0.000000,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^n*(a + a*sin(c + d*x))^2,x)","\int {\cos\left(c+d\,x\right)}^6\,{\sin\left(c+d\,x\right)}^n\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int(cos(c + d*x)^6*sin(c + d*x)^n*(a + a*sin(c + d*x))^2, x)","F"
655,0,-1,129,0.000000,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^n*(a + a*sin(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^6\,{\sin\left(c+d\,x\right)}^n\,\left(a+a\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^6*sin(c + d*x)^n*(a + a*sin(c + d*x)), x)","F"
656,1,93,129,0.095379,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)^6*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^{14}}{14}-\frac{a\,{\sin\left(c+d\,x\right)}^{13}}{13}+\frac{a\,{\sin\left(c+d\,x\right)}^{12}}{4}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^{11}}{11}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^{10}}{10}-\frac{a\,{\sin\left(c+d\,x\right)}^9}{3}+\frac{a\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{a\,{\sin\left(c+d\,x\right)}^7}{7}}{d}","Not used",1,"((a*sin(c + d*x)^7)/7 + (a*sin(c + d*x)^8)/8 - (a*sin(c + d*x)^9)/3 - (3*a*sin(c + d*x)^10)/10 + (3*a*sin(c + d*x)^11)/11 + (a*sin(c + d*x)^12)/4 - (a*sin(c + d*x)^13)/13 - (a*sin(c + d*x)^14)/14)/d","B"
657,1,93,113,8.818373,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)^5*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^{13}}{13}-\frac{a\,{\sin\left(c+d\,x\right)}^{12}}{12}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^{11}}{11}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^{10}}{10}-\frac{a\,{\sin\left(c+d\,x\right)}^9}{3}-\frac{3\,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}{6}}{d}","Not used",1,"((a*sin(c + d*x)^6)/6 + (a*sin(c + d*x)^7)/7 - (3*a*sin(c + d*x)^8)/8 - (a*sin(c + d*x)^9)/3 + (3*a*sin(c + d*x)^10)/10 + (3*a*sin(c + d*x)^11)/11 - (a*sin(c + d*x)^12)/12 - (a*sin(c + d*x)^13)/13)/d","B"
658,1,93,113,0.076087,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)^4*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^{12}}{12}-\frac{a\,{\sin\left(c+d\,x\right)}^{11}}{11}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^{10}}{10}+\frac{a\,{\sin\left(c+d\,x\right)}^9}{3}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^8}{8}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{5}}{d}","Not used",1,"((a*sin(c + d*x)^5)/5 + (a*sin(c + d*x)^6)/6 - (3*a*sin(c + d*x)^7)/7 - (3*a*sin(c + d*x)^8)/8 + (a*sin(c + d*x)^9)/3 + (3*a*sin(c + d*x)^10)/10 - (a*sin(c + d*x)^11)/11 - (a*sin(c + d*x)^12)/12)/d","B"
659,1,93,97,0.075735,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^{11}}{11}-\frac{a\,{\sin\left(c+d\,x\right)}^{10}}{10}+\frac{a\,{\sin\left(c+d\,x\right)}^9}{3}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^8}{8}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{2}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{4}}{d}","Not used",1,"((a*sin(c + d*x)^4)/4 + (a*sin(c + d*x)^5)/5 - (a*sin(c + d*x)^6)/2 - (3*a*sin(c + d*x)^7)/7 + (3*a*sin(c + d*x)^8)/8 + (a*sin(c + d*x)^9)/3 - (a*sin(c + d*x)^10)/10 - (a*sin(c + d*x)^11)/11)/d","B"
660,1,93,97,8.954289,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)^2*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^{10}}{10}-\frac{a\,{\sin\left(c+d\,x\right)}^9}{9}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{3\,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{a\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"((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 + (3*a*sin(c + d*x)^7)/7 + (3*a*sin(c + d*x)^8)/8 - (a*sin(c + d*x)^9)/9 - (a*sin(c + d*x)^10)/10)/d","B"
661,1,93,81,9.024130,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^9}{9}-\frac{a\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{3\,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}+\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"((a*sin(c + d*x)^2)/2 + (a*sin(c + d*x)^3)/3 - (3*a*sin(c + d*x)^4)/4 - (3*a*sin(c + d*x)^5)/5 + (a*sin(c + d*x)^6)/2 + (3*a*sin(c + d*x)^7)/7 - (a*sin(c + d*x)^8)/8 - (a*sin(c + d*x)^9)/9)/d","B"
662,1,160,118,9.163625,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x),x)","\frac{a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a\,{\cos\left(c+d\,x\right)}^2}{2\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^4}{4\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^6}{6\,d}+\frac{16\,a\,\sin\left(c+d\,x\right)}{35\,d}+\frac{8\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{35\,d}+\frac{6\,a\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{35\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^6\,\sin\left(c+d\,x\right)}{7\,d}","Not used",1,"(a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*log(1/cos(c/2 + (d*x)/2)^2))/d + (a*cos(c + d*x)^2)/(2*d) + (a*cos(c + d*x)^4)/(4*d) + (a*cos(c + d*x)^6)/(6*d) + (16*a*sin(c + d*x))/(35*d) + (8*a*cos(c + d*x)^2*sin(c + d*x))/(35*d) + (6*a*cos(c + d*x)^4*sin(c + d*x))/(35*d) + (a*cos(c + d*x)^6*sin(c + d*x))/(7*d)","B"
663,1,340,114,9.325095,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}-\frac{6\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d}+\frac{18\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}-\frac{104\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3\,d}+\frac{44\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d}-\frac{32\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{d}+\frac{32\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3\,d}-\frac{13\,a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{14\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{112\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{136\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{96\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{32\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*log(1/cos(c/2 + (d*x)/2)^2))/d - (6*a*cos(c/2 + (d*x)/2)^2)/d + (18*a*cos(c/2 + (d*x)/2)^4)/d - (104*a*cos(c/2 + (d*x)/2)^6)/(3*d) + (44*a*cos(c/2 + (d*x)/2)^8)/d - (32*a*cos(c/2 + (d*x)/2)^10)/d + (32*a*cos(c/2 + (d*x)/2)^12)/(3*d) - (13*a*cos(c/2 + (d*x)/2))/(2*d*sin(c/2 + (d*x)/2)) - (a*sin(c/2 + (d*x)/2))/(2*d*cos(c/2 + (d*x)/2)) + (14*a*cos(c/2 + (d*x)/2)^3)/(d*sin(c/2 + (d*x)/2)) - (112*a*cos(c/2 + (d*x)/2)^5)/(5*d*sin(c/2 + (d*x)/2)) + (136*a*cos(c/2 + (d*x)/2)^7)/(5*d*sin(c/2 + (d*x)/2)) - (96*a*cos(c/2 + (d*x)/2)^9)/(5*d*sin(c/2 + (d*x)/2)) + (32*a*cos(c/2 + (d*x)/2)^11)/(5*d*sin(c/2 + (d*x)/2))","B"
664,1,311,115,9.172899,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{3\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{26\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-\frac{47\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{2}+74\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-\frac{107\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+\frac{628\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}-51\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+84\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-19\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+34\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(3*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a/2 + 2*a*tan(c/2 + (d*x)/2) + (5*a*tan(c/2 + (d*x)/2)^2)/2 + 34*a*tan(c/2 + (d*x)/2)^3 - 19*a*tan(c/2 + (d*x)/2)^4 + 84*a*tan(c/2 + (d*x)/2)^5 - 51*a*tan(c/2 + (d*x)/2)^6 + (628*a*tan(c/2 + (d*x)/2)^7)/5 - (107*a*tan(c/2 + (d*x)/2)^8)/2 + 74*a*tan(c/2 + (d*x)/2)^9 - (47*a*tan(c/2 + (d*x)/2)^10)/2 + 26*a*tan(c/2 + (d*x)/2)^11)/(d*(4*tan(c/2 + (d*x)/2)^2 + 20*tan(c/2 + (d*x)/2)^4 + 40*tan(c/2 + (d*x)/2)^6 + 40*tan(c/2 + (d*x)/2)^8 + 20*tan(c/2 + (d*x)/2)^10 + 4*tan(c/2 + (d*x)/2)^12)) - (a*tan(c/2 + (d*x)/2))/(2*d) - (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*a*log(tan(c/2 + (d*x)/2)))/d","B"
665,1,300,118,9.070890,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^4,x)","\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{3\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{59\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+47\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{499\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+60\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{562\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+42\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+90\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(11*a*tan(c/2 + (d*x)/2))/(8*d) + (3*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (3*a*log(tan(c/2 + (d*x)/2)))/d + ((29*a*tan(c/2 + (d*x)/2)^2)/3 - a*tan(c/2 + (d*x)/2) - a/3 - 4*a*tan(c/2 + (d*x)/2)^3 + 90*a*tan(c/2 + (d*x)/2)^4 + 42*a*tan(c/2 + (d*x)/2)^5 + (562*a*tan(c/2 + (d*x)/2)^6)/3 + 60*a*tan(c/2 + (d*x)/2)^7 + (499*a*tan(c/2 + (d*x)/2)^8)/3 + 47*a*tan(c/2 + (d*x)/2)^9 + 59*a*tan(c/2 + (d*x)/2)^10)/(d*(8*tan(c/2 + (d*x)/2)^3 + 32*tan(c/2 + (d*x)/2)^5 + 48*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9 + 8*tan(c/2 + (d*x)/2)^11))","B"
666,1,290,118,9.009759,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^5,x)","\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{118\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-27\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{644\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{69\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{4}+160\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{57\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{a}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{3\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(11*a*tan(c/2 + (d*x)/2))/(8*d) + ((17*a*tan(c/2 + (d*x)/2)^2)/4 - (2*a*tan(c/2 + (d*x)/2))/3 - a/4 + 20*a*tan(c/2 + (d*x)/2)^3 + (57*a*tan(c/2 + (d*x)/2)^4)/4 + 160*a*tan(c/2 + (d*x)/2)^5 - (69*a*tan(c/2 + (d*x)/2)^6)/4 + (644*a*tan(c/2 + (d*x)/2)^7)/3 - 27*a*tan(c/2 + (d*x)/2)^8 + 118*a*tan(c/2 + (d*x)/2)^9)/(d*(16*tan(c/2 + (d*x)/2)^4 + 48*tan(c/2 + (d*x)/2)^6 + 48*tan(c/2 + (d*x)/2)^8 + 16*tan(c/2 + (d*x)/2)^10)) - (3*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d + (5*a*tan(c/2 + (d*x)/2)^2)/(16*d) - (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*tan(c/2 + (d*x)/2)^4)/(64*d) + (3*a*log(tan(c/2 + (d*x)/2)))/d","B"
667,1,281,115,9.095975,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^6,x)","\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{3\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{19\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{102\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+54\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+137\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{39\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}+\frac{161\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}","Not used",1,"(5*a*tan(c/2 + (d*x)/2)^2)/(16*d) - (3*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (19*a*tan(c/2 + (d*x)/2))/(16*d) + (3*a*tan(c/2 + (d*x)/2)^3)/(32*d) - (a*tan(c/2 + (d*x)/2)^4)/(64*d) - (a*tan(c/2 + (d*x)/2)^5)/(160*d) + (3*a*log(tan(c/2 + (d*x)/2)))/d - (a/5 + (a*tan(c/2 + (d*x)/2))/2 - (13*a*tan(c/2 + (d*x)/2)^2)/5 - 9*a*tan(c/2 + (d*x)/2)^3 + (161*a*tan(c/2 + (d*x)/2)^4)/5 - (39*a*tan(c/2 + (d*x)/2)^5)/2 + 137*a*tan(c/2 + (d*x)/2)^6 + 54*a*tan(c/2 + (d*x)/2)^7 + 102*a*tan(c/2 + (d*x)/2)^8)/(d*(32*tan(c/2 + (d*x)/2)^5 + 64*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9))","B"
668,1,267,115,10.117969,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^7,x)","\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,d}-\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{19\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{a\,\left(1920\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-1920\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{1920\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{51\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128}+\frac{35\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}+\frac{25\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{80}-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{384}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{160}+\frac{a}{384}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(3*a*tan(c/2 + (d*x)/2)^3)/(32*d) - (29*a*tan(c/2 + (d*x)/2)^2)/(128*d) - (19*a*tan(c/2 + (d*x)/2))/(16*d) + (a*tan(c/2 + (d*x)/2)^4)/(32*d) - (a*tan(c/2 + (d*x)/2)^5)/(160*d) - (a*tan(c/2 + (d*x)/2)^6)/(384*d) - (a*(1920*log(tan(c/2 + (d*x)/2)) - 1920*log(tan(c/2 + (d*x)/2)^2 + 1)))/(1920*d) - (cot(c/2 + (d*x)/2)^6*(a/384 + (a*tan(c/2 + (d*x)/2))/160 - (11*a*tan(c/2 + (d*x)/2)^2)/384 - (7*a*tan(c/2 + (d*x)/2)^3)/80 + (25*a*tan(c/2 + (d*x)/2)^4)/128 + (35*a*tan(c/2 + (d*x)/2)^5)/32 + (29*a*tan(c/2 + (d*x)/2)^6)/128 + (51*a*tan(c/2 + (d*x)/2)^7)/16))/(d*(tan(c/2 + (d*x)/2)^2 + 1))","B"
669,1,270,119,9.315796,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^8,x)","\frac{35\,a\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}+\frac{35\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}+\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{29\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{7\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}+\frac{7\,a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}+\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(35*a*cot(c/2 + (d*x)/2))/(128*d) + (35*a*tan(c/2 + (d*x)/2))/(128*d) + (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (29*a*cot(c/2 + (d*x)/2)^2)/(128*d) - (7*a*cot(c/2 + (d*x)/2)^3)/(128*d) + (a*cot(c/2 + (d*x)/2)^4)/(32*d) + (7*a*cot(c/2 + (d*x)/2)^5)/(640*d) - (a*cot(c/2 + (d*x)/2)^6)/(384*d) - (a*cot(c/2 + (d*x)/2)^7)/(896*d) - (29*a*tan(c/2 + (d*x)/2)^2)/(128*d) - (7*a*tan(c/2 + (d*x)/2)^3)/(128*d) + (a*tan(c/2 + (d*x)/2)^4)/(32*d) + (7*a*tan(c/2 + (d*x)/2)^5)/(640*d) - (a*tan(c/2 + (d*x)/2)^6)/(384*d) - (a*tan(c/2 + (d*x)/2)^7)/(896*d) - (a*log(tan(c/2 + (d*x)/2)))/d","B"
670,1,91,74,9.391902,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^9,x)","-\frac{-a\,{\sin\left(c+d\,x\right)}^7-\frac{a\,{\sin\left(c+d\,x\right)}^6}{2}+a\,{\sin\left(c+d\,x\right)}^5+\frac{3\,a\,{\sin\left(c+d\,x\right)}^4}{4}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^3}{5}-\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{a\,\sin\left(c+d\,x\right)}{7}+\frac{a}{8}}{d\,{\sin\left(c+d\,x\right)}^8}","Not used",1,"-(a/8 + (a*sin(c + d*x))/7 - (a*sin(c + d*x)^2)/2 - (3*a*sin(c + d*x)^3)/5 + (3*a*sin(c + d*x)^4)/4 + a*sin(c + d*x)^5 - (a*sin(c + d*x)^6)/2 - a*sin(c + d*x)^7)/(d*sin(c + d*x)^8)","B"
671,1,92,81,9.229080,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^10,x)","-\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^7}{2}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{3}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^5}{4}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^4}{5}-\frac{a\,{\sin\left(c+d\,x\right)}^3}{2}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^2}{7}+\frac{a\,\sin\left(c+d\,x\right)}{8}+\frac{a}{9}}{d\,{\sin\left(c+d\,x\right)}^9}","Not used",1,"-(a/9 + (a*sin(c + d*x))/8 - (3*a*sin(c + d*x)^2)/7 - (a*sin(c + d*x)^3)/2 + (3*a*sin(c + d*x)^4)/5 + (3*a*sin(c + d*x)^5)/4 - (a*sin(c + d*x)^6)/3 - (a*sin(c + d*x)^7)/2)/(d*sin(c + d*x)^9)","B"
672,1,92,97,9.213511,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^11,x)","-\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^7}{3}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{4}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{2}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^3}{7}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^2}{8}+\frac{a\,\sin\left(c+d\,x\right)}{9}+\frac{a}{10}}{d\,{\sin\left(c+d\,x\right)}^{10}}","Not used",1,"-(a/10 + (a*sin(c + d*x))/9 - (3*a*sin(c + d*x)^2)/8 - (3*a*sin(c + d*x)^3)/7 + (a*sin(c + d*x)^4)/2 + (3*a*sin(c + d*x)^5)/5 - (a*sin(c + d*x)^6)/4 - (a*sin(c + d*x)^7)/3)/(d*sin(c + d*x)^10)","B"
673,1,92,97,9.276724,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^12,x)","-\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^7}{4}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{5}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{2}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^4}{7}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^3}{8}-\frac{a\,{\sin\left(c+d\,x\right)}^2}{3}+\frac{a\,\sin\left(c+d\,x\right)}{10}+\frac{a}{11}}{d\,{\sin\left(c+d\,x\right)}^{11}}","Not used",1,"-(a/11 + (a*sin(c + d*x))/10 - (a*sin(c + d*x)^2)/3 - (3*a*sin(c + d*x)^3)/8 + (3*a*sin(c + d*x)^4)/7 + (a*sin(c + d*x)^5)/2 - (a*sin(c + d*x)^6)/5 - (a*sin(c + d*x)^7)/4)/(d*sin(c + d*x)^11)","B"
674,1,92,113,9.194701,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^13,x)","-\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^7}{5}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^5}{7}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^4}{8}-\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^2}{10}+\frac{a\,\sin\left(c+d\,x\right)}{11}+\frac{a}{12}}{d\,{\sin\left(c+d\,x\right)}^{12}}","Not used",1,"-(a/12 + (a*sin(c + d*x))/11 - (3*a*sin(c + d*x)^2)/10 - (a*sin(c + d*x)^3)/3 + (3*a*sin(c + d*x)^4)/8 + (3*a*sin(c + d*x)^5)/7 - (a*sin(c + d*x)^6)/6 - (a*sin(c + d*x)^7)/5)/(d*sin(c + d*x)^12)","B"
675,1,92,113,9.354944,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^14,x)","-\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^7}{6}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{7}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^5}{8}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{3}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^3}{10}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^2}{11}+\frac{a\,\sin\left(c+d\,x\right)}{12}+\frac{a}{13}}{d\,{\sin\left(c+d\,x\right)}^{13}}","Not used",1,"-(a/13 + (a*sin(c + d*x))/12 - (3*a*sin(c + d*x)^2)/11 - (3*a*sin(c + d*x)^3)/10 + (a*sin(c + d*x)^4)/3 + (3*a*sin(c + d*x)^5)/8 - (a*sin(c + d*x)^6)/7 - (a*sin(c + d*x)^7)/6)/(d*sin(c + d*x)^13)","B"
676,1,92,129,9.239259,"\text{Not used}","int((cos(c + d*x)^7*(a + a*sin(c + d*x)))/sin(c + d*x)^15,x)","-\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{8}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{3}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^4}{10}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^3}{11}-\frac{a\,{\sin\left(c+d\,x\right)}^2}{4}+\frac{a\,\sin\left(c+d\,x\right)}{13}+\frac{a}{14}}{d\,{\sin\left(c+d\,x\right)}^{14}}","Not used",1,"-(a/14 + (a*sin(c + d*x))/13 - (a*sin(c + d*x)^2)/4 - (3*a*sin(c + d*x)^3)/11 + (3*a*sin(c + d*x)^4)/10 + (a*sin(c + d*x)^5)/3 - (a*sin(c + d*x)^6)/8 - (a*sin(c + d*x)^7)/7)/(d*sin(c + d*x)^14)","B"
677,1,83,109,0.079872,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^6)/(a + a*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^7}{7\,a}-\frac{{\sin\left(c+d\,x\right)}^8}{8\,a}-\frac{2\,{\sin\left(c+d\,x\right)}^9}{9\,a}+\frac{{\sin\left(c+d\,x\right)}^{10}}{5\,a}+\frac{{\sin\left(c+d\,x\right)}^{11}}{11\,a}-\frac{{\sin\left(c+d\,x\right)}^{12}}{12\,a}}{d}","Not used",1,"(sin(c + d*x)^7/(7*a) - sin(c + d*x)^8/(8*a) - (2*sin(c + d*x)^9)/(9*a) + sin(c + d*x)^10/(5*a) + sin(c + d*x)^11/(11*a) - sin(c + d*x)^12/(12*a))/d","B"
678,1,83,109,8.986232,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^5)/(a + a*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^6}{6\,a}-\frac{{\sin\left(c+d\,x\right)}^7}{7\,a}-\frac{{\sin\left(c+d\,x\right)}^8}{4\,a}+\frac{2\,{\sin\left(c+d\,x\right)}^9}{9\,a}+\frac{{\sin\left(c+d\,x\right)}^{10}}{10\,a}-\frac{{\sin\left(c+d\,x\right)}^{11}}{11\,a}}{d}","Not used",1,"(sin(c + d*x)^6/(6*a) - sin(c + d*x)^7/(7*a) - sin(c + d*x)^8/(4*a) + (2*sin(c + d*x)^9)/(9*a) + sin(c + d*x)^10/(10*a) - sin(c + d*x)^11/(11*a))/d","B"
679,1,83,109,8.940093,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^4)/(a + a*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^5}{5\,a}-\frac{{\sin\left(c+d\,x\right)}^6}{6\,a}-\frac{2\,{\sin\left(c+d\,x\right)}^7}{7\,a}+\frac{{\sin\left(c+d\,x\right)}^8}{4\,a}+\frac{{\sin\left(c+d\,x\right)}^9}{9\,a}-\frac{{\sin\left(c+d\,x\right)}^{10}}{10\,a}}{d}","Not used",1,"(sin(c + d*x)^5/(5*a) - sin(c + d*x)^6/(6*a) - (2*sin(c + d*x)^7)/(7*a) + sin(c + d*x)^8/(4*a) + sin(c + d*x)^9/(9*a) - sin(c + d*x)^10/(10*a))/d","B"
680,1,83,91,0.058857,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^3)/(a + a*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^4}{4\,a}-\frac{{\sin\left(c+d\,x\right)}^5}{5\,a}-\frac{{\sin\left(c+d\,x\right)}^6}{3\,a}+\frac{2\,{\sin\left(c+d\,x\right)}^7}{7\,a}+\frac{{\sin\left(c+d\,x\right)}^8}{8\,a}-\frac{{\sin\left(c+d\,x\right)}^9}{9\,a}}{d}","Not used",1,"(sin(c + d*x)^4/(4*a) - sin(c + d*x)^5/(5*a) - sin(c + d*x)^6/(3*a) + (2*sin(c + d*x)^7)/(7*a) + sin(c + d*x)^8/(8*a) - sin(c + d*x)^9/(9*a))/d","B"
681,1,83,91,8.962479,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^2)/(a + a*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^3}{3\,a}-\frac{{\sin\left(c+d\,x\right)}^4}{4\,a}-\frac{2\,{\sin\left(c+d\,x\right)}^5}{5\,a}+\frac{{\sin\left(c+d\,x\right)}^6}{3\,a}+\frac{{\sin\left(c+d\,x\right)}^7}{7\,a}-\frac{{\sin\left(c+d\,x\right)}^8}{8\,a}}{d}","Not used",1,"(sin(c + d*x)^3/(3*a) - sin(c + d*x)^4/(4*a) - (2*sin(c + d*x)^5)/(5*a) + sin(c + d*x)^6/(3*a) + sin(c + d*x)^7/(7*a) - sin(c + d*x)^8/(8*a))/d","B"
682,1,83,73,9.127097,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x))/(a + a*sin(c + d*x)),x)","\frac{\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}{2\,a}+\frac{2\,{\sin\left(c+d\,x\right)}^5}{5\,a}+\frac{{\sin\left(c+d\,x\right)}^6}{6\,a}-\frac{{\sin\left(c+d\,x\right)}^7}{7\,a}}{d}","Not used",1,"(sin(c + d*x)^2/(2*a) - sin(c + d*x)^3/(3*a) - sin(c + d*x)^4/(2*a) + (2*sin(c + d*x)^5)/(5*a) + sin(c + d*x)^6/(6*a) - sin(c + d*x)^7/(7*a))/d","B"
683,1,80,68,9.137479,"\text{Not used}","int(cos(c + d*x)^7/(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{2\,{\sin\left(c+d\,x\right)}^3}{3\,a}+\frac{{\sin\left(c+d\,x\right)}^4}{2\,a}+\frac{{\sin\left(c+d\,x\right)}^5}{5\,a}-\frac{{\sin\left(c+d\,x\right)}^6}{6\,a}}{d}","Not used",1,"(sin(c + d*x)/a - sin(c + d*x)^2/(2*a) - (2*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*a))/d","B"
684,1,140,99,9.285704,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{a\,d}-\frac{8\,\sin\left(c+d\,x\right)}{15\,a\,d}+\frac{{\cos\left(c+d\,x\right)}^2}{2\,a\,d}+\frac{{\cos\left(c+d\,x\right)}^4}{4\,a\,d}-\frac{4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{15\,a\,d}-\frac{{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{5\,a\,d}","Not used",1,"log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(a*d) - log(1/cos(c/2 + (d*x)/2)^2)/(a*d) - (8*sin(c + d*x))/(15*a*d) + cos(c + d*x)^2/(2*a*d) + cos(c + d*x)^4/(4*a*d) - (4*cos(c + d*x)^2*sin(c + d*x))/(15*a*d) - (cos(c + d*x)^4*sin(c + d*x))/(5*a*d)","B"
685,1,272,95,9.364272,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a\,d}-\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a\,d}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{a\,d}-\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{a\,d}+\frac{\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{a\,d}-\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}+\frac{20\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,a\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3\,a\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3\,a\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(4*cos(c/2 + (d*x)/2)^2)/(a*d) - (8*cos(c/2 + (d*x)/2)^4)/(a*d) + (8*cos(c/2 + (d*x)/2)^6)/(a*d) - (4*cos(c/2 + (d*x)/2)^8)/(a*d) + log(1/cos(c/2 + (d*x)/2)^2)/(a*d) - log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(a*d) + (20*cos(c/2 + (d*x)/2)^3)/(3*a*d*sin(c/2 + (d*x)/2)) - (16*cos(c/2 + (d*x)/2)^5)/(3*a*d*sin(c/2 + (d*x)/2)) + (8*cos(c/2 + (d*x)/2)^7)/(3*a*d*sin(c/2 + (d*x)/2)) - (9*cos(c/2 + (d*x)/2))/(2*a*d*sin(c/2 + (d*x)/2)) - sin(c/2 + (d*x)/2)/(2*a*d*cos(c/2 + (d*x)/2))","B"
686,1,231,97,9.225264,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{82\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}}{d\,\left(4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}+\frac{2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"(2*tan(c/2 + (d*x)/2) - (3*tan(c/2 + (d*x)/2)^2)/2 + 22*tan(c/2 + (d*x)/2)^3 + (13*tan(c/2 + (d*x)/2)^4)/2 + (82*tan(c/2 + (d*x)/2)^5)/3 + (15*tan(c/2 + (d*x)/2)^6)/2 + 18*tan(c/2 + (d*x)/2)^7 - 1/2)/(d*(4*a*tan(c/2 + (d*x)/2)^2 + 12*a*tan(c/2 + (d*x)/2)^4 + 12*a*tan(c/2 + (d*x)/2)^6 + 4*a*tan(c/2 + (d*x)/2)^8)) - (2*log(tan(c/2 + (d*x)/2)))/(a*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) + tan(c/2 + (d*x)/2)/(2*a*d) + (2*log(tan(c/2 + (d*x)/2)^2 + 1))/(a*d)","B"
687,1,221,97,9.167979,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}+\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}+\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{89\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{3}}{d\,\left(8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - tan(c/2 + (d*x)/2)^3/(24*a*d) + (2*log(tan(c/2 + (d*x)/2)))/(a*d) + (7*tan(c/2 + (d*x)/2))/(8*a*d) + (tan(c/2 + (d*x)/2) + (19*tan(c/2 + (d*x)/2)^2)/3 + 2*tan(c/2 + (d*x)/2)^3 + (89*tan(c/2 + (d*x)/2)^4)/3 - 15*tan(c/2 + (d*x)/2)^5 + 23*tan(c/2 + (d*x)/2)^6 - 1/3)/(d*(8*a*tan(c/2 + (d*x)/2)^3 + 16*a*tan(c/2 + (d*x)/2)^5 + 8*a*tan(c/2 + (d*x)/2)^7)) - (2*log(tan(c/2 + (d*x)/2)^2 + 1))/(a*d)","B"
688,1,214,94,9.342633,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{-46\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{1}{4}}{d\,\left(16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"(3*tan(c/2 + (d*x)/2)^2)/(16*a*d) + tan(c/2 + (d*x)/2)^3/(24*a*d) - tan(c/2 + (d*x)/2)^4/(64*a*d) + log(tan(c/2 + (d*x)/2))/(a*d) + ((2*tan(c/2 + (d*x)/2))/3 + (11*tan(c/2 + (d*x)/2)^2)/4 - (40*tan(c/2 + (d*x)/2)^3)/3 + 3*tan(c/2 + (d*x)/2)^4 - 46*tan(c/2 + (d*x)/2)^5 - 1/4)/(d*(16*a*tan(c/2 + (d*x)/2)^4 + 16*a*tan(c/2 + (d*x)/2)^6)) - (7*tan(c/2 + (d*x)/2))/(8*a*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d)","B"
689,1,204,100,9.239844,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^6*(a + a*sin(c + d*x))),x)","\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,a\,d}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a\,d}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{1}{5}\right)}{32\,a\,d}","Not used",1,"(5*tan(c/2 + (d*x)/2)^3)/(96*a*d) - (3*tan(c/2 + (d*x)/2)^2)/(16*a*d) + tan(c/2 + (d*x)/2)^4/(64*a*d) - tan(c/2 + (d*x)/2)^5/(160*a*d) - log(tan(c/2 + (d*x)/2))/(a*d) - (5*tan(c/2 + (d*x)/2))/(16*a*d) + log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) - (cot(c/2 + (d*x)/2)^5*(6*tan(c/2 + (d*x)/2)^3 - (5*tan(c/2 + (d*x)/2)^2)/3 - tan(c/2 + (d*x)/2)/2 + 10*tan(c/2 + (d*x)/2)^4 + 1/5))/(32*a*d)","B"
690,1,63,68,9.039571,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{{\sin\left(c+d\,x\right)}^5-\frac{{\sin\left(c+d\,x\right)}^4}{2}-\frac{2\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{{\sin\left(c+d\,x\right)}^2}{2}+\frac{\sin\left(c+d\,x\right)}{5}-\frac{1}{6}}{a\,d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"(sin(c + d*x)/5 + sin(c + d*x)^2/2 - (2*sin(c + d*x)^3)/3 - sin(c + d*x)^4/2 + sin(c + d*x)^5 - 1/6)/(a*d*sin(c + d*x)^6)","B"
691,1,66,73,8.974256,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^8*(a + a*sin(c + d*x))),x)","\frac{105\,{\sin\left(c+d\,x\right)}^5-70\,{\sin\left(c+d\,x\right)}^4-105\,{\sin\left(c+d\,x\right)}^3+84\,{\sin\left(c+d\,x\right)}^2+35\,\sin\left(c+d\,x\right)-30}{210\,a\,d\,{\sin\left(c+d\,x\right)}^7}","Not used",1,"(35*sin(c + d*x) + 84*sin(c + d*x)^2 - 105*sin(c + d*x)^3 - 70*sin(c + d*x)^4 + 105*sin(c + d*x)^5 - 30)/(210*a*d*sin(c + d*x)^7)","B"
692,1,66,91,9.035071,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{280\,{\sin\left(c+d\,x\right)}^5-210\,{\sin\left(c+d\,x\right)}^4-336\,{\sin\left(c+d\,x\right)}^3+280\,{\sin\left(c+d\,x\right)}^2+120\,\sin\left(c+d\,x\right)-105}{840\,a\,d\,{\sin\left(c+d\,x\right)}^8}","Not used",1,"(120*sin(c + d*x) + 280*sin(c + d*x)^2 - 336*sin(c + d*x)^3 - 210*sin(c + d*x)^4 + 280*sin(c + d*x)^5 - 105)/(840*a*d*sin(c + d*x)^8)","B"
693,1,65,91,9.040825,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^10*(a + a*sin(c + d*x))),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^5}{4}-\frac{{\sin\left(c+d\,x\right)}^4}{5}-\frac{{\sin\left(c+d\,x\right)}^3}{3}+\frac{2\,{\sin\left(c+d\,x\right)}^2}{7}+\frac{\sin\left(c+d\,x\right)}{8}-\frac{1}{9}}{a\,d\,{\sin\left(c+d\,x\right)}^9}","Not used",1,"(sin(c + d*x)/8 + (2*sin(c + d*x)^2)/7 - sin(c + d*x)^3/3 - sin(c + d*x)^4/5 + sin(c + d*x)^5/4 - 1/9)/(a*d*sin(c + d*x)^9)","B"
694,1,66,109,9.075121,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^11*(a + a*sin(c + d*x))),x)","\frac{252\,{\sin\left(c+d\,x\right)}^5-210\,{\sin\left(c+d\,x\right)}^4-360\,{\sin\left(c+d\,x\right)}^3+315\,{\sin\left(c+d\,x\right)}^2+140\,\sin\left(c+d\,x\right)-126}{1260\,a\,d\,{\sin\left(c+d\,x\right)}^{10}}","Not used",1,"(140*sin(c + d*x) + 315*sin(c + d*x)^2 - 360*sin(c + d*x)^3 - 210*sin(c + d*x)^4 + 252*sin(c + d*x)^5 - 126)/(1260*a*d*sin(c + d*x)^10)","B"
695,1,65,109,9.041184,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^12*(a + a*sin(c + d*x))),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^5}{6}-\frac{{\sin\left(c+d\,x\right)}^4}{7}-\frac{{\sin\left(c+d\,x\right)}^3}{4}+\frac{2\,{\sin\left(c+d\,x\right)}^2}{9}+\frac{\sin\left(c+d\,x\right)}{10}-\frac{1}{11}}{a\,d\,{\sin\left(c+d\,x\right)}^{11}}","Not used",1,"(sin(c + d*x)/10 + (2*sin(c + d*x)^2)/9 - sin(c + d*x)^3/4 - sin(c + d*x)^4/7 + sin(c + d*x)^5/6 - 1/11)/(a*d*sin(c + d*x)^11)","B"
696,1,65,109,9.139704,"\text{Not used}","int(cos(c + d*x)^7/(sin(c + d*x)^13*(a + a*sin(c + d*x))),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^5}{7}-\frac{{\sin\left(c+d\,x\right)}^4}{8}-\frac{2\,{\sin\left(c+d\,x\right)}^3}{9}+\frac{{\sin\left(c+d\,x\right)}^2}{5}+\frac{\sin\left(c+d\,x\right)}{11}-\frac{1}{12}}{a\,d\,{\sin\left(c+d\,x\right)}^{12}}","Not used",1,"(sin(c + d*x)/11 + sin(c + d*x)^2/5 - (2*sin(c + d*x)^3)/9 - sin(c + d*x)^4/8 + sin(c + d*x)^5/7 - 1/12)/(a*d*sin(c + d*x)^12)","B"
697,1,1130,184,17.091488,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)^n*(a + a*sin(c + d*x))^3,x)","\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^n\,\left(11\,n^7+502\,n^6+9800\,n^5+109542\,n^4+755233\,n^3+3058196\,n^2+6117676\,n+3714480\right)}{256\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}-\frac{5\,a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(8\,c+8\,d\,x\right)\,\left(n^7+34\,n^6+472\,n^5+3442\,n^4+14083\,n^3+31804\,n^2+35844\,n+15120\right)}{256\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}+\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(10\,c+10\,d\,x\right)\,\left(n^7+34\,n^6+472\,n^5+3442\,n^4+14083\,n^3+31804\,n^2+35844\,n+15120\right)}{512\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}-\frac{a^3\,\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(n^7\,19{}\mathrm{i}+n^6\,889{}\mathrm{i}+n^5\,18019{}\mathrm{i}+n^4\,215083{}\mathrm{i}+n^3\,1614322{}\mathrm{i}+n^2\,7143148{}\mathrm{i}+n\,16168200{}\mathrm{i}+13759200{}\mathrm{i}\right)\,1{}\mathrm{i}}{128\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}-\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(17\,n^7+706\,n^6+11608\,n^5+97426\,n^4+446515\,n^3+1100668\,n^2+1320260\,n+579600\right)}{512\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}-\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(7\,n^7+334\,n^6+6760\,n^5+71710\,n^4+413653\,n^3+1246276\,n^2+1729500\,n+831600\right)}{64\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}+\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(25\,n^7+1042\,n^6+17176\,n^5+119842\,n^4+122059\,n^3-2395364\,n^2-9293340\,n-6879600\right)}{256\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}+\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\sin\left(9\,c+9\,d\,x\right)\,\left(n^7\,1{}\mathrm{i}+n^6\,35{}\mathrm{i}+n^5\,497{}\mathrm{i}+n^4\,3689{}\mathrm{i}+n^3\,15302{}\mathrm{i}+n^2\,34916{}\mathrm{i}+n\,39640{}\mathrm{i}+16800{}\mathrm{i}\right)\,3{}\mathrm{i}}{256\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}-\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(n^7\,5{}\mathrm{i}+n^6\,191{}\mathrm{i}+n^5\,2741{}\mathrm{i}+n^4\,18845{}\mathrm{i}+n^3\,66110{}\mathrm{i}+n^2\,117044{}\mathrm{i}+n\,97464{}\mathrm{i}+30240{}\mathrm{i}\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}+\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\sin\left(7\,c+7\,d\,x\right)\,\left(n^7\,5{}\mathrm{i}+n^6\,239{}\mathrm{i}+n^5\,4277{}\mathrm{i}+n^4\,37709{}\mathrm{i}+n^3\,177758{}\mathrm{i}+n^2\,445172{}\mathrm{i}+n\,538680{}\mathrm{i}+237600{}\mathrm{i}\right)\,1{}\mathrm{i}}{256\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}-\frac{a^3\,{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(n^7\,5{}\mathrm{i}+n^6\,223{}\mathrm{i}+n^5\,4149{}\mathrm{i}+n^4\,40253{}\mathrm{i}+n^3\,211966{}\mathrm{i}+n^2\,586164{}\mathrm{i}+n\,763320{}\mathrm{i}+352800{}\mathrm{i}\right)\,3{}\mathrm{i}}{64\,d\,\left(n^8+44\,n^7+812\,n^6+8162\,n^5+48503\,n^4+172634\,n^3+353884\,n^2+373560\,n+151200\right)}","Not used",1,"(3*a^3*sin(c + d*x)^n*(6117676*n + 3058196*n^2 + 755233*n^3 + 109542*n^4 + 9800*n^5 + 502*n^6 + 11*n^7 + 3714480))/(256*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) - (5*a^3*sin(c + d*x)^n*cos(8*c + 8*d*x)*(35844*n + 31804*n^2 + 14083*n^3 + 3442*n^4 + 472*n^5 + 34*n^6 + n^7 + 15120))/(256*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) + (a^3*sin(c + d*x)^n*cos(10*c + 10*d*x)*(35844*n + 31804*n^2 + 14083*n^3 + 3442*n^4 + 472*n^5 + 34*n^6 + n^7 + 15120))/(512*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) - (a^3*sin(c + d*x)*sin(c + d*x)^n*(n*16168200i + n^2*7143148i + n^3*1614322i + n^4*215083i + n^5*18019i + n^6*889i + n^7*19i + 13759200i)*1i)/(128*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) - (3*a^3*sin(c + d*x)^n*cos(6*c + 6*d*x)*(1320260*n + 1100668*n^2 + 446515*n^3 + 97426*n^4 + 11608*n^5 + 706*n^6 + 17*n^7 + 579600))/(512*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) - (a^3*sin(c + d*x)^n*cos(4*c + 4*d*x)*(1729500*n + 1246276*n^2 + 413653*n^3 + 71710*n^4 + 6760*n^5 + 334*n^6 + 7*n^7 + 831600))/(64*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) + (a^3*sin(c + d*x)^n*cos(2*c + 2*d*x)*(122059*n^3 - 2395364*n^2 - 9293340*n + 119842*n^4 + 17176*n^5 + 1042*n^6 + 25*n^7 - 6879600))/(256*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) + (a^3*sin(c + d*x)^n*sin(9*c + 9*d*x)*(n*39640i + n^2*34916i + n^3*15302i + n^4*3689i + n^5*497i + n^6*35i + n^7*1i + 16800i)*3i)/(256*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) - (a^3*sin(c + d*x)^n*sin(5*c + 5*d*x)*(n*97464i + n^2*117044i + n^3*66110i + n^4*18845i + n^5*2741i + n^6*191i + n^7*5i + 30240i)*1i)/(64*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) + (a^3*sin(c + d*x)^n*sin(7*c + 7*d*x)*(n*538680i + n^2*445172i + n^3*177758i + n^4*37709i + n^5*4277i + n^6*239i + n^7*5i + 237600i)*1i)/(256*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200)) - (a^3*sin(c + d*x)^n*sin(3*c + 3*d*x)*(n*763320i + n^2*586164i + n^3*211966i + n^4*40253i + n^5*4149i + n^6*223i + n^7*5i + 352800i)*3i)/(64*d*(373560*n + 353884*n^2 + 172634*n^3 + 48503*n^4 + 8162*n^5 + 812*n^6 + 44*n^7 + n^8 + 151200))","B"
698,1,1142,184,16.449499,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)^n*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\left(n^7\,5{}\mathrm{i}+n^6\,208{}\mathrm{i}+n^5\,3702{}\mathrm{i}+n^4\,37844{}\mathrm{i}+n^3\,238585{}\mathrm{i}+n^2\,868332{}\mathrm{i}+n\,1507788{}\mathrm{i}+843696{}\mathrm{i}\right)}{64\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\sin\left(9\,c+9\,d\,x\right)\,\left(n^7+31\,n^6+391\,n^5+2581\,n^4+9544\,n^3+19564\,n^2+20304\,n+8064\right)\,1{}\mathrm{i}}{256\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}+\frac{a^2\,\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(13\,n^7+555\,n^6+10267\,n^5+111993\,n^4+770632\,n^3+3169500\,n^2+6799248\,n+5588352\right)\,1{}\mathrm{i}}{128\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\cos\left(8\,c+8\,d\,x\right)\,\left(n^7\,1{}\mathrm{i}+n^6\,32{}\mathrm{i}+n^5\,414{}\mathrm{i}+n^4\,2788{}\mathrm{i}+n^3\,10469{}\mathrm{i}+n^2\,21708{}\mathrm{i}+n\,22716{}\mathrm{i}+9072{}\mathrm{i}\right)}{64\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(n^7\,1{}\mathrm{i}+n^6\,38{}\mathrm{i}+n^5\,570{}\mathrm{i}+n^4\,4336{}\mathrm{i}+n^3\,17909{}\mathrm{i}+n^2\,39882{}\mathrm{i}+n\,43920{}\mathrm{i}+18144{}\mathrm{i}\right)}{16\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(n^7\,1{}\mathrm{i}+n^6\,44{}\mathrm{i}+n^5\,822{}\mathrm{i}+n^4\,7996{}\mathrm{i}+n^3\,41669{}\mathrm{i}+n^2\,111816{}\mathrm{i}+n\,140868{}\mathrm{i}+63504{}\mathrm{i}\right)}{16\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}+\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(n^7\,1{}\mathrm{i}+n^6\,38{}\mathrm{i}+n^5\,570{}\mathrm{i}+n^4\,3568{}\mathrm{i}+n^3\,2549{}\mathrm{i}-n^2\,59958{}\mathrm{i}-n\,186480{}\mathrm{i}-127008{}\mathrm{i}\right)}{16\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}-\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\sin\left(7\,c+7\,d\,x\right)\,\left(-n^7-15\,n^6-7\,n^5+987\,n^4+6776\,n^3+18900\,n^2+23472\,n+10368\right)\,1{}\mathrm{i}}{256\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}+\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(5\,n^7+183\,n^6+2627\,n^5+19149\,n^4+76280\,n^3+165132\,n^2+178128\,n+72576\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}+\frac{a^2\,{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(11\,n^7+449\,n^6+7661\,n^5+68603\,n^4+338024\,n^3+889556\,n^2+1120944\,n+508032\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8\,1{}\mathrm{i}+n^7\,40{}\mathrm{i}+n^6\,670{}\mathrm{i}+n^5\,6100{}\mathrm{i}+n^4\,32773{}\mathrm{i}+n^3\,105460{}\mathrm{i}+n^2\,196380{}\mathrm{i}+n\,190800{}\mathrm{i}+72576{}\mathrm{i}\right)}","Not used",1,"(a^2*sin(c + d*x)^n*(n*1507788i + n^2*868332i + n^3*238585i + n^4*37844i + n^5*3702i + n^6*208i + n^7*5i + 843696i))/(64*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) - (a^2*sin(c + d*x)^n*sin(9*c + 9*d*x)*(20304*n + 19564*n^2 + 9544*n^3 + 2581*n^4 + 391*n^5 + 31*n^6 + n^7 + 8064)*1i)/(256*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) + (a^2*sin(c + d*x)*sin(c + d*x)^n*(6799248*n + 3169500*n^2 + 770632*n^3 + 111993*n^4 + 10267*n^5 + 555*n^6 + 13*n^7 + 5588352)*1i)/(128*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) - (a^2*sin(c + d*x)^n*cos(8*c + 8*d*x)*(n*22716i + n^2*21708i + n^3*10469i + n^4*2788i + n^5*414i + n^6*32i + n^7*1i + 9072i))/(64*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) - (a^2*sin(c + d*x)^n*cos(6*c + 6*d*x)*(n*43920i + n^2*39882i + n^3*17909i + n^4*4336i + n^5*570i + n^6*38i + n^7*1i + 18144i))/(16*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) - (a^2*sin(c + d*x)^n*cos(4*c + 4*d*x)*(n*140868i + n^2*111816i + n^3*41669i + n^4*7996i + n^5*822i + n^6*44i + n^7*1i + 63504i))/(16*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) + (a^2*sin(c + d*x)^n*cos(2*c + 2*d*x)*(n^3*2549i - n^2*59958i - n*186480i + n^4*3568i + n^5*570i + n^6*38i + n^7*1i - 127008i))/(16*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) - (a^2*sin(c + d*x)^n*sin(7*c + 7*d*x)*(23472*n + 18900*n^2 + 6776*n^3 + 987*n^4 - 7*n^5 - 15*n^6 - n^7 + 10368)*1i)/(256*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) + (a^2*sin(c + d*x)^n*sin(5*c + 5*d*x)*(178128*n + 165132*n^2 + 76280*n^3 + 19149*n^4 + 2627*n^5 + 183*n^6 + 5*n^7 + 72576)*1i)/(64*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i)) + (a^2*sin(c + d*x)^n*sin(3*c + 3*d*x)*(1120944*n + 889556*n^2 + 338024*n^3 + 68603*n^4 + 7661*n^5 + 449*n^6 + 11*n^7 + 508032)*1i)/(64*d*(n*190800i + n^2*196380i + n^3*105460i + n^4*32773i + n^5*6100i + n^6*670i + n^7*40i + n^8*1i + 72576i))","B"
699,1,901,167,15.896520,"\text{Not used}","int(cos(c + d*x)^7*sin(c + d*x)^n*(a + a*sin(c + d*x)),x)","\frac{a\,{\sin\left(c+d\,x\right)}^n\,\left(5\,n^7+188\,n^6+3050\,n^5+28904\,n^4+167669\,n^3+552236\,n^2+879324\,n+468720\right)}{128\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(-n^7-34\,n^6-454\,n^5-2332\,n^4+599\,n^3+41822\,n^2+109872\,n+70560\right)}{32\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\sin\left(7\,c+7\,d\,x\right)\,\left(n^7\,1{}\mathrm{i}+n^6\,29{}\mathrm{i}+n^5\,343{}\mathrm{i}+n^4\,2135{}\mathrm{i}+n^3\,7504{}\mathrm{i}+n^2\,14756{}\mathrm{i}+n\,14832{}\mathrm{i}+5760{}\mathrm{i}\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(n^7\,5{}\mathrm{i}+n^6\,169{}\mathrm{i}+n^5\,2291{}\mathrm{i}+n^4\,16027{}\mathrm{i}+n^3\,62000{}\mathrm{i}+n^2\,131476{}\mathrm{i}+n\,139824{}\mathrm{i}+56448{}\mathrm{i}\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(n^7\,3{}\mathrm{i}+n^6\,111{}\mathrm{i}+n^5\,1733{}\mathrm{i}+n^4\,14445{}\mathrm{i}+n^3\,67472{}\mathrm{i}+n^2\,171084{}\mathrm{i}+n\,210512{}\mathrm{i}+94080{}\mathrm{i}\right)\,3{}\mathrm{i}}{64\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\cos\left(8\,c+8\,d\,x\right)\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}{128\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(n^7+34\,n^6+454\,n^5+3100\,n^4+11689\,n^3+24226\,n^2+25296\,n+10080\right)}{32\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(n^7+40\,n^6+682\,n^5+5968\,n^4+27937\,n^3+68728\,n^2+81396\,n+35280\right)}{32\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{a\,\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(n^7\,5{}\mathrm{i}+n^6\,193{}\mathrm{i}+n^5\,3251{}\mathrm{i}+n^4\,32515{}\mathrm{i}+n^3\,209360{}\mathrm{i}+n^2\,826612{}\mathrm{i}+n\,1735344{}\mathrm{i}+1411200{}\mathrm{i}\right)\,1{}\mathrm{i}}{64\,d\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}","Not used",1,"(a*sin(c + d*x)^n*(879324*n + 552236*n^2 + 167669*n^3 + 28904*n^4 + 3050*n^5 + 188*n^6 + 5*n^7 + 468720))/(128*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a*sin(c + d*x)^n*cos(2*c + 2*d*x)*(109872*n + 41822*n^2 + 599*n^3 - 2332*n^4 - 454*n^5 - 34*n^6 - n^7 + 70560))/(32*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a*sin(c + d*x)^n*sin(7*c + 7*d*x)*(n*14832i + n^2*14756i + n^3*7504i + n^4*2135i + n^5*343i + n^6*29i + n^7*1i + 5760i)*1i)/(64*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a*sin(c + d*x)^n*sin(5*c + 5*d*x)*(n*139824i + n^2*131476i + n^3*62000i + n^4*16027i + n^5*2291i + n^6*169i + n^7*5i + 56448i)*1i)/(64*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a*sin(c + d*x)^n*sin(3*c + 3*d*x)*(n*210512i + n^2*171084i + n^3*67472i + n^4*14445i + n^5*1733i + n^6*111i + n^7*3i + 94080i)*3i)/(64*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a*sin(c + d*x)^n*cos(8*c + 8*d*x)*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040))/(128*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a*sin(c + d*x)^n*cos(6*c + 6*d*x)*(25296*n + 24226*n^2 + 11689*n^3 + 3100*n^4 + 454*n^5 + 34*n^6 + n^7 + 10080))/(32*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a*sin(c + d*x)^n*cos(4*c + 4*d*x)*(81396*n + 68728*n^2 + 27937*n^3 + 5968*n^4 + 682*n^5 + 40*n^6 + n^7 + 35280))/(32*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (a*sin(c + d*x)*sin(c + d*x)^n*(n*1735344i + n^2*826612i + n^3*209360i + n^4*32515i + n^5*3251i + n^6*193i + n^7*5i + 1411200i)*1i)/(64*d*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320))","B"
700,1,568,137,14.291313,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^n)/(a + a*sin(c + d*x)),x)","\frac{{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{32\,a\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{{\sin\left(c+d\,x\right)}^n\,\left(4\,n^5+92\,n^4+948\,n^3+4516\,n^2+8936\,n+5280\right)}{64\,a\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(n^5\,4{}\mathrm{i}+n^4\,96{}\mathrm{i}+n^3\,1052{}\mathrm{i}+n^2\,5904{}\mathrm{i}+n\,15504{}\mathrm{i}+14400{}\mathrm{i}\right)\,1{}\mathrm{i}}{32\,a\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}+\frac{{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(2\,n^5+46\,n^4+346\,n^3+1106\,n^2+1524\,n+720\right)}{32\,a\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}+\frac{{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(-n^5-15\,n^4+43\,n^3+927\,n^2+2670\,n+1800\right)}{32\,a\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(n^5\,2{}\mathrm{i}+n^4\,32{}\mathrm{i}+n^3\,190{}\mathrm{i}+n^2\,520{}\mathrm{i}+n\,648{}\mathrm{i}+288{}\mathrm{i}\right)\,1{}\mathrm{i}}{32\,a\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(n^5\,6{}\mathrm{i}+n^4\,128{}\mathrm{i}+n^3\,986{}\mathrm{i}+n^2\,3352{}\mathrm{i}+n\,4888{}\mathrm{i}+2400{}\mathrm{i}\right)\,1{}\mathrm{i}}{32\,a\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}","Not used",1,"(sin(c + d*x)^n*cos(6*c + 6*d*x)*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(32*a*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (sin(c + d*x)^n*(8936*n + 4516*n^2 + 948*n^3 + 92*n^4 + 4*n^5 + 5280))/(64*a*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (sin(c + d*x)*sin(c + d*x)^n*(n*15504i + n^2*5904i + n^3*1052i + n^4*96i + n^5*4i + 14400i)*1i)/(32*a*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) + (sin(c + d*x)^n*cos(4*c + 4*d*x)*(1524*n + 1106*n^2 + 346*n^3 + 46*n^4 + 2*n^5 + 720))/(32*a*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) + (sin(c + d*x)^n*cos(2*c + 2*d*x)*(2670*n + 927*n^2 + 43*n^3 - 15*n^4 - n^5 + 1800))/(32*a*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (sin(c + d*x)^n*sin(5*c + 5*d*x)*(n*648i + n^2*520i + n^3*190i + n^4*32i + n^5*2i + 288i)*1i)/(32*a*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (sin(c + d*x)^n*sin(3*c + 3*d*x)*(n*4888i + n^2*3352i + n^3*986i + n^4*128i + n^5*6i + 2400i)*1i)/(32*a*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))","B"
701,1,280,92,11.259861,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^n)/(a + a*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^n\,\left(560\,\sin\left(c+d\,x\right)-260\,n+160\,\cos\left(2\,c+2\,d\,x\right)+40\,\cos\left(4\,c+4\,d\,x\right)+40\,\sin\left(3\,c+3\,d\,x\right)-8\,\sin\left(5\,c+5\,d\,x\right)+468\,n\,\sin\left(c+d\,x\right)+192\,n\,\cos\left(2\,c+2\,d\,x\right)+68\,n\,\cos\left(4\,c+4\,d\,x\right)+70\,n\,\sin\left(3\,c+3\,d\,x\right)-14\,n\,\sin\left(5\,c+5\,d\,x\right)+106\,n^2\,\sin\left(c+d\,x\right)+6\,n^3\,\sin\left(c+d\,x\right)-64\,n^2-4\,n^3+32\,n^2\,\cos\left(2\,c+2\,d\,x\right)+32\,n^2\,\cos\left(4\,c+4\,d\,x\right)+4\,n^3\,\cos\left(4\,c+4\,d\,x\right)+35\,n^2\,\sin\left(3\,c+3\,d\,x\right)+5\,n^3\,\sin\left(3\,c+3\,d\,x\right)-7\,n^2\,\sin\left(5\,c+5\,d\,x\right)-n^3\,\sin\left(5\,c+5\,d\,x\right)-200\right)}{16\,a^2\,d\,\left(n^4+12\,n^3+49\,n^2+78\,n+40\right)}","Not used",1,"(sin(c + d*x)^n*(560*sin(c + d*x) - 260*n + 160*cos(2*c + 2*d*x) + 40*cos(4*c + 4*d*x) + 40*sin(3*c + 3*d*x) - 8*sin(5*c + 5*d*x) + 468*n*sin(c + d*x) + 192*n*cos(2*c + 2*d*x) + 68*n*cos(4*c + 4*d*x) + 70*n*sin(3*c + 3*d*x) - 14*n*sin(5*c + 5*d*x) + 106*n^2*sin(c + d*x) + 6*n^3*sin(c + d*x) - 64*n^2 - 4*n^3 + 32*n^2*cos(2*c + 2*d*x) + 32*n^2*cos(4*c + 4*d*x) + 4*n^3*cos(4*c + 4*d*x) + 35*n^2*sin(3*c + 3*d*x) + 5*n^3*sin(3*c + 3*d*x) - 7*n^2*sin(5*c + 5*d*x) - n^3*sin(5*c + 5*d*x) - 200))/(16*a^2*d*(78*n + 49*n^2 + 12*n^3 + n^4 + 40))","B"
702,1,242,92,10.614740,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^n)/(a + a*sin(c + d*x))^3,x)","-\frac{{\sin\left(c+d\,x\right)}^n\,\left(261\,n-336\,\sin\left(c+d\,x\right)-168\,\cos\left(2\,c+2\,d\,x\right)+6\,\cos\left(4\,c+4\,d\,x\right)+48\,\sin\left(3\,c+3\,d\,x\right)-460\,n\,\sin\left(c+d\,x\right)-272\,n\,\cos\left(2\,c+2\,d\,x\right)+11\,n\,\cos\left(4\,c+4\,d\,x\right)+84\,n\,\sin\left(3\,c+3\,d\,x\right)-198\,n^2\,\sin\left(c+d\,x\right)-26\,n^3\,\sin\left(c+d\,x\right)+114\,n^2+15\,n^3-120\,n^2\,\cos\left(2\,c+2\,d\,x\right)-16\,n^3\,\cos\left(2\,c+2\,d\,x\right)+6\,n^2\,\cos\left(4\,c+4\,d\,x\right)+n^3\,\cos\left(4\,c+4\,d\,x\right)+42\,n^2\,\sin\left(3\,c+3\,d\,x\right)+6\,n^3\,\sin\left(3\,c+3\,d\,x\right)+162\right)}{8\,a^3\,d\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}","Not used",1,"-(sin(c + d*x)^n*(261*n - 336*sin(c + d*x) - 168*cos(2*c + 2*d*x) + 6*cos(4*c + 4*d*x) + 48*sin(3*c + 3*d*x) - 460*n*sin(c + d*x) - 272*n*cos(2*c + 2*d*x) + 11*n*cos(4*c + 4*d*x) + 84*n*sin(3*c + 3*d*x) - 198*n^2*sin(c + d*x) - 26*n^3*sin(c + d*x) + 114*n^2 + 15*n^3 - 120*n^2*cos(2*c + 2*d*x) - 16*n^3*cos(2*c + 2*d*x) + 6*n^2*cos(4*c + 4*d*x) + n^3*cos(4*c + 4*d*x) + 42*n^2*sin(3*c + 3*d*x) + 6*n^3*sin(3*c + 3*d*x) + 162))/(8*a^3*d*(50*n + 35*n^2 + 10*n^3 + n^4 + 24))","B"
703,0,-1,109,0.000000,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^n)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\cos\left(c+d\,x\right)}^7\,{\sin\left(c+d\,x\right)}^n}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)^7*sin(c + d*x)^n)/(a + a*sin(c + d*x))^4, x)","F"
704,0,-1,160,0.000000,"\text{Not used}","int((cos(c + d*x)^7*sin(c + d*x)^n)/(a + a*sin(c + d*x))^5,x)","\int \frac{{\cos\left(c+d\,x\right)}^7\,{\sin\left(c+d\,x\right)}^n}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^5} \,d x","Not used",1,"int((cos(c + d*x)^7*sin(c + d*x)^n)/(a + a*sin(c + d*x))^5, x)","F"
705,1,303,209,11.850434,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^5)/(a + a*sin(c + d*x)),x)","-\frac{5\,x}{1024\,a}-\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{23}}{512}+\frac{175\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{1536}+\frac{311\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{512}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{3}-\frac{8361\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{512}-16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+\frac{42259\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{768}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-\frac{25295\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{256}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}+\frac{25295\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{256}-\frac{96\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{7}-\frac{42259\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{768}+\frac{192\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{7}+\frac{8361\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{512}-\frac{352\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{63}-\frac{311\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{512}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{21}-\frac{175\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{1536}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{231}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512}+\frac{16}{693}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{12}}","Not used",1,"- (5*x)/(1024*a) - ((64*tan(c/2 + (d*x)/2)^2)/231 - (5*tan(c/2 + (d*x)/2))/512 - (175*tan(c/2 + (d*x)/2)^3)/1536 + (32*tan(c/2 + (d*x)/2)^4)/21 - (311*tan(c/2 + (d*x)/2)^5)/512 - (352*tan(c/2 + (d*x)/2)^6)/63 + (8361*tan(c/2 + (d*x)/2)^7)/512 + (192*tan(c/2 + (d*x)/2)^8)/7 - (42259*tan(c/2 + (d*x)/2)^9)/768 - (96*tan(c/2 + (d*x)/2)^10)/7 + (25295*tan(c/2 + (d*x)/2)^11)/256 + (32*tan(c/2 + (d*x)/2)^12)/3 - (25295*tan(c/2 + (d*x)/2)^13)/256 + 32*tan(c/2 + (d*x)/2)^14 + (42259*tan(c/2 + (d*x)/2)^15)/768 - 16*tan(c/2 + (d*x)/2)^16 - (8361*tan(c/2 + (d*x)/2)^17)/512 + (32*tan(c/2 + (d*x)/2)^18)/3 + (311*tan(c/2 + (d*x)/2)^19)/512 + (175*tan(c/2 + (d*x)/2)^21)/1536 + (5*tan(c/2 + (d*x)/2)^23)/512 + 16/693)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^12)","B"
706,1,263,183,11.604734,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^4)/(a + a*sin(c + d*x)),x)","\frac{3\,x}{256\,a}+\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{128}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{4}-\frac{3323\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{640}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{3}+\frac{54\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{5}-\frac{80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3}-\frac{841\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{176\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}-48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{841\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{240\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{7}-\frac{54\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}-\frac{48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{7}+\frac{3323\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640}+\frac{80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{63}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{63}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}+\frac{16}{693}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{11}}","Not used",1,"(3*x)/(256*a) + ((16*tan(c/2 + (d*x)/2)^2)/63 - (3*tan(c/2 + (d*x)/2))/128 - tan(c/2 + (d*x)/2)^3/4 + (80*tan(c/2 + (d*x)/2)^4)/63 + (3323*tan(c/2 + (d*x)/2)^5)/640 - (48*tan(c/2 + (d*x)/2)^6)/7 - (54*tan(c/2 + (d*x)/2)^7)/5 + (240*tan(c/2 + (d*x)/2)^8)/7 + (841*tan(c/2 + (d*x)/2)^9)/64 - 48*tan(c/2 + (d*x)/2)^10 + (176*tan(c/2 + (d*x)/2)^12)/3 - (841*tan(c/2 + (d*x)/2)^13)/64 - (80*tan(c/2 + (d*x)/2)^14)/3 + (54*tan(c/2 + (d*x)/2)^15)/5 + (32*tan(c/2 + (d*x)/2)^16)/3 - (3323*tan(c/2 + (d*x)/2)^17)/640 + tan(c/2 + (d*x)/2)^19/4 + (3*tan(c/2 + (d*x)/2)^21)/128 + 16/693)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^11)","B"
707,1,251,165,11.523516,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^3)/(a + a*sin(c + d*x)),x)","-\frac{3\,x}{256\,a}-\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}+\frac{29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-\frac{867\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{160}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3}+\frac{519\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}-\frac{1879\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{1879\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}-\frac{519\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+\frac{72\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{7}+\frac{867\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}-\frac{29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128}+\frac{40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{63}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}+\frac{4}{63}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{10}}","Not used",1,"- (3*x)/(256*a) - ((40*tan(c/2 + (d*x)/2)^2)/63 - (3*tan(c/2 + (d*x)/2))/128 - (29*tan(c/2 + (d*x)/2)^3)/128 - (8*tan(c/2 + (d*x)/2)^4)/7 + (867*tan(c/2 + (d*x)/2)^5)/160 + (72*tan(c/2 + (d*x)/2)^6)/7 - (519*tan(c/2 + (d*x)/2)^7)/32 + (1879*tan(c/2 + (d*x)/2)^9)/64 + 8*tan(c/2 + (d*x)/2)^10 - (1879*tan(c/2 + (d*x)/2)^11)/64 + (40*tan(c/2 + (d*x)/2)^12)/3 + (519*tan(c/2 + (d*x)/2)^13)/32 - (8*tan(c/2 + (d*x)/2)^14)/3 - (867*tan(c/2 + (d*x)/2)^15)/160 + 4*tan(c/2 + (d*x)/2)^16 + (29*tan(c/2 + (d*x)/2)^17)/128 + (3*tan(c/2 + (d*x)/2)^19)/128 + 4/63)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
708,1,224,139,11.603965,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^2)/(a + a*sin(c + d*x)),x)","\frac{5\,x}{128\,a}+\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}-\frac{191\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{96}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\frac{83\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}-\frac{20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}-\frac{145\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{145\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{83\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}-\frac{12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}+\frac{191\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{7}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{4}{63}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(5*x)/(128*a) + ((4*tan(c/2 + (d*x)/2)^2)/7 - (5*tan(c/2 + (d*x)/2))/64 + (191*tan(c/2 + (d*x)/2)^3)/96 - (12*tan(c/2 + (d*x)/2)^4)/7 - (83*tan(c/2 + (d*x)/2)^5)/32 + 12*tan(c/2 + (d*x)/2)^6 + (145*tan(c/2 + (d*x)/2)^7)/32 - 12*tan(c/2 + (d*x)/2)^8 + 20*tan(c/2 + (d*x)/2)^10 - (145*tan(c/2 + (d*x)/2)^11)/32 - (20*tan(c/2 + (d*x)/2)^12)/3 + (83*tan(c/2 + (d*x)/2)^13)/32 + 4*tan(c/2 + (d*x)/2)^14 - (191*tan(c/2 + (d*x)/2)^15)/96 + (5*tan(c/2 + (d*x)/2)^17)/64 + 4/63)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
709,1,225,121,11.681764,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x))/(a + a*sin(c + d*x)),x)","-\frac{5\,x}{128\,a}-\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-\frac{397\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\frac{895\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{192}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{1765\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{1765\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{192}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{895\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{397\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{7}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{2}{7}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"- (5*x)/(128*a) - ((2*tan(c/2 + (d*x)/2)^2)/7 - (5*tan(c/2 + (d*x)/2))/64 + (397*tan(c/2 + (d*x)/2)^3)/192 + 6*tan(c/2 + (d*x)/2)^4 - (895*tan(c/2 + (d*x)/2)^5)/192 + 6*tan(c/2 + (d*x)/2)^6 + (1765*tan(c/2 + (d*x)/2)^7)/192 + 10*tan(c/2 + (d*x)/2)^8 - (1765*tan(c/2 + (d*x)/2)^9)/192 + 10*tan(c/2 + (d*x)/2)^10 + (895*tan(c/2 + (d*x)/2)^11)/192 + 2*tan(c/2 + (d*x)/2)^12 - (397*tan(c/2 + (d*x)/2)^13)/192 + 2*tan(c/2 + (d*x)/2)^14 + (5*tan(c/2 + (d*x)/2)^15)/64 + 2/7)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
710,1,305,143,11.829696,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{5\,\mathrm{atan}\left(\frac{25}{64\,\left(\frac{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{5}{4}\right)}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{5}{4}\right)}\right)}{8\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{92\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}-\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{62\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{46}{15}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(5*atan(25/(64*((25*tan(c/2 + (d*x)/2))/64 + 5/4)) - (5*tan(c/2 + (d*x)/2))/(4*((25*tan(c/2 + (d*x)/2))/64 + 5/4))))/(8*a*d) + log(tan(c/2 + (d*x)/2))/(a*d) + ((62*tan(c/2 + (d*x)/2)^2)/5 - (11*tan(c/2 + (d*x)/2))/8 + (5*tan(c/2 + (d*x)/2)^3)/24 + 28*tan(c/2 + (d*x)/2)^4 - (15*tan(c/2 + (d*x)/2)^5)/4 + (92*tan(c/2 + (d*x)/2)^6)/3 + (15*tan(c/2 + (d*x)/2)^7)/4 + 18*tan(c/2 + (d*x)/2)^8 - (5*tan(c/2 + (d*x)/2)^9)/24 + 6*tan(c/2 + (d*x)/2)^10 + (11*tan(c/2 + (d*x)/2)^11)/8 + 46/15)/(d*(a + 6*a*tan(c/2 + (d*x)/2)^2 + 15*a*tan(c/2 + (d*x)/2)^4 + 20*a*tan(c/2 + (d*x)/2)^6 + 15*a*tan(c/2 + (d*x)/2)^8 + 6*a*tan(c/2 + (d*x)/2)^10 + a*tan(c/2 + (d*x)/2)^12))","B"
711,1,296,137,9.041941,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{15\,\mathrm{atan}\left(\frac{15\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{225\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}-\frac{15}{2}\right)}+\frac{225}{16\,\left(\frac{225\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}-\frac{15}{2}\right)}\right)}{4\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{2}+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{112\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{92\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+1}{d\,\left(2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,a\,{\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)}^3+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}","Not used",1,"(15*atan((15*tan(c/2 + (d*x)/2))/(2*((225*tan(c/2 + (d*x)/2))/16 - 15/2)) + 225/(16*((225*tan(c/2 + (d*x)/2))/16 - 15/2))))/(4*a*d) - log(tan(c/2 + (d*x)/2))/(a*d) - ((92*tan(c/2 + (d*x)/2))/15 + (19*tan(c/2 + (d*x)/2)^2)/2 + (56*tan(c/2 + (d*x)/2)^3)/3 + 15*tan(c/2 + (d*x)/2)^4 + (112*tan(c/2 + (d*x)/2)^5)/3 + 10*tan(c/2 + (d*x)/2)^6 + 24*tan(c/2 + (d*x)/2)^7 + 12*tan(c/2 + (d*x)/2)^9 - (7*tan(c/2 + (d*x)/2)^10)/2 + 1)/(d*(2*a*tan(c/2 + (d*x)/2) + 10*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^5 + 20*a*tan(c/2 + (d*x)/2)^7 + 10*a*tan(c/2 + (d*x)/2)^9 + 2*a*tan(c/2 + (d*x)/2)^11)) + tan(c/2 + (d*x)/2)/(2*a*d)","B"
712,1,303,150,9.019201,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{15\,\mathrm{atan}\left(\frac{225}{16\,\left(\frac{225\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{75}{4}\right)}-\frac{75\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{225\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{75}{4}\right)}\right)}{4\,a\,d}-\frac{5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{49\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+58\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{161\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{62\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{2}}{d\,\left(4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - (15*atan(225/(16*((225*tan(c/2 + (d*x)/2))/16 + 75/4)) - (75*tan(c/2 + (d*x)/2))/(4*((225*tan(c/2 + (d*x)/2))/16 + 75/4))))/(4*a*d) - (5*log(tan(c/2 + (d*x)/2)))/(2*a*d) - ((62*tan(c/2 + (d*x)/2)^2)/3 - 2*tan(c/2 + (d*x)/2) - 17*tan(c/2 + (d*x)/2)^3 + (161*tan(c/2 + (d*x)/2)^4)/3 - 13*tan(c/2 + (d*x)/2)^5 + 58*tan(c/2 + (d*x)/2)^6 - 7*tan(c/2 + (d*x)/2)^7 + (49*tan(c/2 + (d*x)/2)^8)/2 + 7*tan(c/2 + (d*x)/2)^9 + 1/2)/(d*(4*a*tan(c/2 + (d*x)/2)^2 + 16*a*tan(c/2 + (d*x)/2)^4 + 24*a*tan(c/2 + (d*x)/2)^6 + 16*a*tan(c/2 + (d*x)/2)^8 + 4*a*tan(c/2 + (d*x)/2)^10)) - tan(c/2 + (d*x)/2)/(2*a*d)","B"
713,1,290,146,9.064476,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{5\,\mathrm{atan}\left(\frac{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-25}+\frac{25}{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-25}\right)}{a\,d}+\frac{5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+49\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+67\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+34\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{121\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{3}}{d\,\left(8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+24\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) - (5*atan((25*tan(c/2 + (d*x)/2))/(25*tan(c/2 + (d*x)/2) - 25) + 25/(25*tan(c/2 + (d*x)/2) - 25)))/(a*d) + (5*log(tan(c/2 + (d*x)/2)))/(2*a*d) + (tan(c/2 + (d*x)/2) + 8*tan(c/2 + (d*x)/2)^2 + (121*tan(c/2 + (d*x)/2)^3)/3 + 34*tan(c/2 + (d*x)/2)^4 + 67*tan(c/2 + (d*x)/2)^5 + (80*tan(c/2 + (d*x)/2)^6)/3 + 49*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^8 - 1/3)/(d*(8*a*tan(c/2 + (d*x)/2)^3 + 24*a*tan(c/2 + (d*x)/2)^5 + 24*a*tan(c/2 + (d*x)/2)^7 + 8*a*tan(c/2 + (d*x)/2)^9)) - (9*tan(c/2 + (d*x)/2))/(8*a*d)","B"
714,1,286,150,9.034131,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a\,d}+\frac{5\,\mathrm{atan}\left(\frac{25}{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{75}{4}}-\frac{75\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{75}{4}\right)}\right)}{a\,d}+\frac{15\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}+\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{154\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{159\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}-\frac{50\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{1}{4}}{d\,\left(16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+32\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a*d) - tan(c/2 + (d*x)/2)^3/(24*a*d) - tan(c/2 + (d*x)/2)^2/(4*a*d) + (5*atan(25/(25*tan(c/2 + (d*x)/2) + 75/4) - (75*tan(c/2 + (d*x)/2))/(4*(25*tan(c/2 + (d*x)/2) + 75/4))))/(a*d) + (15*log(tan(c/2 + (d*x)/2)))/(8*a*d) + ((2*tan(c/2 + (d*x)/2))/3 + (7*tan(c/2 + (d*x)/2)^2)/2 - (50*tan(c/2 + (d*x)/2)^3)/3 + (159*tan(c/2 + (d*x)/2)^4)/4 - (154*tan(c/2 + (d*x)/2)^5)/3 + 36*tan(c/2 + (d*x)/2)^6 - 2*tan(c/2 + (d*x)/2)^7 - 1/4)/(d*(16*a*tan(c/2 + (d*x)/2)^4 + 32*a*tan(c/2 + (d*x)/2)^6 + 16*a*tan(c/2 + (d*x)/2)^8)) + (9*tan(c/2 + (d*x)/2))/(8*a*d)","B"
715,1,279,138,9.027672,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^6*(a + a*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a\,d}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}+\frac{2\,\mathrm{atan}\left(\frac{15\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{15}{2}\right)}+\frac{4}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{15}{2}}\right)}{a\,d}-\frac{15\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}-\frac{22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+72\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{59\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{1}{5}}{d\,\left(32\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(4*a*d) - (7*tan(c/2 + (d*x)/2)^3)/(96*a*d) - tan(c/2 + (d*x)/2)^4/(64*a*d) + tan(c/2 + (d*x)/2)^5/(160*a*d) + (2*atan((15*tan(c/2 + (d*x)/2))/(2*(4*tan(c/2 + (d*x)/2) - 15/2)) + 4/(4*tan(c/2 + (d*x)/2) - 15/2)))/(a*d) - (15*log(tan(c/2 + (d*x)/2)))/(8*a*d) - ((15*tan(c/2 + (d*x)/2)^3)/2 - (32*tan(c/2 + (d*x)/2)^2)/15 - tan(c/2 + (d*x)/2)/2 + (59*tan(c/2 + (d*x)/2)^4)/3 + 72*tan(c/2 + (d*x)/2)^5 + 22*tan(c/2 + (d*x)/2)^6 + 1/5)/(d*(32*a*tan(c/2 + (d*x)/2)^5 + 32*a*tan(c/2 + (d*x)/2)^7)) + (11*tan(c/2 + (d*x)/2))/(16*a*d)","B"
716,1,413,142,10.387189,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^7*(a + a*sin(c + d*x))),x)","-\frac{5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+12\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-12\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-140\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-225\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+1320\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-1320\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+225\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+140\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3840\,\mathrm{atan}\left(\frac{16\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+600\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1920\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"-(5*cos(c/2 + (d*x)/2)^12 - 5*sin(c/2 + (d*x)/2)^12 + 12*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 - 12*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) + 45*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 - 140*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 - 225*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 1320*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 - 1320*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 + 225*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 140*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 - 45*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 3840*atan((16*cos(c/2 + (d*x)/2) - 5*sin(c/2 + (d*x)/2))/(5*cos(c/2 + (d*x)/2) + 16*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6 + 600*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/(1920*a*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
717,1,387,106,10.615193,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^8*(a + a*sin(c + d*x))),x)","\frac{3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+7\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2688\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(3*sin(c/2 + (d*x)/2)^14 - 3*cos(c/2 + (d*x)/2)^14 - 7*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 + 7*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) - 21*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 + 63*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 + 63*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 - 315*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 - 105*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 105*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 315*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 - 63*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 - 63*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 + 21*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)/(2688*a*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)","B"
718,1,435,134,11.388160,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^9*(a + a*sin(c + d*x))),x)","-\frac{21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-21\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+48\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-48\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+112\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-336\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-168\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+1008\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-336\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-1680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+1680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+336\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-1008\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+168\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+336\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-112\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1680\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{43008\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}","Not used",1,"-(21*cos(c/2 + (d*x)/2)^16 - 21*sin(c/2 + (d*x)/2)^16 + 48*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^15 - 48*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2) + 112*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^14 - 336*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^13 - 168*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 + 1008*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^11 - 336*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 - 1680*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^9 + 1680*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^7 + 336*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 - 1008*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^5 + 168*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 + 336*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^3 - 112*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^2 + 1680*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8)/(43008*a*d*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8)","B"
719,1,435,152,12.553121,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^10*(a + a*sin(c + d*x))),x)","\frac{28\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-28\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-63\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-108\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+336\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-504\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+672\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-1008\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-1512\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+1512\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+1008\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-672\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+504\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-336\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+108\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+5040\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{129024\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"(28*sin(c/2 + (d*x)/2)^18 - 28*cos(c/2 + (d*x)/2)^18 - 63*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^17 + 63*cos(c/2 + (d*x)/2)^17*sin(c/2 + (d*x)/2) - 108*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^16 + 336*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^15 - 504*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^13 + 672*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^12 - 1008*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^11 - 1512*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^10 + 1512*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^8 + 1008*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^7 - 672*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^6 + 504*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^5 - 336*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2)^3 + 108*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^2 + 5040*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^9)/(129024*a*d*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^9)","B"
720,1,483,176,13.995184,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^11*(a + a*sin(c + d*x))),x)","-\frac{126\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}-126\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+280\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}-280\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-1080\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}+630\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-1260\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-15120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+15120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+1260\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-630\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+1080\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+15120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{1290240\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}","Not used",1,"-(126*cos(c/2 + (d*x)/2)^20 - 126*sin(c/2 + (d*x)/2)^20 + 280*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^19 - 280*cos(c/2 + (d*x)/2)^19*sin(c/2 + (d*x)/2) + 315*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^18 - 1080*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^17 + 630*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^16 - 2520*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^14 + 6720*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^13 - 1260*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^12 - 15120*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^11 + 15120*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^9 + 1260*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^8 - 6720*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^7 + 2520*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^6 - 630*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^4 + 1080*cos(c/2 + (d*x)/2)^17*sin(c/2 + (d*x)/2)^3 - 315*cos(c/2 + (d*x)/2)^18*sin(c/2 + (d*x)/2)^2 + 15120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^10)/(1290240*a*d*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^10)","B"
721,1,579,194,16.266273,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^12*(a + a*sin(c + d*x))),x)","\frac{630\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}-630\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}-1386\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}+1386\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-770\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+3465\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}-4950\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+6930\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}+6930\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-27720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+23100\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-13860\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-69300\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+69300\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+13860\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-23100\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+27720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-6930\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-6930\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4950\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3465\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+770\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+166320\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{14192640\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}","Not used",1,"(630*sin(c/2 + (d*x)/2)^22 - 630*cos(c/2 + (d*x)/2)^22 - 1386*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^21 + 1386*cos(c/2 + (d*x)/2)^21*sin(c/2 + (d*x)/2) - 770*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^20 + 3465*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^19 - 4950*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^18 + 6930*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^17 + 6930*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^16 - 27720*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^15 + 23100*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^14 - 13860*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^13 - 69300*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^12 + 69300*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^10 + 13860*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^9 - 23100*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^8 + 27720*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2)^7 - 6930*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^6 - 6930*cos(c/2 + (d*x)/2)^17*sin(c/2 + (d*x)/2)^5 + 4950*cos(c/2 + (d*x)/2)^18*sin(c/2 + (d*x)/2)^4 - 3465*cos(c/2 + (d*x)/2)^19*sin(c/2 + (d*x)/2)^3 + 770*cos(c/2 + (d*x)/2)^20*sin(c/2 + (d*x)/2)^2 + 166320*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^11)/(14192640*a*d*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^11)","B"
722,1,264,203,11.509217,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^5)/(a + a*sin(c + d*x))^2,x)","-\frac{3\,x}{128\,a^2}-\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{64}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{2}+\frac{773\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{320}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{3}-\frac{148\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{5}+\frac{112\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3}+\frac{1207\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}-\frac{848\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{15}+\frac{464\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{5}-\frac{1207\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{32}-\frac{80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{7}+\frac{148\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{7}-\frac{773\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320}+\frac{272\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{63}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{272\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{315}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{272}{3465}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{11}}","Not used",1,"- (3*x)/(128*a^2) - ((272*tan(c/2 + (d*x)/2)^2)/315 - (3*tan(c/2 + (d*x)/2))/64 - tan(c/2 + (d*x)/2)^3/2 + (272*tan(c/2 + (d*x)/2)^4)/63 - (773*tan(c/2 + (d*x)/2)^5)/320 + (16*tan(c/2 + (d*x)/2)^6)/7 + (148*tan(c/2 + (d*x)/2)^7)/5 - (80*tan(c/2 + (d*x)/2)^8)/7 - (1207*tan(c/2 + (d*x)/2)^9)/32 + (464*tan(c/2 + (d*x)/2)^10)/5 - (848*tan(c/2 + (d*x)/2)^12)/15 + (1207*tan(c/2 + (d*x)/2)^13)/32 + (112*tan(c/2 + (d*x)/2)^14)/3 - (148*tan(c/2 + (d*x)/2)^15)/5 + (32*tan(c/2 + (d*x)/2)^16)/3 + (773*tan(c/2 + (d*x)/2)^17)/320 + tan(c/2 + (d*x)/2)^19/2 + (3*tan(c/2 + (d*x)/2)^21)/64 + 272/3465)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^11)","B"
723,1,250,185,11.629449,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^4)/(a + a*sin(c + d*x))^2,x)","\frac{9\,x}{256\,a^2}+\frac{\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}+\frac{87\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{553\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{160}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3}-\frac{491\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}-\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}+\frac{2555\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{5}-\frac{2555\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{491\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}-\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{7}+\frac{553\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}-\frac{87\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{63}-\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}+\frac{32}{315}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{10}}","Not used",1,"(9*x)/(256*a^2) + ((64*tan(c/2 + (d*x)/2)^2)/63 - (9*tan(c/2 + (d*x)/2))/128 - (87*tan(c/2 + (d*x)/2)^3)/128 + (32*tan(c/2 + (d*x)/2)^4)/7 + (553*tan(c/2 + (d*x)/2)^5)/160 - (64*tan(c/2 + (d*x)/2)^6)/7 + (491*tan(c/2 + (d*x)/2)^7)/32 + 32*tan(c/2 + (d*x)/2)^8 - (2555*tan(c/2 + (d*x)/2)^9)/64 + (64*tan(c/2 + (d*x)/2)^10)/5 + (2555*tan(c/2 + (d*x)/2)^11)/64 - (32*tan(c/2 + (d*x)/2)^12)/3 - (491*tan(c/2 + (d*x)/2)^13)/32 + (64*tan(c/2 + (d*x)/2)^14)/3 - (553*tan(c/2 + (d*x)/2)^15)/160 + (87*tan(c/2 + (d*x)/2)^17)/128 + (9*tan(c/2 + (d*x)/2)^19)/128 + 32/315)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
724,1,225,159,11.680867,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^3)/(a + a*sin(c + d*x))^2,x)","-\frac{3\,x}{64\,a^2}-\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{32}+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{16}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-\frac{155\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{16}+\frac{44\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}+\frac{169\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{16}-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{164\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{5}-\frac{169\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{155\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{16}+\frac{68\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}-\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{16}+\frac{52\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32}+\frac{52}{315}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"- (3*x)/(64*a^2) - ((52*tan(c/2 + (d*x)/2)^2)/35 - (3*tan(c/2 + (d*x)/2))/32 - (13*tan(c/2 + (d*x)/2)^3)/16 + (68*tan(c/2 + (d*x)/2)^4)/35 + (155*tan(c/2 + (d*x)/2)^5)/16 - (4*tan(c/2 + (d*x)/2)^6)/5 - (169*tan(c/2 + (d*x)/2)^7)/16 + (164*tan(c/2 + (d*x)/2)^8)/5 - 12*tan(c/2 + (d*x)/2)^10 + (169*tan(c/2 + (d*x)/2)^11)/16 + (44*tan(c/2 + (d*x)/2)^12)/3 - (155*tan(c/2 + (d*x)/2)^13)/16 + 4*tan(c/2 + (d*x)/2)^14 + (13*tan(c/2 + (d*x)/2)^15)/16 + (3*tan(c/2 + (d*x)/2)^17)/32 + 52/315)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
725,1,198,141,11.702777,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^2)/(a + a*sin(c + d*x))^2,x)","\frac{11\,x}{128\,a^2}+\frac{\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}-\frac{259\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{1103\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{192}+\frac{2261\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{2261\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{192}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{1103\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{259\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}-\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{8}{35}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"(11*x)/(128*a^2) + ((64*tan(c/2 + (d*x)/2)^2)/35 - (11*tan(c/2 + (d*x)/2))/64 + (259*tan(c/2 + (d*x)/2)^3)/192 - (8*tan(c/2 + (d*x)/2)^4)/5 + (1103*tan(c/2 + (d*x)/2)^5)/192 + (64*tan(c/2 + (d*x)/2)^6)/5 - (2261*tan(c/2 + (d*x)/2)^7)/192 + 8*tan(c/2 + (d*x)/2)^8 + (2261*tan(c/2 + (d*x)/2)^9)/192 - (1103*tan(c/2 + (d*x)/2)^11)/192 + 8*tan(c/2 + (d*x)/2)^12 - (259*tan(c/2 + (d*x)/2)^13)/192 + (11*tan(c/2 + (d*x)/2)^15)/64 + 8/35)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
726,1,186,124,12.652036,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x))/(a + a*sin(c + d*x))^2,x)","-\frac{x}{8\,a^2}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{31\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{31\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{18}{35}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"- x/(8*a^2) - ((8*tan(c/2 + (d*x)/2)^2)/5 - tan(c/2 + (d*x)/2)/4 + (11*tan(c/2 + (d*x)/2)^3)/3 + (14*tan(c/2 + (d*x)/2)^4)/5 - (31*tan(c/2 + (d*x)/2)^5)/12 + 16*tan(c/2 + (d*x)/2)^6 + 2*tan(c/2 + (d*x)/2)^8 + (31*tan(c/2 + (d*x)/2)^9)/12 + 8*tan(c/2 + (d*x)/2)^10 - (11*tan(c/2 + (d*x)/2)^11)/3 + 2*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^13/4 + 18/35)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
727,1,262,119,10.757996,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{3\,\mathrm{atan}\left(\frac{9}{4\,\left(\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+3\right)}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+3}\right)}{2\,a^2\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{34}{15}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}","Not used",1,"(3*atan(9/(4*((9*tan(c/2 + (d*x)/2))/4 + 3)) - (3*tan(c/2 + (d*x)/2))/((9*tan(c/2 + (d*x)/2))/4 + 3)))/(2*a^2*d) + log(tan(c/2 + (d*x)/2))/(a^2*d) + ((28*tan(c/2 + (d*x)/2)^2)/3 - (5*tan(c/2 + (d*x)/2))/2 - tan(c/2 + (d*x)/2)^3 + (32*tan(c/2 + (d*x)/2)^4)/3 + 12*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^7 + 2*tan(c/2 + (d*x)/2)^8 + (5*tan(c/2 + (d*x)/2)^9)/2 + 34/15)/(d*(5*a^2*tan(c/2 + (d*x)/2)^2 + 10*a^2*tan(c/2 + (d*x)/2)^4 + 10*a^2*tan(c/2 + (d*x)/2)^6 + 5*a^2*tan(c/2 + (d*x)/2)^8 + a^2*tan(c/2 + (d*x)/2)^10 + a^2))","B"
728,1,279,116,9.212352,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{9\,\mathrm{atan}\left(\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{81\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}-9}+\frac{81}{16\,\left(\frac{81\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}-9\right)}\right)}{4\,a^2\,d}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+1}{d\,\left(2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}","Not used",1,"(9*atan((9*tan(c/2 + (d*x)/2))/((81*tan(c/2 + (d*x)/2))/16 - 9) + 81/(16*((81*tan(c/2 + (d*x)/2))/16 - 9))))/(4*a^2*d) - (2*log(tan(c/2 + (d*x)/2)))/(a^2*d) - ((32*tan(c/2 + (d*x)/2))/3 + (7*tan(c/2 + (d*x)/2)^2)/2 + (80*tan(c/2 + (d*x)/2)^3)/3 + (19*tan(c/2 + (d*x)/2)^4)/2 + 32*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^6/2 + 16*tan(c/2 + (d*x)/2)^7 + (3*tan(c/2 + (d*x)/2)^8)/2 + 1)/(d*(8*a^2*tan(c/2 + (d*x)/2)^3 + 12*a^2*tan(c/2 + (d*x)/2)^5 + 8*a^2*tan(c/2 + (d*x)/2)^7 + 2*a^2*tan(c/2 + (d*x)/2)^9 + 2*a^2*tan(c/2 + (d*x)/2))) + tan(c/2 + (d*x)/2)/(2*a^2*d)","B"
729,1,270,97,9.069800,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{6\,\mathrm{atan}\left(\frac{36}{36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}-\frac{6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}\right)}{a^2\,d}+\frac{-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{6}+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}}{d\,\left(4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) - (6*atan(36/(36*tan(c/2 + (d*x)/2) + 6) - (6*tan(c/2 + (d*x)/2))/(36*tan(c/2 + (d*x)/2) + 6)))/(a^2*d) + (4*tan(c/2 + (d*x)/2) + (7*tan(c/2 + (d*x)/2)^2)/6 + 20*tan(c/2 + (d*x)/2)^3 - (3*tan(c/2 + (d*x)/2)^4)/2 + 12*tan(c/2 + (d*x)/2)^5 + (15*tan(c/2 + (d*x)/2)^6)/2 - 4*tan(c/2 + (d*x)/2)^7 - 1/2)/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 + 12*a^2*tan(c/2 + (d*x)/2)^4 + 12*a^2*tan(c/2 + (d*x)/2)^6 + 4*a^2*tan(c/2 + (d*x)/2)^8)) - log(tan(c/2 + (d*x)/2))/(2*a^2*d) - tan(c/2 + (d*x)/2)/(a^2*d)","B"
730,1,253,97,9.155686,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^2\,d}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+34\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{3}}{d\,\left(8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^2\,d}+\frac{\mathrm{atan}\left(\frac{1}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}-\frac{6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}\right)}{a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^2*d) - tan(c/2 + (d*x)/2)^2/(4*a^2*d) + (3*log(tan(c/2 + (d*x)/2)))/(a^2*d) + (2*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2/3 + 36*tan(c/2 + (d*x)/2)^3 - (19*tan(c/2 + (d*x)/2)^4)/3 + 34*tan(c/2 + (d*x)/2)^5 + 9*tan(c/2 + (d*x)/2)^6 - 1/3)/(d*(8*a^2*tan(c/2 + (d*x)/2)^3 + 16*a^2*tan(c/2 + (d*x)/2)^5 + 8*a^2*tan(c/2 + (d*x)/2)^7)) - tan(c/2 + (d*x)/2)/(8*a^2*d) + atan(1/(tan(c/2 + (d*x)/2) + 6) - (6*tan(c/2 + (d*x)/2))/(tan(c/2 + (d*x)/2) + 6))/(a^2*d)","B"
731,1,232,116,9.083034,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^5*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,a^2\,d}+\frac{4\,\mathrm{atan}\left(\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9}+\frac{16}{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9}\right)}{a^2\,d}-\frac{9\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a^2\,d}-\frac{20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{1}{4}}{d\,\left(16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a^2*d) - tan(c/2 + (d*x)/2)^3/(12*a^2*d) + (4*atan((9*tan(c/2 + (d*x)/2))/(16*tan(c/2 + (d*x)/2) - 9) + 16/(16*tan(c/2 + (d*x)/2) - 9)))/(a^2*d) - (9*log(tan(c/2 + (d*x)/2)))/(8*a^2*d) - (tan(c/2 + (d*x)/2)^2/4 - (4*tan(c/2 + (d*x)/2))/3 + (56*tan(c/2 + (d*x)/2)^3)/3 + 32*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^5 + 1/4)/(d*(16*a^2*tan(c/2 + (d*x)/2)^4 + 16*a^2*tan(c/2 + (d*x)/2)^6)) + (5*tan(c/2 + (d*x)/2))/(4*a^2*d)","B"
732,1,365,118,9.851285,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^6*(a + a*sin(c + d*x))^2),x)","-\frac{3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+270\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-270\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+960\,\mathrm{atan}\left(\frac{4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+360\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{480\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(3*cos(c/2 + (d*x)/2)^10 - 3*sin(c/2 + (d*x)/2)^10 + 15*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 - 15*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - 5*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 - 120*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7 + 270*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 - 270*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 120*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3 + 5*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 960*atan((4*cos(c/2 + (d*x)/2) - 3*sin(c/2 + (d*x)/2))/(3*cos(c/2 + (d*x)/2) + 4*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5 + 360*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/(480*a^2*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)","B"
733,1,339,132,10.344464,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^7*(a + a*sin(c + d*x))^2),x)","\frac{5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-24\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-255\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+255\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1920\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"(5*sin(c/2 + (d*x)/2)^12 - 5*cos(c/2 + (d*x)/2)^12 - 24*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 + 24*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) + 15*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 120*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 - 255*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 240*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 240*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 + 255*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 120*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 - 15*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/(1920*a^2*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
734,1,387,124,10.840589,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^8*(a + a*sin(c + d*x))^2),x)","-\frac{15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-15\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+70\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-70\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-210\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+525\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-210\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-1155\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+1155\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+210\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-525\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+210\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1680\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{13440\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(15*cos(c/2 + (d*x)/2)^14 - 15*sin(c/2 + (d*x)/2)^14 + 70*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 - 70*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) - 63*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 210*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 + 525*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 - 210*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 - 1155*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 1155*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 210*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 - 525*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 + 210*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 + 63*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 1680*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)/(13440*a^2*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)","B"
735,1,435,176,11.959391,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^9*(a + a*sin(c + d*x))^2),x)","\frac{105\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-480\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+480\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+672\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-1680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-10080\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+10080\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+1680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-672\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+18480\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{215040\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}","Not used",1,"(105*sin(c/2 + (d*x)/2)^16 - 105*cos(c/2 + (d*x)/2)^16 - 480*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^15 + 480*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2) + 560*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^14 + 672*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^13 - 2520*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 + 3360*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^11 - 1680*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 - 10080*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^9 + 10080*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^7 + 1680*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 - 3360*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^5 + 2520*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 - 672*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^3 - 560*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^2 + 18480*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8)/(215040*a^2*d*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8)","B"
736,1,387,168,12.558025,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^10*(a + a*sin(c + d*x))^2),x)","-\frac{70\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-70\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+315\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-450\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+1008\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-11340\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+11340\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-1008\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+450\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+15120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{322560\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(70*cos(c/2 + (d*x)/2)^18 - 70*sin(c/2 + (d*x)/2)^18 + 315*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^17 - 315*cos(c/2 + (d*x)/2)^17*sin(c/2 + (d*x)/2) - 450*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^16 + 1008*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^14 - 2520*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^13 + 3360*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^12 - 11340*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^10 + 11340*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^8 - 3360*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^6 + 2520*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^5 - 1008*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^4 + 450*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^2 + 15120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^9)/(322560*a^2*d*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^9)","B"
737,1,531,218,14.341925,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^11*(a + a*sin(c + d*x))^2),x)","\frac{126\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}-126\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}-560\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}+560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+945\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-630\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+4032\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-7560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+1260\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-30240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+30240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-1260\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+7560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-4032\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+630\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-945\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+45360\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{1290240\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}","Not used",1,"(126*sin(c/2 + (d*x)/2)^20 - 126*cos(c/2 + (d*x)/2)^20 - 560*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^19 + 560*cos(c/2 + (d*x)/2)^19*sin(c/2 + (d*x)/2) + 945*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^18 - 720*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^17 - 630*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^16 + 4032*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^15 - 7560*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^14 + 6720*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^13 + 1260*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^12 - 30240*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^11 + 30240*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^9 - 1260*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^8 - 6720*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^7 + 7560*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^6 - 4032*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2)^5 + 630*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^4 + 720*cos(c/2 + (d*x)/2)^17*sin(c/2 + (d*x)/2)^3 - 945*cos(c/2 + (d*x)/2)^18*sin(c/2 + (d*x)/2)^2 + 45360*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^10)/(1290240*a^2*d*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^10)","B"
738,1,579,210,16.548098,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^12*(a + a*sin(c + d*x))^2),x)","-\frac{315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}-315\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}+1386\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}-1386\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2695\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+3465\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}-1485\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-6930\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}+18711\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-27720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+25410\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+13860\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-131670\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+131670\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-13860\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-25410\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+27720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-18711\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6930\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+1485\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3465\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2695\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+166320\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{7096320\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}","Not used",1,"-(315*cos(c/2 + (d*x)/2)^22 - 315*sin(c/2 + (d*x)/2)^22 + 1386*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^21 - 1386*cos(c/2 + (d*x)/2)^21*sin(c/2 + (d*x)/2) - 2695*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^20 + 3465*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^19 - 1485*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^18 - 6930*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^17 + 18711*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^16 - 27720*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^15 + 25410*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^14 + 13860*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^13 - 131670*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^12 + 131670*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^10 - 13860*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^9 - 25410*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^8 + 27720*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2)^7 - 18711*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^6 + 6930*cos(c/2 + (d*x)/2)^17*sin(c/2 + (d*x)/2)^5 + 1485*cos(c/2 + (d*x)/2)^18*sin(c/2 + (d*x)/2)^4 - 3465*cos(c/2 + (d*x)/2)^19*sin(c/2 + (d*x)/2)^3 + 2695*cos(c/2 + (d*x)/2)^20*sin(c/2 + (d*x)/2)^2 + 166320*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^11)/(7096320*a^2*d*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^11)","B"
739,1,212,161,11.944200,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^3)/(a + a*sin(c + d*x))^3,x)","-\frac{29\,x}{128\,a^3}-\frac{\frac{29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{667\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{1465\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{192}+\frac{128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}-\frac{5117\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{76\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{5117\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{192}-\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}+\frac{1465\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}+\frac{244\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}-\frac{667\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{608\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{105}-\frac{29\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{76}{105}}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"- (29*x)/(128*a^3) - ((608*tan(c/2 + (d*x)/2)^2)/105 - (29*tan(c/2 + (d*x)/2))/64 - (667*tan(c/2 + (d*x)/2)^3)/192 + (244*tan(c/2 + (d*x)/2)^4)/15 + (1465*tan(c/2 + (d*x)/2)^5)/192 - (32*tan(c/2 + (d*x)/2)^6)/15 + (5117*tan(c/2 + (d*x)/2)^7)/192 + (76*tan(c/2 + (d*x)/2)^8)/3 - (5117*tan(c/2 + (d*x)/2)^9)/192 + (128*tan(c/2 + (d*x)/2)^10)/3 - (1465*tan(c/2 + (d*x)/2)^11)/192 + 4*tan(c/2 + (d*x)/2)^12 + (667*tan(c/2 + (d*x)/2)^13)/192 + (29*tan(c/2 + (d*x)/2)^15)/64 + 76/105)/(a^3*d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
740,1,172,133,12.638583,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x)^2)/(a + a*sin(c + d*x))^3,x)","\frac{5\,x}{16\,a^3}+\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{2}+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{119\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}+\frac{92\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{119\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{20}{21}}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(5*x)/(16*a^3) + ((20*tan(c/2 + (d*x)/2)^2)/3 - (5*tan(c/2 + (d*x)/2))/8 - (3*tan(c/2 + (d*x)/2)^3)/2 + 8*tan(c/2 + (d*x)/2)^4 + (119*tan(c/2 + (d*x)/2)^5)/8 + (8*tan(c/2 + (d*x)/2)^6)/3 + (92*tan(c/2 + (d*x)/2)^8)/3 - (119*tan(c/2 + (d*x)/2)^9)/8 + 12*tan(c/2 + (d*x)/2)^10 + (3*tan(c/2 + (d*x)/2)^11)/2 + (5*tan(c/2 + (d*x)/2)^13)/8 + 20/21)/(a^3*d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
741,1,173,131,12.492816,"\text{Not used}","int((cos(c + d*x)^8*sin(c + d*x))/(a + a*sin(c + d*x))^3,x)","-\frac{7\,x}{16\,a^3}-\frac{\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{73\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{37\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{44\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{37\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{73\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{34\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{22}{15}}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"- (7*x)/(16*a^3) - ((34*tan(c/2 + (d*x)/2)^2)/5 - (7*tan(c/2 + (d*x)/2))/8 + (73*tan(c/2 + (d*x)/2)^3)/24 + 4*tan(c/2 + (d*x)/2)^4 + (37*tan(c/2 + (d*x)/2)^5)/4 + (44*tan(c/2 + (d*x)/2)^6)/3 - (37*tan(c/2 + (d*x)/2)^7)/4 + 18*tan(c/2 + (d*x)/2)^8 - (73*tan(c/2 + (d*x)/2)^9)/24 + 2*tan(c/2 + (d*x)/2)^10 + (7*tan(c/2 + (d*x)/2)^11)/8 + 22/15)/(a^3*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
742,1,222,99,10.995386,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{13\,\mathrm{atan}\left(\frac{169}{16\,\left(\frac{169\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{13}{2}\right)}-\frac{13\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{169\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{13}{2}\right)}\right)}{4\,a^3\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}","Not used",1,"(13*atan(169/(16*((169*tan(c/2 + (d*x)/2))/16 + 13/2)) - (13*tan(c/2 + (d*x)/2))/(2*((169*tan(c/2 + (d*x)/2))/16 + 13/2))))/(4*a^3*d) + log(tan(c/2 + (d*x)/2))/(a^3*d) - ((11*tan(c/2 + (d*x)/2))/4 - 4*tan(c/2 + (d*x)/2)^2 + (19*tan(c/2 + (d*x)/2)^3)/4 - (19*tan(c/2 + (d*x)/2)^5)/4 + 4*tan(c/2 + (d*x)/2)^6 - (11*tan(c/2 + (d*x)/2)^7)/4)/(d*(4*a^3*tan(c/2 + (d*x)/2)^2 + 6*a^3*tan(c/2 + (d*x)/2)^4 + 4*a^3*tan(c/2 + (d*x)/2)^6 + a^3*tan(c/2 + (d*x)/2)^8 + a^3))","B"
743,1,231,92,9.123746,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+24\,{\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+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+1}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{\mathrm{atan}\left(\frac{1}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}-\frac{6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}\right)}{a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - ((32*tan(c/2 + (d*x)/2))/3 - 3*tan(c/2 + (d*x)/2)^2 + 24*tan(c/2 + (d*x)/2)^3 + 3*tan(c/2 + (d*x)/2)^4 + 8*tan(c/2 + (d*x)/2)^5 + 7*tan(c/2 + (d*x)/2)^6 + 1)/(d*(6*a^3*tan(c/2 + (d*x)/2)^3 + 6*a^3*tan(c/2 + (d*x)/2)^5 + 2*a^3*tan(c/2 + (d*x)/2)^7 + 2*a^3*tan(c/2 + (d*x)/2))) - (3*log(tan(c/2 + (d*x)/2)))/(a^3*d) - atan(1/(tan(c/2 + (d*x)/2) + 6) - (6*tan(c/2 + (d*x)/2))/(tan(c/2 + (d*x)/2) + 6))/(a^3*d)","B"
744,1,228,98,9.242228,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^3*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{5\,\mathrm{atan}\left(\frac{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-25}+\frac{25}{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-25}\right)}{a^3\,d}+\frac{5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^3\,d}+\frac{10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{47\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}}{d\,\left(4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^3*d) - (5*atan((25*tan(c/2 + (d*x)/2))/(25*tan(c/2 + (d*x)/2) - 25) + 25/(25*tan(c/2 + (d*x)/2) - 25)))/(a^3*d) + (5*log(tan(c/2 + (d*x)/2)))/(2*a^3*d) + (6*tan(c/2 + (d*x)/2) + 23*tan(c/2 + (d*x)/2)^2 + 8*tan(c/2 + (d*x)/2)^3 + (47*tan(c/2 + (d*x)/2)^4)/2 + 10*tan(c/2 + (d*x)/2)^5 - 1/2)/(d*(4*a^3*tan(c/2 + (d*x)/2)^2 + 8*a^3*tan(c/2 + (d*x)/2)^4 + 4*a^3*tan(c/2 + (d*x)/2)^6)) - (3*tan(c/2 + (d*x)/2))/(2*a^3*d)","B"
745,1,219,92,9.256961,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^3\,d}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{6\,\mathrm{atan}\left(\frac{36}{36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}-\frac{6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6}\right)}{a^3\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^3\,d}+\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}-\frac{11\,{\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+\frac{34\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{3}}{d\,\left(8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^3*d) - (3*tan(c/2 + (d*x)/2)^2)/(8*a^3*d) + (6*atan(36/(36*tan(c/2 + (d*x)/2) + 6) - (6*tan(c/2 + (d*x)/2))/(36*tan(c/2 + (d*x)/2) + 6)))/(a^3*d) + log(tan(c/2 + (d*x)/2))/(2*a^3*d) + (11*tan(c/2 + (d*x)/2))/(8*a^3*d) - ((34*tan(c/2 + (d*x)/2)^2)/3 - 3*tan(c/2 + (d*x)/2) + 13*tan(c/2 + (d*x)/2)^3 + 11*tan(c/2 + (d*x)/2)^4 + 1/3)/(d*(8*a^3*tan(c/2 + (d*x)/2)^3 + 8*a^3*tan(c/2 + (d*x)/2)^5))","B"
746,1,315,97,9.525741,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^5*(a + a*sin(c + d*x))^3),x)","-\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+128\,\mathrm{atan}\left(\frac{8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-13\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{13\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+104\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}","Not used",1,"-(cos(c/2 + (d*x)/2)^8 - sin(c/2 + (d*x)/2)^8 + 8*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^7 - 8*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2) - 24*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^6 + 8*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^5 - 8*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^3 + 24*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2 + 128*atan((8*cos(c/2 + (d*x)/2) - 13*sin(c/2 + (d*x)/2))/(13*cos(c/2 + (d*x)/2) + 8*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4 + 104*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4)/(64*a^3*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4)","B"
747,1,291,100,9.601918,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^6*(a + a*sin(c + d*x))^3),x)","\frac{6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-45\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+130\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-420\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+420\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-130\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{960\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(6*sin(c/2 + (d*x)/2)^10 - 6*cos(c/2 + (d*x)/2)^10 - 45*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 + 45*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) + 130*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 - 120*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7 - 420*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + 420*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 120*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3 - 130*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/(960*a^3*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)","B"
748,1,339,124,10.182206,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^7*(a + a*sin(c + d*x))^3),x)","-\frac{5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+36\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-36\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-600\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+600\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-140\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1920\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"-(5*cos(c/2 + (d*x)/2)^12 - 5*sin(c/2 + (d*x)/2)^12 + 36*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 - 36*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 105*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 140*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 15*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 600*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 600*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 15*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 140*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 105*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/(1920*a^3*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
749,1,387,140,10.858433,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^8*(a + a*sin(c + d*x))^3),x)","\frac{3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-21\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+91\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-609\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+609\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-91\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2688\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(3*sin(c/2 + (d*x)/2)^14 - 3*cos(c/2 + (d*x)/2)^14 - 21*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 + 21*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) + 63*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 105*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 + 91*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 + 63*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 - 609*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 609*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 - 63*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 - 91*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 + 105*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 - 63*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)/(2688*a^3*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)","B"
750,1,435,166,11.500609,"\text{Not used}","int(cos(c + d*x)^8/(sin(c + d*x)^9*(a + a*sin(c + d*x))^3),x)","-\frac{105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-105\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+720\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+4368\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5880\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+3920\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-38640\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+38640\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3920\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+5880\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4368\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+48720\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{215040\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}","Not used",1,"-(105*cos(c/2 + (d*x)/2)^16 - 105*sin(c/2 + (d*x)/2)^16 + 720*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^15 - 720*cos(c/2 + (d*x)/2)^15*sin(c/2 + (d*x)/2) - 2240*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^14 + 4368*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^13 - 5880*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 + 3920*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^11 + 6720*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 - 38640*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^9 + 38640*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^7 - 6720*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 - 3920*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^5 + 5880*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 - 4368*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^3 + 2240*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^2 + 48720*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8)/(215040*a^3*d*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8)","B"
751,1,257,82,14.819746,"\text{Not used}","int((sin(c + d*x)^4*(a + a*sin(c + d*x)))/cos(c + d*x)^2,x)","\frac{\left(\frac{a\,\left(9\,c+9\,d\,x-18\right)}{6}-\frac{3\,a\,\left(c+d\,x\right)}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{9\,a\,\left(c+d\,x\right)}{2}-\frac{a\,\left(27\,c+27\,d\,x-18\right)}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{a\,\left(27\,c+27\,d\,x-48\right)}{6}-\frac{9\,a\,\left(c+d\,x\right)}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{9\,a\,\left(c+d\,x\right)}{2}-\frac{a\,\left(27\,c+27\,d\,x-48\right)}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{a\,\left(27\,c+27\,d\,x-78\right)}{6}-\frac{9\,a\,\left(c+d\,x\right)}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{3\,a\,\left(c+d\,x\right)}{2}-\frac{a\,\left(9\,c+9\,d\,x-14\right)}{6}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\left(9\,c+9\,d\,x-32\right)}{6}-\frac{3\,a\,\left(c+d\,x\right)}{2}}{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)}^3}-\frac{3\,a\,x}{2}","Not used",1,"((a*(9*c + 9*d*x - 32))/6 - tan(c/2 + (d*x)/2)*((a*(9*c + 9*d*x - 14))/6 - (3*a*(c + d*x))/2) - (3*a*(c + d*x))/2 + tan(c/2 + (d*x)/2)^6*((a*(9*c + 9*d*x - 18))/6 - (3*a*(c + d*x))/2) - tan(c/2 + (d*x)/2)^5*((a*(27*c + 27*d*x - 18))/6 - (9*a*(c + d*x))/2) - tan(c/2 + (d*x)/2)^3*((a*(27*c + 27*d*x - 48))/6 - (9*a*(c + d*x))/2) + tan(c/2 + (d*x)/2)^4*((a*(27*c + 27*d*x - 48))/6 - (9*a*(c + d*x))/2) + tan(c/2 + (d*x)/2)^2*((a*(27*c + 27*d*x - 78))/6 - (9*a*(c + d*x))/2))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^3) - (3*a*x)/2","B"
752,1,160,65,11.418276,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x)))/cos(c + d*x)^2,x)","\frac{\left(\frac{a\,\left(3\,d\,x-6\right)}{2}-\frac{3\,a\,d\,x}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(3\,a\,d\,x-\frac{a\,\left(6\,d\,x-6\right)}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{a\,\left(6\,d\,x-10\right)}{2}-3\,a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{3\,a\,d\,x}{2}-\frac{a\,\left(3\,d\,x-2\right)}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\left(3\,d\,x-8\right)}{2}-\frac{3\,a\,d\,x}{2}}{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)}^2}-\frac{3\,a\,x}{2}","Not used",1,"((a*(3*d*x - 8))/2 - tan(c/2 + (d*x)/2)*((a*(3*d*x - 2))/2 - (3*a*d*x)/2) - tan(c/2 + (d*x)/2)^3*((a*(6*d*x - 6))/2 - 3*a*d*x) + tan(c/2 + (d*x)/2)^4*((a*(3*d*x - 6))/2 - (3*a*d*x)/2) + tan(c/2 + (d*x)/2)^2*((a*(6*d*x - 10))/2 - 3*a*d*x) - (3*a*d*x)/2)/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2) - (3*a*x)/2","B"
753,1,99,39,9.213209,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x)))/cos(c + d*x)^2,x)","\frac{\left(a\,\left(d\,x-2\right)-a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(a\,d\,x-a\,\left(d\,x-2\right)\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,\left(d\,x-4\right)-a\,d\,x}{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)}-a\,x","Not used",1,"(a*(d*x - 4) - tan(c/2 + (d*x)/2)*(a*(d*x - 2) - a*d*x) + tan(c/2 + (d*x)/2)^2*(a*(d*x - 2) - a*d*x) - a*d*x)/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)) - a*x","B"
754,1,24,27,8.977399,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x)))/cos(c + d*x)^2,x)","-a\,x-\frac{2\,a}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"- a*x - (2*a)/(d*(tan(c/2 + (d*x)/2) - 1))","B"
755,1,35,36,8.950926,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^2*sin(c + d*x)),x)","\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)))/d - (2*a)/(d*(tan(c/2 + (d*x)/2) - 1))","B"
756,1,77,48,8.966942,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^2*sin(c + d*x)^2),x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a-5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) + (a*log(tan(c/2 + (d*x)/2)))/d - (a - 5*a*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^2))","B"
757,1,113,75,8.897677,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^2*sin(c + d*x)^3),x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + (3*a*tan(c/2 + (d*x)/2))/2 - 10*a*tan(c/2 + (d*x)/2)^2)/(d*(4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^3)) + (a*tan(c/2 + (d*x)/2)^2)/(8*d) + (3*a*log(tan(c/2 + (d*x)/2)))/(2*d)","B"
758,1,144,91,8.990157,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^2*sin(c + d*x)^4),x)","\frac{7\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{-23\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{a}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}+\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}","Not used",1,"(7*a*tan(c/2 + (d*x)/2))/(8*d) - (a/3 + (2*a*tan(c/2 + (d*x)/2))/3 + 6*a*tan(c/2 + (d*x)/2)^2 - 23*a*tan(c/2 + (d*x)/2)^3)/(d*(8*tan(c/2 + (d*x)/2)^3 - 8*tan(c/2 + (d*x)/2)^4)) + (a*tan(c/2 + (d*x)/2)^2)/(8*d) + (a*tan(c/2 + (d*x)/2)^3)/(24*d) + (3*a*log(tan(c/2 + (d*x)/2)))/(2*d)","B"
759,1,288,89,14.710488,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x))^2)/cos(c + d*x)^2,x)","-3\,a^2\,x-\frac{3\,a^2\,\left(c+d\,x\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(9\,c+9\,d\,x-10\right)}{3}\right)-\frac{a^2\,\left(9\,c+9\,d\,x-28\right)}{3}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(9\,c+9\,d\,x-18\right)}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(27\,c+27\,d\,x-18\right)}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(27\,c+27\,d\,x-36\right)}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(9\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(27\,c+27\,d\,x-48\right)}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(9\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(27\,c+27\,d\,x-66\right)}{3}\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)}^3}","Not used",1,"- 3*a^2*x - (3*a^2*(c + d*x) - tan(c/2 + (d*x)/2)*(3*a^2*(c + d*x) - (a^2*(9*c + 9*d*x - 10))/3) - (a^2*(9*c + 9*d*x - 28))/3 + tan(c/2 + (d*x)/2)^6*(3*a^2*(c + d*x) - (a^2*(9*c + 9*d*x - 18))/3) - tan(c/2 + (d*x)/2)^5*(9*a^2*(c + d*x) - (a^2*(27*c + 27*d*x - 18))/3) - tan(c/2 + (d*x)/2)^3*(9*a^2*(c + d*x) - (a^2*(27*c + 27*d*x - 36))/3) + tan(c/2 + (d*x)/2)^4*(9*a^2*(c + d*x) - (a^2*(27*c + 27*d*x - 48))/3) + tan(c/2 + (d*x)/2)^2*(9*a^2*(c + d*x) - (a^2*(27*c + 27*d*x - 66))/3))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
760,1,183,71,11.386068,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x))^2)/cos(c + d*x)^2,x)","-\frac{5\,a^2\,x}{2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,\left(5\,d\,x-6\right)}{2}-\frac{5\,a^2\,d\,x}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2\,\left(5\,d\,x-10\right)}{2}-\frac{5\,a^2\,d\,x}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2\,\left(10\,d\,x-10\right)}{2}-5\,a^2\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2\,\left(10\,d\,x-22\right)}{2}-5\,a^2\,d\,x\right)-\frac{a^2\,\left(5\,d\,x-16\right)}{2}+\frac{5\,a^2\,d\,x}{2}}{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)}^2}","Not used",1,"- (5*a^2*x)/2 - (tan(c/2 + (d*x)/2)*((a^2*(5*d*x - 6))/2 - (5*a^2*d*x)/2) - tan(c/2 + (d*x)/2)^4*((a^2*(5*d*x - 10))/2 - (5*a^2*d*x)/2) + tan(c/2 + (d*x)/2)^3*((a^2*(10*d*x - 10))/2 - 5*a^2*d*x) - tan(c/2 + (d*x)/2)^2*((a^2*(10*d*x - 22))/2 - 5*a^2*d*x) - (a^2*(5*d*x - 16))/2 + (5*a^2*d*x)/2)/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
761,1,117,43,9.179512,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x))^2)/cos(c + d*x)^2,x)","-2\,a^2\,x-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2\,\left(d\,x-1\right)-2\,a^2\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2\,\left(d\,x-2\right)-2\,a^2\,d\,x\right)-2\,a^2\,\left(d\,x-3\right)+2\,a^2\,d\,x}{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,"- 2*a^2*x - (tan(c/2 + (d*x)/2)*(2*a^2*(d*x - 1) - 2*a^2*d*x) - tan(c/2 + (d*x)/2)^2*(2*a^2*(d*x - 2) - 2*a^2*d*x) - 2*a^2*(d*x - 3) + 2*a^2*d*x)/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1))","B"
762,1,39,44,8.889227,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^2*sin(c + d*x)),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{4\,a^2}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d - (4*a^2)/(d*(tan(c/2 + (d*x)/2) - 1))","B"
763,1,86,58,8.926727,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^2*sin(c + d*x)^2),x)","\frac{2\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2-9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(2*a^2*log(tan(c/2 + (d*x)/2)))/d - (a^2 - 9*a^2*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^2)) + (a^2*tan(c/2 + (d*x)/2))/(2*d)","B"
764,1,124,86,8.956171,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^2*sin(c + d*x)^3),x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{5\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}-\frac{-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{7\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a^2}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) + (5*a^2*log(tan(c/2 + (d*x)/2)))/(2*d) + (a^2*tan(c/2 + (d*x)/2))/d - (a^2/2 - 20*a^2*tan(c/2 + (d*x)/2)^2 + (7*a^2*tan(c/2 + (d*x)/2))/2)/(d*(4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^3))","B"
765,1,363,111,14.701128,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x))^3)/cos(c + d*x)^2,x)","-\frac{51\,a^3\,x}{8}-\frac{\frac{51\,a^3\,\left(c+d\,x\right)}{8}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{51\,a^3\,\left(c+d\,x\right)}{8}-\frac{a^3\,\left(51\,c+51\,d\,x-58\right)}{8}\right)-\frac{a^3\,\left(51\,c+51\,d\,x-160\right)}{8}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{51\,a^3\,\left(c+d\,x\right)}{8}-\frac{a^3\,\left(51\,c+51\,d\,x-102\right)}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{51\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(204\,c+204\,d\,x-102\right)}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{51\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(204\,c+204\,d\,x-266\right)}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{51\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(204\,c+204\,d\,x-374\right)}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{51\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(204\,c+204\,d\,x-538\right)}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{153\,a^3\,\left(c+d\,x\right)}{4}-\frac{a^3\,\left(306\,c+306\,d\,x-342\right)}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{153\,a^3\,\left(c+d\,x\right)}{4}-\frac{a^3\,\left(306\,c+306\,d\,x-618\right)}{8}\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)}^4}","Not used",1,"- (51*a^3*x)/8 - ((51*a^3*(c + d*x))/8 - tan(c/2 + (d*x)/2)*((51*a^3*(c + d*x))/8 - (a^3*(51*c + 51*d*x - 58))/8) - (a^3*(51*c + 51*d*x - 160))/8 + tan(c/2 + (d*x)/2)^8*((51*a^3*(c + d*x))/8 - (a^3*(51*c + 51*d*x - 102))/8) - tan(c/2 + (d*x)/2)^7*((51*a^3*(c + d*x))/2 - (a^3*(204*c + 204*d*x - 102))/8) - tan(c/2 + (d*x)/2)^3*((51*a^3*(c + d*x))/2 - (a^3*(204*c + 204*d*x - 266))/8) + tan(c/2 + (d*x)/2)^6*((51*a^3*(c + d*x))/2 - (a^3*(204*c + 204*d*x - 374))/8) + tan(c/2 + (d*x)/2)^2*((51*a^3*(c + d*x))/2 - (a^3*(204*c + 204*d*x - 538))/8) - tan(c/2 + (d*x)/2)^5*((153*a^3*(c + d*x))/4 - (a^3*(306*c + 306*d*x - 342))/8) + tan(c/2 + (d*x)/2)^4*((153*a^3*(c + d*x))/4 - (a^3*(306*c + 306*d*x - 618))/8))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
766,1,288,89,14.759112,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x))^3)/cos(c + d*x)^2,x)","-\frac{11\,a^3\,x}{2}-\frac{\frac{11\,a^3\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{11\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(33\,c+33\,d\,x-38\right)}{6}\right)-\frac{a^3\,\left(33\,c+33\,d\,x-104\right)}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{11\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(33\,c+33\,d\,x-66\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-66\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-120\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-192\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-246\right)}{6}\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)}^3}","Not used",1,"- (11*a^3*x)/2 - ((11*a^3*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((11*a^3*(c + d*x))/2 - (a^3*(33*c + 33*d*x - 38))/6) - (a^3*(33*c + 33*d*x - 104))/6 + tan(c/2 + (d*x)/2)^6*((11*a^3*(c + d*x))/2 - (a^3*(33*c + 33*d*x - 66))/6) - tan(c/2 + (d*x)/2)^5*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 66))/6) - tan(c/2 + (d*x)/2)^3*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 120))/6) + tan(c/2 + (d*x)/2)^4*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 192))/6) + tan(c/2 + (d*x)/2)^2*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 246))/6))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
767,1,183,67,11.393305,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x))^3)/cos(c + d*x)^2,x)","-\frac{9\,a^3\,x}{2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^3\,\left(9\,d\,x-10\right)}{2}-\frac{9\,a^3\,d\,x}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3\,\left(9\,d\,x-18\right)}{2}-\frac{9\,a^3\,d\,x}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^3\,\left(18\,d\,x-14\right)}{2}-9\,a^3\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(18\,d\,x-42\right)}{2}-9\,a^3\,d\,x\right)-\frac{a^3\,\left(9\,d\,x-28\right)}{2}+\frac{9\,a^3\,d\,x}{2}}{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)}^2}","Not used",1,"- (9*a^3*x)/2 - (tan(c/2 + (d*x)/2)*((a^3*(9*d*x - 10))/2 - (9*a^3*d*x)/2) - tan(c/2 + (d*x)/2)^4*((a^3*(9*d*x - 18))/2 - (9*a^3*d*x)/2) + tan(c/2 + (d*x)/2)^3*((a^3*(18*d*x - 14))/2 - 9*a^3*d*x) - tan(c/2 + (d*x)/2)^2*((a^3*(18*d*x - 42))/2 - 9*a^3*d*x) - (a^3*(9*d*x - 28))/2 + (9*a^3*d*x)/2)/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
768,1,112,48,8.925011,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^2*sin(c + d*x)),x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{2\,a^3\,\mathrm{atan}\left(\frac{4\,a^6}{4\,a^6+4\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{4\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^6+4\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{8\,a^3}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d + (2*a^3*atan((4*a^6)/(4*a^6 + 4*a^6*tan(c/2 + (d*x)/2)) - (4*a^6*tan(c/2 + (d*x)/2))/(4*a^6 + 4*a^6*tan(c/2 + (d*x)/2))))/d - (8*a^3)/(d*(tan(c/2 + (d*x)/2) - 1))","B"
769,1,86,56,8.967882,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^2*sin(c + d*x)^2),x)","\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^3-17\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)))/d - (a^3 - 17*a^3*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^2)) + (a^3*tan(c/2 + (d*x)/2))/(2*d)","B"
770,1,125,80,8.947676,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^2*sin(c + d*x)^3),x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{9\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}+\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{-38\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{11\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a^3}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (9*a^3*log(tan(c/2 + (d*x)/2)))/(2*d) + (3*a^3*tan(c/2 + (d*x)/2))/(2*d) - (a^3/2 - 38*a^3*tan(c/2 + (d*x)/2)^2 + (11*a^3*tan(c/2 + (d*x)/2))/2)/(d*(4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^3))","B"
771,1,160,98,8.972173,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^2*sin(c + d*x)^4),x)","\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{-83\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{a^3}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{11\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}+\frac{19\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(3*a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (16*a^3*tan(c/2 + (d*x)/2)^2 - 83*a^3*tan(c/2 + (d*x)/2)^3 + a^3/3 + (8*a^3*tan(c/2 + (d*x)/2))/3)/(d*(8*tan(c/2 + (d*x)/2)^3 - 8*tan(c/2 + (d*x)/2)^4)) + (11*a^3*log(tan(c/2 + (d*x)/2)))/(2*d) + (19*a^3*tan(c/2 + (d*x)/2))/(8*d)","B"
772,1,129,83,13.516037,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{x}{a}-\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{26\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{16}{3}}{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)}^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)}","Not used",1,"x/a - ((26*tan(c/2 + (d*x)/2))/3 + (4*tan(c/2 + (d*x)/2)^2)/3 - (4*tan(c/2 + (d*x)/2)^3)/3 - 4*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^5 + 16/3)/(a*d*(tan(c/2 + (d*x)/2) + 1)^3*(tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1))","B"
773,1,79,70,11.177911,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{4}{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}-\frac{x}{a}","Not used",1,"((2*tan(c/2 + (d*x)/2))/3 - 4*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^3 + 4/3)/(a*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^3) - x/a","B"
774,1,47,50,8.897906,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^2*(a + a*sin(c + d*x))),x)","-\frac{4\,\left(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,"-(4*(2*tan(c/2 + (d*x)/2) + 1))/(3*a*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^3)","B"
775,1,60,37,8.906349,"\text{Not used}","int(sin(c + d*x)/(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)}^2+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*(2*tan(c/2 + (d*x)/2) + 3*tan(c/2 + (d*x)/2)^2 + 1))/(3*a*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^3)","B"
776,1,92,79,9.898936,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{10\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{8}{3}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\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)+a\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a*d) + ((10*tan(c/2 + (d*x)/2))/3 - 2*tan(c/2 + (d*x)/2)^3 + 8/3)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 2*a*tan(c/2 + (d*x)/2)^3 - a*tan(c/2 + (d*x)/2)^4))","B"
777,1,150,93,9.114234,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}-\frac{-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{22\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+1}{d\,\left(-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a*d) - ((22*tan(c/2 + (d*x)/2))/3 + (8*tan(c/2 + (d*x)/2)^2)/3 - 10*tan(c/2 + (d*x)/2)^3 - 9*tan(c/2 + (d*x)/2)^4 + 1)/(d*(2*a*tan(c/2 + (d*x)/2) + 4*a*tan(c/2 + (d*x)/2)^2 - 4*a*tan(c/2 + (d*x)/2)^4 - 2*a*tan(c/2 + (d*x)/2)^5)) - log(tan(c/2 + (d*x)/2))/(a*d)","B"
778,1,172,149,17.672979,"\text{Not used}","int(sin(c + d*x)^6/(cos(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-60\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-60\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{174\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+\frac{84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{212\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}+\frac{268\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{211\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{64}{5}}{a^2\,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)}^5\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}-\frac{9\,x}{2\,a^2}","Not used",1,"((211*tan(c/2 + (d*x)/2))/5 + (268*tan(c/2 + (d*x)/2)^2)/5 + (212*tan(c/2 + (d*x)/2)^3)/5 + (84*tan(c/2 + (d*x)/2)^4)/5 - (174*tan(c/2 + (d*x)/2)^5)/5 - 60*tan(c/2 + (d*x)/2)^6 - 60*tan(c/2 + (d*x)/2)^7 - 36*tan(c/2 + (d*x)/2)^8 - 9*tan(c/2 + (d*x)/2)^9 + 64/5)/(a^2*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^5*(tan(c/2 + (d*x)/2)^2 + 1)^2) - (9*x)/(2*a^2)","B"
779,1,156,120,15.383636,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{2\,x}{a^2}-\frac{-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{68\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}+\frac{144\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{388\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{112}{15}}{a^2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^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)}","Not used",1,"(2*x)/a^2 - ((388*tan(c/2 + (d*x)/2))/15 + (144*tan(c/2 + (d*x)/2)^2)/5 + (36*tan(c/2 + (d*x)/2)^3)/5 - (32*tan(c/2 + (d*x)/2)^4)/3 - (68*tan(c/2 + (d*x)/2)^5)/3 - 16*tan(c/2 + (d*x)/2)^6 - 4*tan(c/2 + (d*x)/2)^7 + 112/15)/(a^2*d*(tan(c/2 + (d*x)/2) + 1)^5*(tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1))","B"
780,1,105,106,14.089318,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{98\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{32}{15}}{a^2\,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)}^5}-\frac{x}{a^2}","Not used",1,"((98*tan(c/2 + (d*x)/2))/15 + (8*tan(c/2 + (d*x)/2)^2)/3 - (28*tan(c/2 + (d*x)/2)^3)/3 - 8*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^5 + 32/15)/(a^2*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^5) - x/a^2","B"
781,1,111,66,9.274900,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{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,"((4*cos(c/2 + (d*x)/2)^6)/5 + (16*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2))/5 + 4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)/(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"
782,1,132,73,9.306507,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}{15\,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,"(8*cos(c/2 + (d*x)/2)^3*(cos(c/2 + (d*x)/2)^3 + 5*sin(c/2 + (d*x)/2)^3 + 5*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^2 + 4*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)))/(15*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"
783,1,159,71,9.385950,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{\frac{2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{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)^6)/15 + (8*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2))/15 + 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + (8*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^3)/3 + (8*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)/3)/(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"
784,1,117,115,10.782110,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{148\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{52}{15}}{a^2\,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)}^5}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) - ((148*tan(c/2 + (d*x)/2))/15 + (28*tan(c/2 + (d*x)/2)^2)/3 - (8*tan(c/2 + (d*x)/2)^3)/3 - 8*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^5 + 52/15)/(a^2*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^5)","B"
785,1,216,130,10.778765,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{-17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-44\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{95\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{571\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{244\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+1}{d\,\left(-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+10\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^2*d) - (2*log(tan(c/2 + (d*x)/2)))/(a^2*d) - ((244*tan(c/2 + (d*x)/2))/15 + (571*tan(c/2 + (d*x)/2)^2)/15 + (64*tan(c/2 + (d*x)/2)^3)/3 - (95*tan(c/2 + (d*x)/2)^4)/3 - 44*tan(c/2 + (d*x)/2)^5 - 17*tan(c/2 + (d*x)/2)^6 + 1)/(d*(8*a^2*tan(c/2 + (d*x)/2)^2 + 10*a^2*tan(c/2 + (d*x)/2)^3 - 10*a^2*tan(c/2 + (d*x)/2)^5 - 8*a^2*tan(c/2 + (d*x)/2)^6 - 2*a^2*tan(c/2 + (d*x)/2)^7 + 2*a^2*tan(c/2 + (d*x)/2)))","B"
786,1,191,158,10.085781,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{9\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{271\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{8}-\frac{41\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}+\frac{197\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{8}+\frac{181\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}+\frac{567\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{40}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{1}{8}\right)}{a^2\,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)}^5}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) + (9*log(tan(c/2 + (d*x)/2)))/(2*a^2*d) - tan(c/2 + (d*x)/2)/(a^2*d) - (cot(c/2 + (d*x)/2)^2*(tan(c/2 + (d*x)/2)/2 + (567*tan(c/2 + (d*x)/2)^2)/40 + (181*tan(c/2 + (d*x)/2)^3)/5 + (197*tan(c/2 + (d*x)/2)^4)/8 - (41*tan(c/2 + (d*x)/2)^5)/2 - (271*tan(c/2 + (d*x)/2)^6)/8 - 13*tan(c/2 + (d*x)/2)^7 - 1/8))/(a^2*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^5)","B"
787,1,182,151,15.499831,"\text{Not used}","int(sin(c + d*x)^6/(cos(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{3\,x}{a^3}-\frac{-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-88\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-108\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{276\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+\frac{164\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{792\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{7}+\frac{804\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{7}+\frac{1902\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}+\frac{352}{35}}{a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^7\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^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)}","Not used",1,"(3*x)/a^3 - ((1902*tan(c/2 + (d*x)/2))/35 + (804*tan(c/2 + (d*x)/2)^2)/7 + (792*tan(c/2 + (d*x)/2)^3)/7 + (164*tan(c/2 + (d*x)/2)^4)/5 - (276*tan(c/2 + (d*x)/2)^5)/5 - 108*tan(c/2 + (d*x)/2)^6 - 88*tan(c/2 + (d*x)/2)^7 - 36*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^9 + 352/35)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^7*(tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1))","B"
788,1,131,142,15.648836,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{82\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{134\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{15}+\frac{364\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{474\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}+\frac{272}{105}}{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)+1\right)}^7}-\frac{x}{a^3}","Not used",1,"((474*tan(c/2 + (d*x)/2))/35 + (364*tan(c/2 + (d*x)/2)^2)/15 + (134*tan(c/2 + (d*x)/2)^3)/15 - 24*tan(c/2 + (d*x)/2)^4 - (82*tan(c/2 + (d*x)/2)^5)/3 - 12*tan(c/2 + (d*x)/2)^6 - 2*tan(c/2 + (d*x)/2)^7 + 272/105)/(a^3*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^7) - x/a^3","B"
789,1,135,102,9.692196,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{35}+\frac{96\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}}{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,"((16*cos(c/2 + (d*x)/2)^8)/35 + (96*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2))/35 + (32*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^3)/5 + (32*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2)/5)/(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"
790,1,158,88,9.734947,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+18\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+42\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+42\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\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,"(4*cos(c/2 + (d*x)/2)^4*(3*cos(c/2 + (d*x)/2)^4 + 35*sin(c/2 + (d*x)/2)^4 + 42*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^3 + 18*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2) + 42*cos(c/2 + (d*x)/2)^2*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"
791,1,183,103,10.151934,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{21}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{7}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{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)\,{\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,"((4*cos(c/2 + (d*x)/2)^8)/21 + (8*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2))/7 + (8*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^5)/3 + 4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4 + (16*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^3)/3 + (8*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2)/3)/(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"
792,1,206,99,10.012293,"\text{Not used}","int(sin(c + d*x)/(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)}^2\,\left(-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+56\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+70\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\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)^2*(35*sin(c/2 + (d*x)/2)^6 - cos(c/2 + (d*x)/2)^6 + 70*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^5 - 6*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2) + 105*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 56*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^3 + 21*cos(c/2 + (d*x)/2)^4*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"
793,1,143,151,11.330754,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{98\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{394\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{15}+\frac{554\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{674\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}+\frac{442}{105}}{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)+1\right)}^7}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) - ((674*tan(c/2 + (d*x)/2))/35 + (554*tan(c/2 + (d*x)/2)^2)/15 + (394*tan(c/2 + (d*x)/2)^3)/15 - 10*tan(c/2 + (d*x)/2)^4 - (98*tan(c/2 + (d*x)/2)^5)/3 - 22*tan(c/2 + (d*x)/2)^6 - 6*tan(c/2 + (d*x)/2)^7 + 442/105)/(a^3*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^7)","B"
794,1,274,162,10.842239,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{-29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-122\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-202\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-106\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{508\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{938\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}+\frac{3854\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{934\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}+1}{d\,\left(-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - ((934*tan(c/2 + (d*x)/2))/35 + (3854*tan(c/2 + (d*x)/2)^2)/35 + (938*tan(c/2 + (d*x)/2)^3)/5 + (508*tan(c/2 + (d*x)/2)^4)/5 - 106*tan(c/2 + (d*x)/2)^5 - 202*tan(c/2 + (d*x)/2)^6 - 122*tan(c/2 + (d*x)/2)^7 - 29*tan(c/2 + (d*x)/2)^8 + 1)/(d*(12*a^3*tan(c/2 + (d*x)/2)^2 + 28*a^3*tan(c/2 + (d*x)/2)^3 + 28*a^3*tan(c/2 + (d*x)/2)^4 - 28*a^3*tan(c/2 + (d*x)/2)^6 - 28*a^3*tan(c/2 + (d*x)/2)^7 - 12*a^3*tan(c/2 + (d*x)/2)^8 - 2*a^3*tan(c/2 + (d*x)/2)^9 + 2*a^3*tan(c/2 + (d*x)/2))) - (3*log(tan(c/2 + (d*x)/2)))/(a^3*d)","B"
795,1,306,117,14.962392,"\text{Not used}","int((sin(c + d*x)^6*(a + a*sin(c + d*x)))/cos(c + d*x)^4,x)","\frac{5\,a\,x}{2}+\frac{\left(5\,a\,d\,x-\frac{a\,\left(30\,d\,x-30\right)}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{a\,\left(45\,d\,x-60\right)}{6}-\frac{15\,a\,d\,x}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(10\,a\,d\,x-\frac{a\,\left(60\,d\,x-80\right)}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{a\,\left(30\,d\,x-100\right)}{6}-5\,a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(5\,a\,d\,x-\frac{a\,\left(30\,d\,x-28\right)}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{a\,\left(60\,d\,x-176\right)}{6}-10\,a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{15\,a\,d\,x}{2}-\frac{a\,\left(45\,d\,x-132\right)}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{a\,\left(30\,d\,x-98\right)}{6}-5\,a\,d\,x\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a\,\left(15\,d\,x-64\right)}{6}+\frac{5\,a\,d\,x}{2}}{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)}^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}","Not used",1,"(5*a*x)/2 + (tan(c/2 + (d*x)/2)*((a*(30*d*x - 98))/6 - 5*a*d*x) - (a*(15*d*x - 64))/6 - tan(c/2 + (d*x)/2)^4*((a*(30*d*x - 28))/6 - 5*a*d*x) - tan(c/2 + (d*x)/2)^9*((a*(30*d*x - 30))/6 - 5*a*d*x) + tan(c/2 + (d*x)/2)^8*((a*(45*d*x - 60))/6 - (15*a*d*x)/2) + tan(c/2 + (d*x)/2)^6*((a*(30*d*x - 100))/6 - 5*a*d*x) - tan(c/2 + (d*x)/2)^7*((a*(60*d*x - 80))/6 - 10*a*d*x) - tan(c/2 + (d*x)/2)^2*((a*(45*d*x - 132))/6 - (15*a*d*x)/2) + tan(c/2 + (d*x)/2)^3*((a*(60*d*x - 176))/6 - 10*a*d*x) + 6*a*tan(c/2 + (d*x)/2)^5 + (5*a*d*x)/2)/(d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1)^3)","B"
796,1,243,101,14.618549,"\text{Not used}","int((sin(c + d*x)^5*(a + a*sin(c + d*x)))/cos(c + d*x)^4,x)","\frac{5\,a\,x}{2}-\frac{\left(\frac{a\,\left(30\,d\,x-30\right)}{6}-5\,a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(5\,a\,d\,x-\frac{a\,\left(30\,d\,x-60\right)}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{a\,\left(30\,d\,x-50\right)}{6}-5\,a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\left(5\,a\,d\,x-\frac{a\,\left(30\,d\,x-14\right)}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{a\,\left(30\,d\,x-4\right)}{6}-5\,a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(5\,a\,d\,x-\frac{a\,\left(30\,d\,x-34\right)}{6}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\left(15\,d\,x-32\right)}{6}-\frac{5\,a\,d\,x}{2}}{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)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(5*a*x)/2 - ((a*(15*d*x - 32))/6 - tan(c/2 + (d*x)/2)*((a*(30*d*x - 34))/6 - 5*a*d*x) + tan(c/2 + (d*x)/2)^2*((a*(30*d*x - 4))/6 - 5*a*d*x) - tan(c/2 + (d*x)/2)^3*((a*(30*d*x - 14))/6 - 5*a*d*x) + tan(c/2 + (d*x)/2)^7*((a*(30*d*x - 30))/6 - 5*a*d*x) + tan(c/2 + (d*x)/2)^5*((a*(30*d*x - 50))/6 - 5*a*d*x) - tan(c/2 + (d*x)/2)^6*((a*(30*d*x - 60))/6 - 5*a*d*x) + (20*a*tan(c/2 + (d*x)/2)^4)/3 - (5*a*d*x)/2)/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
797,1,185,72,12.717865,"\text{Not used}","int((sin(c + d*x)^4*(a + a*sin(c + d*x)))/cos(c + d*x)^4,x)","a\,x+\frac{\left(2\,a\,d\,x-\frac{a\,\left(6\,d\,x-6\right)}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{a\,\left(3\,d\,x-12\right)}{3}-a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\left(a\,d\,x-\frac{a\,\left(3\,d\,x-4\right)}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{a\,\left(6\,d\,x-26\right)}{3}-2\,a\,d\,x\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a\,\left(3\,d\,x-16\right)}{3}+a\,d\,x}{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)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"a*x + (tan(c/2 + (d*x)/2)*((a*(6*d*x - 26))/3 - 2*a*d*x) - (a*(3*d*x - 16))/3 - tan(c/2 + (d*x)/2)^2*((a*(3*d*x - 4))/3 - a*d*x) - tan(c/2 + (d*x)/2)^5*((a*(6*d*x - 6))/3 - 2*a*d*x) + tan(c/2 + (d*x)/2)^4*((a*(3*d*x - 12))/3 - a*d*x) + (4*a*tan(c/2 + (d*x)/2)^3)/3 + a*d*x)/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1))","B"
798,1,117,60,10.137745,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x)))/cos(c + d*x)^4,x)","a\,x-\frac{\left(\frac{a\,\left(6\,d\,x-6\right)}{3}-2\,a\,d\,x\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(2\,a\,d\,x-\frac{a\,\left(6\,d\,x-2\right)}{3}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\left(3\,d\,x-4\right)}{3}-a\,d\,x}{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)}","Not used",1,"a*x - ((a*(3*d*x - 4))/3 - tan(c/2 + (d*x)/2)*((a*(6*d*x - 2))/3 - 2*a*d*x) + tan(c/2 + (d*x)/2)^3*((a*(6*d*x - 6))/3 - 2*a*d*x) + 4*a*tan(c/2 + (d*x)/2)^2 - a*d*x)/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1))","B"
799,1,74,45,9.030241,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x)))/cos(c + d*x)^4,x)","-\frac{4\,a\,\left({\sin\left(c+d\,x\right)}^2+2\,\sin\left(c+d\,x\right)+4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\sin\left(2\,c+2\,d\,x\right)-4\right)}{3\,d\,\left(8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\sin\left(2\,c+2\,d\,x\right)-4\right)}","Not used",1,"-(4*a*(2*sin(c + d*x) + sin(2*c + 2*d*x) + 4*sin(c/2 + (d*x)/2)^2 + sin(c + d*x)^2 - 4))/(3*d*(2*sin(2*c + 2*d*x) + 8*sin(c/2 + (d*x)/2)^2 - 4))","B"
800,1,50,33,9.027980,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x)))/cos(c + d*x)^4,x)","-\frac{2\,a\,\left(\cos\left(c+d\,x\right)+1\right)\,\left(\cos\left(c+d\,x\right)+\sin\left(c+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) + 1)*(cos(c + d*x) + sin(c + d*x) - 2))/(3*d*(2*cos(c + d*x) - sin(2*c + 2*d*x)))","B"
801,1,90,68,9.940714,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^4*sin(c + d*x)),x)","\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{10\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{8\,a}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)))/d - ((8*a)/3 - (10*a*tan(c/2 + (d*x)/2))/3 + 2*a*tan(c/2 + (d*x)/2)^3)/(d*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 - 1))","B"
802,1,145,81,9.099129,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^4*sin(c + d*x)^2),x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{-9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{22\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+a}{d\,\left(-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) + (a*log(tan(c/2 + (d*x)/2)))/d - (a - (22*a*tan(c/2 + (d*x)/2))/3 + (8*a*tan(c/2 + (d*x)/2)^2)/3 + 10*a*tan(c/2 + (d*x)/2)^3 - 9*a*tan(c/2 + (d*x)/2)^4)/(d*(2*tan(c/2 + (d*x)/2) - 4*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^5))","B"
803,1,180,110,8.983595,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^4*sin(c + d*x)^3),x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{-18\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{23\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{67\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{68\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{5\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + a*tan(c/2 + (d*x)/2) - (68*a*tan(c/2 + (d*x)/2)^2)/3 + (67*a*tan(c/2 + (d*x)/2)^3)/3 + (23*a*tan(c/2 + (d*x)/2)^4)/2 - 18*a*tan(c/2 + (d*x)/2)^5)/(d*(4*tan(c/2 + (d*x)/2)^2 - 8*tan(c/2 + (d*x)/2)^3 + 8*tan(c/2 + (d*x)/2)^5 - 4*tan(c/2 + (d*x)/2)^6)) + (a*tan(c/2 + (d*x)/2)^2)/(8*d) + (5*a*log(tan(c/2 + (d*x)/2)))/(2*d)","B"
804,1,287,101,14.686118,"\text{Not used}","int((sin(c + d*x)^4*(a + a*sin(c + d*x))^2)/cos(c + d*x)^4,x)","\frac{7\,a^2\,x}{2}+\frac{\frac{7\,a^2\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{21\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(63\,c+63\,d\,x-150\right)}{6}\right)-\frac{a^2\,\left(21\,c+21\,d\,x-64\right)}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{21\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(63\,c+63\,d\,x-42\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{35\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(105\,c+105\,d\,x-126\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{35\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(105\,c+105\,d\,x-194\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{49\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(147\,c+147\,d\,x-196\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{49\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(147\,c+147\,d\,x-252\right)}{6}\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)}^2}","Not used",1,"(7*a^2*x)/2 + ((7*a^2*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((21*a^2*(c + d*x))/2 - (a^2*(63*c + 63*d*x - 150))/6) - (a^2*(21*c + 21*d*x - 64))/6 + tan(c/2 + (d*x)/2)^6*((21*a^2*(c + d*x))/2 - (a^2*(63*c + 63*d*x - 42))/6) - tan(c/2 + (d*x)/2)^5*((35*a^2*(c + d*x))/2 - (a^2*(105*c + 105*d*x - 126))/6) + tan(c/2 + (d*x)/2)^2*((35*a^2*(c + d*x))/2 - (a^2*(105*c + 105*d*x - 194))/6) + tan(c/2 + (d*x)/2)^4*((49*a^2*(c + d*x))/2 - (a^2*(147*c + 147*d*x - 196))/6) - tan(c/2 + (d*x)/2)^3*((49*a^2*(c + d*x))/2 - (a^2*(147*c + 147*d*x - 252))/6))/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
805,1,182,86,12.161573,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x))^2)/cos(c + d*x)^4,x)","2\,a^2\,x+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,a^2\,\left(9\,d\,x-24\right)}{3}-6\,a^2\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{2\,a^2\,\left(9\,d\,x-6\right)}{3}-6\,a^2\,d\,x\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2\,a^2\,\left(12\,d\,x-18\right)}{3}-8\,a^2\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{2\,a^2\,\left(12\,d\,x-22\right)}{3}-8\,a^2\,d\,x\right)-\frac{2\,a^2\,\left(3\,d\,x-10\right)}{3}+2\,a^2\,d\,x}{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)}","Not used",1,"2*a^2*x + (tan(c/2 + (d*x)/2)*((2*a^2*(9*d*x - 24))/3 - 6*a^2*d*x) - tan(c/2 + (d*x)/2)^4*((2*a^2*(9*d*x - 6))/3 - 6*a^2*d*x) + tan(c/2 + (d*x)/2)^3*((2*a^2*(12*d*x - 18))/3 - 8*a^2*d*x) - tan(c/2 + (d*x)/2)^2*((2*a^2*(12*d*x - 22))/3 - 8*a^2*d*x) - (2*a^2*(3*d*x - 10))/3 + 2*a^2*d*x)/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1))","B"
806,1,102,63,9.289878,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x))^2)/cos(c + d*x)^4,x)","a^2\,x+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,\left(9\,d\,x-18\right)}{3}-3\,a^2\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2\,\left(9\,d\,x-6\right)}{3}-3\,a^2\,d\,x\right)-\frac{a^2\,\left(3\,d\,x-8\right)}{3}+a^2\,d\,x}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3}","Not used",1,"a^2*x + (tan(c/2 + (d*x)/2)*((a^2*(9*d*x - 18))/3 - 3*a^2*d*x) - tan(c/2 + (d*x)/2)^2*((a^2*(9*d*x - 6))/3 - 3*a^2*d*x) - (a^2*(3*d*x - 8))/3 + a^2*d*x)/(d*(tan(c/2 + (d*x)/2) - 1)^3)","B"
807,1,34,60,9.143278,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x))^2)/cos(c + d*x)^4,x)","-\frac{2\,a^2\,\left(3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3}","Not used",1,"-(2*a^2*(3*tan(c/2 + (d*x)/2) - 1))/(3*d*(tan(c/2 + (d*x)/2) - 1)^3)","B"
808,1,98,73,9.497127,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^4*sin(c + d*x)),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{10\,a^2}{3}}{d\,\left({\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+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d - (4*a^2*tan(c/2 + (d*x)/2)^2 + (10*a^2)/3 - 6*a^2*tan(c/2 + (d*x)/2))/(d*(3*tan(c/2 + (d*x)/2) - 3*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1))","B"
809,1,144,87,9.453821,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^4*sin(c + d*x)^2),x)","\frac{2\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{-13\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+23\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{41\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+a^2}{d\,\left(-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(2*a^2*log(tan(c/2 + (d*x)/2)))/d - (23*a^2*tan(c/2 + (d*x)/2)^2 - 13*a^2*tan(c/2 + (d*x)/2)^3 + a^2 - (41*a^2*tan(c/2 + (d*x)/2))/3)/(d*(2*tan(c/2 + (d*x)/2) - 6*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^3 - 2*tan(c/2 + (d*x)/2)^4)) + (a^2*tan(c/2 + (d*x)/2))/(2*d)","B"
810,1,182,125,9.071977,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^4*sin(c + d*x)^3),x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{7\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{-36\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{135\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{239\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{6}+\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a^2}{2}}{d\,\left(-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) + (7*a^2*log(tan(c/2 + (d*x)/2)))/(2*d) - ((135*a^2*tan(c/2 + (d*x)/2)^3)/2 - (239*a^2*tan(c/2 + (d*x)/2)^2)/6 - 36*a^2*tan(c/2 + (d*x)/2)^4 + a^2/2 + (5*a^2*tan(c/2 + (d*x)/2))/2)/(d*(4*tan(c/2 + (d*x)/2)^2 - 12*tan(c/2 + (d*x)/2)^3 + 12*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^5)) + (a^2*tan(c/2 + (d*x)/2))/d","B"
811,1,317,119,14.924038,"\text{Not used}","int((sin(c + d*x)^4*(a + a*sin(c + d*x))^3)/cos(c + d*x)^4,x)","\frac{17\,a^3\,x}{2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^3\,\left(153\,d\,x-378\right)}{6}-\frac{51\,a^3\,d\,x}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^3\,\left(153\,d\,x-102\right)}{6}-\frac{51\,a^3\,d\,x}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{a^3\,\left(306\,d\,x-306\right)}{6}-51\,a^3\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(306\,d\,x-654\right)}{6}-51\,a^3\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^3\,\left(510\,d\,x-578\right)}{6}-85\,a^3\,d\,x\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^3\,\left(510\,d\,x-1022\right)}{6}-85\,a^3\,d\,x\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{a^3\,\left(612\,d\,x-918\right)}{6}-102\,a^3\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3\,\left(612\,d\,x-1002\right)}{6}-102\,a^3\,d\,x\right)-\frac{a^3\,\left(51\,d\,x-160\right)}{6}+\frac{17\,a^3\,d\,x}{2}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^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}","Not used",1,"(17*a^3*x)/2 + (tan(c/2 + (d*x)/2)*((a^3*(153*d*x - 378))/6 - (51*a^3*d*x)/2) - tan(c/2 + (d*x)/2)^8*((a^3*(153*d*x - 102))/6 - (51*a^3*d*x)/2) + tan(c/2 + (d*x)/2)^7*((a^3*(306*d*x - 306))/6 - 51*a^3*d*x) - tan(c/2 + (d*x)/2)^2*((a^3*(306*d*x - 654))/6 - 51*a^3*d*x) - tan(c/2 + (d*x)/2)^6*((a^3*(510*d*x - 578))/6 - 85*a^3*d*x) + tan(c/2 + (d*x)/2)^3*((a^3*(510*d*x - 1022))/6 - 85*a^3*d*x) + tan(c/2 + (d*x)/2)^5*((a^3*(612*d*x - 918))/6 - 102*a^3*d*x) - tan(c/2 + (d*x)/2)^4*((a^3*(612*d*x - 1002))/6 - 102*a^3*d*x) - (a^3*(51*d*x - 160))/6 + (17*a^3*d*x)/2)/(d*(tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1)^3)","B"
812,1,287,101,14.961790,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x))^3)/cos(c + d*x)^4,x)","\frac{11\,a^3\,x}{2}+\frac{\frac{11\,a^3\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-246\right)}{6}\right)-\frac{a^3\,\left(33\,c+33\,d\,x-104\right)}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-66\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{55\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(165\,c+165\,d\,x-198\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{55\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(165\,c+165\,d\,x-322\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{77\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(231\,c+231\,d\,x-308\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{77\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(231\,c+231\,d\,x-420\right)}{6}\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)}^2}","Not used",1,"(11*a^3*x)/2 + ((11*a^3*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 246))/6) - (a^3*(33*c + 33*d*x - 104))/6 + tan(c/2 + (d*x)/2)^6*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 66))/6) - tan(c/2 + (d*x)/2)^5*((55*a^3*(c + d*x))/2 - (a^3*(165*c + 165*d*x - 198))/6) + tan(c/2 + (d*x)/2)^2*((55*a^3*(c + d*x))/2 - (a^3*(165*c + 165*d*x - 322))/6) + tan(c/2 + (d*x)/2)^4*((77*a^3*(c + d*x))/2 - (a^3*(231*c + 231*d*x - 308))/6) - tan(c/2 + (d*x)/2)^3*((77*a^3*(c + d*x))/2 - (a^3*(231*c + 231*d*x - 420))/6))/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
813,1,182,77,12.298925,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x))^3)/cos(c + d*x)^4,x)","3\,a^3\,x+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^3\,\left(27\,d\,x-66\right)}{3}-9\,a^3\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3\,\left(27\,d\,x-18\right)}{3}-9\,a^3\,d\,x\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^3\,\left(36\,d\,x-54\right)}{3}-12\,a^3\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(36\,d\,x-58\right)}{3}-12\,a^3\,d\,x\right)-\frac{a^3\,\left(9\,d\,x-28\right)}{3}+3\,a^3\,d\,x}{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)}","Not used",1,"3*a^3*x + (tan(c/2 + (d*x)/2)*((a^3*(27*d*x - 66))/3 - 9*a^3*d*x) - tan(c/2 + (d*x)/2)^4*((a^3*(27*d*x - 18))/3 - 9*a^3*d*x) + tan(c/2 + (d*x)/2)^3*((a^3*(36*d*x - 54))/3 - 12*a^3*d*x) - tan(c/2 + (d*x)/2)^2*((a^3*(36*d*x - 58))/3 - 12*a^3*d*x) - (a^3*(9*d*x - 28))/3 + 3*a^3*d*x)/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1))","B"
814,1,102,64,9.260742,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x))^3)/cos(c + d*x)^4,x)","a^3\,x+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^3\,\left(9\,d\,x-24\right)}{3}-3\,a^3\,d\,x\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(9\,d\,x-6\right)}{3}-3\,a^3\,d\,x\right)-\frac{a^3\,\left(3\,d\,x-10\right)}{3}+a^3\,d\,x}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3}","Not used",1,"a^3*x + (tan(c/2 + (d*x)/2)*((a^3*(9*d*x - 24))/3 - 3*a^3*d*x) - tan(c/2 + (d*x)/2)^2*((a^3*(9*d*x - 6))/3 - 3*a^3*d*x) - (a^3*(3*d*x - 10))/3 + a^3*d*x)/(d*(tan(c/2 + (d*x)/2) - 1)^3)","B"
815,1,98,72,9.226022,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^4*sin(c + d*x)),x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{14\,a^3}{3}}{d\,\left({\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+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d - (6*a^3*tan(c/2 + (d*x)/2)^2 + (14*a^3)/3 - 8*a^3*tan(c/2 + (d*x)/2))/(d*(3*tan(c/2 + (d*x)/2) - 3*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1))","B"
816,1,144,86,9.205950,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^4*sin(c + d*x)^2),x)","\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{-21\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+35\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{61\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+a^3}{d\,\left(-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)))/d - (35*a^3*tan(c/2 + (d*x)/2)^2 - 21*a^3*tan(c/2 + (d*x)/2)^3 + a^3 - (61*a^3*tan(c/2 + (d*x)/2))/3)/(d*(2*tan(c/2 + (d*x)/2) - 6*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^3 - 2*tan(c/2 + (d*x)/2)^4)) + (a^3*tan(c/2 + (d*x)/2))/(2*d)","B"
817,1,183,110,9.143358,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^4*sin(c + d*x)^3),x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{11\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{-62\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{227\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{403\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{6}+\frac{9\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a^3}{2}}{d\,\left(-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (11*a^3*log(tan(c/2 + (d*x)/2)))/(2*d) - ((227*a^3*tan(c/2 + (d*x)/2)^3)/2 - (403*a^3*tan(c/2 + (d*x)/2)^2)/6 - 62*a^3*tan(c/2 + (d*x)/2)^4 + a^3/2 + (9*a^3*tan(c/2 + (d*x)/2))/2)/(d*(4*tan(c/2 + (d*x)/2)^2 - 12*tan(c/2 + (d*x)/2)^3 + 12*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^5)) + (3*a^3*tan(c/2 + (d*x)/2))/(2*d)","B"
818,1,239,128,11.409345,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^4*sin(c + d*x)^4),x)","\frac{a^3\,\left(6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-581\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+897\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-303\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-181\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-204\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+612\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-612\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+204\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+1\right)}{24\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3}","Not used",1,"(a^3*(6*tan(c/2 + (d*x)/2) + 45*tan(c/2 + (d*x)/2)^2 - 581*tan(c/2 + (d*x)/2)^3 + 897*tan(c/2 + (d*x)/2)^4 - 303*tan(c/2 + (d*x)/2)^5 - 181*tan(c/2 + (d*x)/2)^6 + 45*tan(c/2 + (d*x)/2)^7 + 6*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^9 - 204*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^3 + 612*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^4 - 612*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^5 + 204*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^6 + 1))/(24*d*tan(c/2 + (d*x)/2)^3*(tan(c/2 + (d*x)/2) - 1)^3)","B"
819,1,437,143,16.825121,"\text{Not used}","int((sin(c + d*x)^4*(a + a*sin(c + d*x))^4)/cos(c + d*x)^4,x)","\frac{163\,a^4\,x}{8}+\frac{\frac{163\,a^4\,\left(c+d\,x\right)}{8}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{489\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(1467\,c+1467\,d\,x-3630\right)}{24}\right)-\frac{a^4\,\left(489\,c+489\,d\,x-1536\right)}{24}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{489\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(1467\,c+1467\,d\,x-978\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{1141\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(3423\,c+3423\,d\,x-2934\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{1141\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(3423\,c+3423\,d\,x-7818\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{2119\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(6357\,c+6357\,d\,x-6520\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2119\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(6357\,c+6357\,d\,x-13448\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{1467\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(8802\,c+8802\,d\,x-11736\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{1467\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(8802\,c+8802\,d\,x-15912\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{1793\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(10758\,c+10758\,d\,x-15364\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{1793\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(10758\,c+10758\,d\,x-18428\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,"(163*a^4*x)/8 + ((163*a^4*(c + d*x))/8 - tan(c/2 + (d*x)/2)*((489*a^4*(c + d*x))/8 - (a^4*(1467*c + 1467*d*x - 3630))/24) - (a^4*(489*c + 489*d*x - 1536))/24 + tan(c/2 + (d*x)/2)^10*((489*a^4*(c + d*x))/8 - (a^4*(1467*c + 1467*d*x - 978))/24) - tan(c/2 + (d*x)/2)^9*((1141*a^4*(c + d*x))/8 - (a^4*(3423*c + 3423*d*x - 2934))/24) + tan(c/2 + (d*x)/2)^2*((1141*a^4*(c + d*x))/8 - (a^4*(3423*c + 3423*d*x - 7818))/24) + tan(c/2 + (d*x)/2)^8*((2119*a^4*(c + d*x))/8 - (a^4*(6357*c + 6357*d*x - 6520))/24) - tan(c/2 + (d*x)/2)^3*((2119*a^4*(c + d*x))/8 - (a^4*(6357*c + 6357*d*x - 13448))/24) - tan(c/2 + (d*x)/2)^7*((1467*a^4*(c + d*x))/4 - (a^4*(8802*c + 8802*d*x - 11736))/24) + tan(c/2 + (d*x)/2)^4*((1467*a^4*(c + d*x))/4 - (a^4*(8802*c + 8802*d*x - 15912))/24) + tan(c/2 + (d*x)/2)^6*((1793*a^4*(c + d*x))/4 - (a^4*(10758*c + 10758*d*x - 15364))/24) - tan(c/2 + (d*x)/2)^5*((1793*a^4*(c + d*x))/4 - (a^4*(10758*c + 10758*d*x - 18428))/24))/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
820,1,287,101,14.851111,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x))^4)/cos(c + d*x)^4,x)","\frac{17\,a^4\,x}{2}+\frac{\frac{17\,a^4\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{51\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(153\,c+153\,d\,x-378\right)}{6}\right)-\frac{a^4\,\left(51\,c+51\,d\,x-160\right)}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{51\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(153\,c+153\,d\,x-102\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{85\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(255\,c+255\,d\,x-306\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{85\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(255\,c+255\,d\,x-494\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{119\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(357\,c+357\,d\,x-460\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{119\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(357\,c+357\,d\,x-660\right)}{6}\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)}^2}","Not used",1,"(17*a^4*x)/2 + ((17*a^4*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((51*a^4*(c + d*x))/2 - (a^4*(153*c + 153*d*x - 378))/6) - (a^4*(51*c + 51*d*x - 160))/6 + tan(c/2 + (d*x)/2)^6*((51*a^4*(c + d*x))/2 - (a^4*(153*c + 153*d*x - 102))/6) - tan(c/2 + (d*x)/2)^5*((85*a^4*(c + d*x))/2 - (a^4*(255*c + 255*d*x - 306))/6) + tan(c/2 + (d*x)/2)^2*((85*a^4*(c + d*x))/2 - (a^4*(255*c + 255*d*x - 494))/6) + tan(c/2 + (d*x)/2)^4*((119*a^4*(c + d*x))/2 - (a^4*(357*c + 357*d*x - 460))/6) - tan(c/2 + (d*x)/2)^3*((119*a^4*(c + d*x))/2 - (a^4*(357*c + 357*d*x - 660))/6))/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
821,1,172,117,18.669244,"\text{Not used}","int(sin(c + d*x)^6/(cos(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+\frac{28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{44\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}-\frac{52\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}-\frac{344\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{15}-\frac{52\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{54\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{32}{5}}{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\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{x}{a}","Not used",1,"((54*tan(c/2 + (d*x)/2))/5 - (52*tan(c/2 + (d*x)/2)^2)/5 - (344*tan(c/2 + (d*x)/2)^3)/15 - (52*tan(c/2 + (d*x)/2)^4)/15 + (44*tan(c/2 + (d*x)/2)^5)/15 + (28*tan(c/2 + (d*x)/2)^6)/3 + (8*tan(c/2 + (d*x)/2)^7)/3 - 4*tan(c/2 + (d*x)/2)^8 - 2*tan(c/2 + (d*x)/2)^9 + 32/5)/(a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5*(tan(c/2 + (d*x)/2)^2 + 1)) - x/a","B"
822,1,131,105,16.138631,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{x}{a}-\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{26\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{15}-\frac{92\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{16}{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,"x/a - ((2*tan(c/2 + (d*x)/2))/15 - (92*tan(c/2 + (d*x)/2)^2)/15 - (26*tan(c/2 + (d*x)/2)^3)/15 + (40*tan(c/2 + (d*x)/2)^4)/3 + (14*tan(c/2 + (d*x)/2)^5)/3 - 4*tan(c/2 + (d*x)/2)^6 - 2*tan(c/2 + (d*x)/2)^7 + 16/15)/(a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
823,1,73,69,9.549952,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{16\,\left(-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\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,"(16*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^2 - 6*tan(c/2 + (d*x)/2)^3 + 1))/(15*a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
824,1,86,55,9.857570,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^4*(a + a*sin(c + d*x))),x)","-\frac{4\,\left(15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\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,"-(4*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^3 + 15*tan(c/2 + (d*x)/2)^4 - 1))/(15*a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
825,1,99,73,10.159243,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^4*(a + a*sin(c + d*x))),x)","-\frac{4\,\left(10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\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,"-(4*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^3 + 5*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^5 + 1))/(15*a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
826,1,112,55,10.852304,"\text{Not used}","int(sin(c + d*x)/(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)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,\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*(6*tan(c/2 + (d*x)/2) + 9*tan(c/2 + (d*x)/2)^2 - 8*tan(c/2 + (d*x)/2)^3 + 5*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^5 + 15*tan(c/2 + (d*x)/2)^6 + 3))/(15*a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
827,1,143,115,11.529049,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{26\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{146\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{15}-\frac{62\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{62\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{46}{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,"log(tan(c/2 + (d*x)/2))/(a*d) - ((62*tan(c/2 + (d*x)/2))/15 - (62*tan(c/2 + (d*x)/2)^2)/15 - (146*tan(c/2 + (d*x)/2)^3)/15 + (10*tan(c/2 + (d*x)/2)^4)/3 + (26*tan(c/2 + (d*x)/2)^5)/3 + 2*tan(c/2 + (d*x)/2)^6 - 2*tan(c/2 + (d*x)/2)^7 + 46/15)/(a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
828,1,257,126,10.822447,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-34\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{454\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{15}+\frac{26\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}-\frac{122\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}-1}{d\,\left(-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}","Not used",1,"((26*tan(c/2 + (d*x)/2)^2)/15 - (122*tan(c/2 + (d*x)/2))/15 + (454*tan(c/2 + (d*x)/2)^3)/15 + (84*tan(c/2 + (d*x)/2)^4)/5 - 34*tan(c/2 + (d*x)/2)^5 - 22*tan(c/2 + (d*x)/2)^6 + 14*tan(c/2 + (d*x)/2)^7 + 13*tan(c/2 + (d*x)/2)^8 - 1)/(d*(2*a*tan(c/2 + (d*x)/2) + 4*a*tan(c/2 + (d*x)/2)^2 - 4*a*tan(c/2 + (d*x)/2)^3 - 12*a*tan(c/2 + (d*x)/2)^4 + 12*a*tan(c/2 + (d*x)/2)^6 + 4*a*tan(c/2 + (d*x)/2)^7 - 4*a*tan(c/2 + (d*x)/2)^8 - 2*a*tan(c/2 + (d*x)/2)^9)) - log(tan(c/2 + (d*x)/2))/(a*d) + tan(c/2 + (d*x)/2)/(2*a*d)","B"
829,1,198,155,17.729874,"\text{Not used}","int(sin(c + d*x)^7/(cos(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{44\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3}+\frac{64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{728\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{15}+\frac{352\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}-\frac{1816\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{105}-\frac{7264\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{105}-\frac{4996\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}+\frac{592\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{1012\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}+\frac{288}{35}}{a^2\,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)}^7\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{2\,x}{a^2}","Not used",1,"((1012*tan(c/2 + (d*x)/2))/35 + (592*tan(c/2 + (d*x)/2)^2)/35 - (4996*tan(c/2 + (d*x)/2)^3)/105 - (7264*tan(c/2 + (d*x)/2)^4)/105 - (1816*tan(c/2 + (d*x)/2)^5)/105 + (352*tan(c/2 + (d*x)/2)^6)/15 + (728*tan(c/2 + (d*x)/2)^7)/15 + (64*tan(c/2 + (d*x)/2)^8)/3 - (44*tan(c/2 + (d*x)/2)^9)/3 - 16*tan(c/2 + (d*x)/2)^10 - 4*tan(c/2 + (d*x)/2)^11 + 288/35)/(a^2*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^7*(tan(c/2 + (d*x)/2)^2 + 1)) - (2*x)/a^2","B"
830,1,156,140,16.889807,"\text{Not used}","int(sin(c + d*x)^6/(cos(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{x}{a^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}-\frac{148\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+\frac{104\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+\frac{2096\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}+\frac{88\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}-\frac{186\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}-\frac{64}{35}}{a^2\,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)}^7}","Not used",1,"x/a^2 + ((88*tan(c/2 + (d*x)/2)^2)/35 - (186*tan(c/2 + (d*x)/2))/35 + (2096*tan(c/2 + (d*x)/2)^3)/105 + (104*tan(c/2 + (d*x)/2)^4)/15 - (148*tan(c/2 + (d*x)/2)^5)/5 - (56*tan(c/2 + (d*x)/2)^6)/3 + (16*tan(c/2 + (d*x)/2)^7)/3 + 8*tan(c/2 + (d*x)/2)^8 + 2*tan(c/2 + (d*x)/2)^9 - 64/35)/(a^2*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^7)","B"
831,1,160,85,12.367697,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","-\frac{\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{21}+\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{7}-\frac{128\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{21}-\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}}{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,"-((16*cos(c/2 + (d*x)/2)^10)/21 + (64*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2))/21 - (32*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4)/3 - (128*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3)/21 + (16*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2)/7)/(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"
832,1,184,91,12.384332,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","-\frac{\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{105}+\frac{128\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}-\frac{256\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}-\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}-\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{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)}^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,"-((32*cos(c/2 + (d*x)/2)^10)/105 + (128*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2))/105 - (32*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/5 - (64*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4)/15 - (256*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3)/105 + (32*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2)/35)/(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"
833,1,207,91,14.065431,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{105}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}+\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}-\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}+\frac{52\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{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,"((4*cos(c/2 + (d*x)/2)^10)/105 + (16*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2))/105 + 4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + (16*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/5 + (52*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4)/15 - (32*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3)/105 + (4*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2)/35)/(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"
834,1,231,91,14.343455,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{35}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}+\frac{24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{88\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}-\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}}{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,"((8*cos(c/2 + (d*x)/2)^10)/35 + (32*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2))/35 + (8*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7)/3 + (8*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6)/3 + (16*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/5 - (8*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4)/15 + (88*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3)/105 + (24*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2)/35)/(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"
835,1,254,93,14.349690,"\text{Not used}","int(sin(c + d*x)/(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)}^2\,\left(9\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+36\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+132\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+68\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+14\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-84\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+140\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+140\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+105\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\right)}{105\,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)^2*(9*cos(c/2 + (d*x)/2)^8 + 105*sin(c/2 + (d*x)/2)^8 + 140*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^7 + 36*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2) + 140*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^6 - 84*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^5 + 14*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4 + 68*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^3 + 132*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2))/(105*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"
836,1,169,149,12.342975,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}-\frac{344\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}-\frac{2216\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}+\frac{172\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{1108\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}+\frac{382}{105}}{a^2\,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)}^7}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) - ((1108*tan(c/2 + (d*x)/2))/105 + (172*tan(c/2 + (d*x)/2)^2)/35 - (2216*tan(c/2 + (d*x)/2)^3)/105 - (344*tan(c/2 + (d*x)/2)^4)/15 + (48*tan(c/2 + (d*x)/2)^5)/5 + 28*tan(c/2 + (d*x)/2)^6 + 8*tan(c/2 + (d*x)/2)^7 - 6*tan(c/2 + (d*x)/2)^8 - 4*tan(c/2 + (d*x)/2)^9 + 382/105)/(a^2*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^7)","B"
837,1,331,164,11.237941,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+52\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{462\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{1136\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}+\frac{12734\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{105}+\frac{552\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{35}-\frac{3847\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{105}-\frac{1828\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}-1}{d\,\left(-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+28\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}","Not used",1,"((552*tan(c/2 + (d*x)/2)^3)/35 - (3847*tan(c/2 + (d*x)/2)^2)/105 - (1828*tan(c/2 + (d*x)/2))/105 + (12734*tan(c/2 + (d*x)/2)^4)/105 + (1136*tan(c/2 + (d*x)/2)^5)/15 - (462*tan(c/2 + (d*x)/2)^6)/5 - 120*tan(c/2 + (d*x)/2)^7 + 3*tan(c/2 + (d*x)/2)^8 + 52*tan(c/2 + (d*x)/2)^9 + 21*tan(c/2 + (d*x)/2)^10 - 1)/(d*(8*a^2*tan(c/2 + (d*x)/2)^2 + 6*a^2*tan(c/2 + (d*x)/2)^3 - 16*a^2*tan(c/2 + (d*x)/2)^4 - 28*a^2*tan(c/2 + (d*x)/2)^5 + 28*a^2*tan(c/2 + (d*x)/2)^7 + 16*a^2*tan(c/2 + (d*x)/2)^8 - 6*a^2*tan(c/2 + (d*x)/2)^9 - 8*a^2*tan(c/2 + (d*x)/2)^10 - 2*a^2*tan(c/2 + (d*x)/2)^11 + 2*a^2*tan(c/2 + (d*x)/2))) - (2*log(tan(c/2 + (d*x)/2)))/(a^2*d) + tan(c/2 + (d*x)/2)/(2*a^2*d)","B"
838,1,243,194,10.766141,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{11\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-\frac{319\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{8}+\frac{27\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}+\frac{963\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{8}+\frac{369\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}-\frac{5513\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{60}-\frac{11918\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{105}+\frac{149\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{140}+\frac{4804\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}+\frac{15173\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{840}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{1}{8}\right)}{a^2\,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)}^7}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) + (11*log(tan(c/2 + (d*x)/2)))/(2*a^2*d) - tan(c/2 + (d*x)/2)/(a^2*d) - (cot(c/2 + (d*x)/2)^2*(tan(c/2 + (d*x)/2)/2 + (15173*tan(c/2 + (d*x)/2)^2)/840 + (4804*tan(c/2 + (d*x)/2)^3)/105 + (149*tan(c/2 + (d*x)/2)^4)/140 - (11918*tan(c/2 + (d*x)/2)^5)/105 - (5513*tan(c/2 + (d*x)/2)^6)/60 + (369*tan(c/2 + (d*x)/2)^7)/5 + (963*tan(c/2 + (d*x)/2)^8)/8 + (27*tan(c/2 + (d*x)/2)^9)/2 - (319*tan(c/2 + (d*x)/2)^10)/8 - 17*tan(c/2 + (d*x)/2)^11 - 1/8))/(a^2*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^7)","B"
839,1,169,178,17.807908,"\text{Not used}","int(sin(c + d*x)^7/(cos(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{x}{a^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3}-\frac{308\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}-\frac{1064\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}+\frac{788\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{35}+\frac{2208\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}+\frac{5878\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{315}-\frac{1684\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{105}-\frac{1262\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}-\frac{736}{315}}{a^3\,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)}^9}","Not used",1,"x/a^3 + ((5878*tan(c/2 + (d*x)/2)^3)/315 - (1684*tan(c/2 + (d*x)/2)^2)/105 - (1262*tan(c/2 + (d*x)/2))/105 + (2208*tan(c/2 + (d*x)/2)^4)/35 + (788*tan(c/2 + (d*x)/2)^5)/35 - (1064*tan(c/2 + (d*x)/2)^6)/15 - (308*tan(c/2 + (d*x)/2)^7)/5 + (70*tan(c/2 + (d*x)/2)^9)/3 + 12*tan(c/2 + (d*x)/2)^10 + 2*tan(c/2 + (d*x)/2)^11 - 736/315)/(a^3*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^9)","B"
840,1,184,121,13.173082,"\text{Not used}","int(sin(c + d*x)^6/(cos(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","-\frac{\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{63}+\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}+\frac{128\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{21}+\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{63}-\frac{96\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}-\frac{128\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{7}}{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\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^9}","Not used",1,"-((32*cos(c/2 + (d*x)/2)^12)/63 + (64*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2))/21 - (128*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)/7 - (96*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4)/7 + (64*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3)/63 + (128*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2)/21)/(a^3*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))^9)","B"
841,1,208,105,13.192345,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","-\frac{\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{63}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}+\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{21}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{63}-\frac{48\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}-\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{7}-\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{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\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^9}","Not used",1,"-((16*cos(c/2 + (d*x)/2)^12)/63 + (32*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2))/21 - (32*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/3 - (64*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)/7 - (48*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4)/7 + (32*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3)/63 + (64*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2)/21)/(a^3*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))^9)","B"
842,1,232,127,14.329551,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","-\frac{\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{315}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}+\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{105}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{315}-\frac{48\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}-\frac{288\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{35}-\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}-\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}}{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\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^9}","Not used",1,"-((16*cos(c/2 + (d*x)/2)^12)/315 + (32*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2))/105 - (32*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7)/5 - (32*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/5 - (288*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)/35 - (48*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4)/35 + (32*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3)/315 + (64*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2)/105)/(a^3*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))^9)","B"
843,1,255,105,16.123944,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{45}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{45}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+\frac{112\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}+\frac{24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{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\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^9}","Not used",1,"((4*cos(c/2 + (d*x)/2)^12)/45 + (8*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2))/15 + 4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + (24*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7)/5 + (112*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/15 + (8*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)/5 + (8*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4)/5 + (8*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3)/45 + (16*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2)/15)/(a^3*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))^9)","B"
844,1,279,127,14.870654,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{\frac{44\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{315}+\frac{88\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}+\frac{176\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{105}+\frac{928\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{315}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}+\frac{48\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{35}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{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\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^9}","Not used",1,"((44*cos(c/2 + (d*x)/2)^12)/315 + (88*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2))/105 + (8*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9)/3 + 4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + (32*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7)/5 + (16*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/15 + (48*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)/35 + (8*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4)/35 + (928*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3)/315 + (176*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2)/105)/(a^3*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))^9)","B"
845,1,279,123,15.001035,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{\frac{2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{63}+\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}+\frac{50\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{21}+\frac{256\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{63}+\frac{36\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}-\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{7}-\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{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\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^9}","Not used",1,"((2*cos(c/2 + (d*x)/2)^12)/63 + (4*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2))/21 + 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 4*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 6*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - (4*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/3 - (8*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)/7 + (36*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4)/7 + (256*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3)/63 + (50*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2)/21)/(a^3*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))^9)","B"
846,1,195,187,12.556029,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{50\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3}+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{428\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}+\frac{168\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}-\frac{2348\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{35}-\frac{2608\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}-\frac{2578\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{315}+\frac{3244\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{105}+\frac{2042\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}+\frac{1336}{315}}{a^3\,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)}^9}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) - ((2042*tan(c/2 + (d*x)/2))/105 + (3244*tan(c/2 + (d*x)/2)^2)/105 - (2578*tan(c/2 + (d*x)/2)^3)/315 - (2608*tan(c/2 + (d*x)/2)^4)/35 - (2348*tan(c/2 + (d*x)/2)^5)/35 + (168*tan(c/2 + (d*x)/2)^6)/5 + (428*tan(c/2 + (d*x)/2)^7)/5 + 40*tan(c/2 + (d*x)/2)^8 - (50*tan(c/2 + (d*x)/2)^9)/3 - 20*tan(c/2 + (d*x)/2)^10 - 6*tan(c/2 + (d*x)/2)^11 + 1336/315)/(a^3*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^9)","B"
847,1,390,200,11.316044,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{-33\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-134\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-\frac{484\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}+142\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{2503\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{5}+\frac{4444\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{15}-\frac{11008\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{35}-\frac{16908\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{35}-\frac{41753\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{315}+\frac{14354\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}+\frac{11692\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{105}+\frac{8786\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{315}+1}{d\,\left(-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-24\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+54\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+72\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-72\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-54\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+24\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - (3*log(tan(c/2 + (d*x)/2)))/(a^3*d) - ((8786*tan(c/2 + (d*x)/2))/315 + (11692*tan(c/2 + (d*x)/2)^2)/105 + (14354*tan(c/2 + (d*x)/2)^3)/105 - (41753*tan(c/2 + (d*x)/2)^4)/315 - (16908*tan(c/2 + (d*x)/2)^5)/35 - (11008*tan(c/2 + (d*x)/2)^6)/35 + (4444*tan(c/2 + (d*x)/2)^7)/15 + (2503*tan(c/2 + (d*x)/2)^8)/5 + 142*tan(c/2 + (d*x)/2)^9 - (484*tan(c/2 + (d*x)/2)^10)/3 - 134*tan(c/2 + (d*x)/2)^11 - 33*tan(c/2 + (d*x)/2)^12 + 1)/(d*(12*a^3*tan(c/2 + (d*x)/2)^2 + 24*a^3*tan(c/2 + (d*x)/2)^3 + 4*a^3*tan(c/2 + (d*x)/2)^4 - 54*a^3*tan(c/2 + (d*x)/2)^5 - 72*a^3*tan(c/2 + (d*x)/2)^6 + 72*a^3*tan(c/2 + (d*x)/2)^8 + 54*a^3*tan(c/2 + (d*x)/2)^9 - 4*a^3*tan(c/2 + (d*x)/2)^10 - 24*a^3*tan(c/2 + (d*x)/2)^11 - 12*a^3*tan(c/2 + (d*x)/2)^12 - 2*a^3*tan(c/2 + (d*x)/2)^13 + 2*a^3*tan(c/2 + (d*x)/2)))","B"
848,1,279,145,16.845343,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^4*(a + a*sin(c + d*x))^4),x)","\frac{\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3465}+\frac{512\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3465}+\frac{320\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{693}+\frac{2048\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3465}-\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{315}+\frac{1504\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{315}+\frac{704\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{105}+\frac{320\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{21}+\frac{128\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{15}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{5}}{a^4\,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)}^{11}}","Not used",1,"((64*cos(c/2 + (d*x)/2)^14)/3465 + (512*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2))/3465 + (32*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9)/5 + (128*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8)/15 + (320*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)/21 + (704*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6)/105 + (1504*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5)/315 - (64*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4)/315 + (2048*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3)/3465 + (320*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2)/693)/(a^4*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))^11)","B"
849,1,303,145,15.892594,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^4*(a + a*sin(c + d*x))^4),x)","\frac{\frac{244\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3465}+\frac{1952\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3465}+\frac{1220\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{693}+\frac{7808\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3465}+\frac{1016\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{315}+\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{315}+\frac{584\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{105}+\frac{128\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{21}+\frac{188\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{15}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{5}+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{a^4\,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)}^{11}}","Not used",1,"((244*cos(c/2 + (d*x)/2)^14)/3465 + (1952*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2))/3465 + 4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 + (32*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9)/5 + (188*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8)/15 + (128*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)/21 + (584*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6)/105 + (64*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5)/315 + (1016*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4)/315 + (7808*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3)/3465 + (1220*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2)/693)/(a^4*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))^11)","B"
850,1,327,143,15.996371,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^4*(a + a*sin(c + d*x))^4),x)","\frac{\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{231}+\frac{128\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{231}+\frac{400\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{231}+\frac{376\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{77}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{7}-\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{21}+\frac{80\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{21}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}}{a^4\,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)}^{11}}","Not used",1,"((16*cos(c/2 + (d*x)/2)^14)/231 + (128*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2))/231 + (8*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11)/3 + (16*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10)/3 + (32*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9)/3 + (16*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8)/3 + (80*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)/21 - (32*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6)/21 + (32*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5)/7 + (32*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4)/7 + (376*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3)/77 + (400*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2)/231)/(a^4*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))^11)","B"
851,1,286,133,9.817201,"\text{Not used}","int((sin(c + d*x)^6*(a + a*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{15\,a\,\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)}^{10}-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+4\,{\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)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{9\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{8\,d}-\frac{39\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{8\,d}+\frac{3\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"((3*a*tan(c/2 + (d*x)/2)^2)/2 - (15*a*tan(c/2 + (d*x)/2))/4 + 7*a*tan(c/2 + (d*x)/2)^3 - (7*a*tan(c/2 + (d*x)/2)^4)/2 + (11*a*tan(c/2 + (d*x)/2)^5)/2 - (7*a*tan(c/2 + (d*x)/2)^6)/2 + 7*a*tan(c/2 + (d*x)/2)^7 + (3*a*tan(c/2 + (d*x)/2)^8)/2 - (15*a*tan(c/2 + (d*x)/2)^9)/4)/(d*(tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^5 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 - 2*tan(c/2 + (d*x)/2)^9 + tan(c/2 + (d*x)/2)^10 + 1)) - (9*a*log(tan(c/2 + (d*x)/2) + 1))/(8*d) - (39*a*log(tan(c/2 + (d*x)/2) - 1))/(8*d) + (3*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
852,1,235,115,9.289251,"\text{Not used}","int((sin(c + d*x)^5*(a + a*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{15\,a\,\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)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2\,{\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+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{23\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{8\,d}+\frac{7\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{8\,d}+\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"((11*a*tan(c/2 + (d*x)/2)^2)/2 - (15*a*tan(c/2 + (d*x)/2))/4 + (11*a*tan(c/2 + (d*x)/2)^3)/4 - 5*a*tan(c/2 + (d*x)/2)^4 + (11*a*tan(c/2 + (d*x)/2)^5)/4 + (11*a*tan(c/2 + (d*x)/2)^6)/2 - (15*a*tan(c/2 + (d*x)/2)^7)/4)/(d*(2*tan(c/2 + (d*x)/2)^3 - 2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^4 + 2*tan(c/2 + (d*x)/2)^5 - 2*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^8 + 1)) - (23*a*log(tan(c/2 + (d*x)/2) - 1))/(8*d) + (7*a*log(tan(c/2 + (d*x)/2) + 1))/(8*d) + (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
853,1,205,105,9.258636,"\text{Not used}","int((sin(c + d*x)^4*(a + a*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{5\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{8\,d}-\frac{11\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{8\,d}+\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-\frac{9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{3\,a\,\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)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (5*a*log(tan(c/2 + (d*x)/2) + 1))/(8*d) - (11*a*log(tan(c/2 + (d*x)/2) - 1))/(8*d) + ((3*a*tan(c/2 + (d*x)/2))/4 + (a*tan(c/2 + (d*x)/2)^2)/2 - (9*a*tan(c/2 + (d*x)/2)^3)/2 + (a*tan(c/2 + (d*x)/2)^4)/2 + (3*a*tan(c/2 + (d*x)/2)^5)/4)/(d*(2*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 + 2*tan(c/2 + (d*x)/2)^5 - tan(c/2 + (d*x)/2)^6 - 1))","B"
854,1,167,84,14.457212,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{3\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{3\,a\,\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)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"(3*a*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((3*a*tan(c/2 + (d*x)/2)^2)/2 - (3*a*tan(c/2 + (d*x)/2))/4 + (a*tan(c/2 + (d*x)/2)^3)/2 + (3*a*tan(c/2 + (d*x)/2)^4)/2 - (3*a*tan(c/2 + (d*x)/2)^5)/4)/(d*(2*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 + 2*tan(c/2 + (d*x)/2)^5 - tan(c/2 + (d*x)/2)^6 - 1))","B"
855,1,167,84,14.456144,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x)))/cos(c + d*x)^5,x)","-\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{a\,\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)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"- (a*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((a*tan(c/2 + (d*x)/2))/4 - (a*tan(c/2 + (d*x)/2)^2)/2 + (5*a*tan(c/2 + (d*x)/2)^3)/2 - (a*tan(c/2 + (d*x)/2)^4)/2 + (a*tan(c/2 + (d*x)/2)^5)/4)/(d*(2*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 + 2*tan(c/2 + (d*x)/2)^5 - tan(c/2 + (d*x)/2)^6 - 1))","B"
856,1,167,61,14.586390,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x)))/cos(c + d*x)^5,x)","-\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{a\,\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)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"- (a*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((a*tan(c/2 + (d*x)/2))/4 + (3*a*tan(c/2 + (d*x)/2)^2)/2 - (3*a*tan(c/2 + (d*x)/2)^3)/2 + (3*a*tan(c/2 + (d*x)/2)^4)/2 + (a*tan(c/2 + (d*x)/2)^5)/4)/(d*(2*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 + 2*tan(c/2 + (d*x)/2)^5 - tan(c/2 + (d*x)/2)^6 - 1))","B"
857,1,99,117,0.095022,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^5*sin(c + d*x)),x)","\frac{a\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{\frac{3\,a\,{\sin\left(c+d\,x\right)}^2}{8}+\frac{a\,\sin\left(c+d\,x\right)}{8}-\frac{3\,a}{4}}{d\,\left({\cos\left(c+d\,x\right)}^2+{\sin\left(c+d\,x\right)}^3-\sin\left(c+d\,x\right)\right)}-\frac{11\,a\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{16\,d}-\frac{5\,a\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{16\,d}","Not used",1,"(a*log(sin(c + d*x)))/d - ((a*sin(c + d*x))/8 - (3*a)/4 + (3*a*sin(c + d*x)^2)/8)/(d*(cos(c + d*x)^2 - sin(c + d*x) + sin(c + d*x)^3)) - (11*a*log(sin(c + d*x) - 1))/(16*d) - (5*a*log(sin(c + d*x) + 1))/(16*d)","B"
858,1,118,129,0.096004,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^5*sin(c + d*x)^2),x)","\frac{a\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{\frac{15\,a\,{\sin\left(c+d\,x\right)}^3}{8}-\frac{11\,a\,{\sin\left(c+d\,x\right)}^2}{8}-\frac{7\,a\,\sin\left(c+d\,x\right)}{4}+a}{d\,\left({\sin\left(c+d\,x\right)}^4-{\sin\left(c+d\,x\right)}^3-{\sin\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)\right)}-\frac{23\,a\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{16\,d}+\frac{7\,a\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{16\,d}","Not used",1,"(a*log(sin(c + d*x)))/d - (a - (7*a*sin(c + d*x))/4 - (11*a*sin(c + d*x)^2)/8 + (15*a*sin(c + d*x)^3)/8)/(d*(sin(c + d*x) - sin(c + d*x)^2 - sin(c + d*x)^3 + sin(c + d*x)^4)) - (23*a*log(sin(c + d*x) - 1))/(16*d) + (7*a*log(sin(c + d*x) + 1))/(16*d)","B"
859,1,134,143,9.312135,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^5*sin(c + d*x)^3),x)","\frac{3\,a\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{39\,a\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{16\,d}-\frac{9\,a\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{16\,d}-\frac{\frac{15\,a\,{\sin\left(c+d\,x\right)}^4}{8}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^3}{8}-\frac{11\,a\,{\sin\left(c+d\,x\right)}^2}{4}+\frac{a\,\sin\left(c+d\,x\right)}{2}+\frac{a}{2}}{d\,\left({\sin\left(c+d\,x\right)}^5-{\sin\left(c+d\,x\right)}^4-{\sin\left(c+d\,x\right)}^3+{\sin\left(c+d\,x\right)}^2\right)}","Not used",1,"(3*a*log(sin(c + d*x)))/d - (39*a*log(sin(c + d*x) - 1))/(16*d) - (9*a*log(sin(c + d*x) + 1))/(16*d) - (a/2 + (a*sin(c + d*x))/2 - (11*a*sin(c + d*x)^2)/4 - (3*a*sin(c + d*x)^3)/8 + (15*a*sin(c + d*x)^4)/8)/(d*(sin(c + d*x)^2 - sin(c + d*x)^3 - sin(c + d*x)^4 + sin(c + d*x)^5))","B"
860,1,145,162,0.113958,"\text{Not used}","int((a + a*sin(c + d*x))/(cos(c + d*x)^5*sin(c + d*x)^4),x)","\frac{3\,a\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{\frac{35\,a\,{\sin\left(c+d\,x\right)}^5}{8}-\frac{23\,a\,{\sin\left(c+d\,x\right)}^4}{8}-\frac{53\,a\,{\sin\left(c+d\,x\right)}^3}{12}+\frac{13\,a\,{\sin\left(c+d\,x\right)}^2}{6}+\frac{a\,\sin\left(c+d\,x\right)}{6}+\frac{a}{3}}{d\,\left({\sin\left(c+d\,x\right)}^6-{\sin\left(c+d\,x\right)}^5-{\sin\left(c+d\,x\right)}^4+{\sin\left(c+d\,x\right)}^3\right)}-\frac{59\,a\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{16\,d}+\frac{11\,a\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{16\,d}","Not used",1,"(3*a*log(sin(c + d*x)))/d - (a/3 + (a*sin(c + d*x))/6 + (13*a*sin(c + d*x)^2)/6 - (53*a*sin(c + d*x)^3)/12 - (23*a*sin(c + d*x)^4)/8 + (35*a*sin(c + d*x)^5)/8)/(d*(sin(c + d*x)^3 - sin(c + d*x)^4 - sin(c + d*x)^5 + sin(c + d*x)^6)) - (59*a*log(sin(c + d*x) - 1))/(16*d) + (11*a*log(sin(c + d*x) + 1))/(16*d)","B"
861,1,283,119,9.227173,"\text{Not used}","int((sin(c + d*x)^5*(a + a*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{4\,a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{4\,d}-\frac{\frac{15\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}-22\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{61\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}-36\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{61\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-22\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{15\,a^2\,\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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{31\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{4\,d}","Not used",1,"(4*a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a^2*log(tan(c/2 + (d*x)/2) + 1))/(4*d) - ((61*a^2*tan(c/2 + (d*x)/2)^3)/2 - 22*a^2*tan(c/2 + (d*x)/2)^2 - 36*a^2*tan(c/2 + (d*x)/2)^4 + (61*a^2*tan(c/2 + (d*x)/2)^5)/2 - 22*a^2*tan(c/2 + (d*x)/2)^6 + (15*a^2*tan(c/2 + (d*x)/2)^7)/2 + (15*a^2*tan(c/2 + (d*x)/2))/2)/(d*(8*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 12*tan(c/2 + (d*x)/2)^3 + 14*tan(c/2 + (d*x)/2)^4 - 12*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^6 - 4*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^8 + 1)) - (31*a^2*log(tan(c/2 + (d*x)/2) - 1))/(4*d)","B"
862,1,225,101,9.269887,"\text{Not used}","int((sin(c + d*x)^4*(a + a*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{4\,d}-\frac{17\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{4\,d}-\frac{\frac{9\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}-14\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+17\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-14\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{9\,a^2\,\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)}^6-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}+\frac{2\,a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2) + 1))/(4*d) - (17*a^2*log(tan(c/2 + (d*x)/2) - 1))/(4*d) - (17*a^2*tan(c/2 + (d*x)/2)^3 - 14*a^2*tan(c/2 + (d*x)/2)^2 - 14*a^2*tan(c/2 + (d*x)/2)^4 + (9*a^2*tan(c/2 + (d*x)/2)^5)/2 + (9*a^2*tan(c/2 + (d*x)/2))/2)/(d*(7*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 8*tan(c/2 + (d*x)/2)^3 + 7*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^6 + 1)) + (2*a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
863,1,166,87,9.295545,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{7\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{4\,d}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{4\,d}-\frac{\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{3\,a^2\,\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)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (7*a^2*log(tan(c/2 + (d*x)/2) - 1))/(4*d) - (a^2*log(tan(c/2 + (d*x)/2) + 1))/(4*d) - ((3*a^2*tan(c/2 + (d*x)/2)^3)/2 - 4*a^2*tan(c/2 + (d*x)/2)^2 + (3*a^2*tan(c/2 + (d*x)/2))/2)/(d*(6*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 4*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 + 1))","B"
864,1,123,64,11.551939,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a^2\,\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)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"(a^2*atanh(tan(c/2 + (d*x)/2)))/(2*d) - ((a^2*tan(c/2 + (d*x)/2)^3)/2 - 2*a^2*tan(c/2 + (d*x)/2)^2 + (a^2*tan(c/2 + (d*x)/2))/2)/(d*(6*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 4*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 + 1))","B"
865,1,106,64,11.125944,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{a^2\,\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)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}","Not used",1,"((a^2*tan(c/2 + (d*x)/2)^3)/2 + (a^2*tan(c/2 + (d*x)/2))/2)/(d*(6*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 4*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 + 1)) - (a^2*atanh(tan(c/2 + (d*x)/2)))/(2*d)","B"
866,1,91,101,0.084749,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^5*sin(c + d*x)),x)","\frac{a^2\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{a^2\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{8\,d}-\frac{\frac{3\,a^2\,\sin\left(c+d\,x\right)}{4}-a^2}{d\,\left({\sin\left(c+d\,x\right)}^2-2\,\sin\left(c+d\,x\right)+1\right)}-\frac{7\,a^2\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{8\,d}","Not used",1,"(a^2*log(sin(c + d*x)))/d - (a^2*log(sin(c + d*x) + 1))/(8*d) - ((3*a^2*sin(c + d*x))/4 - a^2)/(d*(sin(c + d*x)^2 - 2*sin(c + d*x) + 1)) - (7*a^2*log(sin(c + d*x) - 1))/(8*d)","B"
867,1,110,116,9.050289,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^5*sin(c + d*x)^2),x)","\frac{a^2\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{8\,d}-\frac{17\,a^2\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{8\,d}+\frac{2\,a^2\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{\frac{9\,a^2\,{\sin\left(c+d\,x\right)}^2}{4}-\frac{7\,a^2\,\sin\left(c+d\,x\right)}{2}+a^2}{d\,\left({\sin\left(c+d\,x\right)}^3-2\,{\sin\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)\right)}","Not used",1,"(a^2*log(sin(c + d*x) + 1))/(8*d) - (17*a^2*log(sin(c + d*x) - 1))/(8*d) + (2*a^2*log(sin(c + d*x)))/d - (a^2 - (7*a^2*sin(c + d*x))/2 + (9*a^2*sin(c + d*x)^2)/4)/(d*(sin(c + d*x) - 2*sin(c + d*x)^2 + sin(c + d*x)^3))","B"
868,1,126,134,0.097656,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^5*sin(c + d*x)^3),x)","\frac{4\,a^2\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{a^2\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{8\,d}-\frac{\frac{15\,a^2\,{\sin\left(c+d\,x\right)}^3}{4}-\frac{11\,a^2\,{\sin\left(c+d\,x\right)}^2}{2}+a^2\,\sin\left(c+d\,x\right)+\frac{a^2}{2}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^3+{\sin\left(c+d\,x\right)}^2\right)}-\frac{31\,a^2\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{8\,d}","Not used",1,"(4*a^2*log(sin(c + d*x)))/d - (a^2*log(sin(c + d*x) + 1))/(8*d) - (a^2*sin(c + d*x) + a^2/2 - (11*a^2*sin(c + d*x)^2)/2 + (15*a^2*sin(c + d*x)^3)/4)/(d*(sin(c + d*x)^2 - 2*sin(c + d*x)^3 + sin(c + d*x)^4)) - (31*a^2*log(sin(c + d*x) - 1))/(8*d)","B"
869,1,140,150,9.054913,"\text{Not used}","int((a + a*sin(c + d*x))^2/(cos(c + d*x)^5*sin(c + d*x)^4),x)","\frac{a^2\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{8\,d}-\frac{49\,a^2\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{8\,d}-\frac{\frac{25\,a^2\,{\sin\left(c+d\,x\right)}^4}{4}-\frac{19\,a^2\,{\sin\left(c+d\,x\right)}^3}{2}+\frac{7\,a^2\,{\sin\left(c+d\,x\right)}^2}{3}+\frac{a^2\,\sin\left(c+d\,x\right)}{3}+\frac{a^2}{3}}{d\,\left({\sin\left(c+d\,x\right)}^5-2\,{\sin\left(c+d\,x\right)}^4+{\sin\left(c+d\,x\right)}^3\right)}+\frac{6\,a^2\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}","Not used",1,"(a^2*log(sin(c + d*x) + 1))/(8*d) - (49*a^2*log(sin(c + d*x) - 1))/(8*d) - ((a^2*sin(c + d*x))/3 + a^2/3 + (7*a^2*sin(c + d*x)^2)/3 - (19*a^2*sin(c + d*x)^3)/2 + (25*a^2*sin(c + d*x)^4)/4)/(d*(sin(c + d*x)^3 - 2*sin(c + d*x)^4 + sin(c + d*x)^5)) + (6*a^2*log(sin(c + d*x)))/d","B"
870,1,321,114,11.558827,"\text{Not used}","int((sin(c + d*x)^5*(a + a*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{10\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{20\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-60\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{320\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{500\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+184\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{500\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{320\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-60\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+20\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{20\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d}","Not used",1,"(10*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d - ((320*a^3*tan(c/2 + (d*x)/2)^3)/3 - 60*a^3*tan(c/2 + (d*x)/2)^2 - (500*a^3*tan(c/2 + (d*x)/2)^4)/3 + 184*a^3*tan(c/2 + (d*x)/2)^5 - (500*a^3*tan(c/2 + (d*x)/2)^6)/3 + (320*a^3*tan(c/2 + (d*x)/2)^7)/3 - 60*a^3*tan(c/2 + (d*x)/2)^8 + 20*a^3*tan(c/2 + (d*x)/2)^9 + 20*a^3*tan(c/2 + (d*x)/2))/(d*(9*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 16*tan(c/2 + (d*x)/2)^3 + 22*tan(c/2 + (d*x)/2)^4 - 24*tan(c/2 + (d*x)/2)^5 + 22*tan(c/2 + (d*x)/2)^6 - 16*tan(c/2 + (d*x)/2)^7 + 9*tan(c/2 + (d*x)/2)^8 - 4*tan(c/2 + (d*x)/2)^9 + tan(c/2 + (d*x)/2)^10 + 1)) - (20*a^3*log(tan(c/2 + (d*x)/2) - 1))/d","B"
871,1,263,96,10.928525,"\text{Not used}","int((sin(c + d*x)^4*(a + a*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{6\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-36\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+52\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-64\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+52\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-36\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+12\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{12\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d}","Not used",1,"(6*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (52*a^3*tan(c/2 + (d*x)/2)^3 - 36*a^3*tan(c/2 + (d*x)/2)^2 - 64*a^3*tan(c/2 + (d*x)/2)^4 + 52*a^3*tan(c/2 + (d*x)/2)^5 - 36*a^3*tan(c/2 + (d*x)/2)^6 + 12*a^3*tan(c/2 + (d*x)/2)^7 + 12*a^3*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 12*tan(c/2 + (d*x)/2)^3 + 14*tan(c/2 + (d*x)/2)^4 - 12*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^6 - 4*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^8 + 1)) - (12*a^3*log(tan(c/2 + (d*x)/2) - 1))/d","B"
872,1,205,78,10.128617,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{3\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{6\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d}-\frac{6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-18\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+20\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-18\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (6*a^3*log(tan(c/2 + (d*x)/2) - 1))/d - (20*a^3*tan(c/2 + (d*x)/2)^3 - 18*a^3*tan(c/2 + (d*x)/2)^2 - 18*a^3*tan(c/2 + (d*x)/2)^4 + 6*a^3*tan(c/2 + (d*x)/2)^5 + 6*a^3*tan(c/2 + (d*x)/2))/(d*(7*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 8*tan(c/2 + (d*x)/2)^3 + 7*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^6 + 1))","B"
873,1,313,64,9.707212,"\text{Not used}","int((sin(c + d*x)^2*(a + a*sin(c + d*x))^3)/cos(c + d*x)^5,x)","-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^3\,\left(2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)+a^3\,\left(4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)-8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)+2\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^3\,\left(2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)+a^3\,\left(4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)-8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)+2\right)\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^3\,\left(2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)+a^3\,\left(6\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)-12\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)+6\right)\right)}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^4}-\frac{a^3\,\left(2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"- (tan(c/2 + (d*x)/2)*(4*a^3*(2*log(tan(c/2 + (d*x)/2) - 1) - log(tan(c/2 + (d*x)/2)^2 + 1)) + a^3*(4*log(tan(c/2 + (d*x)/2)^2 + 1) - 8*log(tan(c/2 + (d*x)/2) - 1) + 2)) + tan(c/2 + (d*x)/2)^3*(4*a^3*(2*log(tan(c/2 + (d*x)/2) - 1) - log(tan(c/2 + (d*x)/2)^2 + 1)) + a^3*(4*log(tan(c/2 + (d*x)/2)^2 + 1) - 8*log(tan(c/2 + (d*x)/2) - 1) + 2)) - tan(c/2 + (d*x)/2)^2*(6*a^3*(2*log(tan(c/2 + (d*x)/2) - 1) - log(tan(c/2 + (d*x)/2)^2 + 1)) + a^3*(6*log(tan(c/2 + (d*x)/2)^2 + 1) - 12*log(tan(c/2 + (d*x)/2) - 1) + 6)))/(d*(tan(c/2 + (d*x)/2) - 1)^4) - (a^3*(2*log(tan(c/2 + (d*x)/2) - 1) - log(tan(c/2 + (d*x)/2)^2 + 1)))/d","B"
874,1,30,31,9.294161,"\text{Not used}","int((sin(c + d*x)*(a + a*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{a^3\,{\sin\left(c+d\,x\right)}^2}{8\,d\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^4}","Not used",1,"(a^3*sin(c + d*x)^2)/(8*d*cos(c/2 + pi/4 + (d*x)/2)^4)","B"
875,1,61,77,9.116961,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^5*sin(c + d*x)),x)","\frac{2\,a^3\,\mathrm{atanh}\left(2\,\sin\left(c+d\,x\right)-1\right)}{d}-\frac{a^3\,\sin\left(c+d\,x\right)-\frac{3\,a^3}{2}}{d\,\left({\sin\left(c+d\,x\right)}^2-2\,\sin\left(c+d\,x\right)+1\right)}","Not used",1,"(2*a^3*atanh(2*sin(c + d*x) - 1))/d - (a^3*sin(c + d*x) - (3*a^3)/2)/(d*(sin(c + d*x)^2 - 2*sin(c + d*x) + 1))","B"
876,1,80,93,0.084691,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^5*sin(c + d*x)^2),x)","\frac{6\,a^3\,\mathrm{atanh}\left(2\,\sin\left(c+d\,x\right)-1\right)}{d}-\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^2-\frac{9\,a^3\,\sin\left(c+d\,x\right)}{2}+a^3}{d\,\left({\sin\left(c+d\,x\right)}^3-2\,{\sin\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)\right)}","Not used",1,"(6*a^3*atanh(2*sin(c + d*x) - 1))/d - (a^3 - (9*a^3*sin(c + d*x))/2 + 3*a^3*sin(c + d*x)^2)/(d*(sin(c + d*x) - 2*sin(c + d*x)^2 + sin(c + d*x)^3))","B"
877,1,97,111,0.093493,"\text{Not used}","int((a + a*sin(c + d*x))^3/(cos(c + d*x)^5*sin(c + d*x)^3),x)","\frac{12\,a^3\,\mathrm{atanh}\left(2\,\sin\left(c+d\,x\right)-1\right)}{d}-\frac{6\,a^3\,{\sin\left(c+d\,x\right)}^3-9\,a^3\,{\sin\left(c+d\,x\right)}^2+2\,a^3\,\sin\left(c+d\,x\right)+\frac{a^3}{2}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^3+{\sin\left(c+d\,x\right)}^2\right)}","Not used",1,"(12*a^3*atanh(2*sin(c + d*x) - 1))/d - (2*a^3*sin(c + d*x) + a^3/2 - 9*a^3*sin(c + d*x)^2 + 6*a^3*sin(c + d*x)^3)/(d*(sin(c + d*x)^2 - 2*sin(c + d*x)^3 + sin(c + d*x)^4))","B"
878,1,567,236,10.636666,"\text{Not used}","int(sin(c + d*x)^11/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{515\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{128\,a\,d}-\frac{1795\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{128\,a\,d}-\frac{-\frac{1155\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{64}-\frac{835\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{32}+\frac{3205\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}+\frac{305\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{4}+\frac{41\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{16}+\frac{53\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{24}-\frac{5521\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{48}-\frac{2387\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{12}+\frac{6697\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}+\frac{6901\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{48}+\frac{6697\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{96}-\frac{2387\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{12}-\frac{5521\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{48}+\frac{53\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{24}+\frac{41\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{16}+\frac{305\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}+\frac{3205\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}-\frac{835\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{1155\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{5\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"(515*log(tan(c/2 + (d*x)/2) - 1))/(128*a*d) - (1795*log(tan(c/2 + (d*x)/2) + 1))/(128*a*d) - ((3205*tan(c/2 + (d*x)/2)^3)/64 - (835*tan(c/2 + (d*x)/2)^2)/32 - (1155*tan(c/2 + (d*x)/2))/64 + (305*tan(c/2 + (d*x)/2)^4)/4 + (41*tan(c/2 + (d*x)/2)^5)/16 + (53*tan(c/2 + (d*x)/2)^6)/24 - (5521*tan(c/2 + (d*x)/2)^7)/48 - (2387*tan(c/2 + (d*x)/2)^8)/12 + (6697*tan(c/2 + (d*x)/2)^9)/96 + (6901*tan(c/2 + (d*x)/2)^10)/48 + (6697*tan(c/2 + (d*x)/2)^11)/96 - (2387*tan(c/2 + (d*x)/2)^12)/12 - (5521*tan(c/2 + (d*x)/2)^13)/48 + (53*tan(c/2 + (d*x)/2)^14)/24 + (41*tan(c/2 + (d*x)/2)^15)/16 + (305*tan(c/2 + (d*x)/2)^16)/4 + (3205*tan(c/2 + (d*x)/2)^17)/64 - (835*tan(c/2 + (d*x)/2)^18)/32 - (1155*tan(c/2 + (d*x)/2)^19)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 2*a*tan(c/2 + (d*x)/2)^2 - 6*a*tan(c/2 + (d*x)/2)^3 - 3*a*tan(c/2 + (d*x)/2)^4 + 8*a*tan(c/2 + (d*x)/2)^6 + 16*a*tan(c/2 + (d*x)/2)^7 + 2*a*tan(c/2 + (d*x)/2)^8 - 12*a*tan(c/2 + (d*x)/2)^9 - 12*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 + 2*a*tan(c/2 + (d*x)/2)^12 + 16*a*tan(c/2 + (d*x)/2)^13 + 8*a*tan(c/2 + (d*x)/2)^14 - 3*a*tan(c/2 + (d*x)/2)^16 - 6*a*tan(c/2 + (d*x)/2)^17 - 2*a*tan(c/2 + (d*x)/2)^18 + 2*a*tan(c/2 + (d*x)/2)^19 + a*tan(c/2 + (d*x)/2)^20)) + (5*log(tan(c/2 + (d*x)/2)^2 + 1))/(a*d)","B"
879,1,512,220,10.337250,"\text{Not used}","int(sin(c + d*x)^10/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{325\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{128\,a\,d}+\frac{955\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{128\,a\,d}+\frac{-\frac{315\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{32}+\frac{265\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{8}+\frac{195\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{32}-\frac{1217\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{16}-\frac{2389\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{96}+\frac{1189\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{24}+\frac{767\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{32}+\frac{6845\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{96}+\frac{767\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{32}+\frac{1189\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{24}-\frac{2389\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{96}-\frac{1217\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{16}+\frac{195\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32}+\frac{265\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{315\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-8\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{5\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"(325*log(tan(c/2 + (d*x)/2) - 1))/(128*a*d) + (955*log(tan(c/2 + (d*x)/2) + 1))/(128*a*d) + ((5*tan(c/2 + (d*x)/2)^2)/32 - (315*tan(c/2 + (d*x)/2))/64 + (265*tan(c/2 + (d*x)/2)^3)/8 + (195*tan(c/2 + (d*x)/2)^4)/32 - (1217*tan(c/2 + (d*x)/2)^5)/16 - (2389*tan(c/2 + (d*x)/2)^6)/96 + (1189*tan(c/2 + (d*x)/2)^7)/24 + (767*tan(c/2 + (d*x)/2)^8)/32 + (6845*tan(c/2 + (d*x)/2)^9)/96 + (767*tan(c/2 + (d*x)/2)^10)/32 + (1189*tan(c/2 + (d*x)/2)^11)/24 - (2389*tan(c/2 + (d*x)/2)^12)/96 - (1217*tan(c/2 + (d*x)/2)^13)/16 + (195*tan(c/2 + (d*x)/2)^14)/32 + (265*tan(c/2 + (d*x)/2)^15)/8 + (5*tan(c/2 + (d*x)/2)^16)/32 - (315*tan(c/2 + (d*x)/2)^17)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 3*a*tan(c/2 + (d*x)/2)^2 - 8*a*tan(c/2 + (d*x)/2)^3 + 8*a*tan(c/2 + (d*x)/2)^5 + 8*a*tan(c/2 + (d*x)/2)^6 + 8*a*tan(c/2 + (d*x)/2)^7 - 6*a*tan(c/2 + (d*x)/2)^8 - 20*a*tan(c/2 + (d*x)/2)^9 - 6*a*tan(c/2 + (d*x)/2)^10 + 8*a*tan(c/2 + (d*x)/2)^11 + 8*a*tan(c/2 + (d*x)/2)^12 + 8*a*tan(c/2 + (d*x)/2)^13 - 8*a*tan(c/2 + (d*x)/2)^15 - 3*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18)) - (5*log(tan(c/2 + (d*x)/2)^2 + 1))/(a*d)","B"
880,1,485,199,10.143705,"\text{Not used}","int(sin(c + d*x)^9/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{\frac{315\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{251\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{32}-\frac{1411\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}-\frac{607\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{16}+\frac{2183\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{6287\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{96}-\frac{2749\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}-\frac{803\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{24}-\frac{2749\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{192}+\frac{6287\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{96}+\frac{2183\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64}-\frac{607\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16}-\frac{1411\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}+\frac{251\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}+\frac{315\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+18\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+18\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{187\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{128\,a\,d}-\frac{443\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{128\,a\,d}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"((315*tan(c/2 + (d*x)/2))/64 + (251*tan(c/2 + (d*x)/2)^2)/32 - (1411*tan(c/2 + (d*x)/2)^3)/64 - (607*tan(c/2 + (d*x)/2)^4)/16 + (2183*tan(c/2 + (d*x)/2)^5)/64 + (6287*tan(c/2 + (d*x)/2)^6)/96 - (2749*tan(c/2 + (d*x)/2)^7)/192 - (803*tan(c/2 + (d*x)/2)^8)/24 - (2749*tan(c/2 + (d*x)/2)^9)/192 + (6287*tan(c/2 + (d*x)/2)^10)/96 + (2183*tan(c/2 + (d*x)/2)^11)/64 - (607*tan(c/2 + (d*x)/2)^12)/16 - (1411*tan(c/2 + (d*x)/2)^13)/64 + (251*tan(c/2 + (d*x)/2)^14)/32 + (315*tan(c/2 + (d*x)/2)^15)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 4*a*tan(c/2 + (d*x)/2)^2 - 10*a*tan(c/2 + (d*x)/2)^3 + 4*a*tan(c/2 + (d*x)/2)^4 + 18*a*tan(c/2 + (d*x)/2)^5 + 4*a*tan(c/2 + (d*x)/2)^6 - 10*a*tan(c/2 + (d*x)/2)^7 - 10*a*tan(c/2 + (d*x)/2)^8 - 10*a*tan(c/2 + (d*x)/2)^9 + 4*a*tan(c/2 + (d*x)/2)^10 + 18*a*tan(c/2 + (d*x)/2)^11 + 4*a*tan(c/2 + (d*x)/2)^12 - 10*a*tan(c/2 + (d*x)/2)^13 - 4*a*tan(c/2 + (d*x)/2)^14 + 2*a*tan(c/2 + (d*x)/2)^15 + a*tan(c/2 + (d*x)/2)^16)) + (187*log(tan(c/2 + (d*x)/2) - 1))/(128*a*d) - (443*log(tan(c/2 + (d*x)/2) + 1))/(128*a*d) + log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d)","B"
881,1,432,188,9.360295,"\text{Not used}","int(sin(c + d*x)^8/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{-\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}+\frac{629\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}-\frac{365\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{96}-\frac{5399\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{203\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{48}+\frac{3019\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{48}+\frac{203\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{48}-\frac{5399\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}-\frac{365\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{96}+\frac{629\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{35\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\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)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{93\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{128\,a\,d}+\frac{163\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{128\,a\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"((29*tan(c/2 + (d*x)/2)^2)/32 - (35*tan(c/2 + (d*x)/2))/64 + (629*tan(c/2 + (d*x)/2)^3)/96 - (365*tan(c/2 + (d*x)/2)^4)/96 - (5399*tan(c/2 + (d*x)/2)^5)/192 + (203*tan(c/2 + (d*x)/2)^6)/48 + (3019*tan(c/2 + (d*x)/2)^7)/48 + (203*tan(c/2 + (d*x)/2)^8)/48 - (5399*tan(c/2 + (d*x)/2)^9)/192 - (365*tan(c/2 + (d*x)/2)^10)/96 + (629*tan(c/2 + (d*x)/2)^11)/96 + (29*tan(c/2 + (d*x)/2)^12)/32 - (35*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14)) + (93*log(tan(c/2 + (d*x)/2) - 1))/(128*a*d) + (163*log(tan(c/2 + (d*x)/2) + 1))/(128*a*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d)","B"
882,1,388,130,17.052129,"\text{Not used}","int(sin(c + d*x)^7/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}-\frac{245\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}-\frac{595\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{96}+\frac{791\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{231\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16}-\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{231\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{16}+\frac{791\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}-\frac{595\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{96}-\frac{245\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}+\frac{35\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\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)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{35\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a\,d}","Not used",1,"((35*tan(c/2 + (d*x)/2))/64 + (35*tan(c/2 + (d*x)/2)^2)/32 - (245*tan(c/2 + (d*x)/2)^3)/96 - (595*tan(c/2 + (d*x)/2)^4)/96 + (791*tan(c/2 + (d*x)/2)^5)/192 + (231*tan(c/2 + (d*x)/2)^6)/16 - (25*tan(c/2 + (d*x)/2)^7)/16 + (231*tan(c/2 + (d*x)/2)^8)/16 + (791*tan(c/2 + (d*x)/2)^9)/192 - (595*tan(c/2 + (d*x)/2)^10)/96 - (245*tan(c/2 + (d*x)/2)^11)/96 + (35*tan(c/2 + (d*x)/2)^12)/32 + (35*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14)) - (35*atanh(tan(c/2 + (d*x)/2)))/(64*a*d)","B"
883,1,388,134,17.116509,"\text{Not used}","int(sin(c + d*x)^6/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}-\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}-\frac{85\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{96}+\frac{113\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{33\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16}+\frac{289\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{33\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{16}+\frac{113\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}-\frac{85\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{96}-\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\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)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a\,d}","Not used",1,"((5*tan(c/2 + (d*x)/2))/64 + (5*tan(c/2 + (d*x)/2)^2)/32 - (35*tan(c/2 + (d*x)/2)^3)/96 - (85*tan(c/2 + (d*x)/2)^4)/96 + (113*tan(c/2 + (d*x)/2)^5)/192 + (33*tan(c/2 + (d*x)/2)^6)/16 + (289*tan(c/2 + (d*x)/2)^7)/16 + (33*tan(c/2 + (d*x)/2)^8)/16 + (113*tan(c/2 + (d*x)/2)^9)/192 - (85*tan(c/2 + (d*x)/2)^10)/96 - (35*tan(c/2 + (d*x)/2)^11)/96 + (5*tan(c/2 + (d*x)/2)^12)/32 + (5*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14)) - (5*atanh(tan(c/2 + (d*x)/2)))/(64*a*d)","B"
884,1,388,152,17.207359,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a\,d}+\frac{-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}+\frac{85\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{96}-\frac{113\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{413\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{48}+\frac{157\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{48}+\frac{413\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{48}-\frac{113\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}+\frac{85\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{96}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\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)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(5*atanh(tan(c/2 + (d*x)/2)))/(64*a*d) + ((35*tan(c/2 + (d*x)/2)^3)/96 - (5*tan(c/2 + (d*x)/2)^2)/32 - (5*tan(c/2 + (d*x)/2))/64 + (85*tan(c/2 + (d*x)/2)^4)/96 - (113*tan(c/2 + (d*x)/2)^5)/192 + (413*tan(c/2 + (d*x)/2)^6)/48 + (157*tan(c/2 + (d*x)/2)^7)/48 + (413*tan(c/2 + (d*x)/2)^8)/48 - (113*tan(c/2 + (d*x)/2)^9)/192 + (85*tan(c/2 + (d*x)/2)^10)/96 + (35*tan(c/2 + (d*x)/2)^11)/96 - (5*tan(c/2 + (d*x)/2)^12)/32 - (5*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14))","B"
885,1,388,150,17.147623,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a\,d}+\frac{-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}+\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{32}+\frac{387\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{43\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{48}+\frac{299\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{48}+\frac{43\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{48}+\frac{387\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64}+\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\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)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2)))/(64*a*d) + ((7*tan(c/2 + (d*x)/2)^3)/32 - (3*tan(c/2 + (d*x)/2)^2)/32 - (3*tan(c/2 + (d*x)/2))/64 + (17*tan(c/2 + (d*x)/2)^4)/32 + (387*tan(c/2 + (d*x)/2)^5)/64 + (43*tan(c/2 + (d*x)/2)^6)/48 + (299*tan(c/2 + (d*x)/2)^7)/48 + (43*tan(c/2 + (d*x)/2)^8)/48 + (387*tan(c/2 + (d*x)/2)^9)/64 + (17*tan(c/2 + (d*x)/2)^10)/32 + (7*tan(c/2 + (d*x)/2)^11)/32 - (3*tan(c/2 + (d*x)/2)^12)/32 - (3*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14))","B"
886,1,388,150,17.024027,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}+\frac{111\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{32}+\frac{125\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{277\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{48}-\frac{43\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{48}+\frac{277\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{48}+\frac{125\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64}+\frac{111\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\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)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a\,d}","Not used",1,"((3*tan(c/2 + (d*x)/2))/64 + (3*tan(c/2 + (d*x)/2)^2)/32 - (7*tan(c/2 + (d*x)/2)^3)/32 + (111*tan(c/2 + (d*x)/2)^4)/32 + (125*tan(c/2 + (d*x)/2)^5)/64 + (277*tan(c/2 + (d*x)/2)^6)/48 - (43*tan(c/2 + (d*x)/2)^7)/48 + (277*tan(c/2 + (d*x)/2)^8)/48 + (125*tan(c/2 + (d*x)/2)^9)/64 + (111*tan(c/2 + (d*x)/2)^10)/32 - (7*tan(c/2 + (d*x)/2)^11)/32 + (3*tan(c/2 + (d*x)/2)^12)/32 + (3*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14)) - (3*atanh(tan(c/2 + (d*x)/2)))/(64*a*d)","B"
887,1,388,148,17.115682,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}+\frac{221\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}+\frac{43\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{96}+\frac{625\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{48}+\frac{355\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{48}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{48}+\frac{625\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}+\frac{43\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{96}+\frac{221\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\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)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a\,d}","Not used",1,"((5*tan(c/2 + (d*x)/2))/64 + (5*tan(c/2 + (d*x)/2)^2)/32 + (221*tan(c/2 + (d*x)/2)^3)/96 + (43*tan(c/2 + (d*x)/2)^4)/96 + (625*tan(c/2 + (d*x)/2)^5)/192 + (35*tan(c/2 + (d*x)/2)^6)/48 + (355*tan(c/2 + (d*x)/2)^7)/48 + (35*tan(c/2 + (d*x)/2)^8)/48 + (625*tan(c/2 + (d*x)/2)^9)/192 + (43*tan(c/2 + (d*x)/2)^10)/96 + (221*tan(c/2 + (d*x)/2)^11)/96 + (5*tan(c/2 + (d*x)/2)^12)/32 + (5*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14)) - (5*atanh(tan(c/2 + (d*x)/2)))/(64*a*d)","B"
888,1,388,130,17.037893,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a\,d}+\frac{-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{59\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}+\frac{163\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}+\frac{149\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{96}-\frac{625\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{95\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16}+\frac{95\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{95\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{16}-\frac{625\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}+\frac{149\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{96}+\frac{163\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{59\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\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)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(5*atanh(tan(c/2 + (d*x)/2)))/(64*a*d) + ((59*tan(c/2 + (d*x)/2)^2)/32 - (5*tan(c/2 + (d*x)/2))/64 + (163*tan(c/2 + (d*x)/2)^3)/96 + (149*tan(c/2 + (d*x)/2)^4)/96 - (625*tan(c/2 + (d*x)/2)^5)/192 + (95*tan(c/2 + (d*x)/2)^6)/16 + (95*tan(c/2 + (d*x)/2)^7)/16 + (95*tan(c/2 + (d*x)/2)^8)/16 - (625*tan(c/2 + (d*x)/2)^9)/192 + (149*tan(c/2 + (d*x)/2)^10)/96 + (163*tan(c/2 + (d*x)/2)^11)/96 + (59*tan(c/2 + (d*x)/2)^12)/32 - (5*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14))","B"
889,1,158,165,0.235258,"\text{Not used}","int(1/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{35\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{128\,a\,d}+\frac{\frac{35\,{\sin\left(c+d\,x\right)}^6}{128}+\frac{35\,{\sin\left(c+d\,x\right)}^5}{128}-\frac{35\,{\sin\left(c+d\,x\right)}^4}{48}-\frac{35\,{\sin\left(c+d\,x\right)}^3}{48}+\frac{77\,{\sin\left(c+d\,x\right)}^2}{128}+\frac{77\,\sin\left(c+d\,x\right)}{128}-\frac{1}{8}}{d\,\left(-a\,{\sin\left(c+d\,x\right)}^7-a\,{\sin\left(c+d\,x\right)}^6+3\,a\,{\sin\left(c+d\,x\right)}^5+3\,a\,{\sin\left(c+d\,x\right)}^4-3\,a\,{\sin\left(c+d\,x\right)}^3-3\,a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)+a\right)}","Not used",1,"(35*atanh(sin(c + d*x)))/(128*a*d) + ((77*sin(c + d*x))/128 + (77*sin(c + d*x)^2)/128 - (35*sin(c + d*x)^3)/48 - (35*sin(c + d*x)^4)/48 + (35*sin(c + d*x)^5)/128 + (35*sin(c + d*x)^6)/128 - 1/8)/(d*(a + a*sin(c + d*x) - 3*a*sin(c + d*x)^2 - 3*a*sin(c + d*x)^3 + 3*a*sin(c + d*x)^4 + 3*a*sin(c + d*x)^5 - a*sin(c + d*x)^6 - a*sin(c + d*x)^7))","B"
890,1,191,202,0.163069,"\text{Not used}","int(1/(cos(c + d*x)^7*sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}-\frac{163\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{256\,a\,d}-\frac{93\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{256\,a\,d}+\frac{-\frac{35\,{\sin\left(c+d\,x\right)}^6}{128}+\frac{29\,{\sin\left(c+d\,x\right)}^5}{128}+\frac{59\,{\sin\left(c+d\,x\right)}^4}{48}-\frac{25\,{\sin\left(c+d\,x\right)}^3}{48}-\frac{237\,{\sin\left(c+d\,x\right)}^2}{128}+\frac{121\,\sin\left(c+d\,x\right)}{384}+\frac{25}{24}}{d\,\left(-a\,{\sin\left(c+d\,x\right)}^7-a\,{\sin\left(c+d\,x\right)}^6+3\,a\,{\sin\left(c+d\,x\right)}^5+3\,a\,{\sin\left(c+d\,x\right)}^4-3\,a\,{\sin\left(c+d\,x\right)}^3-3\,a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)+a\right)}","Not used",1,"log(sin(c + d*x))/(a*d) - (163*log(sin(c + d*x) + 1))/(256*a*d) - (93*log(sin(c + d*x) - 1))/(256*a*d) + ((121*sin(c + d*x))/384 - (237*sin(c + d*x)^2)/128 - (25*sin(c + d*x)^3)/48 + (59*sin(c + d*x)^4)/48 + (29*sin(c + d*x)^5)/128 - (35*sin(c + d*x)^6)/128 + 25/24)/(d*(a + a*sin(c + d*x) - 3*a*sin(c + d*x)^2 - 3*a*sin(c + d*x)^3 + 3*a*sin(c + d*x)^4 + 3*a*sin(c + d*x)^5 - a*sin(c + d*x)^6 - a*sin(c + d*x)^7))","B"
891,1,212,217,9.328648,"\text{Not used}","int(1/(cos(c + d*x)^7*sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{443\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{256\,a\,d}-\frac{187\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{256\,a\,d}-\frac{-\frac{315\,{\sin\left(c+d\,x\right)}^7}{128}-\frac{251\,{\sin\left(c+d\,x\right)}^6}{128}+\frac{113\,{\sin\left(c+d\,x\right)}^5}{16}+\frac{85\,{\sin\left(c+d\,x\right)}^4}{16}-\frac{853\,{\sin\left(c+d\,x\right)}^3}{128}-\frac{1727\,{\sin\left(c+d\,x\right)}^2}{384}+\frac{49\,\sin\left(c+d\,x\right)}{24}+1}{d\,\left(-a\,{\sin\left(c+d\,x\right)}^8-a\,{\sin\left(c+d\,x\right)}^7+3\,a\,{\sin\left(c+d\,x\right)}^6+3\,a\,{\sin\left(c+d\,x\right)}^5-3\,a\,{\sin\left(c+d\,x\right)}^4-3\,a\,{\sin\left(c+d\,x\right)}^3+a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}","Not used",1,"(443*log(sin(c + d*x) + 1))/(256*a*d) - (187*log(sin(c + d*x) - 1))/(256*a*d) - ((49*sin(c + d*x))/24 - (1727*sin(c + d*x)^2)/384 - (853*sin(c + d*x)^3)/128 + (85*sin(c + d*x)^4)/16 + (113*sin(c + d*x)^5)/16 - (251*sin(c + d*x)^6)/128 - (315*sin(c + d*x)^7)/128 + 1)/(d*(a*sin(c + d*x) + a*sin(c + d*x)^2 - 3*a*sin(c + d*x)^3 - 3*a*sin(c + d*x)^4 + 3*a*sin(c + d*x)^5 + 3*a*sin(c + d*x)^6 - a*sin(c + d*x)^7 - a*sin(c + d*x)^8)) - log(sin(c + d*x))/(a*d)","B"
892,1,223,232,9.243615,"\text{Not used}","int(1/(cos(c + d*x)^7*sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{5\,\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}-\frac{955\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{256\,a\,d}-\frac{325\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{256\,a\,d}+\frac{-\frac{315\,{\sin\left(c+d\,x\right)}^8}{128}+\frac{5\,{\sin\left(c+d\,x\right)}^7}{128}+\frac{145\,{\sin\left(c+d\,x\right)}^6}{16}+\frac{5\,{\sin\left(c+d\,x\right)}^5}{16}-\frac{1493\,{\sin\left(c+d\,x\right)}^4}{128}-\frac{319\,{\sin\left(c+d\,x\right)}^3}{384}+\frac{137\,{\sin\left(c+d\,x\right)}^2}{24}+\frac{\sin\left(c+d\,x\right)}{2}-\frac{1}{2}}{d\,\left(-a\,{\sin\left(c+d\,x\right)}^9-a\,{\sin\left(c+d\,x\right)}^8+3\,a\,{\sin\left(c+d\,x\right)}^7+3\,a\,{\sin\left(c+d\,x\right)}^6-3\,a\,{\sin\left(c+d\,x\right)}^5-3\,a\,{\sin\left(c+d\,x\right)}^4+a\,{\sin\left(c+d\,x\right)}^3+a\,{\sin\left(c+d\,x\right)}^2\right)}","Not used",1,"(5*log(sin(c + d*x)))/(a*d) - (955*log(sin(c + d*x) + 1))/(256*a*d) - (325*log(sin(c + d*x) - 1))/(256*a*d) + (sin(c + d*x)/2 + (137*sin(c + d*x)^2)/24 - (319*sin(c + d*x)^3)/384 - (1493*sin(c + d*x)^4)/128 + (5*sin(c + d*x)^5)/16 + (145*sin(c + d*x)^6)/16 + (5*sin(c + d*x)^7)/128 - (315*sin(c + d*x)^8)/128 - 1/2)/(d*(a*sin(c + d*x)^2 + a*sin(c + d*x)^3 - 3*a*sin(c + d*x)^4 - 3*a*sin(c + d*x)^5 + 3*a*sin(c + d*x)^6 + 3*a*sin(c + d*x)^7 - a*sin(c + d*x)^8 - a*sin(c + d*x)^9))","B"
893,1,233,253,9.264345,"\text{Not used}","int(1/(cos(c + d*x)^7*sin(c + d*x)^4*(a + a*sin(c + d*x))),x)","\frac{\frac{1155\,{\sin\left(c+d\,x\right)}^9}{128}+\frac{835\,{\sin\left(c+d\,x\right)}^8}{128}-\frac{425\,{\sin\left(c+d\,x\right)}^7}{16}-\frac{285\,{\sin\left(c+d\,x\right)}^6}{16}+\frac{3341\,{\sin\left(c+d\,x\right)}^5}{128}+\frac{5863\,{\sin\left(c+d\,x\right)}^4}{384}-\frac{209\,{\sin\left(c+d\,x\right)}^3}{24}-\frac{7\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{\sin\left(c+d\,x\right)}{6}-\frac{1}{3}}{d\,\left(-a\,{\sin\left(c+d\,x\right)}^{10}-a\,{\sin\left(c+d\,x\right)}^9+3\,a\,{\sin\left(c+d\,x\right)}^8+3\,a\,{\sin\left(c+d\,x\right)}^7-3\,a\,{\sin\left(c+d\,x\right)}^6-3\,a\,{\sin\left(c+d\,x\right)}^5+a\,{\sin\left(c+d\,x\right)}^4+a\,{\sin\left(c+d\,x\right)}^3\right)}-\frac{515\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{256\,a\,d}+\frac{1795\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{256\,a\,d}-\frac{5\,\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}","Not used",1,"(sin(c + d*x)/6 - (7*sin(c + d*x)^2)/2 - (209*sin(c + d*x)^3)/24 + (5863*sin(c + d*x)^4)/384 + (3341*sin(c + d*x)^5)/128 - (285*sin(c + d*x)^6)/16 - (425*sin(c + d*x)^7)/16 + (835*sin(c + d*x)^8)/128 + (1155*sin(c + d*x)^9)/128 - 1/3)/(d*(a*sin(c + d*x)^3 + a*sin(c + d*x)^4 - 3*a*sin(c + d*x)^5 - 3*a*sin(c + d*x)^6 + 3*a*sin(c + d*x)^7 + 3*a*sin(c + d*x)^8 - a*sin(c + d*x)^9 - a*sin(c + d*x)^10)) - (515*log(sin(c + d*x) - 1))/(256*a*d) + (1795*log(sin(c + d*x) + 1))/(256*a*d) - (5*log(sin(c + d*x)))/(a*d)","B"
894,1,215,91,13.517734,"\text{Not used}","int((sin(c + d*x)^3*(a + a*sin(c + d*x))^2)/cos(c + d*x)^8,x)","\frac{4\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+91\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-84\,{\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\right)}{105\,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,"(4*a^2*cos(c/2 + (d*x)/2)^3*(cos(c/2 + (d*x)/2)^7 + 105*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^6 - 4*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) - 84*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^5 + 91*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^4 + 8*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^3 + 3*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^2))/(105*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"
895,1,648,264,11.204050,"\text{Not used}","int(sin(c + d*x)^12/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{\frac{693\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{128}-\frac{75\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}}{64}-\frac{3153\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{64}-\frac{87\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{64}+\frac{111333\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{640}+\frac{1331\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{40}-\frac{4559\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{16}-\frac{1823\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{20}+\frac{42953\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{320}+\frac{11713\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{160}+\frac{43457\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{160}+\frac{11713\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{160}+\frac{42953\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{320}-\frac{1823\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{20}-\frac{4559\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{1331\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{40}+\frac{111333\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640}-\frac{87\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64}-\frac{3153\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}-\frac{75\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{693\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}+7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+26\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}+5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-22\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-22\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+26\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{843\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{256\,a\,d}-\frac{2229\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{256\,a\,d}+\frac{6\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"((693*tan(c/2 + (d*x)/2))/128 - (75*tan(c/2 + (d*x)/2)^2)/64 - (3153*tan(c/2 + (d*x)/2)^3)/64 - (87*tan(c/2 + (d*x)/2)^4)/64 + (111333*tan(c/2 + (d*x)/2)^5)/640 + (1331*tan(c/2 + (d*x)/2)^6)/40 - (4559*tan(c/2 + (d*x)/2)^7)/16 - (1823*tan(c/2 + (d*x)/2)^8)/20 + (42953*tan(c/2 + (d*x)/2)^9)/320 + (11713*tan(c/2 + (d*x)/2)^10)/160 + (43457*tan(c/2 + (d*x)/2)^11)/160 + (11713*tan(c/2 + (d*x)/2)^12)/160 + (42953*tan(c/2 + (d*x)/2)^13)/320 - (1823*tan(c/2 + (d*x)/2)^14)/20 - (4559*tan(c/2 + (d*x)/2)^15)/16 + (1331*tan(c/2 + (d*x)/2)^16)/40 + (111333*tan(c/2 + (d*x)/2)^17)/640 - (87*tan(c/2 + (d*x)/2)^18)/64 - (3153*tan(c/2 + (d*x)/2)^19)/64 - (75*tan(c/2 + (d*x)/2)^20)/64 + (693*tan(c/2 + (d*x)/2)^21)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 7*a*tan(c/2 + (d*x)/2)^4 + 26*a*tan(c/2 + (d*x)/2)^5 + 5*a*tan(c/2 + (d*x)/2)^6 - 16*a*tan(c/2 + (d*x)/2)^7 - 22*a*tan(c/2 + (d*x)/2)^8 - 28*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 + 56*a*tan(c/2 + (d*x)/2)^11 + 14*a*tan(c/2 + (d*x)/2)^12 - 28*a*tan(c/2 + (d*x)/2)^13 - 22*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 + 5*a*tan(c/2 + (d*x)/2)^16 + 26*a*tan(c/2 + (d*x)/2)^17 + 7*a*tan(c/2 + (d*x)/2)^18 - 12*a*tan(c/2 + (d*x)/2)^19 - 5*a*tan(c/2 + (d*x)/2)^20 + 2*a*tan(c/2 + (d*x)/2)^21 + a*tan(c/2 + (d*x)/2)^22)) - (843*log(tan(c/2 + (d*x)/2) - 1))/(256*a*d) - (2229*log(tan(c/2 + (d*x)/2) + 1))/(256*a*d) + (6*log(tan(c/2 + (d*x)/2)^2 + 1))/(a*d)","B"
896,1,595,247,10.845072,"\text{Not used}","int(sin(c + d*x)^11/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{949\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{256\,a\,d}-\frac{437\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{256\,a\,d}-\frac{\frac{693\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}+\frac{565\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{64}-\frac{4439\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{963\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{16}+\frac{7091\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{80}+\frac{40031\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{240}-\frac{12829\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{120}-\frac{17969\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{80}+\frac{39491\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{960}+\frac{49513\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{480}+\frac{39491\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{960}-\frac{17969\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{80}-\frac{12829\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{120}+\frac{40031\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{240}+\frac{7091\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{80}-\frac{963\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16}-\frac{4439\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128}+\frac{565\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{693\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}+13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"(949*log(tan(c/2 + (d*x)/2) + 1))/(256*a*d) - (437*log(tan(c/2 + (d*x)/2) - 1))/(256*a*d) - ((693*tan(c/2 + (d*x)/2))/128 + (565*tan(c/2 + (d*x)/2)^2)/64 - (4439*tan(c/2 + (d*x)/2)^3)/128 - (963*tan(c/2 + (d*x)/2)^4)/16 + (7091*tan(c/2 + (d*x)/2)^5)/80 + (40031*tan(c/2 + (d*x)/2)^6)/240 - (12829*tan(c/2 + (d*x)/2)^7)/120 - (17969*tan(c/2 + (d*x)/2)^8)/80 + (39491*tan(c/2 + (d*x)/2)^9)/960 + (49513*tan(c/2 + (d*x)/2)^10)/480 + (39491*tan(c/2 + (d*x)/2)^11)/960 - (17969*tan(c/2 + (d*x)/2)^12)/80 - (12829*tan(c/2 + (d*x)/2)^13)/120 + (40031*tan(c/2 + (d*x)/2)^14)/240 + (7091*tan(c/2 + (d*x)/2)^15)/80 - (963*tan(c/2 + (d*x)/2)^16)/16 - (4439*tan(c/2 + (d*x)/2)^17)/128 + (565*tan(c/2 + (d*x)/2)^18)/64 + (693*tan(c/2 + (d*x)/2)^19)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 6*a*tan(c/2 + (d*x)/2)^2 - 14*a*tan(c/2 + (d*x)/2)^3 + 13*a*tan(c/2 + (d*x)/2)^4 + 40*a*tan(c/2 + (d*x)/2)^5 - 8*a*tan(c/2 + (d*x)/2)^6 - 56*a*tan(c/2 + (d*x)/2)^7 - 14*a*tan(c/2 + (d*x)/2)^8 + 28*a*tan(c/2 + (d*x)/2)^9 + 28*a*tan(c/2 + (d*x)/2)^10 + 28*a*tan(c/2 + (d*x)/2)^11 - 14*a*tan(c/2 + (d*x)/2)^12 - 56*a*tan(c/2 + (d*x)/2)^13 - 8*a*tan(c/2 + (d*x)/2)^14 + 40*a*tan(c/2 + (d*x)/2)^15 + 13*a*tan(c/2 + (d*x)/2)^16 - 14*a*tan(c/2 + (d*x)/2)^17 - 6*a*tan(c/2 + (d*x)/2)^18 + 2*a*tan(c/2 + (d*x)/2)^19 + a*tan(c/2 + (d*x)/2)^20)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d)","B"
897,1,539,233,9.400441,"\text{Not used}","int(sin(c + d*x)^10/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{\frac{63\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{65\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}-\frac{233\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}+\frac{413\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{64}+\frac{6527\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{160}-\frac{14911\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{960}-\frac{59737\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{480}+\frac{12763\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{960}+\frac{45791\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{12763\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{960}-\frac{59737\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{480}-\frac{14911\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{960}+\frac{6527\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}+\frac{413\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64}-\frac{233\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}-\frac{65\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{63\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{193\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{256\,a\,d}-\frac{319\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{256\,a\,d}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"((63*tan(c/2 + (d*x)/2))/128 - (65*tan(c/2 + (d*x)/2)^2)/64 - (233*tan(c/2 + (d*x)/2)^3)/32 + (413*tan(c/2 + (d*x)/2)^4)/64 + (6527*tan(c/2 + (d*x)/2)^5)/160 - (14911*tan(c/2 + (d*x)/2)^6)/960 - (59737*tan(c/2 + (d*x)/2)^7)/480 + (12763*tan(c/2 + (d*x)/2)^8)/960 + (45791*tan(c/2 + (d*x)/2)^9)/192 + (12763*tan(c/2 + (d*x)/2)^10)/960 - (59737*tan(c/2 + (d*x)/2)^11)/480 - (14911*tan(c/2 + (d*x)/2)^12)/960 + (6527*tan(c/2 + (d*x)/2)^13)/160 + (413*tan(c/2 + (d*x)/2)^14)/64 - (233*tan(c/2 + (d*x)/2)^15)/32 - (65*tan(c/2 + (d*x)/2)^16)/64 + (63*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18)) - (193*log(tan(c/2 + (d*x)/2) - 1))/(256*a*d) - (319*log(tan(c/2 + (d*x)/2) + 1))/(256*a*d) + log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d)","B"
898,1,497,154,17.054246,"\text{Not used}","int(sin(c + d*x)^9/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{63\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}-\frac{\frac{63\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}+\frac{63\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}-\frac{105\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}-\frac{483\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{64}+\frac{1407\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{160}+\frac{8043\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{320}-\frac{1779\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{160}-\frac{15159\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{320}+\frac{245\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}-\frac{15159\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{320}-\frac{1779\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{160}+\frac{8043\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{320}+\frac{1407\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}-\frac{483\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64}-\frac{105\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}+\frac{63\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{63\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(63*atanh(tan(c/2 + (d*x)/2)))/(128*a*d) - ((63*tan(c/2 + (d*x)/2))/128 + (63*tan(c/2 + (d*x)/2)^2)/64 - (105*tan(c/2 + (d*x)/2)^3)/32 - (483*tan(c/2 + (d*x)/2)^4)/64 + (1407*tan(c/2 + (d*x)/2)^5)/160 + (8043*tan(c/2 + (d*x)/2)^6)/320 - (1779*tan(c/2 + (d*x)/2)^7)/160 - (15159*tan(c/2 + (d*x)/2)^8)/320 + (245*tan(c/2 + (d*x)/2)^9)/64 - (15159*tan(c/2 + (d*x)/2)^10)/320 - (1779*tan(c/2 + (d*x)/2)^11)/160 + (8043*tan(c/2 + (d*x)/2)^12)/320 + (1407*tan(c/2 + (d*x)/2)^13)/160 - (483*tan(c/2 + (d*x)/2)^14)/64 - (105*tan(c/2 + (d*x)/2)^15)/32 + (63*tan(c/2 + (d*x)/2)^16)/64 + (63*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18))","B"
899,1,496,160,16.770464,"\text{Not used}","int(sin(c + d*x)^8/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{7\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}+\frac{-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{96}+\frac{161\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{192}-\frac{469\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{480}-\frac{2681\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{960}+\frac{593\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{480}+\frac{5053\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{960}+\frac{10841\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{5053\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{960}+\frac{593\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{480}-\frac{2681\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{960}-\frac{469\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{480}+\frac{161\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{192}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}-\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(7*atanh(tan(c/2 + (d*x)/2)))/(128*a*d) + ((35*tan(c/2 + (d*x)/2)^3)/96 - (7*tan(c/2 + (d*x)/2)^2)/64 - (7*tan(c/2 + (d*x)/2))/128 + (161*tan(c/2 + (d*x)/2)^4)/192 - (469*tan(c/2 + (d*x)/2)^5)/480 - (2681*tan(c/2 + (d*x)/2)^6)/960 + (593*tan(c/2 + (d*x)/2)^7)/480 + (5053*tan(c/2 + (d*x)/2)^8)/960 + (10841*tan(c/2 + (d*x)/2)^9)/192 + (5053*tan(c/2 + (d*x)/2)^10)/960 + (593*tan(c/2 + (d*x)/2)^11)/480 - (2681*tan(c/2 + (d*x)/2)^12)/960 - (469*tan(c/2 + (d*x)/2)^13)/480 + (161*tan(c/2 + (d*x)/2)^14)/192 + (35*tan(c/2 + (d*x)/2)^15)/96 - (7*tan(c/2 + (d*x)/2)^16)/64 - (7*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18))","B"
900,1,496,178,16.704394,"\text{Not used}","int(sin(c + d*x)^7/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}-\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{96}-\frac{161\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{192}+\frac{469\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{480}+\frac{2681\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{960}-\frac{593\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{480}+\frac{25667\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{960}+\frac{1447\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{25667\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{960}-\frac{593\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{480}+\frac{2681\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{960}+\frac{469\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{480}-\frac{161\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{192}-\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{7\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}","Not used",1,"((7*tan(c/2 + (d*x)/2))/128 + (7*tan(c/2 + (d*x)/2)^2)/64 - (35*tan(c/2 + (d*x)/2)^3)/96 - (161*tan(c/2 + (d*x)/2)^4)/192 + (469*tan(c/2 + (d*x)/2)^5)/480 + (2681*tan(c/2 + (d*x)/2)^6)/960 - (593*tan(c/2 + (d*x)/2)^7)/480 + (25667*tan(c/2 + (d*x)/2)^8)/960 + (1447*tan(c/2 + (d*x)/2)^9)/192 + (25667*tan(c/2 + (d*x)/2)^10)/960 - (593*tan(c/2 + (d*x)/2)^11)/480 + (2681*tan(c/2 + (d*x)/2)^12)/960 + (469*tan(c/2 + (d*x)/2)^13)/480 - (161*tan(c/2 + (d*x)/2)^14)/192 - (35*tan(c/2 + (d*x)/2)^15)/96 + (7*tan(c/2 + (d*x)/2)^16)/64 + (7*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18)) - (7*atanh(tan(c/2 + (d*x)/2)))/(128*a*d)","B"
901,1,496,176,16.644896,"\text{Not used}","int(sin(c + d*x)^6/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}-\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{64}+\frac{67\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{160}+\frac{383\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{320}+\frac{2841\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{160}+\frac{741\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{320}+\frac{1377\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{741\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{320}+\frac{2841\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{160}+\frac{383\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{320}+\frac{67\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}-\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}","Not used",1,"((3*tan(c/2 + (d*x)/2))/128 + (3*tan(c/2 + (d*x)/2)^2)/64 - (5*tan(c/2 + (d*x)/2)^3)/32 - (23*tan(c/2 + (d*x)/2)^4)/64 + (67*tan(c/2 + (d*x)/2)^5)/160 + (383*tan(c/2 + (d*x)/2)^6)/320 + (2841*tan(c/2 + (d*x)/2)^7)/160 + (741*tan(c/2 + (d*x)/2)^8)/320 + (1377*tan(c/2 + (d*x)/2)^9)/64 + (741*tan(c/2 + (d*x)/2)^10)/320 + (2841*tan(c/2 + (d*x)/2)^11)/160 + (383*tan(c/2 + (d*x)/2)^12)/320 + (67*tan(c/2 + (d*x)/2)^13)/160 - (23*tan(c/2 + (d*x)/2)^14)/64 - (5*tan(c/2 + (d*x)/2)^15)/32 + (3*tan(c/2 + (d*x)/2)^16)/64 + (3*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18)) - (3*atanh(tan(c/2 + (d*x)/2)))/(128*a*d)","B"
902,1,496,194,16.617732,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}+\frac{-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}+\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{64}-\frac{67\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{160}+\frac{9091\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{960}+\frac{1717\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{480}+\frac{18257\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{960}-\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{18257\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{960}+\frac{1717\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{480}+\frac{9091\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{960}-\frac{67\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}+\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2)))/(128*a*d) + ((5*tan(c/2 + (d*x)/2)^3)/32 - (3*tan(c/2 + (d*x)/2)^2)/64 - (3*tan(c/2 + (d*x)/2))/128 + (23*tan(c/2 + (d*x)/2)^4)/64 - (67*tan(c/2 + (d*x)/2)^5)/160 + (9091*tan(c/2 + (d*x)/2)^6)/960 + (1717*tan(c/2 + (d*x)/2)^7)/480 + (18257*tan(c/2 + (d*x)/2)^8)/960 - (35*tan(c/2 + (d*x)/2)^9)/192 + (18257*tan(c/2 + (d*x)/2)^10)/960 + (1717*tan(c/2 + (d*x)/2)^11)/480 + (9091*tan(c/2 + (d*x)/2)^12)/960 - (67*tan(c/2 + (d*x)/2)^13)/160 + (23*tan(c/2 + (d*x)/2)^14)/64 + (5*tan(c/2 + (d*x)/2)^15)/32 - (3*tan(c/2 + (d*x)/2)^16)/64 - (3*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18))","B"
903,1,496,192,16.705222,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}+\frac{-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}+\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{64}+\frac{957\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{160}+\frac{899\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{960}+\frac{5813\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{480}+\frac{1873\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{960}+\frac{4061\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{1873\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{960}+\frac{5813\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{480}+\frac{899\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{960}+\frac{957\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}+\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2)))/(128*a*d) + ((5*tan(c/2 + (d*x)/2)^3)/32 - (3*tan(c/2 + (d*x)/2)^2)/64 - (3*tan(c/2 + (d*x)/2))/128 + (23*tan(c/2 + (d*x)/2)^4)/64 + (957*tan(c/2 + (d*x)/2)^5)/160 + (899*tan(c/2 + (d*x)/2)^6)/960 + (5813*tan(c/2 + (d*x)/2)^7)/480 + (1873*tan(c/2 + (d*x)/2)^8)/960 + (4061*tan(c/2 + (d*x)/2)^9)/192 + (1873*tan(c/2 + (d*x)/2)^10)/960 + (5813*tan(c/2 + (d*x)/2)^11)/480 + (899*tan(c/2 + (d*x)/2)^12)/960 + (957*tan(c/2 + (d*x)/2)^13)/160 + (23*tan(c/2 + (d*x)/2)^14)/64 + (5*tan(c/2 + (d*x)/2)^15)/32 - (3*tan(c/2 + (d*x)/2)^16)/64 - (3*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18))","B"
904,1,496,174,17.339110,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}+\frac{233\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{64}+\frac{323\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{160}+\frac{2687\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{320}-\frac{231\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{160}+\frac{5349\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{320}+\frac{353\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{5349\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{320}-\frac{231\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{160}+\frac{2687\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{320}+\frac{323\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}+\frac{233\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}","Not used",1,"((3*tan(c/2 + (d*x)/2))/128 + (3*tan(c/2 + (d*x)/2)^2)/64 - (5*tan(c/2 + (d*x)/2)^3)/32 + (233*tan(c/2 + (d*x)/2)^4)/64 + (323*tan(c/2 + (d*x)/2)^5)/160 + (2687*tan(c/2 + (d*x)/2)^6)/320 - (231*tan(c/2 + (d*x)/2)^7)/160 + (5349*tan(c/2 + (d*x)/2)^8)/320 + (353*tan(c/2 + (d*x)/2)^9)/64 + (5349*tan(c/2 + (d*x)/2)^10)/320 - (231*tan(c/2 + (d*x)/2)^11)/160 + (2687*tan(c/2 + (d*x)/2)^12)/320 + (323*tan(c/2 + (d*x)/2)^13)/160 + (233*tan(c/2 + (d*x)/2)^14)/64 - (5*tan(c/2 + (d*x)/2)^15)/32 + (3*tan(c/2 + (d*x)/2)^16)/64 + (3*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18)) - (3*atanh(tan(c/2 + (d*x)/2)))/(128*a*d)","B"
905,1,496,172,16.880530,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}+\frac{221\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{96}+\frac{95\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{192}+\frac{2261\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{480}+\frac{889\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{960}+\frac{7343\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{480}+\frac{1603\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{960}+\frac{2471\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{1603\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{960}+\frac{7343\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{480}+\frac{889\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{960}+\frac{2261\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{480}+\frac{95\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{192}+\frac{221\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{7\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}","Not used",1,"((7*tan(c/2 + (d*x)/2))/128 + (7*tan(c/2 + (d*x)/2)^2)/64 + (221*tan(c/2 + (d*x)/2)^3)/96 + (95*tan(c/2 + (d*x)/2)^4)/192 + (2261*tan(c/2 + (d*x)/2)^5)/480 + (889*tan(c/2 + (d*x)/2)^6)/960 + (7343*tan(c/2 + (d*x)/2)^7)/480 + (1603*tan(c/2 + (d*x)/2)^8)/960 + (2471*tan(c/2 + (d*x)/2)^9)/192 + (1603*tan(c/2 + (d*x)/2)^10)/960 + (7343*tan(c/2 + (d*x)/2)^11)/480 + (889*tan(c/2 + (d*x)/2)^12)/960 + (2261*tan(c/2 + (d*x)/2)^13)/480 + (95*tan(c/2 + (d*x)/2)^14)/192 + (221*tan(c/2 + (d*x)/2)^15)/96 + (7*tan(c/2 + (d*x)/2)^16)/64 + (7*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18)) - (7*atanh(tan(c/2 + (d*x)/2)))/(128*a*d)","B"
906,1,496,154,16.754458,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{7\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a\,d}+\frac{-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}+\frac{121\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{64}+\frac{163\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{96}+\frac{289\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{192}-\frac{2261\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{480}+\frac{12551\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{960}+\frac{6097\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{480}+\frac{11837\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{960}-\frac{2471\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{11837\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{960}+\frac{6097\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{480}+\frac{12551\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{960}-\frac{2261\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{480}+\frac{289\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{192}+\frac{163\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{121\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}-\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+140\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-112\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(7*atanh(tan(c/2 + (d*x)/2)))/(128*a*d) + ((121*tan(c/2 + (d*x)/2)^2)/64 - (7*tan(c/2 + (d*x)/2))/128 + (163*tan(c/2 + (d*x)/2)^3)/96 + (289*tan(c/2 + (d*x)/2)^4)/192 - (2261*tan(c/2 + (d*x)/2)^5)/480 + (12551*tan(c/2 + (d*x)/2)^6)/960 + (6097*tan(c/2 + (d*x)/2)^7)/480 + (11837*tan(c/2 + (d*x)/2)^8)/960 - (2471*tan(c/2 + (d*x)/2)^9)/192 + (11837*tan(c/2 + (d*x)/2)^10)/960 + (6097*tan(c/2 + (d*x)/2)^11)/480 + (12551*tan(c/2 + (d*x)/2)^12)/960 - (2261*tan(c/2 + (d*x)/2)^13)/480 + (289*tan(c/2 + (d*x)/2)^14)/192 + (163*tan(c/2 + (d*x)/2)^15)/96 + (121*tan(c/2 + (d*x)/2)^16)/64 - (7*tan(c/2 + (d*x)/2)^17)/128)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 7*a*tan(c/2 + (d*x)/2)^2 - 16*a*tan(c/2 + (d*x)/2)^3 + 20*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^5 - 28*a*tan(c/2 + (d*x)/2)^6 - 112*a*tan(c/2 + (d*x)/2)^7 + 14*a*tan(c/2 + (d*x)/2)^8 + 140*a*tan(c/2 + (d*x)/2)^9 + 14*a*tan(c/2 + (d*x)/2)^10 - 112*a*tan(c/2 + (d*x)/2)^11 - 28*a*tan(c/2 + (d*x)/2)^12 + 56*a*tan(c/2 + (d*x)/2)^13 + 20*a*tan(c/2 + (d*x)/2)^14 - 16*a*tan(c/2 + (d*x)/2)^15 - 7*a*tan(c/2 + (d*x)/2)^16 + 2*a*tan(c/2 + (d*x)/2)^17 + a*tan(c/2 + (d*x)/2)^18))","B"
907,1,199,210,9.408807,"\text{Not used}","int(1/(cos(c + d*x)^9*(a + a*sin(c + d*x))),x)","\frac{63\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{256\,a\,d}-\frac{\frac{63\,{\sin\left(c+d\,x\right)}^8}{256}+\frac{63\,{\sin\left(c+d\,x\right)}^7}{256}-\frac{231\,{\sin\left(c+d\,x\right)}^6}{256}-\frac{231\,{\sin\left(c+d\,x\right)}^5}{256}+\frac{1533\,{\sin\left(c+d\,x\right)}^4}{1280}+\frac{1533\,{\sin\left(c+d\,x\right)}^3}{1280}-\frac{837\,{\sin\left(c+d\,x\right)}^2}{1280}-\frac{837\,\sin\left(c+d\,x\right)}{1280}+\frac{1}{10}}{d\,\left(a\,{\sin\left(c+d\,x\right)}^9+a\,{\sin\left(c+d\,x\right)}^8-4\,a\,{\sin\left(c+d\,x\right)}^7-4\,a\,{\sin\left(c+d\,x\right)}^6+6\,a\,{\sin\left(c+d\,x\right)}^5+6\,a\,{\sin\left(c+d\,x\right)}^4-4\,a\,{\sin\left(c+d\,x\right)}^3-4\,a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)+a\right)}","Not used",1,"(63*atanh(sin(c + d*x)))/(256*a*d) - ((1533*sin(c + d*x)^3)/1280 - (837*sin(c + d*x)^2)/1280 - (837*sin(c + d*x))/1280 + (1533*sin(c + d*x)^4)/1280 - (231*sin(c + d*x)^5)/256 - (231*sin(c + d*x)^6)/256 + (63*sin(c + d*x)^7)/256 + (63*sin(c + d*x)^8)/256 + 1/10)/(d*(a + a*sin(c + d*x) - 4*a*sin(c + d*x)^2 - 4*a*sin(c + d*x)^3 + 6*a*sin(c + d*x)^4 + 6*a*sin(c + d*x)^5 - 4*a*sin(c + d*x)^6 - 4*a*sin(c + d*x)^7 + a*sin(c + d*x)^8 + a*sin(c + d*x)^9))","B"
908,1,231,247,0.231847,"\text{Not used}","int(1/(cos(c + d*x)^9*sin(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\frac{63\,{\sin\left(c+d\,x\right)}^8}{256}-\frac{65\,{\sin\left(c+d\,x\right)}^7}{256}-\frac{359\,{\sin\left(c+d\,x\right)}^6}{256}+\frac{217\,{\sin\left(c+d\,x\right)}^5}{256}+\frac{3773\,{\sin\left(c+d\,x\right)}^4}{1280}-\frac{3721\,{\sin\left(c+d\,x\right)}^3}{3840}-\frac{10831\,{\sin\left(c+d\,x\right)}^2}{3840}+\frac{1489\,\sin\left(c+d\,x\right)}{3840}+\frac{137}{120}}{d\,\left(a\,{\sin\left(c+d\,x\right)}^9+a\,{\sin\left(c+d\,x\right)}^8-4\,a\,{\sin\left(c+d\,x\right)}^7-4\,a\,{\sin\left(c+d\,x\right)}^6+6\,a\,{\sin\left(c+d\,x\right)}^5+6\,a\,{\sin\left(c+d\,x\right)}^4-4\,a\,{\sin\left(c+d\,x\right)}^3-4\,a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)+a\right)}-\frac{319\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{512\,a\,d}-\frac{193\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{512\,a\,d}+\frac{\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}","Not used",1,"((1489*sin(c + d*x))/3840 - (10831*sin(c + d*x)^2)/3840 - (3721*sin(c + d*x)^3)/3840 + (3773*sin(c + d*x)^4)/1280 + (217*sin(c + d*x)^5)/256 - (359*sin(c + d*x)^6)/256 - (65*sin(c + d*x)^7)/256 + (63*sin(c + d*x)^8)/256 + 137/120)/(d*(a + a*sin(c + d*x) - 4*a*sin(c + d*x)^2 - 4*a*sin(c + d*x)^3 + 6*a*sin(c + d*x)^4 + 6*a*sin(c + d*x)^5 - 4*a*sin(c + d*x)^6 - 4*a*sin(c + d*x)^7 + a*sin(c + d*x)^8 + a*sin(c + d*x)^9)) - (319*log(sin(c + d*x) + 1))/(512*a*d) - (193*log(sin(c + d*x) - 1))/(512*a*d) + log(sin(c + d*x))/(a*d)","B"
909,1,252,262,9.456273,"\text{Not used}","int(1/(cos(c + d*x)^9*sin(c + d*x)^2*(a + a*sin(c + d*x))),x)","\frac{949\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{512\,a\,d}-\frac{437\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{512\,a\,d}-\frac{\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}-\frac{\frac{693\,{\sin\left(c+d\,x\right)}^9}{256}+\frac{565\,{\sin\left(c+d\,x\right)}^8}{256}-\frac{2669\,{\sin\left(c+d\,x\right)}^7}{256}-\frac{2093\,{\sin\left(c+d\,x\right)}^6}{256}+\frac{19103\,{\sin\left(c+d\,x\right)}^5}{1280}+\frac{42269\,{\sin\left(c+d\,x\right)}^4}{3840}-\frac{35941\,{\sin\left(c+d\,x\right)}^3}{3840}-\frac{23621\,{\sin\left(c+d\,x\right)}^2}{3840}+\frac{257\,\sin\left(c+d\,x\right)}{120}+1}{d\,\left(a\,{\sin\left(c+d\,x\right)}^{10}+a\,{\sin\left(c+d\,x\right)}^9-4\,a\,{\sin\left(c+d\,x\right)}^8-4\,a\,{\sin\left(c+d\,x\right)}^7+6\,a\,{\sin\left(c+d\,x\right)}^6+6\,a\,{\sin\left(c+d\,x\right)}^5-4\,a\,{\sin\left(c+d\,x\right)}^4-4\,a\,{\sin\left(c+d\,x\right)}^3+a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)\right)}","Not used",1,"(949*log(sin(c + d*x) + 1))/(512*a*d) - (437*log(sin(c + d*x) - 1))/(512*a*d) - log(sin(c + d*x))/(a*d) - ((257*sin(c + d*x))/120 - (23621*sin(c + d*x)^2)/3840 - (35941*sin(c + d*x)^3)/3840 + (42269*sin(c + d*x)^4)/3840 + (19103*sin(c + d*x)^5)/1280 - (2093*sin(c + d*x)^6)/256 - (2669*sin(c + d*x)^7)/256 + (565*sin(c + d*x)^8)/256 + (693*sin(c + d*x)^9)/256 + 1)/(d*(a*sin(c + d*x) + a*sin(c + d*x)^2 - 4*a*sin(c + d*x)^3 - 4*a*sin(c + d*x)^4 + 6*a*sin(c + d*x)^5 + 6*a*sin(c + d*x)^6 - 4*a*sin(c + d*x)^7 - 4*a*sin(c + d*x)^8 + a*sin(c + d*x)^9 + a*sin(c + d*x)^10))","B"
910,1,263,279,9.636923,"\text{Not used}","int(1/(cos(c + d*x)^9*sin(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{\frac{693\,{\sin\left(c+d\,x\right)}^{10}}{256}-\frac{75\,{\sin\left(c+d\,x\right)}^9}{256}-\frac{3309\,{\sin\left(c+d\,x\right)}^8}{256}+\frac{147\,{\sin\left(c+d\,x\right)}^7}{256}+\frac{30303\,{\sin\left(c+d\,x\right)}^6}{1280}+\frac{223\,{\sin\left(c+d\,x\right)}^5}{1280}-\frac{25847\,{\sin\left(c+d\,x\right)}^4}{1280}-\frac{1207\,{\sin\left(c+d\,x\right)}^3}{1280}+\frac{147\,{\sin\left(c+d\,x\right)}^2}{20}+\frac{\sin\left(c+d\,x\right)}{2}-\frac{1}{2}}{d\,\left(a\,{\sin\left(c+d\,x\right)}^{11}+a\,{\sin\left(c+d\,x\right)}^{10}-4\,a\,{\sin\left(c+d\,x\right)}^9-4\,a\,{\sin\left(c+d\,x\right)}^8+6\,a\,{\sin\left(c+d\,x\right)}^7+6\,a\,{\sin\left(c+d\,x\right)}^6-4\,a\,{\sin\left(c+d\,x\right)}^5-4\,a\,{\sin\left(c+d\,x\right)}^4+a\,{\sin\left(c+d\,x\right)}^3+a\,{\sin\left(c+d\,x\right)}^2\right)}-\frac{2229\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{512\,a\,d}-\frac{843\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{512\,a\,d}+\frac{6\,\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}","Not used",1,"(sin(c + d*x)/2 + (147*sin(c + d*x)^2)/20 - (1207*sin(c + d*x)^3)/1280 - (25847*sin(c + d*x)^4)/1280 + (223*sin(c + d*x)^5)/1280 + (30303*sin(c + d*x)^6)/1280 + (147*sin(c + d*x)^7)/256 - (3309*sin(c + d*x)^8)/256 - (75*sin(c + d*x)^9)/256 + (693*sin(c + d*x)^10)/256 - 1/2)/(d*(a*sin(c + d*x)^2 + a*sin(c + d*x)^3 - 4*a*sin(c + d*x)^4 - 4*a*sin(c + d*x)^5 + 6*a*sin(c + d*x)^6 + 6*a*sin(c + d*x)^7 - 4*a*sin(c + d*x)^8 - 4*a*sin(c + d*x)^9 + a*sin(c + d*x)^10 + a*sin(c + d*x)^11)) - (2229*log(sin(c + d*x) + 1))/(512*a*d) - (843*log(sin(c + d*x) - 1))/(512*a*d) + (6*log(sin(c + d*x)))/(a*d)","B"
911,0,-1,127,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(g/cos(e + f*x))^p*(a + a*sin(e + f*x))^m,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(\frac{g}{\cos\left(e+f\,x\right)}\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((d*sin(e + f*x))^n*(g/cos(e + f*x))^p*(a + a*sin(e + f*x))^m, x)","F"
912,0,-1,88,0.000000,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int \cos\left(e+f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
913,1,863,175,18.137565,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))^4*(c + d*sin(e + f*x))^n,x)","\frac{a^4\,\sin\left(5\,e+5\,f\,x\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)\,1{}\mathrm{i}}{16\,f\,\left(n^5\,1{}\mathrm{i}+n^4\,15{}\mathrm{i}+n^3\,85{}\mathrm{i}+n^2\,225{}\mathrm{i}+n\,274{}\mathrm{i}+120{}\mathrm{i}\right)}+\frac{a^4\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(c^5\,192{}\mathrm{i}-c^4\,d\,n\,192{}\mathrm{i}-c^4\,d\,960{}\mathrm{i}+c^3\,d^2\,n^2\,144{}\mathrm{i}+c^3\,d^2\,n\,912{}\mathrm{i}+c^3\,d^2\,1920{}\mathrm{i}-c^2\,d^3\,n^3\,80{}\mathrm{i}-c^2\,d^3\,n^2\,672{}\mathrm{i}-c^2\,d^3\,n\,1744{}\mathrm{i}-c^2\,d^3\,1920{}\mathrm{i}+c\,d^4\,n^4\,35{}\mathrm{i}+c\,d^4\,n^3\,370{}\mathrm{i}+c\,d^4\,n^2\,1297{}\mathrm{i}+c\,d^4\,n\,1730{}\mathrm{i}+c\,d^4\,960{}\mathrm{i}+d^5\,n^4\,28{}\mathrm{i}+d^5\,n^3\,340{}\mathrm{i}+d^5\,n^2\,1436{}\mathrm{i}+d^5\,n\,2444{}\mathrm{i}+d^5\,1320{}\mathrm{i}\right)}{8\,d^5\,f\,\left(n^5\,1{}\mathrm{i}+n^4\,15{}\mathrm{i}+n^3\,85{}\mathrm{i}+n^2\,225{}\mathrm{i}+n\,274{}\mathrm{i}+120{}\mathrm{i}\right)}+\frac{a^4\,\sin\left(e+f\,x\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(-192\,c^4\,n+192\,c^3\,d\,n^2+960\,c^3\,d\,n-120\,c^2\,d^2\,n^3-936\,c^2\,d^2\,n^2-1968\,c^2\,d^2\,n+56\,c\,d^3\,n^4+576\,c\,d^3\,n^3+1912\,c\,d^3\,n^2+2160\,c\,d^3\,n+49\,d^4\,n^4+594\,d^4\,n^3+2507\,d^4\,n^2+4290\,d^4\,n+2520\,d^4\right)\,1{}\mathrm{i}}{8\,d^4\,f\,\left(n^5\,1{}\mathrm{i}+n^4\,15{}\mathrm{i}+n^3\,85{}\mathrm{i}+n^2\,225{}\mathrm{i}+n\,274{}\mathrm{i}+120{}\mathrm{i}\right)}+\frac{a^4\,\cos\left(4\,e+4\,f\,x\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(d\,20{}\mathrm{i}+c\,n\,1{}\mathrm{i}+d\,n\,4{}\mathrm{i}\right)\,\left(n^3+6\,n^2+11\,n+6\right)}{8\,d\,f\,\left(n^5\,1{}\mathrm{i}+n^4\,15{}\mathrm{i}+n^3\,85{}\mathrm{i}+n^2\,225{}\mathrm{i}+n\,274{}\mathrm{i}+120{}\mathrm{i}\right)}-\frac{a^4\,\sin\left(3\,e+3\,f\,x\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(n^2+3\,n+2\right)\,\left(-16\,c^2\,n+16\,c\,d\,n^2+80\,c\,d\,n+29\,d^2\,n^2+251\,d^2\,n+540\,d^2\right)\,1{}\mathrm{i}}{16\,d^2\,f\,\left(n^5\,1{}\mathrm{i}+n^4\,15{}\mathrm{i}+n^3\,85{}\mathrm{i}+n^2\,225{}\mathrm{i}+n\,274{}\mathrm{i}+120{}\mathrm{i}\right)}-\frac{a^4\,\cos\left(2\,e+2\,f\,x\right)\,\left(n+1\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(c^3\,n\,12{}\mathrm{i}-c^2\,d\,n^2\,12{}\mathrm{i}-c^2\,d\,n\,60{}\mathrm{i}+c\,d^2\,n^3\,7{}\mathrm{i}+c\,d^2\,n^2\,59{}\mathrm{i}+c\,d^2\,n\,126{}\mathrm{i}+d^3\,n^3\,8{}\mathrm{i}+d^3\,n^2\,88{}\mathrm{i}+d^3\,n\,312{}\mathrm{i}+d^3\,360{}\mathrm{i}\right)}{2\,d^3\,f\,\left(n^5\,1{}\mathrm{i}+n^4\,15{}\mathrm{i}+n^3\,85{}\mathrm{i}+n^2\,225{}\mathrm{i}+n\,274{}\mathrm{i}+120{}\mathrm{i}\right)}","Not used",1,"(a^4*sin(5*e + 5*f*x)*(c + d*sin(e + f*x))^n*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)*1i)/(16*f*(n*274i + n^2*225i + n^3*85i + n^4*15i + n^5*1i + 120i)) + (a^4*(c + d*sin(e + f*x))^n*(c*d^4*960i - c^4*d*960i + d^5*n*2444i + c^5*192i + d^5*1320i - c^2*d^3*1920i + c^3*d^2*1920i + d^5*n^2*1436i + d^5*n^3*340i + d^5*n^4*28i - c^2*d^3*n*1744i + c^3*d^2*n*912i + c*d^4*n^2*1297i + c*d^4*n^3*370i + c*d^4*n^4*35i - c^2*d^3*n^2*672i + c^3*d^2*n^2*144i - c^2*d^3*n^3*80i + c*d^4*n*1730i - c^4*d*n*192i))/(8*d^5*f*(n*274i + n^2*225i + n^3*85i + n^4*15i + n^5*1i + 120i)) + (a^4*sin(e + f*x)*(c + d*sin(e + f*x))^n*(4290*d^4*n - 192*c^4*n + 2520*d^4 + 2507*d^4*n^2 + 594*d^4*n^3 + 49*d^4*n^4 - 1968*c^2*d^2*n + 1912*c*d^3*n^2 + 192*c^3*d*n^2 + 576*c*d^3*n^3 + 56*c*d^3*n^4 - 936*c^2*d^2*n^2 - 120*c^2*d^2*n^3 + 2160*c*d^3*n + 960*c^3*d*n)*1i)/(8*d^4*f*(n*274i + n^2*225i + n^3*85i + n^4*15i + n^5*1i + 120i)) + (a^4*cos(4*e + 4*f*x)*(c + d*sin(e + f*x))^n*(d*20i + c*n*1i + d*n*4i)*(11*n + 6*n^2 + n^3 + 6))/(8*d*f*(n*274i + n^2*225i + n^3*85i + n^4*15i + n^5*1i + 120i)) - (a^4*sin(3*e + 3*f*x)*(c + d*sin(e + f*x))^n*(3*n + n^2 + 2)*(251*d^2*n - 16*c^2*n + 540*d^2 + 29*d^2*n^2 + 80*c*d*n + 16*c*d*n^2)*1i)/(16*d^2*f*(n*274i + n^2*225i + n^3*85i + n^4*15i + n^5*1i + 120i)) - (a^4*cos(2*e + 2*f*x)*(n + 1)*(c + d*sin(e + f*x))^n*(c^3*n*12i + d^3*n*312i + d^3*360i + d^3*n^2*88i + d^3*n^3*8i + c*d^2*n^2*59i - c^2*d*n^2*12i + c*d^2*n^3*7i + c*d^2*n*126i - c^2*d*n*60i))/(2*d^3*f*(n*274i + n^2*225i + n^3*85i + n^4*15i + n^5*1i + 120i))","B"
914,1,617,139,13.583872,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^n,x)","\frac{a^3\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(192\,c\,d^3+192\,c^3\,d+261\,d^4\,n+336\,d^4\,\sin\left(e+f\,x\right)-48\,c^4+162\,d^4-288\,c^2\,d^2-168\,d^4\,\cos\left(2\,e+2\,f\,x\right)+6\,d^4\,\cos\left(4\,e+4\,f\,x\right)+114\,d^4\,n^2+15\,d^4\,n^3-48\,d^4\,\sin\left(3\,e+3\,f\,x\right)+460\,d^4\,n\,\sin\left(e+f\,x\right)-180\,c^2\,d^2\,n+132\,c\,d^3\,n^2+20\,c\,d^3\,n^3-272\,d^4\,n\,\cos\left(2\,e+2\,f\,x\right)+11\,d^4\,n\,\cos\left(4\,e+4\,f\,x\right)-84\,d^4\,n\,\sin\left(3\,e+3\,f\,x\right)+198\,d^4\,n^2\,\sin\left(e+f\,x\right)+26\,d^4\,n^3\,\sin\left(e+f\,x\right)-36\,c^2\,d^2\,n^2-120\,d^4\,n^2\,\cos\left(2\,e+2\,f\,x\right)-16\,d^4\,n^3\,\cos\left(2\,e+2\,f\,x\right)+6\,d^4\,n^2\,\cos\left(4\,e+4\,f\,x\right)+d^4\,n^3\,\cos\left(4\,e+4\,f\,x\right)-42\,d^4\,n^2\,\sin\left(3\,e+3\,f\,x\right)-6\,d^4\,n^3\,\sin\left(3\,e+3\,f\,x\right)+256\,c\,d^3\,n+48\,c^3\,d\,n+12\,c^2\,d^2\,n\,\cos\left(2\,e+2\,f\,x\right)-60\,c\,d^3\,n^2\,\cos\left(2\,e+2\,f\,x\right)-12\,c\,d^3\,n^3\,\cos\left(2\,e+2\,f\,x\right)-6\,c\,d^3\,n^2\,\sin\left(3\,e+3\,f\,x\right)-2\,c\,d^3\,n^3\,\sin\left(3\,e+3\,f\,x\right)-48\,c^2\,d^2\,n^2\,\sin\left(e+f\,x\right)+300\,c\,d^3\,n\,\sin\left(e+f\,x\right)+48\,c^3\,d\,n\,\sin\left(e+f\,x\right)+12\,c^2\,d^2\,n^2\,\cos\left(2\,e+2\,f\,x\right)-48\,c\,d^3\,n\,\cos\left(2\,e+2\,f\,x\right)-4\,c\,d^3\,n\,\sin\left(3\,e+3\,f\,x\right)-192\,c^2\,d^2\,n\,\sin\left(e+f\,x\right)+186\,c\,d^3\,n^2\,\sin\left(e+f\,x\right)+30\,c\,d^3\,n^3\,\sin\left(e+f\,x\right)\right)}{8\,d^4\,f\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}","Not used",1,"(a^3*(c + d*sin(e + f*x))^n*(192*c*d^3 + 192*c^3*d + 261*d^4*n + 336*d^4*sin(e + f*x) - 48*c^4 + 162*d^4 - 288*c^2*d^2 - 168*d^4*cos(2*e + 2*f*x) + 6*d^4*cos(4*e + 4*f*x) + 114*d^4*n^2 + 15*d^4*n^3 - 48*d^4*sin(3*e + 3*f*x) + 460*d^4*n*sin(e + f*x) - 180*c^2*d^2*n + 132*c*d^3*n^2 + 20*c*d^3*n^3 - 272*d^4*n*cos(2*e + 2*f*x) + 11*d^4*n*cos(4*e + 4*f*x) - 84*d^4*n*sin(3*e + 3*f*x) + 198*d^4*n^2*sin(e + f*x) + 26*d^4*n^3*sin(e + f*x) - 36*c^2*d^2*n^2 - 120*d^4*n^2*cos(2*e + 2*f*x) - 16*d^4*n^3*cos(2*e + 2*f*x) + 6*d^4*n^2*cos(4*e + 4*f*x) + d^4*n^3*cos(4*e + 4*f*x) - 42*d^4*n^2*sin(3*e + 3*f*x) - 6*d^4*n^3*sin(3*e + 3*f*x) + 256*c*d^3*n + 48*c^3*d*n + 12*c^2*d^2*n*cos(2*e + 2*f*x) - 60*c*d^3*n^2*cos(2*e + 2*f*x) - 12*c*d^3*n^3*cos(2*e + 2*f*x) - 6*c*d^3*n^2*sin(3*e + 3*f*x) - 2*c*d^3*n^3*sin(3*e + 3*f*x) - 48*c^2*d^2*n^2*sin(e + f*x) + 300*c*d^3*n*sin(e + f*x) + 48*c^3*d*n*sin(e + f*x) + 12*c^2*d^2*n^2*cos(2*e + 2*f*x) - 48*c*d^3*n*cos(2*e + 2*f*x) - 4*c*d^3*n*sin(3*e + 3*f*x) - 192*c^2*d^2*n*sin(e + f*x) + 186*c*d^3*n^2*sin(e + f*x) + 30*c*d^3*n^3*sin(e + f*x)))/(8*d^4*f*(50*n + 35*n^2 + 10*n^3 + n^4 + 24))","B"
915,1,302,101,11.258608,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n,x)","\frac{a^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(24\,c\,d^2-24\,c^2\,d+16\,d^3\,n+30\,d^3\,\sin\left(e+f\,x\right)+8\,c^3+12\,d^3-12\,d^3\,\cos\left(2\,e+2\,f\,x\right)+4\,d^3\,n^2-2\,d^3\,\sin\left(3\,e+3\,f\,x\right)+29\,d^3\,n\,\sin\left(e+f\,x\right)+6\,c\,d^2\,n^2-16\,d^3\,n\,\cos\left(2\,e+2\,f\,x\right)-3\,d^3\,n\,\sin\left(3\,e+3\,f\,x\right)+7\,d^3\,n^2\,\sin\left(e+f\,x\right)-4\,d^3\,n^2\,\cos\left(2\,e+2\,f\,x\right)-d^3\,n^2\,\sin\left(3\,e+3\,f\,x\right)+22\,c\,d^2\,n-8\,c^2\,d\,n-2\,c\,d^2\,n^2\,\cos\left(2\,e+2\,f\,x\right)+24\,c\,d^2\,n\,\sin\left(e+f\,x\right)-8\,c^2\,d\,n\,\sin\left(e+f\,x\right)-2\,c\,d^2\,n\,\cos\left(2\,e+2\,f\,x\right)+8\,c\,d^2\,n^2\,\sin\left(e+f\,x\right)\right)}{4\,d^3\,f\,\left(n^3+6\,n^2+11\,n+6\right)}","Not used",1,"(a^2*(c + d*sin(e + f*x))^n*(24*c*d^2 - 24*c^2*d + 16*d^3*n + 30*d^3*sin(e + f*x) + 8*c^3 + 12*d^3 - 12*d^3*cos(2*e + 2*f*x) + 4*d^3*n^2 - 2*d^3*sin(3*e + 3*f*x) + 29*d^3*n*sin(e + f*x) + 6*c*d^2*n^2 - 16*d^3*n*cos(2*e + 2*f*x) - 3*d^3*n*sin(3*e + 3*f*x) + 7*d^3*n^2*sin(e + f*x) - 4*d^3*n^2*cos(2*e + 2*f*x) - d^3*n^2*sin(3*e + 3*f*x) + 22*c*d^2*n - 8*c^2*d*n - 2*c*d^2*n^2*cos(2*e + 2*f*x) + 24*c*d^2*n*sin(e + f*x) - 8*c^2*d*n*sin(e + f*x) - 2*c*d^2*n*cos(2*e + 2*f*x) + 8*c*d^2*n^2*sin(e + f*x)))/(4*d^3*f*(11*n + 6*n^2 + n^3 + 6))","B"
916,1,121,61,10.082266,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n,x)","\frac{a\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(4\,c\,d+d^2\,n+4\,d^2\,\sin\left(e+f\,x\right)+d^2\,\left(2\,{\sin\left(e+f\,x\right)}^2-1\right)-2\,c^2+d^2+2\,d^2\,n\,\sin\left(e+f\,x\right)+d^2\,n\,\left(2\,{\sin\left(e+f\,x\right)}^2-1\right)+2\,c\,d\,n+2\,c\,d\,n\,\sin\left(e+f\,x\right)\right)}{2\,d^2\,f\,\left(n^2+3\,n+2\right)}","Not used",1,"(a*(c + d*sin(e + f*x))^n*(4*c*d + d^2*n + 4*d^2*sin(e + f*x) + d^2*(2*sin(e + f*x)^2 - 1) - 2*c^2 + d^2 + 2*d^2*n*sin(e + f*x) + d^2*n*(2*sin(e + f*x)^2 - 1) + 2*c*d*n + 2*c*d*n*sin(e + f*x)))/(2*d^2*f*(3*n + n^2 + 2))","B"
917,0,-1,60,0.000000,"\text{Not used}","int((cos(e + f*x)*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)),x)","\int \frac{\cos\left(e+f\,x\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((cos(e + f*x)*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)), x)","F"
918,0,-1,60,0.000000,"\text{Not used}","int((cos(e + f*x)*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2,x)","\int \frac{\cos\left(e+f\,x\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(e + f*x)*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2, x)","F"
919,0,-1,63,0.000000,"\text{Not used}","int((cos(e + f*x)*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^3,x)","\int \frac{\cos\left(e+f\,x\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(e + f*x)*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^3, x)","F"
920,1,1656,170,16.866925,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^4,x)","{\mathrm{e}}^{-e\,5{}\mathrm{i}-f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)\right)}^m\,\left(-\frac{d^4\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}{32\,f\,\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)}-\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(16\,c^4\,m^4+224\,c^4\,m^3+1136\,c^4\,m^2+2464\,c^4\,m+1920\,c^4+64\,c^3\,d\,m^4+768\,c^3\,d\,m^3+3008\,c^3\,d\,m^2+3840\,c^3\,d\,m+72\,c^2\,d^2\,m^4+672\,c^2\,d^2\,m^3+1800\,c^2\,d^2\,m^2+1776\,c^2\,d^2\,m+2880\,c^2\,d^2+48\,c\,d^3\,m^4+384\,c\,d^3\,m^3+1200\,c\,d^3\,m^2+2400\,c\,d^3\,m+10\,d^4\,m^4+52\,d^4\,m^3+206\,d^4\,m^2+20\,d^4\,m+240\,d^4\right)}{32\,f\,\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)}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(16\,c^4\,m^4+224\,c^4\,m^3+1136\,c^4\,m^2+2464\,c^4\,m+1920\,c^4+64\,c^3\,d\,m^4+768\,c^3\,d\,m^3+3008\,c^3\,d\,m^2+3840\,c^3\,d\,m+72\,c^2\,d^2\,m^4+672\,c^2\,d^2\,m^3+1800\,c^2\,d^2\,m^2+1776\,c^2\,d^2\,m+2880\,c^2\,d^2+48\,c\,d^3\,m^4+384\,c\,d^3\,m^3+1200\,c\,d^3\,m^2+2400\,c\,d^3\,m+10\,d^4\,m^4+52\,d^4\,m^3+206\,d^4\,m^2+20\,d^4\,m+240\,d^4\right)}{32\,f\,\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)}+\frac{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(c^4\,m^4\,32{}\mathrm{i}+c^4\,m^3\,448{}\mathrm{i}+c^4\,m^2\,2272{}\mathrm{i}+c^4\,m\,4928{}\mathrm{i}+c^4\,3840{}\mathrm{i}+c^3\,d\,m^4\,64{}\mathrm{i}+c^3\,d\,m^3\,704{}\mathrm{i}+c^3\,d\,m^2\,2240{}\mathrm{i}+c^3\,d\,m\,832{}\mathrm{i}-c^3\,d\,3840{}\mathrm{i}+c^2\,d^2\,m^4\,96{}\mathrm{i}+c^2\,d^2\,m^3\,960{}\mathrm{i}+c^2\,d^2\,m^2\,3168{}\mathrm{i}+c^2\,d^2\,m\,5376{}\mathrm{i}+c^2\,d^2\,7680{}\mathrm{i}+c\,d^3\,m^4\,48{}\mathrm{i}+c\,d^3\,m^3\,336{}\mathrm{i}+c\,d^3\,m^2\,816{}\mathrm{i}+c\,d^3\,m\,1200{}\mathrm{i}-c\,d^3\,2400{}\mathrm{i}+d^4\,m^4\,12{}\mathrm{i}+d^4\,m^3\,72{}\mathrm{i}+d^4\,m^2\,324{}\mathrm{i}+d^4\,m\,264{}\mathrm{i}+d^4\,768{}\mathrm{i}\right)}{32\,f\,\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)}+\frac{d^4\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}{32\,f\,\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)}+\frac{d^2\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(m^2+3\,m+2\right)\,\left(24\,c^2\,m^2+216\,c^2\,m+480\,c^2+16\,c\,d\,m^2+80\,c\,d\,m+5\,d^2\,m^2+19\,d^2\,m+60\,d^2\right)}{32\,f\,\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)}-\frac{d^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\left(m^2+3\,m+2\right)\,\left(24\,c^2\,m^2+216\,c^2\,m+480\,c^2+16\,c\,d\,m^2+80\,c\,d\,m+5\,d^2\,m^2+19\,d^2\,m+60\,d^2\right)}{32\,f\,\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)}-\frac{d\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(m+1\right)\,\left(c^3\,m^3\,4{}\mathrm{i}+c^3\,m^2\,48{}\mathrm{i}+c^3\,m\,188{}\mathrm{i}+c^3\,240{}\mathrm{i}+c^2\,d\,m^3\,6{}\mathrm{i}+c^2\,d\,m^2\,54{}\mathrm{i}+c^2\,d\,m\,120{}\mathrm{i}+c\,d^2\,m^3\,4{}\mathrm{i}+c\,d^2\,m^2\,28{}\mathrm{i}+c\,d^2\,m\,64{}\mathrm{i}+c\,d^2\,120{}\mathrm{i}+d^3\,m^3\,1{}\mathrm{i}+d^3\,m^2\,5{}\mathrm{i}+d^3\,m\,18{}\mathrm{i}\right)}{4\,f\,\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)}-\frac{d\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\left(m+1\right)\,\left(c^3\,m^3\,4{}\mathrm{i}+c^3\,m^2\,48{}\mathrm{i}+c^3\,m\,188{}\mathrm{i}+c^3\,240{}\mathrm{i}+c^2\,d\,m^3\,6{}\mathrm{i}+c^2\,d\,m^2\,54{}\mathrm{i}+c^2\,d\,m\,120{}\mathrm{i}+c\,d^2\,m^3\,4{}\mathrm{i}+c\,d^2\,m^2\,28{}\mathrm{i}+c\,d^2\,m\,64{}\mathrm{i}+c\,d^2\,120{}\mathrm{i}+d^3\,m^3\,1{}\mathrm{i}+d^3\,m^2\,5{}\mathrm{i}+d^3\,m\,18{}\mathrm{i}\right)}{4\,f\,\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)}+\frac{d^3\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(c\,20{}\mathrm{i}+c\,m\,4{}\mathrm{i}+d\,m\,1{}\mathrm{i}\right)\,\left(m^3+6\,m^2+11\,m+6\right)}{16\,f\,\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)}+\frac{d^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\left(c\,20{}\mathrm{i}+c\,m\,4{}\mathrm{i}+d\,m\,1{}\mathrm{i}\right)\,\left(m^3+6\,m^2+11\,m+6\right)}{16\,f\,\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)}\right)","Not used",1,"exp(- e*5i - f*x*5i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^m*((exp(e*6i + f*x*6i)*(2464*c^4*m + 20*d^4*m + 1920*c^4 + 240*d^4 + 2880*c^2*d^2 + 1136*c^4*m^2 + 224*c^4*m^3 + 16*c^4*m^4 + 206*d^4*m^2 + 52*d^4*m^3 + 10*d^4*m^4 + 1776*c^2*d^2*m + 1200*c*d^3*m^2 + 3008*c^3*d*m^2 + 384*c*d^3*m^3 + 768*c^3*d*m^3 + 48*c*d^3*m^4 + 64*c^3*d*m^4 + 1800*c^2*d^2*m^2 + 672*c^2*d^2*m^3 + 72*c^2*d^2*m^4 + 2400*c*d^3*m + 3840*c^3*d*m))/(32*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) - (exp(e*4i + f*x*4i)*(2464*c^4*m + 20*d^4*m + 1920*c^4 + 240*d^4 + 2880*c^2*d^2 + 1136*c^4*m^2 + 224*c^4*m^3 + 16*c^4*m^4 + 206*d^4*m^2 + 52*d^4*m^3 + 10*d^4*m^4 + 1776*c^2*d^2*m + 1200*c*d^3*m^2 + 3008*c^3*d*m^2 + 384*c*d^3*m^3 + 768*c^3*d*m^3 + 48*c*d^3*m^4 + 64*c^3*d*m^4 + 1800*c^2*d^2*m^2 + 672*c^2*d^2*m^3 + 72*c^2*d^2*m^4 + 2400*c*d^3*m + 3840*c^3*d*m))/(32*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) - (d^4*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))/(32*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) + (exp(e*5i + f*x*5i)*(c^4*m*4928i - c^3*d*3840i - c*d^3*2400i + d^4*m*264i + c^4*3840i + d^4*768i + c^2*d^2*7680i + c^4*m^2*2272i + c^4*m^3*448i + c^4*m^4*32i + d^4*m^2*324i + d^4*m^3*72i + d^4*m^4*12i + c^2*d^2*m*5376i + c*d^3*m^2*816i + c^3*d*m^2*2240i + c*d^3*m^3*336i + c^3*d*m^3*704i + c*d^3*m^4*48i + c^3*d*m^4*64i + c^2*d^2*m^2*3168i + c^2*d^2*m^3*960i + c^2*d^2*m^4*96i + c*d^3*m*1200i + c^3*d*m*832i))/(32*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) + (d^4*exp(e*10i + f*x*10i)*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))/(32*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) + (d^2*exp(e*2i + f*x*2i)*(3*m + m^2 + 2)*(216*c^2*m + 19*d^2*m + 480*c^2 + 60*d^2 + 24*c^2*m^2 + 5*d^2*m^2 + 80*c*d*m + 16*c*d*m^2))/(32*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) - (d^2*exp(e*8i + f*x*8i)*(3*m + m^2 + 2)*(216*c^2*m + 19*d^2*m + 480*c^2 + 60*d^2 + 24*c^2*m^2 + 5*d^2*m^2 + 80*c*d*m + 16*c*d*m^2))/(32*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) - (d*exp(e*3i + f*x*3i)*(m + 1)*(c*d^2*120i + c^3*m*188i + d^3*m*18i + c^3*240i + c^3*m^2*48i + c^3*m^3*4i + d^3*m^2*5i + d^3*m^3*1i + c*d^2*m^2*28i + c^2*d*m^2*54i + c*d^2*m^3*4i + c^2*d*m^3*6i + c*d^2*m*64i + c^2*d*m*120i))/(4*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) - (d*exp(e*7i + f*x*7i)*(m + 1)*(c*d^2*120i + c^3*m*188i + d^3*m*18i + c^3*240i + c^3*m^2*48i + c^3*m^3*4i + d^3*m^2*5i + d^3*m^3*1i + c*d^2*m^2*28i + c^2*d*m^2*54i + c*d^2*m^3*4i + c^2*d*m^3*6i + c*d^2*m*64i + c^2*d*m*120i))/(4*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) + (d^3*exp(e*1i + f*x*1i)*(c*20i + c*m*4i + d*m*1i)*(11*m + 6*m^2 + m^3 + 6))/(16*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)) + (d^3*exp(e*9i + f*x*9i)*(c*20i + c*m*4i + d*m*1i)*(11*m + 6*m^2 + m^3 + 6))/(16*f*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i)))","B"
921,1,703,133,13.442455,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^3,x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(192\,c\,d^2-144\,c^2\,d+208\,c^3\,m+21\,d^3\,m+192\,c^3\,\sin\left(e+f\,x\right)+192\,c^3-30\,d^3-24\,d^3\,\cos\left(2\,e+2\,f\,x\right)+6\,d^3\,\cos\left(4\,e+4\,f\,x\right)+72\,c^3\,m^2+8\,c^3\,m^3+6\,d^3\,m^2+3\,d^3\,m^3+208\,c^3\,m\,\sin\left(e+f\,x\right)+60\,d^3\,m\,\sin\left(e+f\,x\right)-144\,c^2\,d\,\cos\left(2\,e+2\,f\,x\right)+60\,c\,d^2\,m^2+72\,c^2\,d\,m^2+12\,c\,d^2\,m^3+12\,c^2\,d\,m^3-32\,d^3\,m\,\cos\left(2\,e+2\,f\,x\right)+11\,d^3\,m\,\cos\left(4\,e+4\,f\,x\right)-48\,c\,d^2\,\sin\left(3\,e+3\,f\,x\right)+72\,c^3\,m^2\,\sin\left(e+f\,x\right)+8\,c^3\,m^3\,\sin\left(e+f\,x\right)-4\,d^3\,m\,\sin\left(3\,e+3\,f\,x\right)+18\,d^3\,m^2\,\sin\left(e+f\,x\right)+6\,d^3\,m^3\,\sin\left(e+f\,x\right)-12\,d^3\,m^2\,\cos\left(2\,e+2\,f\,x\right)-4\,d^3\,m^3\,\cos\left(2\,e+2\,f\,x\right)+6\,d^3\,m^2\,\cos\left(4\,e+4\,f\,x\right)+d^3\,m^3\,\cos\left(4\,e+4\,f\,x\right)-6\,d^3\,m^2\,\sin\left(3\,e+3\,f\,x\right)-2\,d^3\,m^3\,\sin\left(3\,e+3\,f\,x\right)+96\,c\,d^2\,m+60\,c^2\,d\,m+144\,c\,d^2\,\sin\left(e+f\,x\right)-60\,c\,d^2\,m^2\,\cos\left(2\,e+2\,f\,x\right)-96\,c^2\,d\,m^2\,\cos\left(2\,e+2\,f\,x\right)-12\,c\,d^2\,m^3\,\cos\left(2\,e+2\,f\,x\right)-12\,c^2\,d\,m^3\,\cos\left(2\,e+2\,f\,x\right)-42\,c\,d^2\,m^2\,\sin\left(3\,e+3\,f\,x\right)-6\,c\,d^2\,m^3\,\sin\left(3\,e+3\,f\,x\right)+60\,c\,d^2\,m\,\sin\left(e+f\,x\right)+288\,c^2\,d\,m\,\sin\left(e+f\,x\right)-48\,c\,d^2\,m\,\cos\left(2\,e+2\,f\,x\right)-228\,c^2\,d\,m\,\cos\left(2\,e+2\,f\,x\right)-84\,c\,d^2\,m\,\sin\left(3\,e+3\,f\,x\right)+78\,c\,d^2\,m^2\,\sin\left(e+f\,x\right)+168\,c^2\,d\,m^2\,\sin\left(e+f\,x\right)+18\,c\,d^2\,m^3\,\sin\left(e+f\,x\right)+24\,c^2\,d\,m^3\,\sin\left(e+f\,x\right)\right)}{8\,f\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(192*c*d^2 - 144*c^2*d + 208*c^3*m + 21*d^3*m + 192*c^3*sin(e + f*x) + 192*c^3 - 30*d^3 - 24*d^3*cos(2*e + 2*f*x) + 6*d^3*cos(4*e + 4*f*x) + 72*c^3*m^2 + 8*c^3*m^3 + 6*d^3*m^2 + 3*d^3*m^3 + 208*c^3*m*sin(e + f*x) + 60*d^3*m*sin(e + f*x) - 144*c^2*d*cos(2*e + 2*f*x) + 60*c*d^2*m^2 + 72*c^2*d*m^2 + 12*c*d^2*m^3 + 12*c^2*d*m^3 - 32*d^3*m*cos(2*e + 2*f*x) + 11*d^3*m*cos(4*e + 4*f*x) - 48*c*d^2*sin(3*e + 3*f*x) + 72*c^3*m^2*sin(e + f*x) + 8*c^3*m^3*sin(e + f*x) - 4*d^3*m*sin(3*e + 3*f*x) + 18*d^3*m^2*sin(e + f*x) + 6*d^3*m^3*sin(e + f*x) - 12*d^3*m^2*cos(2*e + 2*f*x) - 4*d^3*m^3*cos(2*e + 2*f*x) + 6*d^3*m^2*cos(4*e + 4*f*x) + d^3*m^3*cos(4*e + 4*f*x) - 6*d^3*m^2*sin(3*e + 3*f*x) - 2*d^3*m^3*sin(3*e + 3*f*x) + 96*c*d^2*m + 60*c^2*d*m + 144*c*d^2*sin(e + f*x) - 60*c*d^2*m^2*cos(2*e + 2*f*x) - 96*c^2*d*m^2*cos(2*e + 2*f*x) - 12*c*d^2*m^3*cos(2*e + 2*f*x) - 12*c^2*d*m^3*cos(2*e + 2*f*x) - 42*c*d^2*m^2*sin(3*e + 3*f*x) - 6*c*d^2*m^3*sin(3*e + 3*f*x) + 60*c*d^2*m*sin(e + f*x) + 288*c^2*d*m*sin(e + f*x) - 48*c*d^2*m*cos(2*e + 2*f*x) - 228*c^2*d*m*cos(2*e + 2*f*x) - 84*c*d^2*m*sin(3*e + 3*f*x) + 78*c*d^2*m^2*sin(e + f*x) + 168*c^2*d*m^2*sin(e + f*x) + 18*c*d^2*m^3*sin(e + f*x) + 24*c^2*d*m^3*sin(e + f*x)))/(8*f*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))","B"
922,1,305,96,11.480365,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^2,x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(20\,c^2\,m-12\,c\,d+2\,d^2\,m+24\,c^2\,\sin\left(e+f\,x\right)+6\,d^2\,\sin\left(e+f\,x\right)+24\,c^2+8\,d^2+4\,c^2\,m^2+2\,d^2\,m^2-2\,d^2\,\sin\left(3\,e+3\,f\,x\right)+20\,c^2\,m\,\sin\left(e+f\,x\right)+d^2\,m\,\sin\left(e+f\,x\right)-2\,d^2\,m\,\cos\left(2\,e+2\,f\,x\right)+4\,c^2\,m^2\,\sin\left(e+f\,x\right)-3\,d^2\,m\,\sin\left(3\,e+3\,f\,x\right)+3\,d^2\,m^2\,\sin\left(e+f\,x\right)+8\,c\,d\,m-2\,d^2\,m^2\,\cos\left(2\,e+2\,f\,x\right)-d^2\,m^2\,\sin\left(3\,e+3\,f\,x\right)-12\,c\,d\,\cos\left(2\,e+2\,f\,x\right)+4\,c\,d\,m^2+24\,c\,d\,m\,\sin\left(e+f\,x\right)-16\,c\,d\,m\,\cos\left(2\,e+2\,f\,x\right)+8\,c\,d\,m^2\,\sin\left(e+f\,x\right)-4\,c\,d\,m^2\,\cos\left(2\,e+2\,f\,x\right)\right)}{4\,f\,\left(m^3+6\,m^2+11\,m+6\right)}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(20*c^2*m - 12*c*d + 2*d^2*m + 24*c^2*sin(e + f*x) + 6*d^2*sin(e + f*x) + 24*c^2 + 8*d^2 + 4*c^2*m^2 + 2*d^2*m^2 - 2*d^2*sin(3*e + 3*f*x) + 20*c^2*m*sin(e + f*x) + d^2*m*sin(e + f*x) - 2*d^2*m*cos(2*e + 2*f*x) + 4*c^2*m^2*sin(e + f*x) - 3*d^2*m*sin(3*e + 3*f*x) + 3*d^2*m^2*sin(e + f*x) + 8*c*d*m - 2*d^2*m^2*cos(2*e + 2*f*x) - d^2*m^2*sin(3*e + 3*f*x) - 12*c*d*cos(2*e + 2*f*x) + 4*c*d*m^2 + 24*c*d*m*sin(e + f*x) - 16*c*d*m*cos(2*e + 2*f*x) + 8*c*d*m^2*sin(e + f*x) - 4*c*d*m^2*cos(2*e + 2*f*x)))/(4*f*(11*m + 6*m^2 + m^3 + 6))","B"
923,1,99,59,9.763714,"\text{Not used}","int(cos(e + f*x)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x)),x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(4\,c-d+2\,c\,m+d\,m+4\,c\,\sin\left(e+f\,x\right)+d\,\left(2\,{\sin\left(e+f\,x\right)}^2-1\right)+2\,c\,m\,\sin\left(e+f\,x\right)+2\,d\,m\,\sin\left(e+f\,x\right)+d\,m\,\left(2\,{\sin\left(e+f\,x\right)}^2-1\right)\right)}{2\,f\,\left(m^2+3\,m+2\right)}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(4*c - d + 2*c*m + d*m + 4*c*sin(e + f*x) + d*(2*sin(e + f*x)^2 - 1) + 2*c*m*sin(e + f*x) + 2*d*m*sin(e + f*x) + d*m*(2*sin(e + f*x)^2 - 1)))/(2*f*(3*m + m^2 + 2))","B"
924,0,-1,59,0.000000,"\text{Not used}","int((cos(e + f*x)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x)),x)","\int \frac{\cos\left(e+f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((cos(e + f*x)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x)), x)","F"
925,0,-1,59,0.000000,"\text{Not used}","int((cos(e + f*x)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^2,x)","\int \frac{\cos\left(e+f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(e + f*x)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^2, x)","F"
926,0,-1,59,0.000000,"\text{Not used}","int((cos(e + f*x)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^3,x)","\int \frac{\cos\left(e+f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(e + f*x)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^3, x)","F"
927,0,-1,54,0.000000,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^n*(a + a*sin(c + d*x))^m,x)","\int \cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int(cos(c + d*x)*sin(c + d*x)^n*(a + a*sin(c + d*x))^m, x)","F"
928,1,349,134,12.194407,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^4*(a + a*sin(c + d*x))^m,x)","\frac{{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m\,\left(132\,m+240\,\sin\left(c+d\,x\right)-120\,\sin\left(3\,c+3\,d\,x\right)+24\,\sin\left(5\,c+5\,d\,x\right)+20\,m\,\sin\left(c+d\,x\right)-144\,m\,\cos\left(2\,c+2\,d\,x\right)+12\,m\,\cos\left(4\,c+4\,d\,x\right)-218\,m\,\sin\left(3\,c+3\,d\,x\right)+50\,m\,\sin\left(5\,c+5\,d\,x\right)+206\,m^2\,\sin\left(c+d\,x\right)+52\,m^3\,\sin\left(c+d\,x\right)+10\,m^4\,\sin\left(c+d\,x\right)+162\,m^2+36\,m^3+6\,m^4-184\,m^2\,\cos\left(2\,c+2\,d\,x\right)-48\,m^3\,\cos\left(2\,c+2\,d\,x\right)-8\,m^4\,\cos\left(2\,c+2\,d\,x\right)+22\,m^2\,\cos\left(4\,c+4\,d\,x\right)+12\,m^3\,\cos\left(4\,c+4\,d\,x\right)+2\,m^4\,\cos\left(4\,c+4\,d\,x\right)-127\,m^2\,\sin\left(3\,c+3\,d\,x\right)-34\,m^3\,\sin\left(3\,c+3\,d\,x\right)-5\,m^4\,\sin\left(3\,c+3\,d\,x\right)+35\,m^2\,\sin\left(5\,c+5\,d\,x\right)+10\,m^3\,\sin\left(5\,c+5\,d\,x\right)+m^4\,\sin\left(5\,c+5\,d\,x\right)+384\right)}{16\,d\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}","Not used",1,"((a*(sin(c + d*x) + 1))^m*(132*m + 240*sin(c + d*x) - 120*sin(3*c + 3*d*x) + 24*sin(5*c + 5*d*x) + 20*m*sin(c + d*x) - 144*m*cos(2*c + 2*d*x) + 12*m*cos(4*c + 4*d*x) - 218*m*sin(3*c + 3*d*x) + 50*m*sin(5*c + 5*d*x) + 206*m^2*sin(c + d*x) + 52*m^3*sin(c + d*x) + 10*m^4*sin(c + d*x) + 162*m^2 + 36*m^3 + 6*m^4 - 184*m^2*cos(2*c + 2*d*x) - 48*m^3*cos(2*c + 2*d*x) - 8*m^4*cos(2*c + 2*d*x) + 22*m^2*cos(4*c + 4*d*x) + 12*m^3*cos(4*c + 4*d*x) + 2*m^4*cos(4*c + 4*d*x) - 127*m^2*sin(3*c + 3*d*x) - 34*m^3*sin(3*c + 3*d*x) - 5*m^4*sin(3*c + 3*d*x) + 35*m^2*sin(5*c + 5*d*x) + 10*m^3*sin(5*c + 5*d*x) + m^4*sin(5*c + 5*d*x) + 384))/(16*d*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))","B"
929,1,224,108,10.740709,"\text{Not used}","int(cos(c + d*x)*sin(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(21\,m-24\,\cos\left(2\,c+2\,d\,x\right)+6\,\cos\left(4\,c+4\,d\,x\right)+60\,m\,\sin\left(c+d\,x\right)-32\,m\,\cos\left(2\,c+2\,d\,x\right)+11\,m\,\cos\left(4\,c+4\,d\,x\right)-4\,m\,\sin\left(3\,c+3\,d\,x\right)+18\,m^2\,\sin\left(c+d\,x\right)+6\,m^3\,\sin\left(c+d\,x\right)+6\,m^2+3\,m^3-12\,m^2\,\cos\left(2\,c+2\,d\,x\right)-4\,m^3\,\cos\left(2\,c+2\,d\,x\right)+6\,m^2\,\cos\left(4\,c+4\,d\,x\right)+m^3\,\cos\left(4\,c+4\,d\,x\right)-6\,m^2\,\sin\left(3\,c+3\,d\,x\right)-2\,m^3\,\sin\left(3\,c+3\,d\,x\right)-30\right)}{8\,d\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}","Not used",1,"((a*(sin(c + d*x) + 1))^m*(21*m - 24*cos(2*c + 2*d*x) + 6*cos(4*c + 4*d*x) + 60*m*sin(c + d*x) - 32*m*cos(2*c + 2*d*x) + 11*m*cos(4*c + 4*d*x) - 4*m*sin(3*c + 3*d*x) + 18*m^2*sin(c + d*x) + 6*m^3*sin(c + d*x) + 6*m^2 + 3*m^3 - 12*m^2*cos(2*c + 2*d*x) - 4*m^3*cos(2*c + 2*d*x) + 6*m^2*cos(4*c + 4*d*x) + m^3*cos(4*c + 4*d*x) - 6*m^2*sin(3*c + 3*d*x) - 2*m^3*sin(3*c + 3*d*x) - 30))/(8*d*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))","B"
930,1,138,80,9.919458,"\text{Not used}","int(cos(c + d*x)*sin(c + d*x)^2*(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+6\,\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)-3\,m\,\sin\left(3\,c+3\,d\,x\right)+3\,m^2\,\sin\left(c+d\,x\right)+2\,m^2\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)+2\,m^2-m^2\,\sin\left(3\,c+3\,d\,x\right)+8\right)}{4\,d\,\left(m^3+6\,m^2+11\,m+6\right)}","Not used",1,"((a*(sin(c + d*x) + 1))^m*(2*m + 6*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) - 3*m*sin(3*c + 3*d*x) + 3*m^2*sin(c + d*x) + 2*m^2*(2*sin(c + d*x)^2 - 1) + 2*m^2 - m^2*sin(3*c + 3*d*x) + 8))/(4*d*(11*m + 6*m^2 + m^3 + 6))","B"
931,1,62,54,9.418694,"\text{Not used}","int(cos(c + d*x)*sin(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(\frac{m}{2}+m\,\sin\left(c+d\,x\right)+\frac{m\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)}{2}+{\sin\left(c+d\,x\right)}^2-1\right)}{d\,\left(m^2+3\,m+2\right)}","Not used",1,"((a*(sin(c + d*x) + 1))^m*(m/2 + m*sin(c + d*x) + (m*(2*sin(c + d*x)^2 - 1))/2 + sin(c + d*x)^2 - 1))/(d*(3*m + m^2 + 2))","B"
932,0,-1,43,0.000000,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^m)/sin(c + d*x),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)*(a + a*sin(c + d*x))^m)/sin(c + d*x), x)","F"
933,0,-1,42,0.000000,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^m)/sin(c + d*x)^2,x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)*(a + a*sin(c + d*x))^m)/sin(c + d*x)^2, x)","F"
934,0,-1,43,0.000000,"\text{Not used}","int((cos(c + d*x)*(a + a*sin(c + d*x))^m)/sin(c + d*x)^3,x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)*(a + a*sin(c + d*x))^m)/sin(c + d*x)^3, x)","F"
935,1,276,79,10.239629,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))*(c + d*sin(e + f*x)),x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,c+d\right)}{4\,\left(a\,c+\frac{a\,d}{4}\right)}\right)\,\left(4\,c+d\right)}{4\,f}-\frac{\left(a\,c-\frac{a\,d}{4}\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+\left(2\,a\,c+2\,a\,d\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+\left(a\,c+\frac{7\,a\,d}{4}\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+\left(2\,a\,c+2\,a\,d\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+\left(-a\,c-\frac{7\,a\,d}{4}\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+\left(\frac{2\,a\,c}{3}+\frac{2\,a\,d}{3}\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\left(\frac{a\,d}{4}-a\,c\right)\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{2\,a\,c}{3}+\frac{2\,a\,d}{3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{a\,\left(4\,c+d\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{4\,f}","Not used",1,"(a*atan((a*tan(e/2 + (f*x)/2)*(4*c + d))/(4*(a*c + (a*d)/4)))*(4*c + d))/(4*f) - ((2*a*c)/3 + (2*a*d)/3 + tan(e/2 + (f*x)/2)^4*(2*a*c + 2*a*d) + tan(e/2 + (f*x)/2)^6*(2*a*c + 2*a*d) + tan(e/2 + (f*x)/2)^2*((2*a*c)/3 + (2*a*d)/3) + tan(e/2 + (f*x)/2)^7*(a*c - (a*d)/4) - tan(e/2 + (f*x)/2)^3*(a*c + (7*a*d)/4) + tan(e/2 + (f*x)/2)^5*(a*c + (7*a*d)/4) - tan(e/2 + (f*x)/2)*(a*c - (a*d)/4))/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1)) - (a*(4*c + d)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(4*f)","B"
936,0,-1,123,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))), x)","F"
937,0,-1,141,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(cos(e + f*x)^2/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
938,0,-1,135,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
939,0,-1,119,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^n, x)","F"
940,0,-1,119,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n, x)","F"
941,0,-1,117,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^2*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n, x)","F"
942,0,-1,119,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)), x)","F"
943,0,-1,119,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2,x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2, x)","F"
944,0,-1,119,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^3,x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^3, x)","F"
945,0,-1,135,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^4*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
946,0,-1,121,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^4*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n, x)","F"
947,0,-1,119,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^4\,\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^4*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n, x)","F"
948,0,-1,121,0.000000,"\text{Not used}","int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)),x)","\int \frac{{\cos\left(e+f\,x\right)}^4\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)), x)","F"
949,0,-1,121,0.000000,"\text{Not used}","int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2,x)","\int \frac{{\cos\left(e+f\,x\right)}^4\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2, x)","F"
950,0,-1,121,0.000000,"\text{Not used}","int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^3,x)","\int \frac{{\cos\left(e+f\,x\right)}^4\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^3, x)","F"
951,0,-1,121,0.000000,"\text{Not used}","int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^4,x)","\int \frac{{\cos\left(e+f\,x\right)}^4\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^4} \,d x","Not used",1,"int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^4, x)","F"
952,0,-1,121,0.000000,"\text{Not used}","int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^5,x)","\int \frac{{\cos\left(e+f\,x\right)}^4\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^5} \,d x","Not used",1,"int((cos(e + f*x)^4*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^5, x)","F"
953,1,134,134,0.122298,"\text{Not used}","int(cos(c + d*x)^7*(A + B*sin(c + d*x))*(a + a*sin(c + d*x)),x)","-\frac{\frac{B\,a\,{\sin\left(c+d\,x\right)}^9}{9}+\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{a\,\left(A-3\,B\right)\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^6}{2}-\frac{3\,a\,\left(A-B\right)\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{3\,a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{a\,\left(3\,A-B\right)\,{\sin\left(c+d\,x\right)}^3}{3}-\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^2}{2}-A\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-((a*sin(c + d*x)^3*(3*A - B))/3 - A*a*sin(c + d*x) - (a*sin(c + d*x)^2*(A + B))/2 + (3*a*sin(c + d*x)^4*(A + B))/4 - (a*sin(c + d*x)^6*(A + B))/2 + (a*sin(c + d*x)^8*(A + B))/8 - (3*a*sin(c + d*x)^5*(A - B))/5 + (a*sin(c + d*x)^7*(A - 3*B))/7 + (B*a*sin(c + d*x)^9)/9)/d","B"
954,1,102,102,0.081005,"\text{Not used}","int(cos(c + d*x)^5*(A + B*sin(c + d*x))*(a + a*sin(c + d*x)),x)","\frac{\frac{B\,a\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{a\,\left(A-2\,B\right)\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^4}{2}-\frac{a\,\left(2\,A-B\right)\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^2}{2}+A\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(A*a*sin(c + d*x) - (a*sin(c + d*x)^3*(2*A - B))/3 + (a*sin(c + d*x)^2*(A + B))/2 - (a*sin(c + d*x)^4*(A + B))/2 + (a*sin(c + d*x)^6*(A + B))/6 + (a*sin(c + d*x)^5*(A - 2*B))/5 + (B*a*sin(c + d*x)^7)/7)/d","B"
955,1,72,78,9.007461,"\text{Not used}","int(cos(c + d*x)^3*(A + B*sin(c + d*x))*(a + a*sin(c + d*x)),x)","-\frac{\frac{B\,a\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{a\,\left(A-B\right)\,{\sin\left(c+d\,x\right)}^3}{3}-\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^2}{2}-A\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-((a*sin(c + d*x)^4*(A + B))/4 - (a*sin(c + d*x)^2*(A + B))/2 - A*a*sin(c + d*x) + (a*sin(c + d*x)^3*(A - B))/3 + (B*a*sin(c + d*x)^5)/5)/d","B"
956,1,40,49,0.069075,"\text{Not used}","int(cos(c + d*x)*(A + B*sin(c + d*x))*(a + a*sin(c + d*x)),x)","\frac{\frac{B\,a\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a\,\left(A+B\right)\,{\sin\left(c+d\,x\right)}^2}{2}+A\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(A*a*sin(c + d*x) + (a*sin(c + d*x)^2*(A + B))/2 + (B*a*sin(c + d*x)^3)/3)/d","B"
957,1,35,34,0.069449,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x),x)","-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(A\,a+B\,a\right)}{d}-\frac{B\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"- (log(sin(c + d*x) - 1)*(A*a + B*a))/d - (B*a*sin(c + d*x))/d","B"
958,1,43,47,9.120811,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x)^3,x)","\frac{a\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(A-B\right)}{2\,d}-\frac{\frac{A\,a}{2}+\frac{B\,a}{2}}{d\,\left(\sin\left(c+d\,x\right)-1\right)}","Not used",1,"(a*atanh(sin(c + d*x))*(A - B))/(2*d) - ((A*a)/2 + (B*a)/2)/(d*(sin(c + d*x) - 1))","B"
959,1,98,100,0.137452,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{a\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(3\,A-B\right)}{8\,d}-\frac{\left(\frac{B\,a}{8}-\frac{3\,A\,a}{8}\right)\,{\sin\left(c+d\,x\right)}^2+\left(\frac{3\,A\,a}{8}-\frac{B\,a}{8}\right)\,\sin\left(c+d\,x\right)+\frac{A\,a}{4}+\frac{B\,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,"(a*atanh(sin(c + d*x))*(3*A - B))/(8*d) - ((A*a)/4 + (B*a)/4 + sin(c + d*x)*((3*A*a)/8 - (B*a)/8) - sin(c + d*x)^2*((3*A*a)/8 - (B*a)/8))/(d*(sin(c + d*x) + sin(c + d*x)^2 - sin(c + d*x)^3 - 1))","B"
960,1,155,157,9.256848,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x)^7,x)","\frac{a\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(5\,A-B\right)}{16\,d}-\frac{\left(\frac{5\,A\,a}{16}-\frac{B\,a}{16}\right)\,{\sin\left(c+d\,x\right)}^4+\left(\frac{B\,a}{16}-\frac{5\,A\,a}{16}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{5\,B\,a}{48}-\frac{25\,A\,a}{48}\right)\,{\sin\left(c+d\,x\right)}^2+\left(\frac{25\,A\,a}{48}-\frac{5\,B\,a}{48}\right)\,\sin\left(c+d\,x\right)+\frac{A\,a}{6}+\frac{B\,a}{6}}{d\,\left({\sin\left(c+d\,x\right)}^5-{\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^3+2\,{\sin\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)-1\right)}","Not used",1,"(a*atanh(sin(c + d*x))*(5*A - B))/(16*d) - ((A*a)/6 + (B*a)/6 + sin(c + d*x)*((25*A*a)/48 - (5*B*a)/48) - sin(c + d*x)^3*((5*A*a)/16 - (B*a)/16) + sin(c + d*x)^4*((5*A*a)/16 - (B*a)/16) - sin(c + d*x)^2*((25*A*a)/48 - (5*B*a)/48))/(d*(sin(c + d*x) + 2*sin(c + d*x)^2 - 2*sin(c + d*x)^3 - sin(c + d*x)^4 + sin(c + d*x)^5 - 1))","B"
961,1,504,138,10.724745,"\text{Not used}","int(cos(c + d*x)^6*(A + B*sin(c + d*x))*(a + a*sin(c + d*x)),x)","\frac{5\,a\,\mathrm{atan}\left(\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A+B\right)}{64\,\left(\frac{5\,A\,a}{8}+\frac{5\,B\,a}{64}\right)}\right)\,\left(8\,A+B\right)}{64\,d}-\frac{5\,a\,\left(8\,A+B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{64\,d}-\frac{\left(\frac{11\,A\,a}{8}-\frac{5\,B\,a}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+\left(2\,A\,a+2\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\left(\frac{61\,A\,a}{24}+\frac{397\,B\,a}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(2\,A\,a+2\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\left(\frac{113\,A\,a}{24}-\frac{895\,B\,a}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(10\,A\,a+10\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(\frac{85\,A\,a}{24}+\frac{1765\,B\,a}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(10\,A\,a+10\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(-\frac{85\,A\,a}{24}-\frac{1765\,B\,a}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a+6\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{895\,B\,a}{192}-\frac{113\,A\,a}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,a+6\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{61\,A\,a}{24}-\frac{397\,B\,a}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{2\,A\,a}{7}+\frac{2\,B\,a}{7}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{5\,B\,a}{64}-\frac{11\,A\,a}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2\,A\,a}{7}+\frac{2\,B\,a}{7}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(5*a*atan((5*a*tan(c/2 + (d*x)/2)*(8*A + B))/(64*((5*A*a)/8 + (5*B*a)/64)))*(8*A + B))/(64*d) - (5*a*(8*A + B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(64*d) - ((2*A*a)/7 + (2*B*a)/7 - tan(c/2 + (d*x)/2)*((11*A*a)/8 - (5*B*a)/64) + tan(c/2 + (d*x)/2)^4*(6*A*a + 6*B*a) + tan(c/2 + (d*x)/2)^12*(2*A*a + 2*B*a) + tan(c/2 + (d*x)/2)^6*(6*A*a + 6*B*a) + tan(c/2 + (d*x)/2)^14*(2*A*a + 2*B*a) + tan(c/2 + (d*x)/2)^2*((2*A*a)/7 + (2*B*a)/7) + tan(c/2 + (d*x)/2)^8*(10*A*a + 10*B*a) + tan(c/2 + (d*x)/2)^10*(10*A*a + 10*B*a) + tan(c/2 + (d*x)/2)^15*((11*A*a)/8 - (5*B*a)/64) - tan(c/2 + (d*x)/2)^3*((61*A*a)/24 + (397*B*a)/192) + tan(c/2 + (d*x)/2)^13*((61*A*a)/24 + (397*B*a)/192) - tan(c/2 + (d*x)/2)^5*((113*A*a)/24 - (895*B*a)/192) + tan(c/2 + (d*x)/2)^11*((113*A*a)/24 - (895*B*a)/192) - tan(c/2 + (d*x)/2)^7*((85*A*a)/24 + (1765*B*a)/192) + tan(c/2 + (d*x)/2)^9*((85*A*a)/24 + (1765*B*a)/192))/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1))","B"
962,1,391,111,10.506340,"\text{Not used}","int(cos(c + d*x)^4*(A + B*sin(c + d*x))*(a + a*sin(c + d*x)),x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,A+B\right)}{8\,\left(\frac{3\,A\,a}{4}+\frac{B\,a}{8}\right)}\right)\,\left(6\,A+B\right)}{8\,d}-\frac{a\,\left(6\,A+B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}-\frac{\left(\frac{5\,A\,a}{4}-\frac{B\,a}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(2\,A\,a+2\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(\frac{7\,A\,a}{4}+\frac{47\,B\,a}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,A\,a+2\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(\frac{A\,a}{2}-\frac{13\,B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(4\,A\,a+4\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{13\,B\,a}{4}-\frac{A\,a}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A\,a+4\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{7\,A\,a}{4}-\frac{47\,B\,a}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{2\,A\,a}{5}+\frac{2\,B\,a}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{B\,a}{8}-\frac{5\,A\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2\,A\,a}{5}+\frac{2\,B\,a}{5}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(6*A + B))/(8*((3*A*a)/4 + (B*a)/8)))*(6*A + B))/(8*d) - (a*(6*A + B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d) - ((2*A*a)/5 + (2*B*a)/5 - tan(c/2 + (d*x)/2)*((5*A*a)/4 - (B*a)/8) + tan(c/2 + (d*x)/2)^4*(4*A*a + 4*B*a) + tan(c/2 + (d*x)/2)^8*(2*A*a + 2*B*a) + tan(c/2 + (d*x)/2)^6*(4*A*a + 4*B*a) + tan(c/2 + (d*x)/2)^10*(2*A*a + 2*B*a) + tan(c/2 + (d*x)/2)^2*((2*A*a)/5 + (2*B*a)/5) - tan(c/2 + (d*x)/2)^5*((A*a)/2 - (13*B*a)/4) + tan(c/2 + (d*x)/2)^7*((A*a)/2 - (13*B*a)/4) + tan(c/2 + (d*x)/2)^11*((5*A*a)/4 - (B*a)/8) - tan(c/2 + (d*x)/2)^3*((7*A*a)/4 + (47*B*a)/24) + tan(c/2 + (d*x)/2)^9*((7*A*a)/4 + (47*B*a)/24))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
963,1,276,84,10.553341,"\text{Not used}","int(cos(c + d*x)^2*(A + B*sin(c + d*x))*(a + a*sin(c + d*x)),x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+B\right)}{4\,\left(A\,a+\frac{B\,a}{4}\right)}\right)\,\left(4\,A+B\right)}{4\,d}-\frac{a\,\left(4\,A+B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}-\frac{\left(A\,a-\frac{B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(2\,A\,a+2\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(A\,a+\frac{7\,B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,A\,a+2\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-A\,a-\frac{7\,B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{2\,A\,a}{3}+\frac{2\,B\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{B\,a}{4}-A\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2\,A\,a}{3}+\frac{2\,B\,a}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(4*A + B))/(4*(A*a + (B*a)/4)))*(4*A + B))/(4*d) - (a*(4*A + B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d) - ((2*A*a)/3 + (2*B*a)/3 - tan(c/2 + (d*x)/2)*(A*a - (B*a)/4) + tan(c/2 + (d*x)/2)^4*(2*A*a + 2*B*a) + tan(c/2 + (d*x)/2)^6*(2*A*a + 2*B*a) + tan(c/2 + (d*x)/2)^2*((2*A*a)/3 + (2*B*a)/3) + tan(c/2 + (d*x)/2)^7*(A*a - (B*a)/4) - tan(c/2 + (d*x)/2)^3*(A*a + (7*B*a)/4) + tan(c/2 + (d*x)/2)^5*(A*a + (7*B*a)/4))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
964,1,33,29,9.165831,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x)^2,x)","-\frac{2\,A\,a+2\,B\,a}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}-B\,a\,x","Not used",1,"- (2*A*a + 2*B*a)/(d*(tan(c/2 + (d*x)/2) - 1)) - B*a*x","B"
965,1,107,50,9.247074,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x)^4,x)","\frac{\frac{2\,a\,\left(\frac{3\,B}{2}+A\,\cos\left(c+d\,x\right)+B\,\cos\left(c+d\,x\right)+2\,A\,\sin\left(c+d\,x\right)-B\,\sin\left(c+d\,x\right)+A\,\cos\left(2\,c+2\,d\,x\right)-\frac{B\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}{3}-\frac{4\,a\,\cos\left(c+d\,x\right)\,\left(\frac{A}{2}+\frac{B}{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*((3*B)/2 + A*cos(c + d*x) + B*cos(c + d*x) + 2*A*sin(c + d*x) - B*sin(c + d*x) + A*cos(2*c + 2*d*x) - (B*cos(2*c + 2*d*x))/2))/3 - (4*a*cos(c + d*x)*(A/2 + B/2))/3)/(d*(2*cos(c + d*x) - sin(2*c + 2*d*x)))","B"
966,1,224,73,11.137142,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x)^6,x)","-\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{4}-\frac{9\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{4}-A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)-\frac{15\,B\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{3\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{2}-B\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+\frac{B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{4}-\frac{73\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{25\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}-\frac{19\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{3\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}+\frac{7\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{5\,B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{3\,B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}\right)}{120\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^3\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(a*cos(c/2 + (d*x)/2)*((A*cos((5*c)/2 + (5*d*x)/2))/4 - (9*A*cos((3*c)/2 + (3*d*x)/2))/4 - A*cos((7*c)/2 + (7*d*x)/2) - (15*B*cos(c/2 + (d*x)/2))/4 + (3*B*cos((3*c)/2 + (3*d*x)/2))/2 - B*cos((5*c)/2 + (5*d*x)/2) + (B*cos((7*c)/2 + (7*d*x)/2))/4 - (73*A*sin(c/2 + (d*x)/2))/8 + (25*A*sin((3*c)/2 + (3*d*x)/2))/8 - (19*A*sin((5*c)/2 + (5*d*x)/2))/8 + (3*A*sin((7*c)/2 + (7*d*x)/2))/8 + (7*B*sin(c/2 + (d*x)/2))/8 + (5*B*sin((3*c)/2 + (3*d*x)/2))/8 + (B*sin((5*c)/2 + (5*d*x)/2))/8 + (3*B*sin((7*c)/2 + (7*d*x)/2))/8))/(120*d*cos(c/2 - pi/4 + (d*x)/2)^3*cos(c/2 + pi/4 + (d*x)/2)^5)","B"
967,1,320,96,12.638762,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x)^8,x)","-\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{15\,A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}-\frac{75\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}-\frac{105\,A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}+\frac{9\,A\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}-\frac{3\,A\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{2}-\frac{35\,B\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{65\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}-\frac{55\,B\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{35\,B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}-\frac{19\,B\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}+\frac{B\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{4}-\frac{843\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{363\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{16}-\frac{651\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{32}+\frac{171\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{32}-\frac{111\,A\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{32}+\frac{15\,A\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{32}+\frac{53\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{27\,B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{16}+\frac{21\,B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{32}+\frac{59\,B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{32}+\frac{B\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{32}+\frac{15\,B\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{32}\right)}{3360\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^5\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(a*cos(c/2 + (d*x)/2)*((15*A*cos((5*c)/2 + (5*d*x)/2))/8 - (75*A*cos((3*c)/2 + (3*d*x)/2))/8 - (105*A*cos((7*c)/2 + (7*d*x)/2))/16 + (9*A*cos((9*c)/2 + (9*d*x)/2))/16 - (3*A*cos((11*c)/2 + (11*d*x)/2))/2 - (35*B*cos(c/2 + (d*x)/2))/2 + (65*B*cos((3*c)/2 + (3*d*x)/2))/8 - (55*B*cos((5*c)/2 + (5*d*x)/2))/8 + (35*B*cos((7*c)/2 + (7*d*x)/2))/16 - (19*B*cos((9*c)/2 + (9*d*x)/2))/16 + (B*cos((11*c)/2 + (11*d*x)/2))/4 - (843*A*sin(c/2 + (d*x)/2))/16 + (363*A*sin((3*c)/2 + (3*d*x)/2))/16 - (651*A*sin((5*c)/2 + (5*d*x)/2))/32 + (171*A*sin((7*c)/2 + (7*d*x)/2))/32 - (111*A*sin((9*c)/2 + (9*d*x)/2))/32 + (15*A*sin((11*c)/2 + (11*d*x)/2))/32 + (53*B*sin(c/2 + (d*x)/2))/16 + (27*B*sin((3*c)/2 + (3*d*x)/2))/16 + (21*B*sin((5*c)/2 + (5*d*x)/2))/32 + (59*B*sin((7*c)/2 + (7*d*x)/2))/32 + (B*sin((9*c)/2 + (9*d*x)/2))/32 + (15*B*sin((11*c)/2 + (11*d*x)/2))/32))/(3360*d*cos(c/2 - pi/4 + (d*x)/2)^5*cos(c/2 + pi/4 + (d*x)/2)^7)","B"
968,1,416,119,13.295071,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x)))/cos(c + d*x)^10,x)","-\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{329\,A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{64}-\frac{1225\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{64}-\frac{133\,A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}+\frac{21\,A\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{8}-\frac{413\,A\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{64}+\frac{29\,A\,\cos\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{64}-A\,\cos\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)-\frac{315\,B\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{1295\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{64}-\frac{1183\,B\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{64}+7\,B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)-\frac{21\,B\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{4}+\frac{91\,B\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{64}-\frac{43\,B\,\cos\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{64}+\frac{B\,\cos\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{8}-\frac{17609\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}+\frac{8649\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{128}-\frac{8159\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{128}+\frac{2783\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{128}-\frac{2293\,A\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{128}+\frac{501\,A\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{128}-\frac{291\,A\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{128}+\frac{35\,A\,\sin\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{128}+\frac{823\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}+\frac{297\,B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{128}+\frac{193\,B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{128}+\frac{479\,B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{128}+\frac{11\,B\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{128}+\frac{213\,B\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{128}-\frac{3\,B\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{128}+\frac{35\,B\,\sin\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{128}\right)}{40320\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^7\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(a*cos(c/2 + (d*x)/2)*((329*A*cos((5*c)/2 + (5*d*x)/2))/64 - (1225*A*cos((3*c)/2 + (3*d*x)/2))/64 - (133*A*cos((7*c)/2 + (7*d*x)/2))/8 + (21*A*cos((9*c)/2 + (9*d*x)/2))/8 - (413*A*cos((11*c)/2 + (11*d*x)/2))/64 + (29*A*cos((13*c)/2 + (13*d*x)/2))/64 - A*cos((15*c)/2 + (15*d*x)/2) - (315*B*cos(c/2 + (d*x)/2))/8 + (1295*B*cos((3*c)/2 + (3*d*x)/2))/64 - (1183*B*cos((5*c)/2 + (5*d*x)/2))/64 + 7*B*cos((7*c)/2 + (7*d*x)/2) - (21*B*cos((9*c)/2 + (9*d*x)/2))/4 + (91*B*cos((11*c)/2 + (11*d*x)/2))/64 - (43*B*cos((13*c)/2 + (13*d*x)/2))/64 + (B*cos((15*c)/2 + (15*d*x)/2))/8 - (17609*A*sin(c/2 + (d*x)/2))/128 + (8649*A*sin((3*c)/2 + (3*d*x)/2))/128 - (8159*A*sin((5*c)/2 + (5*d*x)/2))/128 + (2783*A*sin((7*c)/2 + (7*d*x)/2))/128 - (2293*A*sin((9*c)/2 + (9*d*x)/2))/128 + (501*A*sin((11*c)/2 + (11*d*x)/2))/128 - (291*A*sin((13*c)/2 + (13*d*x)/2))/128 + (35*A*sin((15*c)/2 + (15*d*x)/2))/128 + (823*B*sin(c/2 + (d*x)/2))/128 + (297*B*sin((3*c)/2 + (3*d*x)/2))/128 + (193*B*sin((5*c)/2 + (5*d*x)/2))/128 + (479*B*sin((7*c)/2 + (7*d*x)/2))/128 + (11*B*sin((9*c)/2 + (9*d*x)/2))/128 + (213*B*sin((11*c)/2 + (11*d*x)/2))/128 - (3*B*sin((13*c)/2 + (13*d*x)/2))/128 + (35*B*sin((15*c)/2 + (15*d*x)/2))/128))/(40320*d*cos(c/2 - pi/4 + (d*x)/2)^7*cos(c/2 + pi/4 + (d*x)/2)^9)","B"
969,1,168,134,9.199212,"\text{Not used}","int(cos(c + d*x)^7*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2,x)","-\frac{\frac{2\,a^2\,{\sin\left(c+d\,x\right)}^3\,\left(A-B\right)}{3}-\frac{a^2\,{\sin\left(c+d\,x\right)}^2\,\left(2\,A+B\right)}{2}-A\,a^2\,{\sin\left(c+d\,x\right)}^6+\frac{a^2\,{\sin\left(c+d\,x\right)}^4\,\left(3\,A+B\right)}{2}+\frac{a^2\,{\sin\left(c+d\,x\right)}^8\,\left(A-B\right)}{4}-\frac{2\,a^2\,{\sin\left(c+d\,x\right)}^7\,\left(A+3\,B\right)}{7}+\frac{a^2\,{\sin\left(c+d\,x\right)}^9\,\left(A+2\,B\right)}{9}+\frac{6\,B\,a^2\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{B\,a^2\,{\sin\left(c+d\,x\right)}^{10}}{10}-A\,a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-((2*a^2*sin(c + d*x)^3*(A - B))/3 - (a^2*sin(c + d*x)^2*(2*A + B))/2 - A*a^2*sin(c + d*x)^6 + (a^2*sin(c + d*x)^4*(3*A + B))/2 + (a^2*sin(c + d*x)^8*(A - B))/4 - (2*a^2*sin(c + d*x)^7*(A + 3*B))/7 + (a^2*sin(c + d*x)^9*(A + 2*B))/9 + (6*B*a^2*sin(c + d*x)^5)/5 + (B*a^2*sin(c + d*x)^10)/10 - A*a^2*sin(c + d*x))/d","B"
970,1,140,105,0.122559,"\text{Not used}","int(cos(c + d*x)^5*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2,x)","\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^2\,\left(2\,A+B\right)}{2}-\frac{a^2\,{\sin\left(c+d\,x\right)}^3\,\left(A-2\,B\right)}{3}-\frac{a^2\,{\sin\left(c+d\,x\right)}^4\,\left(4\,A+B\right)}{4}-\frac{a^2\,{\sin\left(c+d\,x\right)}^5\,\left(A+4\,B\right)}{5}+\frac{a^2\,{\sin\left(c+d\,x\right)}^7\,\left(A+2\,B\right)}{7}+\frac{B\,a^2\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{a^2\,{\sin\left(c+d\,x\right)}^6\,\left(2\,A-B\right)}{6}+A\,a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"((a^2*sin(c + d*x)^2*(2*A + B))/2 - (a^2*sin(c + d*x)^3*(A - 2*B))/3 - (a^2*sin(c + d*x)^4*(4*A + B))/4 - (a^2*sin(c + d*x)^5*(A + 4*B))/5 + (a^2*sin(c + d*x)^7*(A + 2*B))/7 + (B*a^2*sin(c + d*x)^8)/8 + (a^2*sin(c + d*x)^6*(2*A - B))/6 + A*a^2*sin(c + d*x))/d","B"
971,1,96,78,9.075108,"\text{Not used}","int(cos(c + d*x)^3*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2,x)","-\frac{\frac{A\,a^2\,{\sin\left(c+d\,x\right)}^4}{2}-\frac{a^2\,{\sin\left(c+d\,x\right)}^2\,\left(2\,A+B\right)}{2}+\frac{a^2\,{\sin\left(c+d\,x\right)}^5\,\left(A+2\,B\right)}{5}-\frac{2\,B\,a^2\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{B\,a^2\,{\sin\left(c+d\,x\right)}^6}{6}-A\,a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-((A*a^2*sin(c + d*x)^4)/2 - (a^2*sin(c + d*x)^2*(2*A + B))/2 + (a^2*sin(c + d*x)^5*(A + 2*B))/5 - (2*B*a^2*sin(c + d*x)^3)/3 + (B*a^2*sin(c + d*x)^6)/6 - A*a^2*sin(c + d*x))/d","B"
972,1,66,51,9.095389,"\text{Not used}","int(cos(c + d*x)*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2,x)","\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^2\,\left(2\,A+B\right)}{2}+\frac{a^2\,{\sin\left(c+d\,x\right)}^3\,\left(A+2\,B\right)}{3}+\frac{B\,a^2\,{\sin\left(c+d\,x\right)}^4}{4}+A\,a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"((a^2*sin(c + d*x)^2*(2*A + B))/2 + (a^2*sin(c + d*x)^3*(A + 2*B))/3 + (B*a^2*sin(c + d*x)^4)/4 + A*a^2*sin(c + d*x))/d","B"
973,1,63,60,0.075316,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x),x)","-\frac{\sin\left(c+d\,x\right)\,\left(a^2\,\left(A+B\right)+B\,a^2\right)+\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(2\,A\,a^2+2\,B\,a^2\right)+\frac{B\,a^2\,{\sin\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"-(sin(c + d*x)*(a^2*(A + B) + B*a^2) + log(sin(c + d*x) - 1)*(2*A*a^2 + 2*B*a^2) + (B*a^2*sin(c + d*x)^2)/2)/d","B"
974,1,44,43,0.064549,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x)^3,x)","\frac{B\,a^2\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{d}-\frac{A\,a^2+B\,a^2}{d\,\left(\sin\left(c+d\,x\right)-1\right)}","Not used",1,"(B*a^2*log(sin(c + d*x) - 1))/d - (A*a^2 + B*a^2)/(d*(sin(c + d*x) - 1))","B"
975,1,73,77,0.109299,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\frac{A\,a^2}{2}-\sin\left(c+d\,x\right)\,\left(\frac{A\,a^2}{4}-\frac{B\,a^2}{4}\right)}{d\,\left({\sin\left(c+d\,x\right)}^2-2\,\sin\left(c+d\,x\right)+1\right)}+\frac{a^2\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(A-B\right)}{4\,d}","Not used",1,"((A*a^2)/2 - sin(c + d*x)*((A*a^2)/4 - (B*a^2)/4))/(d*(sin(c + d*x)^2 - 2*sin(c + d*x) + 1)) + (a^2*atanh(sin(c + d*x))*(A - B))/(4*d)","B"
976,1,136,132,9.215756,"\text{Not used}","int(((A + B*sin(c + d*x))*(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)\,\left(2\,A-B\right)}{8\,d}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{A\,a^2}{4}-\frac{B\,a^2}{8}\right)-{\sin\left(c+d\,x\right)}^2\,\left(\frac{A\,a^2}{2}-\frac{B\,a^2}{4}\right)+\frac{A\,a^2}{3}+\frac{B\,a^2}{12}+\sin\left(c+d\,x\right)\,\left(\frac{A\,a^2}{12}-\frac{B\,a^2}{24}\right)}{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))*(2*A - B))/(8*d) - (sin(c + d*x)^3*((A*a^2)/4 - (B*a^2)/8) - sin(c + d*x)^2*((A*a^2)/2 - (B*a^2)/4) + (A*a^2)/3 + (B*a^2)/12 + sin(c + d*x)*((A*a^2)/12 - (B*a^2)/24))/(d*(2*sin(c + d*x) - 2*sin(c + d*x)^3 + sin(c + d*x)^4 - 1))","B"
977,1,622,196,10.805825,"\text{Not used}","int(cos(c + d*x)^6*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2,x)","\frac{5\,a^2\,\mathrm{atan}\left(\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A+2\,B\right)}{64\,\left(\frac{45\,A\,a^2}{64}+\frac{5\,B\,a^2}{32}\right)}\right)\,\left(9\,A+2\,B\right)}{64\,d}-\frac{5\,a^2\,\left(9\,A+2\,B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{64\,d}-\frac{\frac{4\,A\,a^2}{7}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{83\,A\,a^2}{64}-\frac{5\,B\,a^2}{32}\right)+\frac{22\,B\,a^2}{63}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(4\,A\,a^2+2\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(8\,A\,a^2+8\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{8\,A\,a^2}{7}+\frac{8\,B\,a^2}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(32\,A\,a^2+4\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(24\,A\,a^2+24\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(24\,A\,a^2+\frac{16\,B\,a^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(40\,A\,a^2+40\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{88\,A\,a^2}{7}+\frac{32\,B\,a^2}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{83\,A\,a^2}{64}-\frac{5\,B\,a^2}{32}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{149\,A\,a^2}{32}-\frac{83\,B\,a^2}{16}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{149\,A\,a^2}{32}-\frac{83\,B\,a^2}{16}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{189\,A\,a^2}{32}+\frac{191\,B\,a^2}{48}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{189\,A\,a^2}{32}+\frac{191\,B\,a^2}{48}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{409\,A\,a^2}{32}+\frac{145\,B\,a^2}{16}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{409\,A\,a^2}{32}+\frac{145\,B\,a^2}{16}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(5*a^2*atan((5*a^2*tan(c/2 + (d*x)/2)*(9*A + 2*B))/(64*((45*A*a^2)/64 + (5*B*a^2)/32)))*(9*A + 2*B))/(64*d) - (5*a^2*(9*A + 2*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(64*d) - ((4*A*a^2)/7 - tan(c/2 + (d*x)/2)*((83*A*a^2)/64 - (5*B*a^2)/32) + (22*B*a^2)/63 + tan(c/2 + (d*x)/2)^16*(4*A*a^2 + 2*B*a^2) + tan(c/2 + (d*x)/2)^14*(8*A*a^2 + 8*B*a^2) + tan(c/2 + (d*x)/2)^2*((8*A*a^2)/7 + (8*B*a^2)/7) + tan(c/2 + (d*x)/2)^8*(32*A*a^2 + 4*B*a^2) + tan(c/2 + (d*x)/2)^6*(24*A*a^2 + 24*B*a^2) + tan(c/2 + (d*x)/2)^12*(24*A*a^2 + (16*B*a^2)/3) + tan(c/2 + (d*x)/2)^10*(40*A*a^2 + 40*B*a^2) + tan(c/2 + (d*x)/2)^4*((88*A*a^2)/7 + (32*B*a^2)/7) + tan(c/2 + (d*x)/2)^17*((83*A*a^2)/64 - (5*B*a^2)/32) - tan(c/2 + (d*x)/2)^5*((149*A*a^2)/32 - (83*B*a^2)/16) + tan(c/2 + (d*x)/2)^13*((149*A*a^2)/32 - (83*B*a^2)/16) - tan(c/2 + (d*x)/2)^3*((189*A*a^2)/32 + (191*B*a^2)/48) + tan(c/2 + (d*x)/2)^15*((189*A*a^2)/32 + (191*B*a^2)/48) - tan(c/2 + (d*x)/2)^7*((409*A*a^2)/32 + (145*B*a^2)/16) + tan(c/2 + (d*x)/2)^11*((409*A*a^2)/32 + (145*B*a^2)/16))/(d*(9*tan(c/2 + (d*x)/2)^2 + 36*tan(c/2 + (d*x)/2)^4 + 84*tan(c/2 + (d*x)/2)^6 + 126*tan(c/2 + (d*x)/2)^8 + 126*tan(c/2 + (d*x)/2)^10 + 84*tan(c/2 + (d*x)/2)^12 + 36*tan(c/2 + (d*x)/2)^14 + 9*tan(c/2 + (d*x)/2)^16 + tan(c/2 + (d*x)/2)^18 + 1))","B"
978,1,494,165,10.998378,"\text{Not used}","int(cos(c + d*x)^4*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,A+2\,B\right)}{8\,\left(\frac{7\,A\,a^2}{8}+\frac{B\,a^2}{4}\right)}\right)\,\left(7\,A+2\,B\right)}{8\,d}-\frac{a^2\,\left(7\,A+2\,B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}-\frac{\frac{4\,A\,a^2}{5}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A\,a^2}{8}-\frac{B\,a^2}{4}\right)+\frac{18\,B\,a^2}{35}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(4\,A\,a^2+2\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(12\,A\,a^2+2\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(8\,A\,a^2+8\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{8\,A\,a^2}{5}+\frac{8\,B\,a^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{9\,A\,a^2}{8}-\frac{B\,a^2}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(16\,A\,a^2+16\,B\,a^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{29\,A\,a^2}{6}+\frac{11\,B\,a^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{29\,A\,a^2}{6}+\frac{11\,B\,a^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{44\,A\,a^2}{5}+\frac{14\,B\,a^2}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{23\,A\,a^2}{24}-\frac{31\,B\,a^2}{12}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{23\,A\,a^2}{24}-\frac{31\,B\,a^2}{12}\right)}{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,"(a^2*atan((a^2*tan(c/2 + (d*x)/2)*(7*A + 2*B))/(8*((7*A*a^2)/8 + (B*a^2)/4)))*(7*A + 2*B))/(8*d) - (a^2*(7*A + 2*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d) - ((4*A*a^2)/5 - tan(c/2 + (d*x)/2)*((9*A*a^2)/8 - (B*a^2)/4) + (18*B*a^2)/35 + tan(c/2 + (d*x)/2)^12*(4*A*a^2 + 2*B*a^2) + tan(c/2 + (d*x)/2)^8*(12*A*a^2 + 2*B*a^2) + tan(c/2 + (d*x)/2)^10*(8*A*a^2 + 8*B*a^2) + tan(c/2 + (d*x)/2)^2*((8*A*a^2)/5 + (8*B*a^2)/5) + tan(c/2 + (d*x)/2)^13*((9*A*a^2)/8 - (B*a^2)/4) + tan(c/2 + (d*x)/2)^6*(16*A*a^2 + 16*B*a^2) - tan(c/2 + (d*x)/2)^3*((29*A*a^2)/6 + (11*B*a^2)/3) + tan(c/2 + (d*x)/2)^11*((29*A*a^2)/6 + (11*B*a^2)/3) + tan(c/2 + (d*x)/2)^4*((44*A*a^2)/5 + (14*B*a^2)/5) - tan(c/2 + (d*x)/2)^5*((23*A*a^2)/24 - (31*B*a^2)/12) + tan(c/2 + (d*x)/2)^9*((23*A*a^2)/24 - (31*B*a^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"
979,1,367,134,10.465004,"\text{Not used}","int(cos(c + d*x)^2*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A+2\,B\right)}{4\,\left(\frac{5\,A\,a^2}{4}+\frac{B\,a^2}{2}\right)}\right)\,\left(5\,A+2\,B\right)}{4\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}-\frac{\frac{4\,A\,a^2}{3}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A\,a^2}{4}-\frac{B\,a^2}{2}\right)+\frac{14\,B\,a^2}{15}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(4\,A\,a^2+2\,B\,a^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{7\,A\,a^2}{2}+3\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{7\,A\,a^2}{2}+3\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{3\,A\,a^2}{4}-\frac{B\,a^2}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(8\,A\,a^2+8\,B\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{8\,A\,a^2}{3}+\frac{8\,B\,a^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{16\,A\,a^2}{3}+\frac{4\,B\,a^2}{3}\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)}","Not used",1,"(a^2*atan((a^2*tan(c/2 + (d*x)/2)*(5*A + 2*B))/(4*((5*A*a^2)/4 + (B*a^2)/2)))*(5*A + 2*B))/(4*d) - (a^2*(5*A + 2*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d) - ((4*A*a^2)/3 - tan(c/2 + (d*x)/2)*((3*A*a^2)/4 - (B*a^2)/2) + (14*B*a^2)/15 + tan(c/2 + (d*x)/2)^8*(4*A*a^2 + 2*B*a^2) - tan(c/2 + (d*x)/2)^3*((7*A*a^2)/2 + 3*B*a^2) + tan(c/2 + (d*x)/2)^7*((7*A*a^2)/2 + 3*B*a^2) + tan(c/2 + (d*x)/2)^9*((3*A*a^2)/4 - (B*a^2)/2) + tan(c/2 + (d*x)/2)^6*(8*A*a^2 + 8*B*a^2) + tan(c/2 + (d*x)/2)^2*((8*A*a^2)/3 + (8*B*a^2)/3) + tan(c/2 + (d*x)/2)^4*((16*A*a^2)/3 + (4*B*a^2)/3))/(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))","B"
980,1,110,55,9.296549,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x)^2,x)","-\frac{4\,A\,a^2+6\,B\,a^2+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,A\,a^2+4\,B\,a^2\right)-2\,B\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^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)}-A\,a^2\,x-2\,B\,a^2\,x","Not used",1,"- (4*A*a^2 + 6*B*a^2 + tan(c/2 + (d*x)/2)^2*(4*A*a^2 + 4*B*a^2) - 2*B*a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1)) - A*a^2*x - 2*B*a^2*x","B"
981,1,77,73,9.147619,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x)^4,x)","-\frac{\sqrt{2}\,a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B}{2}-\frac{5\,A}{2}+\frac{A\,\cos\left(c+d\,x\right)}{2}+\frac{B\,\cos\left(c+d\,x\right)}{2}+\frac{3\,A\,\sin\left(c+d\,x\right)}{2}-\frac{3\,B\,\sin\left(c+d\,x\right)}{2}\right)}{6\,d\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^3}","Not used",1,"-(2^(1/2)*a^2*cos(c/2 + (d*x)/2)*(B/2 - (5*A)/2 + (A*cos(c + d*x))/2 + (B*cos(c + d*x))/2 + (3*A*sin(c + d*x))/2 - (3*B*sin(c + d*x))/2))/(6*d*cos(c/2 + pi/4 + (d*x)/2)^3)","B"
982,1,175,104,9.361123,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x)^6,x)","\frac{2\,a^2\,\left(\frac{5\,B\,\sin\left(c+d\,x\right)}{2}-\frac{15\,A\,\cos\left(c+d\,x\right)}{4}-\frac{5\,B\,\cos\left(c+d\,x\right)}{8}-\frac{15\,A\,\sin\left(c+d\,x\right)}{4}-\frac{5\,B}{2}-3\,A\,\cos\left(2\,c+2\,d\,x\right)+\frac{3\,A\,\cos\left(3\,c+3\,d\,x\right)}{4}+2\,B\,\cos\left(2\,c+2\,d\,x\right)+\frac{B\,\cos\left(3\,c+3\,d\,x\right)}{8}+3\,A\,\sin\left(2\,c+2\,d\,x\right)+\frac{3\,A\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,\sin\left(2\,c+2\,d\,x\right)}{2}-\frac{B\,\sin\left(3\,c+3\,d\,x\right)}{2}\right)}{15\,d\,\left(\frac{\cos\left(3\,c+3\,d\,x\right)}{4}-\frac{5\,\cos\left(c+d\,x\right)}{4}+\sin\left(2\,c+2\,d\,x\right)\right)}","Not used",1,"(2*a^2*((5*B*sin(c + d*x))/2 - (15*A*cos(c + d*x))/4 - (5*B*cos(c + d*x))/8 - (15*A*sin(c + d*x))/4 - (5*B)/2 - 3*A*cos(2*c + 2*d*x) + (3*A*cos(3*c + 3*d*x))/4 + 2*B*cos(2*c + 2*d*x) + (B*cos(3*c + 3*d*x))/8 + 3*A*sin(2*c + 2*d*x) + (3*A*sin(3*c + 3*d*x))/4 + (B*sin(2*c + 2*d*x))/2 - (B*sin(3*c + 3*d*x))/2))/(15*d*(cos(3*c + 3*d*x)/4 - (5*cos(c + d*x))/4 + sin(2*c + 2*d*x)))","B"
983,1,274,129,12.231108,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x)^8,x)","-\frac{a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{25\,A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{4}-\frac{105\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{4}-\frac{95\,A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}+\frac{15\,A\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{8}-21\,B\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{105\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}-\frac{41\,B\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{55\,B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}+\frac{9\,B\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}-\frac{125\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{55\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{2}-\frac{25\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{2}+5\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+\frac{5\,A\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{2}+\frac{37\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{19\,B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{4}-\frac{B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{4}+\frac{13\,B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{4}-B\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\right)}{1680\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^3\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(a^2*cos(c/2 + (d*x)/2)*((25*A*cos((5*c)/2 + (5*d*x)/2))/4 - (105*A*cos((3*c)/2 + (3*d*x)/2))/4 - (95*A*cos((7*c)/2 + (7*d*x)/2))/8 + (15*A*cos((9*c)/2 + (9*d*x)/2))/8 - 21*B*cos(c/2 + (d*x)/2) + (105*B*cos((3*c)/2 + (3*d*x)/2))/8 - (41*B*cos((5*c)/2 + (5*d*x)/2))/8 + (55*B*cos((7*c)/2 + (7*d*x)/2))/16 + (9*B*cos((9*c)/2 + (9*d*x)/2))/16 - (125*A*sin(c/2 + (d*x)/2))/2 + (55*A*sin((3*c)/2 + (3*d*x)/2))/2 - (25*A*sin((5*c)/2 + (5*d*x)/2))/2 + 5*A*sin((7*c)/2 + (7*d*x)/2) + (5*A*sin((9*c)/2 + (9*d*x)/2))/2 + (37*B*sin(c/2 + (d*x)/2))/4 + (19*B*sin((3*c)/2 + (3*d*x)/2))/4 - (B*sin((5*c)/2 + (5*d*x)/2))/4 + (13*B*sin((7*c)/2 + (7*d*x)/2))/4 - B*sin((9*c)/2 + (9*d*x)/2)))/(1680*d*cos(c/2 - pi/4 + (d*x)/2)^3*cos(c/2 + pi/4 + (d*x)/2)^7)","B"
984,1,370,154,12.954031,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x)^10,x)","-\frac{a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{455\,A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{32}-\frac{1575\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{32}-35\,A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+7\,A\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)-\frac{259\,A\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{32}+\frac{35\,A\,\cos\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{32}-45\,B\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1755\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{64}-\frac{1115\,B\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{64}+10\,B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)-2\,B\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)+\frac{103\,B\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{64}+\frac{25\,B\,\cos\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{64}-\frac{623\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+77\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)-\frac{441\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{175\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}-\frac{35\,A\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{8}+\frac{21\,A\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{8}+\frac{7\,A\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{4}+\frac{131\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{49\,B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{27\,B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{16}+\frac{125\,B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}-\frac{25\,B\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}+\frac{33\,B\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{16}-\frac{B\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{2}\right)}{20160\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^5\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(a^2*cos(c/2 + (d*x)/2)*((455*A*cos((5*c)/2 + (5*d*x)/2))/32 - (1575*A*cos((3*c)/2 + (3*d*x)/2))/32 - 35*A*cos((7*c)/2 + (7*d*x)/2) + 7*A*cos((9*c)/2 + (9*d*x)/2) - (259*A*cos((11*c)/2 + (11*d*x)/2))/32 + (35*A*cos((13*c)/2 + (13*d*x)/2))/32 - 45*B*cos(c/2 + (d*x)/2) + (1755*B*cos((3*c)/2 + (3*d*x)/2))/64 - (1115*B*cos((5*c)/2 + (5*d*x)/2))/64 + 10*B*cos((7*c)/2 + (7*d*x)/2) - 2*B*cos((9*c)/2 + (9*d*x)/2) + (103*B*cos((11*c)/2 + (11*d*x)/2))/64 + (25*B*cos((13*c)/2 + (13*d*x)/2))/64 - (623*A*sin(c/2 + (d*x)/2))/4 + 77*A*sin((3*c)/2 + (3*d*x)/2) - (441*A*sin((5*c)/2 + (5*d*x)/2))/8 + (175*A*sin((7*c)/2 + (7*d*x)/2))/8 - (35*A*sin((9*c)/2 + (9*d*x)/2))/8 + (21*A*sin((11*c)/2 + (11*d*x)/2))/8 + (7*A*sin((13*c)/2 + (13*d*x)/2))/4 + (131*B*sin(c/2 + (d*x)/2))/8 + (49*B*sin((3*c)/2 + (3*d*x)/2))/8 + (27*B*sin((5*c)/2 + (5*d*x)/2))/16 + (125*B*sin((7*c)/2 + (7*d*x)/2))/16 - (25*B*sin((9*c)/2 + (9*d*x)/2))/16 + (33*B*sin((11*c)/2 + (11*d*x)/2))/16 - (B*sin((13*c)/2 + (13*d*x)/2))/2))/(20160*d*cos(c/2 - pi/4 + (d*x)/2)^5*cos(c/2 + pi/4 + (d*x)/2)^9)","B"
985,1,466,179,13.960048,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^2)/cos(c + d*x)^12,x)","-\frac{a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{8127\,A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{64}-\frac{24255\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{64}-\frac{21357\,A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{64}+\frac{5229\,A\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{64}-\frac{8379\,A\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{64}+\frac{1467\,A\,\cos\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{64}-\frac{2619\,A\,\cos\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{128}+\frac{315\,A\,\cos\left(\frac{17\,c}{2}+\frac{17\,d\,x}{2}\right)}{128}-385\,B\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{30415\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{128}-\frac{23247\,B\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{128}+\frac{12957\,B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{128}-\frac{5789\,B\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{128}+\frac{3339\,B\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{128}-\frac{267\,B\,\cos\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{128}+\frac{779\,B\,\cos\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{256}+\frac{245\,B\,\cos\left(\frac{17\,c}{2}+\frac{17\,d\,x}{2}\right)}{256}-\frac{47889\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32}+\frac{25713\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{32}-\frac{21303\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{32}+\frac{9207\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{32}-\frac{4797\,A\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{32}+\frac{1917\,A\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{32}-\frac{27\,A\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{32}+\frac{171\,A\,\sin\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{32}+\frac{9\,A\,\sin\left(\frac{17\,c}{2}+\frac{17\,d\,x}{2}\right)}{2}+\frac{7809\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{2047\,B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{64}+\frac{1383\,B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{64}+\frac{3993\,B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{64}-\frac{563\,B\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{64}+\frac{1843\,B\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{64}-\frac{373\,B\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{64}+\frac{309\,B\,\sin\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{64}-B\,\sin\left(\frac{17\,c}{2}+\frac{17\,d\,x}{2}\right)\right)}{887040\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^7\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^{11}}","Not used",1,"-(a^2*cos(c/2 + (d*x)/2)*((8127*A*cos((5*c)/2 + (5*d*x)/2))/64 - (24255*A*cos((3*c)/2 + (3*d*x)/2))/64 - (21357*A*cos((7*c)/2 + (7*d*x)/2))/64 + (5229*A*cos((9*c)/2 + (9*d*x)/2))/64 - (8379*A*cos((11*c)/2 + (11*d*x)/2))/64 + (1467*A*cos((13*c)/2 + (13*d*x)/2))/64 - (2619*A*cos((15*c)/2 + (15*d*x)/2))/128 + (315*A*cos((17*c)/2 + (17*d*x)/2))/128 - 385*B*cos(c/2 + (d*x)/2) + (30415*B*cos((3*c)/2 + (3*d*x)/2))/128 - (23247*B*cos((5*c)/2 + (5*d*x)/2))/128 + (12957*B*cos((7*c)/2 + (7*d*x)/2))/128 - (5789*B*cos((9*c)/2 + (9*d*x)/2))/128 + (3339*B*cos((11*c)/2 + (11*d*x)/2))/128 - (267*B*cos((13*c)/2 + (13*d*x)/2))/128 + (779*B*cos((15*c)/2 + (15*d*x)/2))/256 + (245*B*cos((17*c)/2 + (17*d*x)/2))/256 - (47889*A*sin(c/2 + (d*x)/2))/32 + (25713*A*sin((3*c)/2 + (3*d*x)/2))/32 - (21303*A*sin((5*c)/2 + (5*d*x)/2))/32 + (9207*A*sin((7*c)/2 + (7*d*x)/2))/32 - (4797*A*sin((9*c)/2 + (9*d*x)/2))/32 + (1917*A*sin((11*c)/2 + (11*d*x)/2))/32 - (27*A*sin((13*c)/2 + (13*d*x)/2))/32 + (171*A*sin((15*c)/2 + (15*d*x)/2))/32 + (9*A*sin((17*c)/2 + (17*d*x)/2))/2 + (7809*B*sin(c/2 + (d*x)/2))/64 + (2047*B*sin((3*c)/2 + (3*d*x)/2))/64 + (1383*B*sin((5*c)/2 + (5*d*x)/2))/64 + (3993*B*sin((7*c)/2 + (7*d*x)/2))/64 - (563*B*sin((9*c)/2 + (9*d*x)/2))/64 + (1843*B*sin((11*c)/2 + (11*d*x)/2))/64 - (373*B*sin((13*c)/2 + (13*d*x)/2))/64 + (309*B*sin((15*c)/2 + (15*d*x)/2))/64 - B*sin((17*c)/2 + (17*d*x)/2)))/(887040*d*cos(c/2 - pi/4 + (d*x)/2)^7*cos(c/2 + pi/4 + (d*x)/2)^11)","B"
986,1,177,134,0.199954,"\text{Not used}","int(cos(c + d*x)^7*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^2\,\left(3\,A+B\right)}{2}-\frac{A\,a^3\,{\sin\left(c+d\,x\right)}^9}{3}-2\,A\,a^3\,{\sin\left(c+d\,x\right)}^4+a^3\,{\sin\left(c+d\,x\right)}^6\,\left(A-B\right)-\frac{a^3\,{\sin\left(c+d\,x\right)}^{10}\,\left(A+3\,B\right)}{10}+B\,a^3\,{\sin\left(c+d\,x\right)}^3+B\,a^3\,{\sin\left(c+d\,x\right)}^8-\frac{B\,a^3\,{\sin\left(c+d\,x\right)}^{11}}{11}-\frac{2\,a^3\,{\sin\left(c+d\,x\right)}^5\,\left(3\,A+4\,B\right)}{5}+\frac{2\,a^3\,{\sin\left(c+d\,x\right)}^7\,\left(4\,A+3\,B\right)}{7}+A\,a^3\,\sin\left(c+d\,x\right)}{d}","Not used",1,"((a^3*sin(c + d*x)^2*(3*A + B))/2 - (A*a^3*sin(c + d*x)^9)/3 - 2*A*a^3*sin(c + d*x)^4 + a^3*sin(c + d*x)^6*(A - B) - (a^3*sin(c + d*x)^10*(A + 3*B))/10 + B*a^3*sin(c + d*x)^3 + B*a^3*sin(c + d*x)^8 - (B*a^3*sin(c + d*x)^11)/11 - (2*a^3*sin(c + d*x)^5*(3*A + 4*B))/5 + (2*a^3*sin(c + d*x)^7*(4*A + 3*B))/7 + A*a^3*sin(c + d*x))/d","B"
987,1,156,105,0.143690,"\text{Not used}","int(cos(c + d*x)^5*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^2\,\left(3\,A+B\right)}{2}+\frac{a^3\,{\sin\left(c+d\,x\right)}^3\,\left(A+3\,B\right)}{3}+\frac{a^3\,{\sin\left(c+d\,x\right)}^7\,\left(3\,A+B\right)}{7}+\frac{a^3\,{\sin\left(c+d\,x\right)}^6\,\left(A-5\,B\right)}{6}+\frac{a^3\,{\sin\left(c+d\,x\right)}^8\,\left(A+3\,B\right)}{8}+\frac{B\,a^3\,{\sin\left(c+d\,x\right)}^9}{9}-\frac{a^3\,{\sin\left(c+d\,x\right)}^4\,\left(5\,A-B\right)}{4}+A\,a^3\,\sin\left(c+d\,x\right)-a^3\,{\sin\left(c+d\,x\right)}^5\,\left(A+B\right)}{d}","Not used",1,"((a^3*sin(c + d*x)^2*(3*A + B))/2 + (a^3*sin(c + d*x)^3*(A + 3*B))/3 + (a^3*sin(c + d*x)^7*(3*A + B))/7 + (a^3*sin(c + d*x)^6*(A - 5*B))/6 + (a^3*sin(c + d*x)^8*(A + 3*B))/8 + (B*a^3*sin(c + d*x)^9)/9 - (a^3*sin(c + d*x)^4*(5*A - B))/4 + A*a^3*sin(c + d*x) - a^3*sin(c + d*x)^5*(A + B))/d","B"
988,1,126,78,9.142079,"\text{Not used}","int(cos(c + d*x)^3*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","-\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^4\,\left(A-B\right)}{2}-\frac{a^3\,{\sin\left(c+d\,x\right)}^2\,\left(3\,A+B\right)}{2}+\frac{a^3\,{\sin\left(c+d\,x\right)}^6\,\left(A+3\,B\right)}{6}+\frac{B\,a^3\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{a^3\,{\sin\left(c+d\,x\right)}^3\,\left(2\,A+3\,B\right)}{3}+\frac{a^3\,{\sin\left(c+d\,x\right)}^5\,\left(3\,A+2\,B\right)}{5}-A\,a^3\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-((a^3*sin(c + d*x)^4*(A - B))/2 - (a^3*sin(c + d*x)^2*(3*A + B))/2 + (a^3*sin(c + d*x)^6*(A + 3*B))/6 + (B*a^3*sin(c + d*x)^7)/7 - (a^3*sin(c + d*x)^3*(2*A + 3*B))/3 + (a^3*sin(c + d*x)^5*(3*A + 2*B))/5 - A*a^3*sin(c + d*x))/d","B"
989,1,81,51,9.073187,"\text{Not used}","int(cos(c + d*x)*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^2\,\left(3\,A+B\right)}{2}+\frac{a^3\,{\sin\left(c+d\,x\right)}^4\,\left(A+3\,B\right)}{4}+\frac{B\,a^3\,{\sin\left(c+d\,x\right)}^5}{5}+A\,a^3\,\sin\left(c+d\,x\right)+a^3\,{\sin\left(c+d\,x\right)}^3\,\left(A+B\right)}{d}","Not used",1,"((a^3*sin(c + d*x)^2*(3*A + B))/2 + (a^3*sin(c + d*x)^4*(A + 3*B))/4 + (B*a^3*sin(c + d*x)^5)/5 + A*a^3*sin(c + d*x) + a^3*sin(c + d*x)^3*(A + B))/d","B"
990,1,100,81,0.087539,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x),x)","-\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{a^3\,\left(A+2\,B\right)}{2}+\frac{B\,a^3}{2}\right)+\sin\left(c+d\,x\right)\,\left(a^3\,\left(A+2\,B\right)+a^3\,\left(2\,A+B\right)+B\,a^3\right)+\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(4\,A\,a^3+4\,B\,a^3\right)+\frac{B\,a^3\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"-(sin(c + d*x)^2*((a^3*(A + 2*B))/2 + (B*a^3)/2) + sin(c + d*x)*(a^3*(A + 2*B) + a^3*(2*A + B) + B*a^3) + log(sin(c + d*x) - 1)*(4*A*a^3 + 4*B*a^3) + (B*a^3*sin(c + d*x)^3)/3)/d","B"
991,1,63,62,0.083517,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x)^3,x)","\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(A\,a^3+3\,B\,a^3\right)-\frac{2\,A\,a^3+2\,B\,a^3}{\sin\left(c+d\,x\right)-1}+B\,a^3\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(log(sin(c + d*x) - 1)*(A*a^3 + 3*B*a^3) - (2*A*a^3 + 2*B*a^3)/(sin(c + d*x) - 1) + B*a^3*sin(c + d*x))/d","B"
992,1,36,43,9.154420,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{\frac{a^3\,\left(A-B\right)}{2}+B\,a^3\,\sin\left(c+d\,x\right)}{d\,{\left(\sin\left(c+d\,x\right)-1\right)}^2}","Not used",1,"((a^3*(A - B))/2 + B*a^3*sin(c + d*x))/(d*(sin(c + d*x) - 1)^2)","B"
993,1,112,105,9.141571,"\text{Not used}","int(((A + B*sin(c + d*x))*(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)\,\left(A-B\right)}{8\,d}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{A\,a^3}{8}-\frac{B\,a^3}{8}\right)+\frac{5\,A\,a^3}{12}-\frac{B\,a^3}{12}-\sin\left(c+d\,x\right)\,\left(\frac{3\,A\,a^3}{8}-\frac{3\,B\,a^3}{8}\right)}{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))*(A - B))/(8*d) - (sin(c + d*x)^2*((A*a^3)/8 - (B*a^3)/8) + (5*A*a^3)/12 - (B*a^3)/12 - sin(c + d*x)*((3*A*a^3)/8 - (3*B*a^3)/8))/(d*(3*sin(c + d*x) - 3*sin(c + d*x)^2 + sin(c + d*x)^3 - 1))","B"
994,1,172,162,9.183716,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x)^9,x)","\frac{a^3\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(5\,A-3\,B\right)}{32\,d}-\frac{{\sin\left(c+d\,x\right)}^4\,\left(\frac{5\,A\,a^3}{32}-\frac{3\,B\,a^3}{32}\right)-{\sin\left(c+d\,x\right)}^3\,\left(\frac{15\,A\,a^3}{32}-\frac{9\,B\,a^3}{32}\right)+{\sin\left(c+d\,x\right)}^2\,\left(\frac{35\,A\,a^3}{96}-\frac{7\,B\,a^3}{32}\right)-\frac{A\,a^3}{3}+\sin\left(c+d\,x\right)\,\left(\frac{5\,A\,a^3}{32}-\frac{3\,B\,a^3}{32}\right)}{d\,\left({\sin\left(c+d\,x\right)}^5-3\,{\sin\left(c+d\,x\right)}^4+2\,{\sin\left(c+d\,x\right)}^3+2\,{\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))*(5*A - 3*B))/(32*d) - (sin(c + d*x)^4*((5*A*a^3)/32 - (3*B*a^3)/32) - sin(c + d*x)^3*((15*A*a^3)/32 - (9*B*a^3)/32) + sin(c + d*x)^2*((35*A*a^3)/96 - (7*B*a^3)/32) - (A*a^3)/3 + sin(c + d*x)*((5*A*a^3)/32 - (3*B*a^3)/32))/(d*(2*sin(c + d*x)^2 - 3*sin(c + d*x) + 2*sin(c + d*x)^3 - 3*sin(c + d*x)^4 + sin(c + d*x)^5 + 1))","B"
995,1,711,231,10.831991,"\text{Not used}","int(cos(c + d*x)^6*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{11\,a^3\,\mathrm{atan}\left(\frac{11\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,A+3\,B\right)}{128\,\left(\frac{55\,A\,a^3}{64}+\frac{33\,B\,a^3}{128}\right)}\right)\,\left(10\,A+3\,B\right)}{128\,d}-\frac{11\,a^3\,\left(10\,A+3\,B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{128\,d}-\frac{\frac{58\,A\,a^3}{63}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{73\,A\,a^3}{64}-\frac{33\,B\,a^3}{128}\right)+\frac{10\,B\,a^3}{21}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(6\,A\,a^3+2\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(22\,A\,a^3+18\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(84\,A\,a^3+28\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{136\,A\,a^3}{3}+8\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{136\,A\,a^3}{7}+\frac{24\,B\,a^3}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(116\,A\,a^3+60\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,\left(\frac{73\,A\,a^3}{64}-\frac{33\,B\,a^3}{128}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{202\,A\,a^3}{63}+\frac{58\,B\,a^3}{21}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{328\,A\,a^3}{3}+72\,B\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{341\,A\,a^3}{16}-\frac{333\,B\,a^3}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{341\,A\,a^3}{16}-\frac{333\,B\,a^3}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{456\,A\,a^3}{7}+\frac{344\,B\,a^3}{7}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{449\,A\,a^3}{48}+\frac{577\,B\,a^3}{160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{449\,A\,a^3}{48}+\frac{577\,B\,a^3}{160}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2117\,A\,a^3}{192}+\frac{705\,B\,a^3}{128}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{2117\,A\,a^3}{192}+\frac{705\,B\,a^3}{128}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{699\,A\,a^3}{32}+\frac{2749\,B\,a^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{699\,A\,a^3}{32}+\frac{2749\,B\,a^3}{64}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+252\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(11*a^3*atan((11*a^3*tan(c/2 + (d*x)/2)*(10*A + 3*B))/(128*((55*A*a^3)/64 + (33*B*a^3)/128)))*(10*A + 3*B))/(128*d) - (11*a^3*(10*A + 3*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(128*d) - ((58*A*a^3)/63 - tan(c/2 + (d*x)/2)*((73*A*a^3)/64 - (33*B*a^3)/128) + (10*B*a^3)/21 + tan(c/2 + (d*x)/2)^18*(6*A*a^3 + 2*B*a^3) + tan(c/2 + (d*x)/2)^16*(22*A*a^3 + 18*B*a^3) + tan(c/2 + (d*x)/2)^8*(84*A*a^3 + 28*B*a^3) + tan(c/2 + (d*x)/2)^14*((136*A*a^3)/3 + 8*B*a^3) + tan(c/2 + (d*x)/2)^4*((136*A*a^3)/7 + (24*B*a^3)/7) + tan(c/2 + (d*x)/2)^10*(116*A*a^3 + 60*B*a^3) + tan(c/2 + (d*x)/2)^19*((73*A*a^3)/64 - (33*B*a^3)/128) + tan(c/2 + (d*x)/2)^2*((202*A*a^3)/63 + (58*B*a^3)/21) + tan(c/2 + (d*x)/2)^12*((328*A*a^3)/3 + 72*B*a^3) - tan(c/2 + (d*x)/2)^7*((341*A*a^3)/16 - (333*B*a^3)/32) + tan(c/2 + (d*x)/2)^13*((341*A*a^3)/16 - (333*B*a^3)/32) + tan(c/2 + (d*x)/2)^6*((456*A*a^3)/7 + (344*B*a^3)/7) - tan(c/2 + (d*x)/2)^5*((449*A*a^3)/48 + (577*B*a^3)/160) + tan(c/2 + (d*x)/2)^15*((449*A*a^3)/48 + (577*B*a^3)/160) - tan(c/2 + (d*x)/2)^3*((2117*A*a^3)/192 + (705*B*a^3)/128) + tan(c/2 + (d*x)/2)^17*((2117*A*a^3)/192 + (705*B*a^3)/128) - tan(c/2 + (d*x)/2)^9*((699*A*a^3)/32 + (2749*B*a^3)/64) + tan(c/2 + (d*x)/2)^11*((699*A*a^3)/32 + (2749*B*a^3)/64))/(d*(10*tan(c/2 + (d*x)/2)^2 + 45*tan(c/2 + (d*x)/2)^4 + 120*tan(c/2 + (d*x)/2)^6 + 210*tan(c/2 + (d*x)/2)^8 + 252*tan(c/2 + (d*x)/2)^10 + 210*tan(c/2 + (d*x)/2)^12 + 120*tan(c/2 + (d*x)/2)^14 + 45*tan(c/2 + (d*x)/2)^16 + 10*tan(c/2 + (d*x)/2)^18 + tan(c/2 + (d*x)/2)^20 + 1))","B"
996,1,584,200,10.689701,"\text{Not used}","int(cos(c + d*x)^4*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{9\,a^3\,\mathrm{atan}\left(\frac{9\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A+3\,B\right)}{64\,\left(\frac{9\,A\,a^3}{8}+\frac{27\,B\,a^3}{64}\right)}\right)\,\left(8\,A+3\,B\right)}{64\,d}-\frac{9\,a^3\,\left(8\,A+3\,B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{64\,d}-\frac{\frac{46\,A\,a^3}{35}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7\,A\,a^3}{8}-\frac{27\,B\,a^3}{64}\right)+\frac{26\,B\,a^3}{35}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(6\,A\,a^3+2\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(30\,A\,a^3+10\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(22\,A\,a^3+18\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(46\,A\,a^3+26\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{74\,A\,a^3}{5}+\frac{14\,B\,a^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{7\,A\,a^3}{8}-\frac{27\,B\,a^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{158\,A\,a^3}{35}+\frac{138\,B\,a^3}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{218\,A\,a^3}{5}+\frac{158\,B\,a^3}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{75\,A\,a^3}{8}+\frac{305\,B\,a^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{75\,A\,a^3}{8}+\frac{305\,B\,a^3}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{55\,A\,a^3}{8}+\frac{437\,B\,a^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{55\,A\,a^3}{8}+\frac{437\,B\,a^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{13\,A\,a^3}{8}+\frac{919\,B\,a^3}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{13\,A\,a^3}{8}+\frac{919\,B\,a^3}{64}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(9*a^3*atan((9*a^3*tan(c/2 + (d*x)/2)*(8*A + 3*B))/(64*((9*A*a^3)/8 + (27*B*a^3)/64)))*(8*A + 3*B))/(64*d) - (9*a^3*(8*A + 3*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(64*d) - ((46*A*a^3)/35 - tan(c/2 + (d*x)/2)*((7*A*a^3)/8 - (27*B*a^3)/64) + (26*B*a^3)/35 + tan(c/2 + (d*x)/2)^14*(6*A*a^3 + 2*B*a^3) + tan(c/2 + (d*x)/2)^10*(30*A*a^3 + 10*B*a^3) + tan(c/2 + (d*x)/2)^12*(22*A*a^3 + 18*B*a^3) + tan(c/2 + (d*x)/2)^8*(46*A*a^3 + 26*B*a^3) + tan(c/2 + (d*x)/2)^4*((74*A*a^3)/5 + (14*B*a^3)/5) + tan(c/2 + (d*x)/2)^15*((7*A*a^3)/8 - (27*B*a^3)/64) + tan(c/2 + (d*x)/2)^2*((158*A*a^3)/35 + (138*B*a^3)/35) + tan(c/2 + (d*x)/2)^6*((218*A*a^3)/5 + (158*B*a^3)/5) - tan(c/2 + (d*x)/2)^3*((75*A*a^3)/8 + (305*B*a^3)/64) + tan(c/2 + (d*x)/2)^13*((75*A*a^3)/8 + (305*B*a^3)/64) - tan(c/2 + (d*x)/2)^5*((55*A*a^3)/8 + (437*B*a^3)/64) + tan(c/2 + (d*x)/2)^11*((55*A*a^3)/8 + (437*B*a^3)/64) + tan(c/2 + (d*x)/2)^7*((13*A*a^3)/8 + (919*B*a^3)/64) - tan(c/2 + (d*x)/2)^9*((13*A*a^3)/8 + (919*B*a^3)/64))/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1))","B"
997,1,451,159,10.729062,"\text{Not used}","int(cos(c + d*x)^2*(A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{7\,a^3\,\mathrm{atan}\left(\frac{7\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A+B\right)}{8\,\left(\frac{7\,A\,a^3}{4}+\frac{7\,B\,a^3}{8}\right)}\right)\,\left(2\,A+B\right)}{8\,d}-\frac{\frac{34\,A\,a^3}{15}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A\,a^3}{4}-\frac{7\,B\,a^3}{8}\right)+\frac{22\,B\,a^3}{15}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(6\,A\,a^3+2\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,A\,a^3+4\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{A\,a^3}{4}-\frac{7\,B\,a^3}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(22\,A\,a^3+18\,B\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{13\,A\,a^3}{2}+\frac{37\,B\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{13\,A\,a^3}{2}+\frac{37\,B\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{38\,A\,a^3}{5}+\frac{34\,B\,a^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{68\,A\,a^3}{3}+\frac{44\,B\,a^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{27\,A\,a^3}{4}+\frac{73\,B\,a^3}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{27\,A\,a^3}{4}+\frac{73\,B\,a^3}{24}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{7\,a^3\,\left(2\,A+B\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,"(7*a^3*atan((7*a^3*tan(c/2 + (d*x)/2)*(2*A + B))/(8*((7*A*a^3)/4 + (7*B*a^3)/8)))*(2*A + B))/(8*d) - ((34*A*a^3)/15 - tan(c/2 + (d*x)/2)*((A*a^3)/4 - (7*B*a^3)/8) + (22*B*a^3)/15 + tan(c/2 + (d*x)/2)^10*(6*A*a^3 + 2*B*a^3) + tan(c/2 + (d*x)/2)^4*(12*A*a^3 + 4*B*a^3) + tan(c/2 + (d*x)/2)^11*((A*a^3)/4 - (7*B*a^3)/8) + tan(c/2 + (d*x)/2)^8*(22*A*a^3 + 18*B*a^3) - tan(c/2 + (d*x)/2)^5*((13*A*a^3)/2 + (37*B*a^3)/4) + tan(c/2 + (d*x)/2)^7*((13*A*a^3)/2 + (37*B*a^3)/4) + tan(c/2 + (d*x)/2)^2*((38*A*a^3)/5 + (34*B*a^3)/5) + tan(c/2 + (d*x)/2)^6*((68*A*a^3)/3 + (44*B*a^3)/3) - tan(c/2 + (d*x)/2)^3*((27*A*a^3)/4 + (73*B*a^3)/24) + tan(c/2 + (d*x)/2)^9*((27*A*a^3)/4 + (73*B*a^3)/24))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - (7*a^3*(2*A + B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d)","B"
998,1,234,91,11.511944,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x)^2,x)","-\frac{10\,A\,a^3-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^3+5\,B\,a^3\right)+14\,B\,a^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,a^3+7\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,A\,a^3+9\,B\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(18\,A\,a^3+21\,B\,a^3\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,{\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)}-\frac{3\,a^3\,\mathrm{atan}\left(\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A+3\,B\right)}{6\,A\,a^3+9\,B\,a^3}\right)\,\left(2\,A+3\,B\right)}{d}","Not used",1,"- (10*A*a^3 - tan(c/2 + (d*x)/2)*(2*A*a^3 + 5*B*a^3) + 14*B*a^3 - tan(c/2 + (d*x)/2)^3*(2*A*a^3 + 7*B*a^3) + tan(c/2 + (d*x)/2)^4*(8*A*a^3 + 9*B*a^3) + tan(c/2 + (d*x)/2)^2*(18*A*a^3 + 21*B*a^3))/(d*(tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^3 - tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^5 - 1)) - (3*a^3*atan((3*a^3*tan(c/2 + (d*x)/2)*(2*A + 3*B))/(6*A*a^3 + 9*B*a^3))*(2*A + 3*B))/d","B"
999,1,140,69,9.812622,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x)^4,x)","B\,a^3\,x-\frac{\frac{a^3\,\left(2\,A-10\,B+3\,B\,\left(c+d\,x\right)\right)}{3}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(6\,A-6\,B+9\,B\,\left(c+d\,x\right)\right)}{3}-3\,B\,a^3\,\left(c+d\,x\right)\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^3\,\left(24\,B-9\,B\,\left(c+d\,x\right)\right)}{3}+3\,B\,a^3\,\left(c+d\,x\right)\right)-B\,a^3\,\left(c+d\,x\right)}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3}","Not used",1,"B*a^3*x - ((a^3*(2*A - 10*B + 3*B*(c + d*x)))/3 + tan(c/2 + (d*x)/2)^2*((a^3*(6*A - 6*B + 9*B*(c + d*x)))/3 - 3*B*a^3*(c + d*x)) + tan(c/2 + (d*x)/2)*((a^3*(24*B - 9*B*(c + d*x)))/3 + 3*B*a^3*(c + d*x)) - B*a^3*(c + d*x))/(d*(tan(c/2 + (d*x)/2) - 1)^3)","B"
1000,1,113,107,11.305486,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x)^6,x)","-\frac{\sqrt{2}\,a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,B-\frac{53\,A}{4}+4\,A\,\cos\left(c+d\,x\right)+\frac{3\,B\,\cos\left(c+d\,x\right)}{2}+\frac{25\,A\,\sin\left(c+d\,x\right)}{2}-\frac{15\,B\,\sin\left(c+d\,x\right)}{2}+\frac{9\,A\,\cos\left(2\,c+2\,d\,x\right)}{4}-\frac{3\,B\,\cos\left(2\,c+2\,d\,x\right)}{2}-\frac{5\,A\,\sin\left(2\,c+2\,d\,x\right)}{4}\right)}{60\,d\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(2^(1/2)*a^3*cos(c/2 + (d*x)/2)*(3*B - (53*A)/4 + 4*A*cos(c + d*x) + (3*B*cos(c + d*x))/2 + (25*A*sin(c + d*x))/2 - (15*B*sin(c + d*x))/2 + (9*A*cos(2*c + 2*d*x))/4 - (3*B*cos(2*c + 2*d*x))/2 - (5*A*sin(2*c + 2*d*x))/4))/(60*d*cos(c/2 + pi/4 + (d*x)/2)^5)","B"
1001,1,213,115,11.176825,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x)^8,x)","-\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{35\,A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{4}-\frac{91\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{4}+A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)-\frac{35\,B\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{21\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{2}-\frac{3\,B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{4}-\frac{233\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{121\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{61\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}-\frac{13\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}+\frac{61\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{23\,B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}-\frac{37\,B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}\right)}{280\,d\,\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(a^3*cos(c/2 + (d*x)/2)*((35*A*cos((5*c)/2 + (5*d*x)/2))/4 - (91*A*cos((3*c)/2 + (3*d*x)/2))/4 + A*cos((7*c)/2 + (7*d*x)/2) - (35*B*cos(c/2 + (d*x)/2))/4 + (21*B*cos((3*c)/2 + (3*d*x)/2))/2 - (3*B*cos((7*c)/2 + (7*d*x)/2))/4 - (233*A*sin(c/2 + (d*x)/2))/8 + (121*A*sin((3*c)/2 + (3*d*x)/2))/8 + (61*A*sin((5*c)/2 + (5*d*x)/2))/8 - (13*A*sin((7*c)/2 + (7*d*x)/2))/8 + (61*B*sin(c/2 + (d*x)/2))/8 + (23*B*sin((3*c)/2 + (3*d*x)/2))/8 - (37*B*sin((5*c)/2 + (5*d*x)/2))/8 + (B*sin((7*c)/2 + (7*d*x)/2))/8))/(280*d*cos(c/2 - pi/4 + (d*x)/2)*cos(c/2 + pi/4 + (d*x)/2)^7)","B"
1002,1,322,140,12.213178,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + a*sin(c + d*x))^3)/cos(c + d*x)^10,x)","-\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{63\,A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}-\frac{171\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}-\frac{145\,A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}+\frac{49\,A\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}+\frac{A\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{2}-\frac{21\,B\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{75\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}-\frac{21\,B\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{41\,B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}+\frac{7\,B\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}-\frac{B\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{4}-\frac{617\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{329\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{16}-\frac{145\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{32}+\frac{113\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{32}+\frac{115\,A\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{32}-\frac{19\,A\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{32}+\frac{109\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}+\frac{35\,B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{16}-\frac{43\,B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{32}+\frac{59\,B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{32}-\frac{47\,B\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{32}-\frac{B\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{32}\right)}{2016\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^3\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(a^3*cos(c/2 + (d*x)/2)*((63*A*cos((5*c)/2 + (5*d*x)/2))/8 - (171*A*cos((3*c)/2 + (3*d*x)/2))/8 - (145*A*cos((7*c)/2 + (7*d*x)/2))/16 + (49*A*cos((9*c)/2 + (9*d*x)/2))/16 + (A*cos((11*c)/2 + (11*d*x)/2))/2 - (21*B*cos(c/2 + (d*x)/2))/2 + (75*B*cos((3*c)/2 + (3*d*x)/2))/8 - (21*B*cos((5*c)/2 + (5*d*x)/2))/8 + (41*B*cos((7*c)/2 + (7*d*x)/2))/16 + (7*B*cos((9*c)/2 + (9*d*x)/2))/16 - (B*cos((11*c)/2 + (11*d*x)/2))/4 - (617*A*sin(c/2 + (d*x)/2))/16 + (329*A*sin((3*c)/2 + (3*d*x)/2))/16 - (145*A*sin((5*c)/2 + (5*d*x)/2))/32 + (113*A*sin((7*c)/2 + (7*d*x)/2))/32 + (115*A*sin((9*c)/2 + (9*d*x)/2))/32 - (19*A*sin((11*c)/2 + (11*d*x)/2))/32 + (109*B*sin(c/2 + (d*x)/2))/16 + (35*B*sin((3*c)/2 + (3*d*x)/2))/16 - (43*B*sin((5*c)/2 + (5*d*x)/2))/32 + (59*B*sin((7*c)/2 + (7*d*x)/2))/32 - (47*B*sin((9*c)/2 + (9*d*x)/2))/32 - (B*sin((11*c)/2 + (11*d*x)/2))/32))/(2016*d*cos(c/2 - pi/4 + (d*x)/2)^3*cos(c/2 + pi/4 + (d*x)/2)^9)","B"
1003,1,124,105,0.107637,"\text{Not used}","int((cos(c + d*x)^7*(A + B*sin(c + d*x)))/(a + a*sin(c + d*x)),x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^2\,\left(A-B\right)}{2\,a}+\frac{{\sin\left(c+d\,x\right)}^3\,\left(2\,A+B\right)}{3\,a}-\frac{{\sin\left(c+d\,x\right)}^5\,\left(A+2\,B\right)}{5\,a}+\frac{{\sin\left(c+d\,x\right)}^6\,\left(A-B\right)}{6\,a}+\frac{B\,{\sin\left(c+d\,x\right)}^7}{7\,a}-\frac{{\sin\left(c+d\,x\right)}^4\,\left(2\,A-2\,B\right)}{4\,a}-\frac{A\,\sin\left(c+d\,x\right)}{a}}{d}","Not used",1,"-((sin(c + d*x)^2*(A - B))/(2*a) + (sin(c + d*x)^3*(2*A + B))/(3*a) - (sin(c + d*x)^5*(A + 2*B))/(5*a) + (sin(c + d*x)^6*(A - B))/(6*a) + (B*sin(c + d*x)^7)/(7*a) - (sin(c + d*x)^4*(2*A - 2*B))/(4*a) - (A*sin(c + d*x))/a)/d","B"
1004,1,82,79,9.200796,"\text{Not used}","int((cos(c + d*x)^5*(A + B*sin(c + d*x)))/(a + a*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^4\,\left(A-B\right)}{4\,a}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(A-B\right)}{2\,a}+\frac{B\,{\sin\left(c+d\,x\right)}^5}{5\,a}+\frac{A\,\sin\left(c+d\,x\right)}{a}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(A+B\right)}{3\,a}}{d}","Not used",1,"((sin(c + d*x)^4*(A - B))/(4*a) - (sin(c + d*x)^2*(A - B))/(2*a) + (B*sin(c + d*x)^5)/(5*a) + (A*sin(c + d*x))/a - (sin(c + d*x)^3*(A + B))/(3*a))/d","B"
1005,1,47,57,0.076127,"\text{Not used}","int((cos(c + d*x)^3*(A + B*sin(c + d*x)))/(a + a*sin(c + d*x)),x)","\frac{\sin\left(c+d\,x\right)\,\left(6\,A-3\,A\,\sin\left(c+d\,x\right)+3\,B\,\sin\left(c+d\,x\right)-2\,B\,{\sin\left(c+d\,x\right)}^2\right)}{6\,a\,d}","Not used",1,"(sin(c + d*x)*(6*A - 3*A*sin(c + d*x) + 3*B*sin(c + d*x) - 2*B*sin(c + d*x)^2))/(6*a*d)","B"
1006,1,36,36,9.232574,"\text{Not used}","int((cos(c + d*x)*(A + B*sin(c + d*x)))/(a + a*sin(c + d*x)),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(A-B\right)}{a\,d}+\frac{B\,\sin\left(c+d\,x\right)}{a\,d}","Not used",1,"(log(sin(c + d*x) + 1)*(A - B))/(a*d) + (B*sin(c + d*x))/(a*d)","B"
1007,1,43,45,0.102794,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(A+B\right)}{2\,a\,d}-\frac{\frac{A}{2}-\frac{B}{2}}{d\,\left(a+a\,\sin\left(c+d\,x\right)\right)}","Not used",1,"(atanh(sin(c + d*x))*(A + B))/(2*a*d) - (A/2 - B/2)/(d*(a + a*sin(c + d*x)))","B"
1008,1,96,91,0.127659,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{\left(\frac{3\,A}{8}+\frac{B}{8}\right)\,{\sin\left(c+d\,x\right)}^2+\left(\frac{3\,A}{8}+\frac{B}{8}\right)\,\sin\left(c+d\,x\right)-\frac{A}{4}+\frac{B}{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)}+\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(3\,A+B\right)}{8\,a\,d}","Not used",1,"(B/4 - A/4 + sin(c + d*x)*((3*A)/8 + B/8) + sin(c + d*x)^2*((3*A)/8 + B/8))/(d*(a + a*sin(c + d*x) - a*sin(c + d*x)^2 - a*sin(c + d*x)^3)) + (atanh(sin(c + d*x))*(3*A + B))/(8*a*d)","B"
1009,1,151,146,9.183874,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(5\,A+B\right)}{16\,a\,d}-\frac{\left(\frac{5\,A}{16}+\frac{B}{16}\right)\,{\sin\left(c+d\,x\right)}^4+\left(\frac{5\,A}{16}+\frac{B}{16}\right)\,{\sin\left(c+d\,x\right)}^3+\left(-\frac{25\,A}{48}-\frac{5\,B}{48}\right)\,{\sin\left(c+d\,x\right)}^2+\left(-\frac{25\,A}{48}-\frac{5\,B}{48}\right)\,\sin\left(c+d\,x\right)+\frac{A}{6}-\frac{B}{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,"(atanh(sin(c + d*x))*(5*A + B))/(16*a*d) - (A/6 - B/6 - sin(c + d*x)*((25*A)/48 + (5*B)/48) + sin(c + d*x)^3*((5*A)/16 + B/16) + sin(c + d*x)^4*((5*A)/16 + B/16) - sin(c + d*x)^2*((25*A)/48 + (5*B)/48))/(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"
1010,1,206,205,9.346790,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^7*(a + a*sin(c + d*x))),x)","\frac{\left(\frac{35\,A}{128}+\frac{5\,B}{128}\right)\,{\sin\left(c+d\,x\right)}^6+\left(\frac{35\,A}{128}+\frac{5\,B}{128}\right)\,{\sin\left(c+d\,x\right)}^5+\left(-\frac{35\,A}{48}-\frac{5\,B}{48}\right)\,{\sin\left(c+d\,x\right)}^4+\left(-\frac{35\,A}{48}-\frac{5\,B}{48}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{77\,A}{128}+\frac{11\,B}{128}\right)\,{\sin\left(c+d\,x\right)}^2+\left(\frac{77\,A}{128}+\frac{11\,B}{128}\right)\,\sin\left(c+d\,x\right)-\frac{A}{8}+\frac{B}{8}}{d\,\left(-a\,{\sin\left(c+d\,x\right)}^7-a\,{\sin\left(c+d\,x\right)}^6+3\,a\,{\sin\left(c+d\,x\right)}^5+3\,a\,{\sin\left(c+d\,x\right)}^4-3\,a\,{\sin\left(c+d\,x\right)}^3-3\,a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)+a\right)}+\frac{5\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(7\,A+B\right)}{128\,a\,d}","Not used",1,"(B/8 - A/8 + sin(c + d*x)*((77*A)/128 + (11*B)/128) - sin(c + d*x)^3*((35*A)/48 + (5*B)/48) - sin(c + d*x)^4*((35*A)/48 + (5*B)/48) + sin(c + d*x)^5*((35*A)/128 + (5*B)/128) + sin(c + d*x)^6*((35*A)/128 + (5*B)/128) + sin(c + d*x)^2*((77*A)/128 + (11*B)/128))/(d*(a + a*sin(c + d*x) - 3*a*sin(c + d*x)^2 - 3*a*sin(c + d*x)^3 + 3*a*sin(c + d*x)^4 + 3*a*sin(c + d*x)^5 - a*sin(c + d*x)^6 - a*sin(c + d*x)^7)) + (5*atanh(sin(c + d*x))*(7*A + B))/(128*a*d)","B"
1011,1,98,79,0.075015,"\text{Not used}","int((cos(c + d*x)^7*(A + B*sin(c + d*x)))/(a + a*sin(c + d*x))^2,x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^5\,\left(A-2\,B\right)}{5\,a^2}-\frac{A\,{\sin\left(c+d\,x\right)}^4}{2\,a^2}+\frac{2\,B\,{\sin\left(c+d\,x\right)}^3}{3\,a^2}+\frac{B\,{\sin\left(c+d\,x\right)}^6}{6\,a^2}+\frac{{\sin\left(c+d\,x\right)}^2\,\left(2\,A-B\right)}{2\,a^2}-\frac{A\,\sin\left(c+d\,x\right)}{a^2}}{d}","Not used",1,"-((sin(c + d*x)^5*(A - 2*B))/(5*a^2) - (A*sin(c + d*x)^4)/(2*a^2) + (2*B*sin(c + d*x)^3)/(3*a^2) + (B*sin(c + d*x)^6)/(6*a^2) + (sin(c + d*x)^2*(2*A - B))/(2*a^2) - (A*sin(c + d*x))/a^2)/d","B"
1012,1,68,51,9.122295,"\text{Not used}","int((cos(c + d*x)^5*(A + B*sin(c + d*x)))/(a + a*sin(c + d*x))^2,x)","\frac{\frac{{\sin\left(c+d\,x\right)}^3\,\left(A-2\,B\right)}{3\,a^2}+\frac{B\,{\sin\left(c+d\,x\right)}^4}{4\,a^2}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(2\,A-B\right)}{2\,a^2}+\frac{A\,\sin\left(c+d\,x\right)}{a^2}}{d}","Not used",1,"((sin(c + d*x)^3*(A - 2*B))/(3*a^2) + (B*sin(c + d*x)^4)/(4*a^2) - (sin(c + d*x)^2*(2*A - B))/(2*a^2) + (A*sin(c + d*x))/a^2)/d","B"
1013,1,61,66,0.072903,"\text{Not used}","int((cos(c + d*x)^3*(A + B*sin(c + d*x)))/(a + a*sin(c + d*x))^2,x)","-\frac{2\,A\,\sin\left(c+d\,x\right)-4\,B\,\sin\left(c+d\,x\right)+B\,{\sin\left(c+d\,x\right)}^2-4\,A\,\ln\left(\sin\left(c+d\,x\right)+1\right)+4\,B\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{2\,a^2\,d}","Not used",1,"-(2*A*sin(c + d*x) - 4*B*sin(c + d*x) + B*sin(c + d*x)^2 - 4*A*log(sin(c + d*x) + 1) + 4*B*log(sin(c + d*x) + 1))/(2*a^2*d)","B"
1014,1,41,44,0.055881,"\text{Not used}","int((cos(c + d*x)*(A + B*sin(c + d*x)))/(a + a*sin(c + d*x))^2,x)","\frac{B\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^2\,d}-\frac{A-B}{a^2\,d\,\left(\sin\left(c+d\,x\right)+1\right)}","Not used",1,"(B*log(sin(c + d*x) + 1))/(a^2*d) - (A - B)/(a^2*d*(sin(c + d*x) + 1))","B"
1015,1,71,71,9.247590,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(A+B\right)}{4\,a^2\,d}-\frac{\frac{A}{2}+\sin\left(c+d\,x\right)\,\left(\frac{A}{4}+\frac{B}{4}\right)}{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))*(A + B))/(4*a^2*d) - (A/2 + sin(c + d*x)*(A/4 + B/4))/(d*(2*a^2*sin(c + d*x) + a^2 + a^2*sin(c + d*x)^2))","B"
1016,1,121,123,0.150728,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{\left(\frac{A}{4}+\frac{B}{8}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{A}{2}+\frac{B}{4}\right)\,{\sin\left(c+d\,x\right)}^2+\left(\frac{A}{12}+\frac{B}{24}\right)\,\sin\left(c+d\,x\right)-\frac{A}{3}+\frac{B}{12}}{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)\,\left(2\,A+B\right)}{8\,a^2\,d}","Not used",1,"(B/12 - A/3 + sin(c + d*x)*(A/12 + B/24) + sin(c + d*x)^2*(A/2 + B/4) + sin(c + d*x)^3*(A/4 + B/8))/(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))*(2*A + B))/(8*a^2*d)","B"
1017,1,193,179,9.498800,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^5*(a + a*sin(c + d*x))^2),x)","\frac{\left(-\frac{15\,A}{64}-\frac{5\,B}{64}\right)\,{\sin\left(c+d\,x\right)}^5+\left(-\frac{15\,A}{32}-\frac{5\,B}{32}\right)\,{\sin\left(c+d\,x\right)}^4+\left(\frac{5\,A}{32}+\frac{5\,B}{96}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{25\,A}{32}+\frac{25\,B}{96}\right)\,{\sin\left(c+d\,x\right)}^2+\left(\frac{17\,A}{64}+\frac{17\,B}{192}\right)\,\sin\left(c+d\,x\right)-\frac{A}{4}+\frac{B}{12}}{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)}+\frac{5\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(3\,A+B\right)}{64\,a^2\,d}","Not used",1,"(B/12 - A/4 + sin(c + d*x)*((17*A)/64 + (17*B)/192) - sin(c + d*x)^4*((15*A)/32 + (5*B)/32) + sin(c + d*x)^3*((5*A)/32 + (5*B)/96) - sin(c + d*x)^5*((15*A)/64 + (5*B)/64) + sin(c + d*x)^2*((25*A)/32 + (25*B)/96))/(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)) + (5*atanh(sin(c + d*x))*(3*A + B))/(64*a^2*d)","B"
1018,1,240,236,9.596729,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^7*(a + a*sin(c + d*x))^2),x)","\frac{\left(\frac{7\,A}{32}+\frac{7\,B}{128}\right)\,{\sin\left(c+d\,x\right)}^7+\left(\frac{7\,A}{16}+\frac{7\,B}{64}\right)\,{\sin\left(c+d\,x\right)}^6+\left(-\frac{35\,A}{96}-\frac{35\,B}{384}\right)\,{\sin\left(c+d\,x\right)}^5+\left(-\frac{7\,A}{6}-\frac{7\,B}{24}\right)\,{\sin\left(c+d\,x\right)}^4+\left(-\frac{49\,A}{480}-\frac{49\,B}{1920}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{77\,A}{80}+\frac{77\,B}{320}\right)\,{\sin\left(c+d\,x\right)}^2+\left(\frac{61\,A}{160}+\frac{61\,B}{640}\right)\,\sin\left(c+d\,x\right)-\frac{A}{5}+\frac{3\,B}{40}}{d\,\left(-a^2\,{\sin\left(c+d\,x\right)}^8-2\,a^2\,{\sin\left(c+d\,x\right)}^7+2\,a^2\,{\sin\left(c+d\,x\right)}^6+6\,a^2\,{\sin\left(c+d\,x\right)}^5-6\,a^2\,{\sin\left(c+d\,x\right)}^3-2\,a^2\,{\sin\left(c+d\,x\right)}^2+2\,a^2\,\sin\left(c+d\,x\right)+a^2\right)}+\frac{7\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(4\,A+B\right)}{128\,a^2\,d}","Not used",1,"((3*B)/40 - A/5 + sin(c + d*x)*((61*A)/160 + (61*B)/640) - sin(c + d*x)^4*((7*A)/6 + (7*B)/24) + sin(c + d*x)^6*((7*A)/16 + (7*B)/64) + sin(c + d*x)^7*((7*A)/32 + (7*B)/128) - sin(c + d*x)^5*((35*A)/96 + (35*B)/384) + sin(c + d*x)^2*((77*A)/80 + (77*B)/320) - sin(c + d*x)^3*((49*A)/480 + (49*B)/1920))/(d*(2*a^2*sin(c + d*x) + a^2 - 2*a^2*sin(c + d*x)^2 - 6*a^2*sin(c + d*x)^3 + 6*a^2*sin(c + d*x)^5 + 2*a^2*sin(c + d*x)^6 - 2*a^2*sin(c + d*x)^7 - a^2*sin(c + d*x)^8)) + (7*atanh(sin(c + d*x))*(4*A + B))/(128*a^2*d)","B"
1019,0,-1,170,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^p\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((g*cos(e + f*x))^p*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m, x)","F"
1020,1,783,159,17.898948,"\text{Not used}","int(cos(e + f*x)^7*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","-{\mathrm{e}}^{-e\,8{}\mathrm{i}-f\,x\,8{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(-\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\left(786432\,A-58800\,B+237056\,A\,m+53644\,B\,m+32320\,A\,m^2+2512\,A\,m^3+80\,A\,m^4+4814\,B\,m^2+332\,B\,m^3+10\,B\,m^4\right)}{256\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}+\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\left(23520\,B-8448\,A\,m+17864\,B\,m-4320\,A\,m^2-600\,A\,m^3-24\,A\,m^4+3956\,B\,m^2+208\,B\,m^3+4\,B\,m^4\right)}{128\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}-\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(77184\,A\,m-47040\,B-35728\,B\,m+20112\,A\,m^2+1788\,A\,m^3+60\,A\,m^4-376\,B\,m^2+76\,B\,m^3+4\,B\,m^4\right)}{128\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}+\frac{B\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(8\,e+8\,f\,x\right)\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}{128\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}+\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\left(A\,8{}\mathrm{i}+A\,m\,1{}\mathrm{i}+B\,m\,1{}\mathrm{i}\right)\,\left(5\,m^3+123\,m^2+706\,m+1176\right)\,1{}\mathrm{i}}{64\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}+\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\left(A\,8{}\mathrm{i}+A\,m\,1{}\mathrm{i}+B\,m\,1{}\mathrm{i}\right)\,\left(3\,m^3+93\,m^2+1070\,m+1960\right)\,3{}\mathrm{i}}{64\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}+\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\left(m^2+9\,m+20\right)\,\left(84\,B-8\,A\,m+26\,B\,m-A\,m^2+B\,m^2\right)}{32\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}+\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\left(A\,8{}\mathrm{i}+A\,m\,1{}\mathrm{i}+B\,m\,1{}\mathrm{i}\right)\,\left(m^3+15\,m^2+74\,m+120\right)\,1{}\mathrm{i}}{64\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}+\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(A\,8{}\mathrm{i}+A\,m\,1{}\mathrm{i}+B\,m\,1{}\mathrm{i}\right)\,\left(5\,m^3+171\,m^2+2578\,m+29400\right)\,1{}\mathrm{i}}{64\,f\,\left(m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720\right)}\right)","Not used",1,"-exp(- e*8i - f*x*8i)*(a + a*sin(e + f*x))^m*((exp(e*8i + f*x*8i)*cos(4*e + 4*f*x)*(23520*B - 8448*A*m + 17864*B*m - 4320*A*m^2 - 600*A*m^3 - 24*A*m^4 + 3956*B*m^2 + 208*B*m^3 + 4*B*m^4))/(128*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)) - (exp(e*8i + f*x*8i)*(786432*A - 58800*B + 237056*A*m + 53644*B*m + 32320*A*m^2 + 2512*A*m^3 + 80*A*m^4 + 4814*B*m^2 + 332*B*m^3 + 10*B*m^4))/(256*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)) - (exp(e*8i + f*x*8i)*cos(2*e + 2*f*x)*(77184*A*m - 47040*B - 35728*B*m + 20112*A*m^2 + 1788*A*m^3 + 60*A*m^4 - 376*B*m^2 + 76*B*m^3 + 4*B*m^4))/(128*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)) + (B*exp(e*8i + f*x*8i)*cos(8*e + 8*f*x)*(638*m + 179*m^2 + 22*m^3 + m^4 + 840))/(128*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)) + (exp(e*8i + f*x*8i)*sin(5*e + 5*f*x)*(A*8i + A*m*1i + B*m*1i)*(706*m + 123*m^2 + 5*m^3 + 1176)*1i)/(64*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)) + (exp(e*8i + f*x*8i)*sin(3*e + 3*f*x)*(A*8i + A*m*1i + B*m*1i)*(1070*m + 93*m^2 + 3*m^3 + 1960)*3i)/(64*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)) + (exp(e*8i + f*x*8i)*cos(6*e + 6*f*x)*(9*m + m^2 + 20)*(84*B - 8*A*m + 26*B*m - A*m^2 + B*m^2))/(32*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)) + (exp(e*8i + f*x*8i)*sin(7*e + 7*f*x)*(A*8i + A*m*1i + B*m*1i)*(74*m + 15*m^2 + m^3 + 120)*1i)/(64*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)) + (exp(e*8i + f*x*8i)*sin(e + f*x)*(A*8i + A*m*1i + B*m*1i)*(2578*m + 171*m^2 + 5*m^3 + 29400)*1i)/(64*f*(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720)))","B"
1021,1,517,123,15.820424,"\text{Not used}","int(cos(e + f*x)^5*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","-{\mathrm{e}}^{-e\,6{}\mathrm{i}-f\,x\,6{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(-\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(12288\,A-1200\,B+4016\,A\,m+1108\,B\,m+472\,A\,m^2+24\,A\,m^3+88\,B\,m^2+4\,B\,m^3\right)}{64\,f\,\left(m^4+18\,m^3+119\,m^2+342\,m+360\right)}-\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(1056\,A\,m-900\,B-705\,B\,m+272\,A\,m^2+16\,A\,m^3-4\,B\,m^2+B\,m^3\right)}{32\,f\,\left(m^4+18\,m^3+119\,m^2+342\,m+360\right)}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\left(m+3\right)\,\left(60\,B-12\,A\,m+27\,B\,m-2\,A\,m^2+B\,m^2\right)}{16\,f\,\left(m^4+18\,m^3+119\,m^2+342\,m+360\right)}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(A\,6{}\mathrm{i}+A\,m\,1{}\mathrm{i}+B\,m\,1{}\mathrm{i}\right)\,\left(m^2+23\,m+300\right)\,1{}\mathrm{i}}{8\,f\,\left(m^4+18\,m^3+119\,m^2+342\,m+360\right)}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\left(A\,6{}\mathrm{i}+A\,m\,1{}\mathrm{i}+B\,m\,1{}\mathrm{i}\right)\,\left(m^2+7\,m+12\right)\,1{}\mathrm{i}}{16\,f\,\left(m^4+18\,m^3+119\,m^2+342\,m+360\right)}+\frac{B\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\left(m^3+12\,m^2+47\,m+60\right)}{32\,f\,\left(m^4+18\,m^3+119\,m^2+342\,m+360\right)}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\left(A\,6{}\mathrm{i}+A\,m\,1{}\mathrm{i}+B\,m\,1{}\mathrm{i}\right)\,\left(3\,m^2+53\,m+100\right)\,1{}\mathrm{i}}{16\,f\,\left(m^4+18\,m^3+119\,m^2+342\,m+360\right)}\right)","Not used",1,"-exp(- e*6i - f*x*6i)*(a + a*sin(e + f*x))^m*((exp(e*6i + f*x*6i)*cos(4*e + 4*f*x)*(m + 3)*(60*B - 12*A*m + 27*B*m - 2*A*m^2 + B*m^2))/(16*f*(342*m + 119*m^2 + 18*m^3 + m^4 + 360)) - (exp(e*6i + f*x*6i)*cos(2*e + 2*f*x)*(1056*A*m - 900*B - 705*B*m + 272*A*m^2 + 16*A*m^3 - 4*B*m^2 + B*m^3))/(32*f*(342*m + 119*m^2 + 18*m^3 + m^4 + 360)) - (exp(e*6i + f*x*6i)*(12288*A - 1200*B + 4016*A*m + 1108*B*m + 472*A*m^2 + 24*A*m^3 + 88*B*m^2 + 4*B*m^3))/(64*f*(342*m + 119*m^2 + 18*m^3 + m^4 + 360)) + (exp(e*6i + f*x*6i)*sin(e + f*x)*(A*6i + A*m*1i + B*m*1i)*(23*m + m^2 + 300)*1i)/(8*f*(342*m + 119*m^2 + 18*m^3 + m^4 + 360)) + (exp(e*6i + f*x*6i)*sin(5*e + 5*f*x)*(A*6i + A*m*1i + B*m*1i)*(7*m + m^2 + 12)*1i)/(16*f*(342*m + 119*m^2 + 18*m^3 + m^4 + 360)) + (B*exp(e*6i + f*x*6i)*cos(6*e + 6*f*x)*(47*m + 12*m^2 + m^3 + 60))/(32*f*(342*m + 119*m^2 + 18*m^3 + m^4 + 360)) + (exp(e*6i + f*x*6i)*sin(3*e + 3*f*x)*(A*6i + A*m*1i + B*m*1i)*(53*m + 3*m^2 + 100)*1i)/(16*f*(342*m + 119*m^2 + 18*m^3 + m^4 + 360)))","B"
1022,1,272,93,11.741461,"\text{Not used}","int(cos(e + f*x)^3*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(128\,A-18\,B+48\,A\,m+17\,B\,m+144\,A\,\sin\left(e+f\,x\right)-24\,B\,\cos\left(2\,e+2\,f\,x\right)-6\,B\,\cos\left(4\,e+4\,f\,x\right)+4\,A\,m^2+B\,m^2+16\,A\,\sin\left(3\,e+3\,f\,x\right)+4\,A\,m^2\,\cos\left(2\,e+2\,f\,x\right)-B\,m^2\,\cos\left(4\,e+4\,f\,x\right)+2\,A\,m^2\,\sin\left(3\,e+3\,f\,x\right)+2\,B\,m^2\,\sin\left(3\,e+3\,f\,x\right)+44\,A\,m\,\sin\left(e+f\,x\right)+36\,B\,m\,\sin\left(e+f\,x\right)+16\,A\,m\,\cos\left(2\,e+2\,f\,x\right)-20\,B\,m\,\cos\left(2\,e+2\,f\,x\right)-5\,B\,m\,\cos\left(4\,e+4\,f\,x\right)+12\,A\,m\,\sin\left(3\,e+3\,f\,x\right)+2\,A\,m^2\,\sin\left(e+f\,x\right)+4\,B\,m\,\sin\left(3\,e+3\,f\,x\right)+2\,B\,m^2\,\sin\left(e+f\,x\right)\right)}{8\,f\,\left(m^3+9\,m^2+26\,m+24\right)}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(128*A - 18*B + 48*A*m + 17*B*m + 144*A*sin(e + f*x) - 24*B*cos(2*e + 2*f*x) - 6*B*cos(4*e + 4*f*x) + 4*A*m^2 + B*m^2 + 16*A*sin(3*e + 3*f*x) + 4*A*m^2*cos(2*e + 2*f*x) - B*m^2*cos(4*e + 4*f*x) + 2*A*m^2*sin(3*e + 3*f*x) + 2*B*m^2*sin(3*e + 3*f*x) + 44*A*m*sin(e + f*x) + 36*B*m*sin(e + f*x) + 16*A*m*cos(2*e + 2*f*x) - 20*B*m*cos(2*e + 2*f*x) - 5*B*m*cos(4*e + 4*f*x) + 12*A*m*sin(3*e + 3*f*x) + 2*A*m^2*sin(e + f*x) + 4*B*m*sin(3*e + 3*f*x) + 2*B*m^2*sin(e + f*x)))/(8*f*(26*m + 9*m^2 + m^3 + 24))","B"
1023,1,99,59,10.166005,"\text{Not used}","int(cos(e + f*x)*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(4\,A-B+2\,A\,m+B\,m+4\,A\,\sin\left(e+f\,x\right)+B\,\left(2\,{\sin\left(e+f\,x\right)}^2-1\right)+2\,A\,m\,\sin\left(e+f\,x\right)+2\,B\,m\,\sin\left(e+f\,x\right)+B\,m\,\left(2\,{\sin\left(e+f\,x\right)}^2-1\right)\right)}{2\,f\,\left(m^2+3\,m+2\right)}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(4*A - B + 2*A*m + B*m + 4*A*sin(e + f*x) + B*(2*sin(e + f*x)^2 - 1) + 2*A*m*sin(e + f*x) + 2*B*m*sin(e + f*x) + B*m*(2*sin(e + f*x)^2 - 1)))/(2*f*(3*m + m^2 + 2))","B"
1024,0,-1,80,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\cos\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x), x)","F"
1025,0,-1,100,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^3,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\cos\left(e+f\,x\right)}^3} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^3, x)","F"
1026,0,-1,104,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^5,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\cos\left(e+f\,x\right)}^5} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^5, x)","F"
1027,0,-1,129,0.000000,"\text{Not used}","int(cos(e + f*x)^6*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\int {\cos\left(e+f\,x\right)}^6\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cos(e + f*x)^6*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m, x)","F"
1028,0,-1,129,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\int {\cos\left(e+f\,x\right)}^4\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cos(e + f*x)^4*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m, x)","F"
1029,0,-1,127,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\int {\cos\left(e+f\,x\right)}^2\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cos(e + f*x)^2*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m, x)","F"
1030,0,-1,123,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\cos\left(e+f\,x\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^2, x)","F"
1031,0,-1,135,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^4,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\cos\left(e+f\,x\right)}^4} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^4, x)","F"
1032,0,-1,135,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^6,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\cos\left(e+f\,x\right)}^6} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/cos(e + f*x)^6, x)","F"
1033,1,441,239,18.419291,"\text{Not used}","int(((g*cos(e + f*x))^p*(A + B*sin(e + f*x)))/(c - c*sin(e + f*x))^(p + 4),x)","\frac{\cos\left(e+f\,x\right)\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^p\,\left(A\,168{}\mathrm{i}-B\,84{}\mathrm{i}+A\,p\,170{}\mathrm{i}-B\,p\,48{}\mathrm{i}+A\,p^2\,48{}\mathrm{i}+A\,p^3\,4{}\mathrm{i}-B\,p^2\,6{}\mathrm{i}\right)}{4\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{p+4}\,\left(p^4\,1{}\mathrm{i}+p^3\,16{}\mathrm{i}+p^2\,86{}\mathrm{i}+p\,176{}\mathrm{i}+105{}\mathrm{i}\right)}-\frac{\sin\left(4\,e+4\,f\,x\right)\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^p\,\left(4\,B-3\,A+B\,p\right)\,1{}\mathrm{i}}{4\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{p+4}\,\left(p^4\,1{}\mathrm{i}+p^3\,16{}\mathrm{i}+p^2\,86{}\mathrm{i}+p\,176{}\mathrm{i}+105{}\mathrm{i}\right)}+\frac{\cos\left(3\,e+3\,f\,x\right)\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^p\,\left(p+4\right)\,\left(-A\,3{}\mathrm{i}+B\,4{}\mathrm{i}+B\,p\,1{}\mathrm{i}\right)}{2\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{p+4}\,\left(p^4\,1{}\mathrm{i}+p^3\,16{}\mathrm{i}+p^2\,86{}\mathrm{i}+p\,176{}\mathrm{i}+105{}\mathrm{i}\right)}+\frac{\sin\left(2\,e+2\,f\,x\right)\,{\left(g\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}}{2}\right)\right)}^p\,\left(4\,B-3\,A+B\,p\right)\,\left(p^2+8\,p+14\right)\,1{}\mathrm{i}}{2\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{p+4}\,\left(p^4\,1{}\mathrm{i}+p^3\,16{}\mathrm{i}+p^2\,86{}\mathrm{i}+p\,176{}\mathrm{i}+105{}\mathrm{i}\right)}","Not used",1,"(cos(e + f*x)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^p*(A*168i - B*84i + A*p*170i - B*p*48i + A*p^2*48i + A*p^3*4i - B*p^2*6i))/(4*f*(c - c*sin(e + f*x))^(p + 4)*(p*176i + p^2*86i + p^3*16i + p^4*1i + 105i)) - (sin(4*e + 4*f*x)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^p*(4*B - 3*A + B*p)*1i)/(4*f*(c - c*sin(e + f*x))^(p + 4)*(p*176i + p^2*86i + p^3*16i + p^4*1i + 105i)) + (cos(3*e + 3*f*x)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^p*(p + 4)*(B*4i - A*3i + B*p*1i))/(2*f*(c - c*sin(e + f*x))^(p + 4)*(p*176i + p^2*86i + p^3*16i + p^4*1i + 105i)) + (sin(2*e + 2*f*x)*(g*(exp(- e*1i - f*x*1i)/2 + exp(e*1i + f*x*1i)/2))^p*(4*B - 3*A + B*p)*(8*p + p^2 + 14)*1i)/(2*f*(c - c*sin(e + f*x))^(p + 4)*(p*176i + p^2*86i + p^3*16i + p^4*1i + 105i))","B"
1034,1,234,168,11.939507,"\text{Not used}","int(((g*cos(e + f*x))^p*(A + B*sin(e + f*x)))/(c - c*sin(e + f*x))^(p + 3),x)","-\frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,\left(30\,A\,\cos\left(e+f\,x\right)-15\,B\,\cos\left(e+f\,x\right)-2\,A\,\cos\left(3\,e+3\,f\,x\right)+3\,B\,\cos\left(3\,e+3\,f\,x\right)-12\,A\,\sin\left(2\,e+2\,f\,x\right)+18\,B\,\sin\left(2\,e+2\,f\,x\right)+2\,B\,p^2\,\sin\left(2\,e+2\,f\,x\right)+24\,A\,p\,\cos\left(e+f\,x\right)-5\,B\,p\,\cos\left(e+f\,x\right)+4\,A\,p^2\,\cos\left(e+f\,x\right)+B\,p\,\cos\left(3\,e+3\,f\,x\right)-4\,A\,p\,\sin\left(2\,e+2\,f\,x\right)+12\,B\,p\,\sin\left(2\,e+2\,f\,x\right)\right)}{c^3\,f\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^p\,\left(p^3+9\,p^2+23\,p+15\right)\,\left(15\,\sin\left(e+f\,x\right)+6\,\cos\left(2\,e+2\,f\,x\right)-\sin\left(3\,e+3\,f\,x\right)-10\right)}","Not used",1,"-((g*cos(e + f*x))^p*(30*A*cos(e + f*x) - 15*B*cos(e + f*x) - 2*A*cos(3*e + 3*f*x) + 3*B*cos(3*e + 3*f*x) - 12*A*sin(2*e + 2*f*x) + 18*B*sin(2*e + 2*f*x) + 2*B*p^2*sin(2*e + 2*f*x) + 24*A*p*cos(e + f*x) - 5*B*p*cos(e + f*x) + 4*A*p^2*cos(e + f*x) + B*p*cos(3*e + 3*f*x) - 4*A*p*sin(2*e + 2*f*x) + 12*B*p*sin(2*e + 2*f*x)))/(c^3*f*(-c*(sin(e + f*x) - 1))^p*(23*p + 9*p^2 + p^3 + 15)*(15*sin(e + f*x) + 6*cos(2*e + 2*f*x) - sin(3*e + 3*f*x) - 10))","B"
1035,1,129,102,1.278908,"\text{Not used}","int(((g*cos(e + f*x))^p*(A + B*sin(e + f*x)))/(c - c*sin(e + f*x))^(p + 2),x)","-\frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,\left(4\,A\,\cos\left(e+f\,x\right)-2\,B\,\cos\left(e+f\,x\right)-A\,\sin\left(2\,e+2\,f\,x\right)+2\,B\,\sin\left(2\,e+2\,f\,x\right)+2\,A\,p\,\cos\left(e+f\,x\right)+B\,p\,\sin\left(2\,e+2\,f\,x\right)\right)}{c^2\,f\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^p\,\left(4\,\sin\left(e+f\,x\right)+\cos\left(2\,e+2\,f\,x\right)-3\right)\,\left(p^2+4\,p+3\right)}","Not used",1,"-((g*cos(e + f*x))^p*(4*A*cos(e + f*x) - 2*B*cos(e + f*x) - A*sin(2*e + 2*f*x) + 2*B*sin(2*e + 2*f*x) + 2*A*p*cos(e + f*x) + B*p*sin(2*e + 2*f*x)))/(c^2*f*(-c*(sin(e + f*x) - 1))^p*(4*sin(e + f*x) + cos(2*e + 2*f*x) - 3)*(4*p + p^2 + 3))","B"
1036,0,-1,151,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^p*(A + B*sin(e + f*x)))/(c - c*sin(e + f*x))^(p + 1),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,\left(A+B\,\sin\left(e+f\,x\right)\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{p+1}} \,d x","Not used",1,"int(((g*cos(e + f*x))^p*(A + B*sin(e + f*x)))/(c - c*sin(e + f*x))^(p + 1), x)","F"
1037,0,-1,147,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^p*(A + B*sin(e + f*x)))/(c - c*sin(e + f*x))^p,x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,\left(A+B\,\sin\left(e+f\,x\right)\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^p} \,d x","Not used",1,"int(((g*cos(e + f*x))^p*(A + B*sin(e + f*x)))/(c - c*sin(e + f*x))^p, x)","F"
1038,0,-1,160,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p*(A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1 - p),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^p\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{1-p} \,d x","Not used",1,"int((g*cos(e + f*x))^p*(A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1 - p), x)","F"
1039,0,-1,163,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p*(A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(2 - p),x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^p\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{2-p} \,d x","Not used",1,"int((g*cos(e + f*x))^p*(A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(2 - p), x)","F"
1040,1,33,32,9.704765,"\text{Not used}","int((g*cos(e + f*x))^p*(A*m - A*sin(e + f*x)*(m + p + 1))*(a + a*sin(e + f*x))^m,x)","\frac{A\,\cos\left(e+f\,x\right)\,{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m}{f}","Not used",1,"(A*cos(e + f*x)*(g*cos(e + f*x))^p*(a*(sin(e + f*x) + 1))^m)/f","B"
1041,1,35,34,0.515723,"\text{Not used}","int((g*cos(e + f*x))^p*(A*m + A*sin(e + f*x)*(m + p + 1))*(a - a*sin(e + f*x))^m,x)","-\frac{A\,\cos\left(e+f\,x\right)\,{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(-a\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m}{f}","Not used",1,"-(A*cos(e + f*x)*(g*cos(e + f*x))^p*(-a*(sin(e + f*x) - 1))^m)/f","B"
1042,0,-1,168,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((g*cos(e + f*x))^p*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
1043,0,-1,149,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((g*cos(e + f*x))^p*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n, x)","F"
1044,0,-1,145,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n,x)","\int {\left(g\,\cos\left(e+f\,x\right)\right)}^p\,\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((g*cos(e + f*x))^p*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n, x)","F"
1045,0,-1,149,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^p*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*cos(e + f*x))^p*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)), x)","F"
1046,0,-1,149,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^p*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((g*cos(e + f*x))^p*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2, x)","F"
1047,0,-1,149,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^p*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^3,x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((g*cos(e + f*x))^p*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^3, x)","F"
1048,0,-1,149,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^p*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^4,x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^4} \,d x","Not used",1,"int(((g*cos(e + f*x))^p*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^4, x)","F"
1049,0,-1,175,0.000000,"\text{Not used}","int((g/cos(e + f*x))^p*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int {\left(\frac{g}{\cos\left(e+f\,x\right)}\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((g/cos(e + f*x))^p*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
1050,1,153,105,12.982626,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^3*(a + b*sin(c + d*x)),x)","\frac{b\,x}{16}-\frac{-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}-\frac{17\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{19\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}-\frac{19\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{17\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{4\,a}{15}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(b*x)/16 - ((4*a)/15 + (b*tan(c/2 + (d*x)/2))/8 + (8*a*tan(c/2 + (d*x)/2)^2)/5 + (8*a*tan(c/2 + (d*x)/2)^6)/3 + 4*a*tan(c/2 + (d*x)/2)^8 + (17*b*tan(c/2 + (d*x)/2)^3)/24 - (19*b*tan(c/2 + (d*x)/2)^5)/4 + (19*b*tan(c/2 + (d*x)/2)^7)/4 - (17*b*tan(c/2 + (d*x)/2)^9)/24 - (b*tan(c/2 + (d*x)/2)^11)/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
1051,1,125,81,12.891633,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^2*(a + b*sin(c + d*x)),x)","\frac{a\,x}{8}-\frac{-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\frac{3\,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)}^6-\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{4\,b}{15}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(a*x)/8 - ((4*b)/15 + (a*tan(c/2 + (d*x)/2))/4 - (3*a*tan(c/2 + (d*x)/2)^3)/2 + (3*a*tan(c/2 + (d*x)/2)^7)/2 - (a*tan(c/2 + (d*x)/2)^9)/4 + (4*b*tan(c/2 + (d*x)/2)^2)/3 - (4*b*tan(c/2 + (d*x)/2)^4)/3 + 4*b*tan(c/2 + (d*x)/2)^6)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
1052,1,125,65,12.661034,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)*(a + b*sin(c + d*x)),x)","\frac{b\,x}{8}-\frac{-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{2\,a}{3}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(b*x)/8 - ((2*a)/3 + (b*tan(c/2 + (d*x)/2))/4 + (2*a*tan(c/2 + (d*x)/2)^2)/3 + 2*a*tan(c/2 + (d*x)/2)^4 + 2*a*tan(c/2 + (d*x)/2)^6 - (7*b*tan(c/2 + (d*x)/2)^3)/4 + (7*b*tan(c/2 + (d*x)/2)^5)/4 - (b*tan(c/2 + (d*x)/2)^7)/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
1053,1,157,51,9.874046,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x)))/sin(c + d*x),x)","\frac{b\,\mathrm{atan}\left(\frac{b^2}{2\,a\,b-b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,b-b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{-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+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,a}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(b*atan(b^2/(2*a*b - b^2*tan(c/2 + (d*x)/2)) + (2*a*b*tan(c/2 + (d*x)/2))/(2*a*b - b^2*tan(c/2 + (d*x)/2))))/d + (2*a + b*tan(c/2 + (d*x)/2) + 2*a*tan(c/2 + (d*x)/2)^2 - b*tan(c/2 + (d*x)/2)^3)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) + (a*log(tan(c/2 + (d*x)/2)))/d","B"
1054,1,158,41,9.544823,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,b\,a}-\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,b\,a}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) + (b*log(tan(c/2 + (d*x)/2)))/d - (a - 4*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)/(d*(2*tan(c/2 + (d*x)/2) + 2*tan(c/2 + (d*x)/2)^3)) + (2*a*atan((4*a^2)/(4*a*b + 4*a^2*tan(c/2 + (d*x)/2)) - (4*a*b*tan(c/2 + (d*x)/2))/(4*a*b + 4*a^2*tan(c/2 + (d*x)/2))))/d","B"
1055,1,151,52,9.359886,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{b\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,d}-\frac{2\,b\,\mathrm{atan}\left(\frac{2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(2*d) - (b*cot(c/2 + (d*x)/2))/(2*d) - (a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(2*d) - (2*b*atan((2*b*cos(c/2 + (d*x)/2) + a*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2) - 2*b*sin(c/2 + (d*x)/2))))/d - (a*cot(c/2 + (d*x)/2)^2)/(8*d) + (a*tan(c/2 + (d*x)/2)^2)/(8*d)","B"
1056,1,111,52,9.308770,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x)))/sin(c + d*x)^4,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{3}\right)}{8\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*tan(c/2 + (d*x)/2))/(8*d) + (b*tan(c/2 + (d*x)/2)^2)/(8*d) - (b*log(tan(c/2 + (d*x)/2)))/(2*d) - (cot(c/2 + (d*x)/2)^3*(a/3 + b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))/(8*d)","B"
1057,1,112,74,9.327066,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x)))/sin(c + d*x)^5,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{a}{4}\right)}{16\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^4)/(64*d) - (b*tan(c/2 + (d*x)/2))/(8*d) + (b*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*log(tan(c/2 + (d*x)/2)))/(8*d) - (cot(c/2 + (d*x)/2)^4*(a/4 + (2*b*tan(c/2 + (d*x)/2))/3 - 2*b*tan(c/2 + (d*x)/2)^3))/(16*d)","B"
1058,1,143,90,9.332728,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x)))/sin(c + d*x)^6,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-2\,a\,{\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)}^2}{3}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}\right)}{32\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^3)/(96*d) - (a*tan(c/2 + (d*x)/2))/(16*d) + (a*tan(c/2 + (d*x)/2)^5)/(160*d) + (b*tan(c/2 + (d*x)/2)^4)/(64*d) - (b*log(tan(c/2 + (d*x)/2)))/(8*d) - (cot(c/2 + (d*x)/2)^5*(a/5 + (b*tan(c/2 + (d*x)/2))/2 + (a*tan(c/2 + (d*x)/2)^2)/3 - 2*a*tan(c/2 + (d*x)/2)^4))/(32*d)","B"
1059,1,233,190,12.973797,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^3*(a + b*sin(c + d*x))^2,x)","\frac{a\,b\,x}{8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{8\,a^2}{3}-\frac{16\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{8\,a^2}{5}+\frac{16\,b^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{20\,a^2}{3}+\frac{32\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{28\,a^2}{15}+\frac{16\,b^2}{15}\right)+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{4\,a^2}{15}+\frac{16\,b^2}{105}+\frac{5\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{97\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{97\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}-\frac{5\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+\frac{a\,b\,\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)}^7}","Not used",1,"(a*b*x)/8 - (tan(c/2 + (d*x)/2)^6*((8*a^2)/3 - (16*b^2)/3) + tan(c/2 + (d*x)/2)^4*((8*a^2)/5 + (16*b^2)/5) + tan(c/2 + (d*x)/2)^8*((20*a^2)/3 + (32*b^2)/3) + tan(c/2 + (d*x)/2)^2*((28*a^2)/15 + (16*b^2)/15) + 4*a^2*tan(c/2 + (d*x)/2)^10 + (4*a^2)/15 + (16*b^2)/105 + (5*a*b*tan(c/2 + (d*x)/2)^3)/3 - (97*a*b*tan(c/2 + (d*x)/2)^5)/12 + (97*a*b*tan(c/2 + (d*x)/2)^9)/12 - (5*a*b*tan(c/2 + (d*x)/2)^11)/3 - (a*b*tan(c/2 + (d*x)/2)^13)/4 + (a*b*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
1060,1,112,163,9.615050,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)^2*(a + b*sin(c + d*x))^2,x)","-\frac{\frac{15\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{2}+\frac{15\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{15\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{4}-\frac{5\,b^2\,\sin\left(6\,c+6\,d\,x\right)}{4}+60\,a\,b\,\cos\left(c+d\,x\right)+10\,a\,b\,\cos\left(3\,c+3\,d\,x\right)-6\,a\,b\,\cos\left(5\,c+5\,d\,x\right)-30\,a^2\,d\,x-15\,b^2\,d\,x}{240\,d}","Not used",1,"-((15*a^2*sin(4*c + 4*d*x))/2 + (15*b^2*sin(2*c + 2*d*x))/4 + (15*b^2*sin(4*c + 4*d*x))/4 - (5*b^2*sin(6*c + 6*d*x))/4 + 60*a*b*cos(c + d*x) + 10*a*b*cos(3*c + 3*d*x) - 6*a*b*cos(5*c + 5*d*x) - 30*a^2*d*x - 15*b^2*d*x)/(240*d)","B"
1061,1,180,106,12.772320,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)*(a + b*sin(c + d*x))^2,x)","\frac{a\,b\,x}{4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{4\,a^2}{3}+\frac{4\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{8\,a^2}{3}-\frac{4\,b^2}{3}\right)+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{2\,a^2}{3}+\frac{4\,b^2}{15}-3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}+\frac{a\,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)}^2+1\right)}^5}","Not used",1,"(a*b*x)/4 - (tan(c/2 + (d*x)/2)^6*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^2*((4*a^2)/3 + (4*b^2)/3) + tan(c/2 + (d*x)/2)^4*((8*a^2)/3 - (4*b^2)/3) + 2*a^2*tan(c/2 + (d*x)/2)^8 + (2*a^2)/3 + (4*b^2)/15 - 3*a*b*tan(c/2 + (d*x)/2)^3 + 3*a*b*tan(c/2 + (d*x)/2)^7 - (a*b*tan(c/2 + (d*x)/2)^9)/2 + (a*b*tan(c/2 + (d*x)/2))/2)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
1062,1,225,90,9.868098,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2-2\,b^2\right)+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2-\frac{2\,b^2}{3}-2\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{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\,a\,b\,\mathrm{atan}\left(\frac{4\,a^2\,b^2}{4\,a^3\,b-4\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{4\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^3\,b-4\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (tan(c/2 + (d*x)/2)^4*(2*a^2 - 2*b^2) + 4*a^2*tan(c/2 + (d*x)/2)^2 + 2*a^2 - (2*b^2)/3 - 2*a*b*tan(c/2 + (d*x)/2)^5 + 2*a*b*tan(c/2 + (d*x)/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*a*b*atan((4*a^2*b^2)/(4*a^3*b - 4*a^2*b^2*tan(c/2 + (d*x)/2)) + (4*a^3*b*tan(c/2 + (d*x)/2))/(4*a^3*b - 4*a^2*b^2*tan(c/2 + (d*x)/2))))/d","B"
1063,1,277,78,9.706964,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{b^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)-2\,a^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)+2\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a^2\,\cos\left(c+d\,x\right)-\frac{b^2\,\cos\left(c+d\,x\right)}{8}+\frac{b^2\,\cos\left(3\,c+3\,d\,x\right)}{8}-a\,b\,\sin\left(2\,c+2\,d\,x\right)}{d\,\sin\left(c+d\,x\right)}","Not used",1,"(b^2*atan((b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 4*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - b^2*sin(c/2 + (d*x)/2) + 4*a*b*cos(c/2 + (d*x)/2))) - 2*a^2*atan((b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 4*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - b^2*sin(c/2 + (d*x)/2) + 4*a*b*cos(c/2 + (d*x)/2))) + 2*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a^2*cos(c + d*x) - (b^2*cos(c + d*x))/8 + (b^2*cos(3*c + 3*d*x))/8 - a*b*sin(2*c + 2*d*x))/(d*sin(c + d*x))","B"
1064,1,397,89,10.198312,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{\cos\left(c+d\,x\right)\,\left(\frac{a^2}{2}-\frac{b^2}{4}\right)-\frac{b^2}{2}+\frac{a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}-\frac{b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{b^2\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{b^2\,\cos\left(3\,c+3\,d\,x\right)}{4}-2\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\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}{-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)-\frac{a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{4}+\frac{b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+a\,b\,\sin\left(2\,c+2\,d\,x\right)+2\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\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}{-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\cos\left(2\,c+2\,d\,x\right)}{d\,\left({\cos\left(c+d\,x\right)}^2-1\right)}","Not used",1,"(cos(c + d*x)*(a^2/2 - b^2/4) - b^2/2 + (a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 - (b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (b^2*cos(2*c + 2*d*x))/2 + (b^2*cos(3*c + 3*d*x))/4 - 2*a*b*atan((a^2*sin(c/2 + (d*x)/2) - 2*b^2*sin(c/2 + (d*x)/2) + 4*a*b*cos(c/2 + (d*x)/2))/(2*b^2*cos(c/2 + (d*x)/2) - a^2*cos(c/2 + (d*x)/2) + 4*a*b*sin(c/2 + (d*x)/2))) - (a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/4 + (b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + a*b*sin(2*c + 2*d*x) + 2*a*b*atan((a^2*sin(c/2 + (d*x)/2) - 2*b^2*sin(c/2 + (d*x)/2) + 4*a*b*cos(c/2 + (d*x)/2))/(2*b^2*cos(c/2 + (d*x)/2) - a^2*cos(c/2 + (d*x)/2) + 4*a*b*sin(c/2 + (d*x)/2)))*cos(2*c + 2*d*x))/(d*(cos(c + d*x)^2 - 1))","B"
1065,1,231,96,9.479700,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^2)/sin(c + d*x)^4,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}+\frac{a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{b^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,b\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (a^2*cot(c/2 + (d*x)/2)^3)/(24*d) + (a^2*cot(c/2 + (d*x)/2))/(8*d) - (b^2*cot(c/2 + (d*x)/2))/(2*d) - (a^2*tan(c/2 + (d*x)/2))/(8*d) + (b^2*tan(c/2 + (d*x)/2))/(2*d) - (2*b^2*atan((b*cos(c/2 + (d*x)/2) + a*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2))))/d - (a*b*cot(c/2 + (d*x)/2)^2)/(4*d) + (a*b*tan(c/2 + (d*x)/2)^2)/(4*d) - (a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
1066,1,165,123,9.328240,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^2)/sin(c + d*x)^5,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{a^2}{8}+\frac{b^2}{2}\right)}{d}+\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{4}-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{16\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,d}-\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^4)/(64*d) - (log(tan(c/2 + (d*x)/2))*(a^2/8 + b^2/2))/d + (b^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (cot(c/2 + (d*x)/2)^4*(2*b^2*tan(c/2 + (d*x)/2)^2 + a^2/4 - 4*a*b*tan(c/2 + (d*x)/2)^3 + (4*a*b*tan(c/2 + (d*x)/2))/3))/(16*d) + (a*b*tan(c/2 + (d*x)/2)^3)/(12*d) - (a*b*tan(c/2 + (d*x)/2))/(4*d)","B"
1067,1,187,148,9.356805,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^2)/sin(c + d*x)^6,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{3}+\frac{4\,b^2}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2+4\,b^2\right)+\frac{a^2}{5}+a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{32\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2}{16}+\frac{b^2}{8}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2}{96}+\frac{b^2}{24}\right)}{d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}-\frac{a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^5)/(160*d) - (cot(c/2 + (d*x)/2)^5*(tan(c/2 + (d*x)/2)^2*(a^2/3 + (4*b^2)/3) - tan(c/2 + (d*x)/2)^4*(2*a^2 + 4*b^2) + a^2/5 + a*b*tan(c/2 + (d*x)/2)))/(32*d) - (tan(c/2 + (d*x)/2)*(a^2/16 + b^2/8))/d + (tan(c/2 + (d*x)/2)^3*(a^2/96 + b^2/24))/d + (a*b*tan(c/2 + (d*x)/2)^4)/(32*d) - (a*b*log(tan(c/2 + (d*x)/2)))/(4*d)","B"
1068,1,245,170,9.444199,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^2)/sin(c + d*x)^7,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{a^2}{16}+\frac{b^2}{8}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^2}{6}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{2}+b^2\right)+\frac{4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}\right)}{64\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{128}+\frac{b^2}{64}\right)}{d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{48\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{80\,d}-\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^6)/(384*d) - (a^2*tan(c/2 + (d*x)/2)^2)/(128*d) - (log(tan(c/2 + (d*x)/2))*(a^2/16 + b^2/8))/d - (cot(c/2 + (d*x)/2)^6*(a^2/6 - (a^2*tan(c/2 + (d*x)/2)^4)/2 + tan(c/2 + (d*x)/2)^2*(a^2/2 + b^2) + (4*a*b*tan(c/2 + (d*x)/2)^3)/3 - 8*a*b*tan(c/2 + (d*x)/2)^5 + (4*a*b*tan(c/2 + (d*x)/2))/5))/(64*d) + (tan(c/2 + (d*x)/2)^4*(a^2/128 + b^2/64))/d + (a*b*tan(c/2 + (d*x)/2)^3)/(48*d) + (a*b*tan(c/2 + (d*x)/2)^5)/(80*d) - (a*b*tan(c/2 + (d*x)/2))/(8*d)","B"
1069,1,455,232,10.658357,"\text{Not used}","int(cos(c + d*x)^2*sin(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(2\,a^2+3\,b^2\right)}{8\,\left(\frac{a^3}{4}+\frac{3\,a\,b^2}{8}\right)}\right)\,\left(2\,a^2+3\,b^2\right)}{8\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^3}{4}+\frac{3\,a\,b^2}{8}\right)+\frac{4\,a^2\,b}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,a\,b^2}{2}-a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{5\,a\,b^2}{2}-a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{a^3}{4}+\frac{3\,a\,b^2}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{11\,a^3}{4}+\frac{97\,a\,b^2}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{11\,a^3}{4}+\frac{97\,a\,b^2}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(8\,a^2\,b-\frac{16\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{24\,a^2\,b}{5}+\frac{16\,b^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(20\,a^2\,b+\frac{32\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{28\,a^2\,b}{5}+\frac{16\,b^3}{15}\right)+\frac{16\,b^3}{105}+12\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{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{a\,\left(2\,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)}{8\,d}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(2*a^2 + 3*b^2))/(8*((3*a*b^2)/8 + a^3/4)))*(2*a^2 + 3*b^2))/(8*d) - (tan(c/2 + (d*x)/2)*((3*a*b^2)/8 + a^3/4) + (4*a^2*b)/5 + tan(c/2 + (d*x)/2)^3*((5*a*b^2)/2 - a^3) - tan(c/2 + (d*x)/2)^11*((5*a*b^2)/2 - a^3) - tan(c/2 + (d*x)/2)^13*((3*a*b^2)/8 + a^3/4) - tan(c/2 + (d*x)/2)^5*((97*a*b^2)/8 + (11*a^3)/4) + tan(c/2 + (d*x)/2)^9*((97*a*b^2)/8 + (11*a^3)/4) + tan(c/2 + (d*x)/2)^6*(8*a^2*b - (16*b^3)/3) + tan(c/2 + (d*x)/2)^4*((24*a^2*b)/5 + (16*b^3)/5) + tan(c/2 + (d*x)/2)^8*(20*a^2*b + (32*b^3)/3) + tan(c/2 + (d*x)/2)^2*((28*a^2*b)/5 + (16*b^3)/15) + (16*b^3)/105 + 12*a^2*b*tan(c/2 + (d*x)/2)^10)/(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)) - (a*(2*a^2 + 3*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d)","B"
1070,1,425,163,10.746328,"\text{Not used}","int(cos(c + d*x)^2*sin(c + d*x)*(a + b*sin(c + d*x))^3,x)","\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2+b^2\right)}{8\,\left(\frac{3\,a^2\,b}{4}+\frac{b^3}{8}\right)}\right)\,\left(6\,a^2+b^2\right)}{8\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a^2\,b}{4}+\frac{b^3}{8}\right)+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{4\,a\,b^2}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(6\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^3+\frac{24\,a\,b^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{20\,a^3}{3}+8\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{3\,a^2\,b}{4}+\frac{b^3}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{9\,a^2\,b}{2}+\frac{19\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{9\,a^2\,b}{2}+\frac{19\,b^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{15\,a^2\,b}{4}-\frac{17\,b^3}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{15\,a^2\,b}{4}-\frac{17\,b^3}{24}\right)+\frac{2\,a^3}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{b\,\left(6\,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,"(b*atan((b*tan(c/2 + (d*x)/2)*(6*a^2 + b^2))/(8*((3*a^2*b)/4 + b^3/8)))*(6*a^2 + b^2))/(8*d) - (tan(c/2 + (d*x)/2)*((3*a^2*b)/4 + b^3/8) + 4*a^3*tan(c/2 + (d*x)/2)^4 + 2*a^3*tan(c/2 + (d*x)/2)^10 + (4*a*b^2)/5 + tan(c/2 + (d*x)/2)^8*(12*a*b^2 + 6*a^3) + tan(c/2 + (d*x)/2)^2*((24*a*b^2)/5 + 2*a^3) + tan(c/2 + (d*x)/2)^6*(8*a*b^2 + (20*a^3)/3) - tan(c/2 + (d*x)/2)^11*((3*a^2*b)/4 + b^3/8) - tan(c/2 + (d*x)/2)^5*((9*a^2*b)/2 + (19*b^3)/4) + tan(c/2 + (d*x)/2)^7*((9*a^2*b)/2 + (19*b^3)/4) - tan(c/2 + (d*x)/2)^3*((15*a^2*b)/4 - (17*b^3)/24) + tan(c/2 + (d*x)/2)^9*((15*a^2*b)/4 - (17*b^3)/24) + (2*a^3)/3)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - (b*(6*a^2 + b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d)","B"
1071,1,567,136,11.122230,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^3)/sin(c + d*x),x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a\,b^2-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2\,b-\frac{b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a\,b^2-6\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(6\,a\,b^2-2\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a\,b^2-6\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(3\,a^2\,b-\frac{b^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2\,b+\frac{7\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^2\,b+\frac{7\,b^3}{4}\right)-2\,a^3}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(12\,a^2+b^2\right)\,\left(3\,a^2\,b+\frac{b^3}{4}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2+b^2\right)\,3{}\mathrm{i}}{4}\right)}{8}+\frac{b\,\left(12\,a^2+b^2\right)\,\left(3\,a^2\,b+\frac{b^3}{4}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2+b^2\right)\,3{}\mathrm{i}}{4}\right)}{8}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^4\,b^2+\frac{3\,a^2\,b^4}{2}+\frac{b^6}{16}\right)+6\,a^5\,b+\frac{a^3\,b^3}{2}-\frac{b\,\left(12\,a^2+b^2\right)\,\left(3\,a^2\,b+\frac{b^3}{4}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2+b^2\right)\,3{}\mathrm{i}}{4}\right)\,1{}\mathrm{i}}{8}+\frac{b\,\left(12\,a^2+b^2\right)\,\left(3\,a^2\,b+\frac{b^3}{4}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2+b^2\right)\,3{}\mathrm{i}}{4}\right)\,1{}\mathrm{i}}{8}}\right)\,\left(12\,a^2+b^2\right)}{4\,d}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d - (2*a*b^2 - tan(c/2 + (d*x)/2)*(3*a^2*b - b^3/4) + tan(c/2 + (d*x)/2)^2*(2*a*b^2 - 6*a^3) + tan(c/2 + (d*x)/2)^6*(6*a*b^2 - 2*a^3) + tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^3) + tan(c/2 + (d*x)/2)^7*(3*a^2*b - b^3/4) - tan(c/2 + (d*x)/2)^3*(3*a^2*b + (7*b^3)/4) + tan(c/2 + (d*x)/2)^5*(3*a^2*b + (7*b^3)/4) - 2*a^3)/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (b*atan(((b*(12*a^2 + b^2)*(3*a^2*b + b^3/4 + 2*a^3*tan(c/2 + (d*x)/2) - (b*tan(c/2 + (d*x)/2)*(12*a^2 + b^2)*3i)/4))/8 + (b*(12*a^2 + b^2)*(3*a^2*b + b^3/4 + 2*a^3*tan(c/2 + (d*x)/2) + (b*tan(c/2 + (d*x)/2)*(12*a^2 + b^2)*3i)/4))/8)/(2*tan(c/2 + (d*x)/2)*(b^6/16 + (3*a^2*b^4)/2 + 9*a^4*b^2) + 6*a^5*b + (a^3*b^3)/2 - (b*(12*a^2 + b^2)*(3*a^2*b + b^3/4 + 2*a^3*tan(c/2 + (d*x)/2) - (b*tan(c/2 + (d*x)/2)*(12*a^2 + b^2)*3i)/4)*1i)/8 + (b*(12*a^2 + b^2)*(3*a^2*b + b^3/4 + 2*a^3*tan(c/2 + (d*x)/2) + (b*tan(c/2 + (d*x)/2)*(12*a^2 + b^2)*3i)/4)*1i)/8))*(12*a^2 + b^2))/(4*d)","B"
1072,1,289,102,9.474275,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^3)/sin(c + d*x)^2,x)","\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(\frac{a\,b^2\,3{}\mathrm{i}}{2}-a^3\,1{}\mathrm{i}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2\,b-\frac{4\,b^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3+6\,a\,b^2\right)-3\,a^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\,\left(6\,a\,b^2-3\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(12\,a^2\,b-4\,b^3\right)-a^3+24\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{3\,a^2\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(2\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2))/(2*d) - (log(tan(c/2 + (d*x)/2) - 1i)*((a*b^2*3i)/2 - a^3*1i))/d + (tan(c/2 + (d*x)/2)*(12*a^2*b - (4*b^3)/3) - tan(c/2 + (d*x)/2)^6*(6*a*b^2 + a^3) - 3*a^3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^2*(6*a*b^2 - 3*a^3) + tan(c/2 + (d*x)/2)^5*(12*a^2*b - 4*b^3) - a^3 + 24*a^2*b*tan(c/2 + (d*x)/2)^3)/(d*(2*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^3 + 6*tan(c/2 + (d*x)/2)^5 + 2*tan(c/2 + (d*x)/2)^7)) + (3*a^2*b*log(tan(c/2 + (d*x)/2)))/d - (a*log(tan(c/2 + (d*x)/2) + 1i)*(2*a^2 - 3*b^2)*1i)/(2*d)","B"
1073,1,585,138,9.462940,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^3)/sin(c + d*x)^3,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a\,b^2-\frac{a^3}{2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^2\,b+4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(24\,a\,b^2-\frac{a^3}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(24\,a\,b^2-a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b-4\,b^3\right)+\frac{a^3}{2}+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(6\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-a^3\right)-6\,a^2\,b+b^3-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2-b^2\right)\,3{}\mathrm{i}\right)}{2}+\frac{b\,\left(6\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-a^3\right)-6\,a^2\,b+b^3+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2-b^2\right)\,3{}\mathrm{i}\right)}{2}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^4\,b^2-12\,a^2\,b^4+b^6\right)+6\,a\,b^5+6\,a^5\,b-37\,a^3\,b^3-\frac{b\,\left(6\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-a^3\right)-6\,a^2\,b+b^3-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2-b^2\right)\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\frac{b\,\left(6\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-a^3\right)-6\,a^2\,b+b^3+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2-b^2\right)\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}}\right)\,\left(6\,a^2-b^2\right)}{d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (log(tan(c/2 + (d*x)/2))*(3*a*b^2 - a^3/2))/d - (tan(c/2 + (d*x)/2)^5*(6*a^2*b + 4*b^3) - tan(c/2 + (d*x)/2)^4*(24*a*b^2 - a^3/2) - tan(c/2 + (d*x)/2)^2*(24*a*b^2 - a^3) + tan(c/2 + (d*x)/2)^3*(12*a^2*b - 4*b^3) + a^3/2 + 6*a^2*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 8*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6)) + (3*a^2*b*tan(c/2 + (d*x)/2))/(2*d) + (b*atan(((b*(6*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(6*a*b^2 - a^3) - 6*a^2*b + b^3 - b*tan(c/2 + (d*x)/2)*(6*a^2 - b^2)*3i))/2 + (b*(6*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(6*a*b^2 - a^3) - 6*a^2*b + b^3 + b*tan(c/2 + (d*x)/2)*(6*a^2 - b^2)*3i))/2)/(2*tan(c/2 + (d*x)/2)*(b^6 - 12*a^2*b^4 + 36*a^4*b^2) + 6*a*b^5 + 6*a^5*b - 37*a^3*b^3 - (b*(6*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(6*a*b^2 - a^3) - 6*a^2*b + b^3 - b*tan(c/2 + (d*x)/2)*(6*a^2 - b^2)*3i)*1i)/2 + (b*(6*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(6*a*b^2 - a^3) - 6*a^2*b + b^3 + b*tan(c/2 + (d*x)/2)*(6*a^2 - b^2)*3i)*1i)/2))*(6*a^2 - b^2))/d","B"
1074,1,477,138,10.709032,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^3)/sin(c + d*x)^4,x)","-\frac{\frac{a^3\,\cos\left(c+d\,x\right)}{4}-\frac{3\,b^3\,\sin\left(c+d\,x\right)}{4}+\frac{a^3\,\cos\left(3\,c+3\,d\,x\right)}{12}-\frac{b^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{b^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{b^3\,\sin\left(4\,c+4\,d\,x\right)}{8}-\frac{3\,a\,b^2\,\cos\left(3\,c+3\,d\,x\right)}{4}-\frac{3\,b^3\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{3\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,a\,b^2\,\cos\left(c+d\,x\right)}{4}-\frac{3\,a^2\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{8}-\frac{9\,a\,b^2\,\mathrm{atan}\left(\frac{3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\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}{-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{2}+\frac{3\,a\,b^2\,\mathrm{atan}\left(\frac{3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\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}{-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{9\,a^2\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}}{d\,{\sin\left(c+d\,x\right)}^3}","Not used",1,"-((a^3*cos(c + d*x))/4 - (3*b^3*sin(c + d*x))/4 + (a^3*cos(3*c + 3*d*x))/12 - (b^3*sin(2*c + 2*d*x))/4 + (b^3*sin(3*c + 3*d*x))/4 + (b^3*sin(4*c + 4*d*x))/8 - (3*a*b^2*cos(3*c + 3*d*x))/4 - (3*b^3*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (3*a^2*b*sin(2*c + 2*d*x))/4 + (b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/4 + (3*a*b^2*cos(c + d*x))/4 - (3*a^2*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/8 - (9*a*b^2*atan((3*a^2*sin(c/2 + (d*x)/2) - 2*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2))/(2*b^2*cos(c/2 + (d*x)/2) - 3*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2)))*sin(c + d*x))/2 + (3*a*b^2*atan((3*a^2*sin(c/2 + (d*x)/2) - 2*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2))/(2*b^2*cos(c/2 + (d*x)/2) - 3*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/2 + (9*a^2*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8)/(d*sin(c + d*x)^3)","B"
1075,1,348,152,9.865077,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^3)/sin(c + d*x)^5,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8\,d}-\frac{b^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{2\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2+8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+12\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)}{d}-\frac{3\,a\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,d}+\frac{3\,a^2\,b\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{3\,a\,b^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a^2\,b\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}+\frac{3\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^4)/(64*d) - (a^3*cot(c/2 + (d*x)/2)^4)/(64*d) - (a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(8*d) - (b^3*cot(c/2 + (d*x)/2))/(2*d) + (b^3*tan(c/2 + (d*x)/2))/(2*d) - (2*b^3*atan((8*b^3*cos(c/2 + (d*x)/2) + a^3*sin(c/2 + (d*x)/2) + 12*a*b^2*sin(c/2 + (d*x)/2))/(a^3*cos(c/2 + (d*x)/2) - 8*b^3*sin(c/2 + (d*x)/2) + 12*a*b^2*cos(c/2 + (d*x)/2))))/d - (3*a*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(2*d) + (3*a^2*b*cot(c/2 + (d*x)/2))/(8*d) - (3*a^2*b*tan(c/2 + (d*x)/2))/(8*d) - (3*a*b^2*cot(c/2 + (d*x)/2)^2)/(8*d) - (a^2*b*cot(c/2 + (d*x)/2)^3)/(8*d) + (3*a*b^2*tan(c/2 + (d*x)/2)^2)/(8*d) + (a^2*b*tan(c/2 + (d*x)/2)^3)/(8*d)","B"
1076,1,241,183,9.438721,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^3)/sin(c + d*x)^6,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^3}{96}+\frac{a\,b^2}{8}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^2\,b}{8}+\frac{b^3}{2}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3}{3}+4\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^3+12\,a\,b^2\right)+\frac{a^3}{5}+\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{32\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^3}{16}+\frac{3\,a\,b^2}{8}\right)}{d}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^5)/(160*d) + (b^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (tan(c/2 + (d*x)/2)^3*((a*b^2)/8 + a^3/96))/d - (log(tan(c/2 + (d*x)/2))*((3*a^2*b)/8 + b^3/2))/d - (cot(c/2 + (d*x)/2)^5*(4*b^3*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^2*(4*a*b^2 + a^3/3) - tan(c/2 + (d*x)/2)^4*(12*a*b^2 + 2*a^3) + a^3/5 + (3*a^2*b*tan(c/2 + (d*x)/2))/2))/(32*d) - (tan(c/2 + (d*x)/2)*((3*a*b^2)/8 + a^3/16))/d + (3*a^2*b*tan(c/2 + (d*x)/2)^4)/(64*d)","B"
1077,1,292,212,9.689200,"\text{Not used}","int((cos(c + d*x)^2*(a + b*sin(c + d*x))^3)/sin(c + d*x)^7,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3}{2}+3\,a\,b^2\right)-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^2\,b+\frac{8\,b^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(12\,a^2\,b+8\,b^3\right)+\frac{a^3}{6}+\frac{6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}\right)}{64\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3}{128}+\frac{3\,a\,b^2}{64}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2\,b}{32}+\frac{b^3}{24}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{a^3}{16}+\frac{3\,a\,b^2}{8}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a^2\,b}{16}+\frac{b^3}{8}\right)}{d}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^6)/(384*d) - (a^3*tan(c/2 + (d*x)/2)^2)/(128*d) - (cot(c/2 + (d*x)/2)^6*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 + a^3/2) - (a^3*tan(c/2 + (d*x)/2)^4)/2 + tan(c/2 + (d*x)/2)^3*(2*a^2*b + (8*b^3)/3) - tan(c/2 + (d*x)/2)^5*(12*a^2*b + 8*b^3) + a^3/6 + (6*a^2*b*tan(c/2 + (d*x)/2))/5))/(64*d) + (tan(c/2 + (d*x)/2)^4*((3*a*b^2)/64 + a^3/128))/d + (tan(c/2 + (d*x)/2)^3*((a^2*b)/32 + b^3/24))/d - (log(tan(c/2 + (d*x)/2))*((3*a*b^2)/8 + a^3/16))/d - (tan(c/2 + (d*x)/2)*((3*a^2*b)/16 + b^3/8))/d + (3*a^2*b*tan(c/2 + (d*x)/2)^5)/(160*d)","B"
1078,1,1688,188,11.852686,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^3)/(a + b*sin(c + d*x))^2,x)","\frac{\frac{28\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b^3}-\frac{2\,\left(a\,b^2-12\,a^3\right)}{3\,b^4}+\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3+a\,b^2\right)}{b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a\,b^2-12\,a^3\right)}{b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,a\,b^2-36\,a^3\right)}{3\,b^4}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^2-b^2\right)}{3\,b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(5\,a^2-b^2\right)}{b^3}}{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+4\,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\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,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{\mathrm{atan}\left(\frac{64\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^4-\frac{256\,a^6}{b^2}}+\frac{256\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,a^6-64\,a^4\,b^2}\right)\,\left(a\,b^2\,1{}\mathrm{i}-a^3\,4{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^5\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(16\,a^8\,b^4-8\,a^6\,b^6+a^4\,b^8\right)}{b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32\,a^9\,b^4+64\,a^7\,b^6-26\,a^5\,b^8+2\,a^3\,b^{10}\right)}{b^{12}}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(a^2\,b^{12}-2\,a^4\,b^{10}\right)}{b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^3\,b^{12}-8\,a^5\,b^{10}\right)}{b^{12}}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a\,b^{16}-2\,a^3\,b^{14}\right)}{b^{12}}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}\right)\,1{}\mathrm{i}}{b^7-a^2\,b^5}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(16\,a^8\,b^4-8\,a^6\,b^6+a^4\,b^8\right)}{b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32\,a^9\,b^4+64\,a^7\,b^6-26\,a^5\,b^8+2\,a^3\,b^{10}\right)}{b^{12}}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(a^2\,b^{12}-2\,a^4\,b^{10}\right)}{b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^3\,b^{12}-8\,a^5\,b^{10}\right)}{b^{12}}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a\,b^{16}-2\,a^3\,b^{14}\right)}{b^{12}}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}\right)\,1{}\mathrm{i}}{b^7-a^2\,b^5}}{\frac{64\,\left(32\,a^{10}-32\,a^8\,b^2+6\,a^6\,b^4\right)}{b^{11}}+\frac{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{11}-160\,a^9\,b^2+56\,a^7\,b^4-6\,a^5\,b^6\right)}{b^{12}}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(16\,a^8\,b^4-8\,a^6\,b^6+a^4\,b^8\right)}{b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32\,a^9\,b^4+64\,a^7\,b^6-26\,a^5\,b^8+2\,a^3\,b^{10}\right)}{b^{12}}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(a^2\,b^{12}-2\,a^4\,b^{10}\right)}{b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^3\,b^{12}-8\,a^5\,b^{10}\right)}{b^{12}}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a\,b^{16}-2\,a^3\,b^{14}\right)}{b^{12}}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(16\,a^8\,b^4-8\,a^6\,b^6+a^4\,b^8\right)}{b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32\,a^9\,b^4+64\,a^7\,b^6-26\,a^5\,b^8+2\,a^3\,b^{10}\right)}{b^{12}}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(a^2\,b^{12}-2\,a^4\,b^{10}\right)}{b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^3\,b^{12}-8\,a^5\,b^{10}\right)}{b^{12}}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a\,b^{16}-2\,a^3\,b^{14}\right)}{b^{12}}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^7-a^2\,b^5\right)}","Not used",1,"((28*a^2*tan(c/2 + (d*x)/2)^3)/b^3 - (2*(a*b^2 - 12*a^3))/(3*b^4) + (4*a^2*tan(c/2 + (d*x)/2)^7)/b^3 + (2*tan(c/2 + (d*x)/2)^6*(a*b^2 + 4*a^3))/b^4 - (2*tan(c/2 + (d*x)/2)^4*(a*b^2 - 12*a^3))/b^4 - (2*tan(c/2 + (d*x)/2)^2*(7*a*b^2 - 36*a^3))/(3*b^4) + (4*tan(c/2 + (d*x)/2)*(9*a^2 - b^2))/(3*b^3) + (4*tan(c/2 + (d*x)/2)^5*(5*a^2 - b^2))/b^3)/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 + 4*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)) + (atan((64*a^4*tan(c/2 + (d*x)/2))/(64*a^4 - (256*a^6)/b^2) + (256*a^6*tan(c/2 + (d*x)/2))/(256*a^6 - 64*a^4*b^2))*(a*b^2*1i - a^3*4i)*2i)/(b^5*d) + (a^2*atan(((a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a^4*b^8 - 8*a^6*b^6 + 16*a^8*b^4))/b^11 + (32*tan(c/2 + (d*x)/2)*(2*a^3*b^10 - 26*a^5*b^8 + 64*a^7*b^6 - 32*a^9*b^4))/b^12 + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a^2*b^12 - 2*a^4*b^10))/b^11 + (32*tan(c/2 + (d*x)/2)*(6*a^3*b^12 - 8*a^5*b^10))/b^12 + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(32*a^2*b^3 + (32*tan(c/2 + (d*x)/2)*(3*a*b^16 - 2*a^3*b^14))/b^12))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5))*1i)/(b^7 - a^2*b^5) + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a^4*b^8 - 8*a^6*b^6 + 16*a^8*b^4))/b^11 + (32*tan(c/2 + (d*x)/2)*(2*a^3*b^10 - 26*a^5*b^8 + 64*a^7*b^6 - 32*a^9*b^4))/b^12 - (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a^2*b^12 - 2*a^4*b^10))/b^11 + (32*tan(c/2 + (d*x)/2)*(6*a^3*b^12 - 8*a^5*b^10))/b^12 - (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(32*a^2*b^3 + (32*tan(c/2 + (d*x)/2)*(3*a*b^16 - 2*a^3*b^14))/b^12))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5))*1i)/(b^7 - a^2*b^5))/((64*(32*a^10 + 6*a^6*b^4 - 32*a^8*b^2))/b^11 + (64*tan(c/2 + (d*x)/2)*(128*a^11 - 6*a^5*b^6 + 56*a^7*b^4 - 160*a^9*b^2))/b^12 - (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a^4*b^8 - 8*a^6*b^6 + 16*a^8*b^4))/b^11 + (32*tan(c/2 + (d*x)/2)*(2*a^3*b^10 - 26*a^5*b^8 + 64*a^7*b^6 - 32*a^9*b^4))/b^12 + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a^2*b^12 - 2*a^4*b^10))/b^11 + (32*tan(c/2 + (d*x)/2)*(6*a^3*b^12 - 8*a^5*b^10))/b^12 + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(32*a^2*b^3 + (32*tan(c/2 + (d*x)/2)*(3*a*b^16 - 2*a^3*b^14))/b^12))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5) + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a^4*b^8 - 8*a^6*b^6 + 16*a^8*b^4))/b^11 + (32*tan(c/2 + (d*x)/2)*(2*a^3*b^10 - 26*a^5*b^8 + 64*a^7*b^6 - 32*a^9*b^4))/b^12 - (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a^2*b^12 - 2*a^4*b^10))/b^11 + (32*tan(c/2 + (d*x)/2)*(6*a^3*b^12 - 8*a^5*b^10))/b^12 - (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(32*a^2*b^3 + (32*tan(c/2 + (d*x)/2)*(3*a*b^16 - 2*a^3*b^14))/b^12))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5)))*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*2i)/(d*(b^7 - a^2*b^5))","B"
1079,1,479,153,10.400296,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^2)/(a + b*sin(c + d*x))^2,x)","-\frac{\frac{6\,a^2}{b^3}+\frac{9\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^2+b^2\right)}{b^3}+\frac{12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b^2}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{b^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^2-b^2\right)}{b^3}}{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{\ln\left(b+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sqrt{b^2-a^2}\right)\,\left(3\,a^3\,\sqrt{b^2-a^2}-2\,a\,b^2\,\sqrt{b^2-a^2}\right)}{b^4\,d\,\left(a^2-b^2\right)}-\frac{a\,\ln\left(b+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-2\,b^2\right)}{d\,\left(b^6-a^2\,b^4\right)}+\frac{\mathrm{atan}\left(\frac{24\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{24\,a^3-8\,a\,b^2+\frac{144\,a^5}{b^2}}+\frac{144\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{144\,a^5+24\,a^3\,b^2-8\,a\,b^4}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{24\,a^3}{b^2}-8\,a+\frac{144\,a^5}{b^4}}\right)\,\left(a^2\,6{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4\,d}","Not used",1,"(atan((24*a^3*tan(c/2 + (d*x)/2))/(24*a^3 - 8*a*b^2 + (144*a^5)/b^2) + (144*a^5*tan(c/2 + (d*x)/2))/(144*a^5 - 8*a*b^4 + 24*a^3*b^2) - (8*a*tan(c/2 + (d*x)/2))/((24*a^3)/b^2 - 8*a + (144*a^5)/b^4))*(a^2*6i - b^2*1i)*1i)/(b^4*d) - ((6*a^2)/b^3 + (9*a*tan(c/2 + (d*x)/2))/b^2 + (2*tan(c/2 + (d*x)/2)^4*(3*a^2 + b^2))/b^3 + (12*a*tan(c/2 + (d*x)/2)^3)/b^2 + (3*a*tan(c/2 + (d*x)/2)^5)/b^2 + (2*tan(c/2 + (d*x)/2)^2*(6*a^2 - b^2))/b^3)/(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)) - (log(b + a*tan(c/2 + (d*x)/2) - (b^2 - a^2)^(1/2))*(3*a^3*(b^2 - a^2)^(1/2) - 2*a*b^2*(b^2 - a^2)^(1/2)))/(b^4*d*(a^2 - b^2)) - (a*log(b + a*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 2*b^2))/(d*(b^6 - a^2*b^4))","B"
1080,1,269,106,10.024176,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x))/(a + b*sin(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b}+\frac{4\,a}{b^2}+\frac{6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^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\,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{2\,a\,x}{b^3}-\frac{\ln\left(b+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sqrt{b^2-a^2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)}{d\,\left(b^5-a^2\,b^3\right)}-\frac{\ln\left(b+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\left(2\,a^2\,\sqrt{b^2-a^2}-b^2\,\sqrt{b^2-a^2}\right)}{b^3\,d\,\left(a^2-b^2\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3)/b + (4*a)/b^2 + (6*tan(c/2 + (d*x)/2))/b + (4*a*tan(c/2 + (d*x)/2)^2)/b^2)/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4 + 2*b*tan(c/2 + (d*x)/2)^3)) + (2*a*x)/b^3 - (log(b + a*tan(c/2 + (d*x)/2) - (b^2 - a^2)^(1/2))*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2))/(d*(b^5 - a^2*b^3)) - (log(b + a*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(2*a^2*(b^2 - a^2)^(1/2) - b^2*(b^2 - a^2)^(1/2)))/(b^3*d*(a^2 - b^2))","B"
1081,1,523,92,10.162166,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)*(a + b*sin(c + d*x))^2),x)","\frac{a^3\,\cos\left(c+d\,x\right)-a\,b^2-b^3\,\sin\left(c+d\,x\right)+a^3+a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-a\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-b^3\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-a\,b^2\,\cos\left(c+d\,x\right)+a^2\,b\,\sin\left(c+d\,x\right)+a^2\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+b^2\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{-a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+a\,b\,\mathrm{atan}\left(\frac{-a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^2\,d\,\left(a^2-b^2\right)\,\left(a+b\,\sin\left(c+d\,x\right)\right)}","Not used",1,"(a^3*cos(c + d*x) - a*b^2 - b^3*sin(c + d*x) + a^3 + a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - a*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - b^3*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - a*b^2*cos(c + d*x) + a^2*b*sin(c + d*x) + b^2*sin(c + d*x)*atan((b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - a^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + a*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i)/(a^3*cos(c/2 + (d*x)/2) - 4*b^3*sin(c/2 + (d*x)/2) - 2*a*b^2*cos(c/2 + (d*x)/2) + 3*a^2*b*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i + a*b*atan((b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - a^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + a*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i)/(a^3*cos(c/2 + (d*x)/2) - 4*b^3*sin(c/2 + (d*x)/2) - 2*a*b^2*cos(c/2 + (d*x)/2) + 3*a^2*b*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i + a^2*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^2*d*(a^2 - b^2)*(a + b*sin(c + d*x)))","B"
1082,1,1616,115,11.414026,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","-\frac{a^4\,\cos\left(c+d\,x\right)-\frac{b^4}{2}-b^4\,\ln\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^2\,b^2}{2}+\frac{b^4\,\cos\left(2\,c+2\,d\,x\right)}{2}-a^2\,b^2\,\cos\left(c+d\,x\right)-a\,b^3\,\sin\left(2\,c+2\,d\,x\right)+a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+a^2\,b^2\,\ln\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\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+b^3\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-\frac{a^2\,b^2\,\cos\left(2\,c+2\,d\,x\right)}{2}-a\,b^3\,\sin\left(c+d\,x\right)+a^3\,b\,\sin\left(c+d\,x\right)-a^2\,b\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^3\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-a^2\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)-b^3\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-2\,a\,b^3\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,a^3\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+a\,b^2\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{2\,a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{b}{4}+\frac{a\,\sin\left(c+d\,x\right)}{2}-\frac{b\,\cos\left(2\,c+2\,d\,x\right)}{4}\right)}","Not used",1,"-(a^4*cos(c + d*x) - b^4/2 - b^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (a^2*b^2)/2 + (b^4*cos(2*c + 2*d*x))/2 - a^2*b^2*cos(c + d*x) - a*b^3*sin(2*c + 2*d*x) + a^3*b*sin(2*c + 2*d*x) + a^2*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + b^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + b^3*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i - (a^2*b^2*cos(2*c + 2*d*x))/2 - a*b^3*sin(c + d*x) + a^3*b*sin(c + d*x) - a^2*b*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*1i - a^3*sin(c + d*x)*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i - a^2*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) - b^3*cos(2*c + 2*d*x)*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i - 2*a*b^3*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*a^3*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + a*b^2*sin(c + d*x)*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*4i + a^2*b*cos(2*c + 2*d*x)*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*1i)/(2*a^3*d*(a^2 - b^2)*(b/4 + (a*sin(c + d*x))/2 - (b*cos(2*c + 2*d*x))/4))","B"
1083,1,966,157,9.894953,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^3*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{2}-16\,b^2\right)+\frac{a^2}{2}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2\,b+2\,b^3\right)}{a}-3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,b\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-6\,b^2\right)}{2\,a^4\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{5\,a^6\,b-12\,a^4\,b^3}{a^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-16\,a^4\,b^2+24\,a^2\,b^4\right)}{a^5}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-8\,a^6\,b^2\right)}{a^5}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-16\,a^4\,b^2+24\,a^2\,b^4\right)}{a^5}-\frac{5\,a^6\,b-12\,a^4\,b^3}{a^6}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-8\,a^6\,b^2\right)}{a^5}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{2\,\left(2\,a^4\,b-15\,a^2\,b^3+18\,b^5\right)}{a^6}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,b^4-12\,a^2\,b^2\right)}{a^5}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{5\,a^6\,b-12\,a^4\,b^3}{a^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-16\,a^4\,b^2+24\,a^2\,b^4\right)}{a^5}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-8\,a^6\,b^2\right)}{a^5}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-16\,a^4\,b^2+24\,a^2\,b^4\right)}{a^5}-\frac{5\,a^6\,b-12\,a^4\,b^3}{a^6}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-8\,a^6\,b^2\right)}{a^5}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) - (tan(c/2 + (d*x)/2)^2*(a^2/2 - 16*b^2) + a^2/2 - (4*tan(c/2 + (d*x)/2)^3*(a^2*b + 2*b^3))/a - 3*a*b*tan(c/2 + (d*x)/2))/(d*(4*a^4*tan(c/2 + (d*x)/2)^2 + 4*a^4*tan(c/2 + (d*x)/2)^4 + 8*a^3*b*tan(c/2 + (d*x)/2)^3)) - (b*tan(c/2 + (d*x)/2))/(a^3*d) - (log(tan(c/2 + (d*x)/2))*(a^2 - 6*b^2))/(2*a^4*d) - (b*atan(((b*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((5*a^6*b - 12*a^4*b^3)/a^6 - (tan(c/2 + (d*x)/2)*(a^6 + 24*a^2*b^4 - 16*a^4*b^2))/a^5 + (b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^8 - 8*a^6*b^2))/a^5)*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) - (b*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((tan(c/2 + (d*x)/2)*(a^6 + 24*a^2*b^4 - 16*a^4*b^2))/a^5 - (5*a^6*b - 12*a^4*b^3)/a^6 + (b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^8 - 8*a^6*b^2))/a^5)*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2))/((2*(2*a^4*b + 18*b^5 - 15*a^2*b^3))/a^6 + (2*tan(c/2 + (d*x)/2)*(18*b^4 - 12*a^2*b^2))/a^5 + (b*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((5*a^6*b - 12*a^4*b^3)/a^6 - (tan(c/2 + (d*x)/2)*(a^6 + 24*a^2*b^4 - 16*a^4*b^2))/a^5 + (b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^8 - 8*a^6*b^2))/a^5)*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) + (b*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((tan(c/2 + (d*x)/2)*(a^6 + 24*a^2*b^4 - 16*a^4*b^2))/a^5 - (5*a^6*b - 12*a^4*b^3)/a^6 + (b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^8 - 8*a^6*b^2))/a^5)*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*2i)/(d*(a^6 - a^4*b^2))","B"
1084,1,1089,193,9.988873,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^4*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a\,b^2-\frac{2\,a^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^2\,b-40\,b^3\right)+\frac{a^3}{3}-\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-a^4+12\,a^2\,b^2+16\,b^4\right)}{a}}{d\,\left(8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,b\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1}{8\,a^2}-\frac{16\,a^2+32\,b^2}{64\,a^4}+\frac{2\,b^2}{a^4}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^3\,d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-4\,b^2\right)}{a^5\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{2\,\left(8\,a^5\,b^4-4\,a^7\,b^2\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7\,b-12\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\left(3\,a^2-4\,b^2\right)}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{2\,\left(8\,a^5\,b^4-4\,a^7\,b^2\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7\,b-12\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\left(3\,a^2-4\,b^2\right)}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}}{\frac{4\,\left(3\,a^4\,b^3-16\,a^2\,b^5+16\,b^7\right)}{a^8}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,b^6-12\,a^2\,b^4\right)}{a^7}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{2\,\left(8\,a^5\,b^4-4\,a^7\,b^2\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7\,b-12\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\left(3\,a^2-4\,b^2\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{2\,\left(8\,a^5\,b^4-4\,a^7\,b^2\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7\,b-12\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\left(3\,a^2-4\,b^2\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^7-a^5\,b^2\right)}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^2*d) - (tan(c/2 + (d*x)/2)^2*(8*a*b^2 - (2*a^3)/3) - tan(c/2 + (d*x)/2)^3*(4*a^2*b - 40*b^3) + a^3/3 - (4*a^2*b*tan(c/2 + (d*x)/2))/3 + (tan(c/2 + (d*x)/2)^4*(16*b^4 - a^4 + 12*a^2*b^2))/a)/(d*(8*a^5*tan(c/2 + (d*x)/2)^3 + 8*a^5*tan(c/2 + (d*x)/2)^5 + 16*a^4*b*tan(c/2 + (d*x)/2)^4)) + (tan(c/2 + (d*x)/2)*(1/(8*a^2) - (16*a^2 + 32*b^2)/(64*a^4) + (2*b^2)/a^4))/d - (b*tan(c/2 + (d*x)/2)^2)/(4*a^3*d) + (b*log(tan(c/2 + (d*x)/2))*(a^2 - 4*b^2))/(a^5*d) - (b^2*atan(((b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((2*(8*a^5*b^4 - 4*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(a^7*b + 16*a^3*b^5 - 12*a^5*b^3))/a^7 + (b^2*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(3*a^2 - 4*b^2))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2) + (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((2*(8*a^5*b^4 - 4*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(a^7*b + 16*a^3*b^5 - 12*a^5*b^3))/a^7 - (b^2*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(3*a^2 - 4*b^2))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2))/((4*(16*b^7 - 16*a^2*b^5 + 3*a^4*b^3))/a^8 + (4*tan(c/2 + (d*x)/2)*(16*b^6 - 12*a^2*b^4))/a^7 + (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((2*(8*a^5*b^4 - 4*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(a^7*b + 16*a^3*b^5 - 12*a^5*b^3))/a^7 + (b^2*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(3*a^2 - 4*b^2))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2) - (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((2*(8*a^5*b^4 - 4*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(a^7*b + 16*a^3*b^5 - 12*a^5*b^3))/a^7 - (b^2*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(3*a^2 - 4*b^2))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2)))*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*2i)/(d*(a^7 - a^5*b^2))","B"
1085,1,4943,266,17.721647,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^3)/(a + b*sin(c + d*x))^3,x)","-\frac{\frac{12\,a^5-11\,a^3\,b^2}{b^4\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,a^4-5\,a^2\,b^2\right)}{b^3\,\left(a^2-b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-54\,a^4+45\,a^2\,b^2+4\,b^4\right)}{b^3\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(90\,a^4-87\,a^2\,b^2+4\,b^4\right)}{b^3\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(12\,a^5+5\,a^3\,b^2-14\,a\,b^4\right)}{b^4\,\left(a^2-b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-36\,a^5+a^3\,b^2+30\,a\,b^4\right)}{b^4\,\left(a^2-b^2\right)}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(14\,a^4-13\,a^2\,b^2\right)}{b^3\,\left(a^2-b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(11\,a\,b^2-12\,a^3\right)\,\left(3\,a^2+4\,b^2\right)}{b^4\,\left(a^2-b^2\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2+8\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+a^2+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,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)}^7+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(288\,a^{10}\,b^4-624\,a^8\,b^6+386\,a^6\,b^8-52\,a^4\,b^{10}+2\,a^2\,b^{12}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(-24\,a^7\,b^{10}+56\,a^5\,b^{12}-36\,a^3\,b^{14}+4\,a\,b^{16}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-48\,a^8\,b^{10}+124\,a^6\,b^{12}-100\,a^4\,b^{14}+24\,a^2\,b^{16}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(8\,a^6\,b^{14}-16\,a^4\,b^{16}+8\,a^2\,b^{18}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{14}+28\,a^5\,b^{16}-32\,a^3\,b^{18}+12\,a\,b^{20}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)}{2\,b^5}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{11}\,b^4+1056\,a^9\,b^6-1322\,a^7\,b^8+640\,a^5\,b^{10}-89\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)\,1{}\mathrm{i}}{2\,b^5}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(288\,a^{10}\,b^4-624\,a^8\,b^6+386\,a^6\,b^8-52\,a^4\,b^{10}+2\,a^2\,b^{12}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(-24\,a^7\,b^{10}+56\,a^5\,b^{12}-36\,a^3\,b^{14}+4\,a\,b^{16}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-48\,a^8\,b^{10}+124\,a^6\,b^{12}-100\,a^4\,b^{14}+24\,a^2\,b^{16}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(8\,a^6\,b^{14}-16\,a^4\,b^{16}+8\,a^2\,b^{18}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{14}+28\,a^5\,b^{16}-32\,a^3\,b^{18}+12\,a\,b^{20}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)}{2\,b^5}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{11}\,b^4+1056\,a^9\,b^6-1322\,a^7\,b^8+640\,a^5\,b^{10}-89\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)\,1{}\mathrm{i}}{2\,b^5}}{\frac{8\,\left(864\,a^{11}-2160\,a^9\,b^2+1746\,a^7\,b^4-491\,a^5\,b^6+30\,a^3\,b^8\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1728\,a^{12}-4752\,a^{10}\,b^2+4356\,a^8\,b^4-1495\,a^6\,b^6+169\,a^4\,b^8-6\,a^2\,b^{10}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(288\,a^{10}\,b^4-624\,a^8\,b^6+386\,a^6\,b^8-52\,a^4\,b^{10}+2\,a^2\,b^{12}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(-24\,a^7\,b^{10}+56\,a^5\,b^{12}-36\,a^3\,b^{14}+4\,a\,b^{16}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-48\,a^8\,b^{10}+124\,a^6\,b^{12}-100\,a^4\,b^{14}+24\,a^2\,b^{16}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(8\,a^6\,b^{14}-16\,a^4\,b^{16}+8\,a^2\,b^{18}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{14}+28\,a^5\,b^{16}-32\,a^3\,b^{18}+12\,a\,b^{20}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)}{2\,b^5}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{11}\,b^4+1056\,a^9\,b^6-1322\,a^7\,b^8+640\,a^5\,b^{10}-89\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)}{2\,b^5}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(288\,a^{10}\,b^4-624\,a^8\,b^6+386\,a^6\,b^8-52\,a^4\,b^{10}+2\,a^2\,b^{12}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(-24\,a^7\,b^{10}+56\,a^5\,b^{12}-36\,a^3\,b^{14}+4\,a\,b^{16}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-48\,a^8\,b^{10}+124\,a^6\,b^{12}-100\,a^4\,b^{14}+24\,a^2\,b^{16}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(8\,a^6\,b^{14}-16\,a^4\,b^{16}+8\,a^2\,b^{18}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{14}+28\,a^5\,b^{16}-32\,a^3\,b^{18}+12\,a\,b^{20}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)}{2\,b^5}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{11}\,b^4+1056\,a^9\,b^6-1322\,a^7\,b^8+640\,a^5\,b^{10}-89\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)}{2\,b^5}}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(288\,a^{10}\,b^4-624\,a^8\,b^6+386\,a^6\,b^8-52\,a^4\,b^{10}+2\,a^2\,b^{12}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{11}\,b^4+1056\,a^9\,b^6-1322\,a^7\,b^8+640\,a^5\,b^{10}-89\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(-24\,a^7\,b^{10}+56\,a^5\,b^{12}-36\,a^3\,b^{14}+4\,a\,b^{16}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-48\,a^8\,b^{10}+124\,a^6\,b^{12}-100\,a^4\,b^{14}+24\,a^2\,b^{16}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(8\,a^6\,b^{14}-16\,a^4\,b^{16}+8\,a^2\,b^{18}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{14}+28\,a^5\,b^{16}-32\,a^3\,b^{18}+12\,a\,b^{20}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(288\,a^{10}\,b^4-624\,a^8\,b^6+386\,a^6\,b^8-52\,a^4\,b^{10}+2\,a^2\,b^{12}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{11}\,b^4+1056\,a^9\,b^6-1322\,a^7\,b^8+640\,a^5\,b^{10}-89\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(-24\,a^7\,b^{10}+56\,a^5\,b^{12}-36\,a^3\,b^{14}+4\,a\,b^{16}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-48\,a^8\,b^{10}+124\,a^6\,b^{12}-100\,a^4\,b^{14}+24\,a^2\,b^{16}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(8\,a^6\,b^{14}-16\,a^4\,b^{16}+8\,a^2\,b^{18}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{14}+28\,a^5\,b^{16}-32\,a^3\,b^{18}+12\,a\,b^{20}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}}{\frac{8\,\left(864\,a^{11}-2160\,a^9\,b^2+1746\,a^7\,b^4-491\,a^5\,b^6+30\,a^3\,b^8\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1728\,a^{12}-4752\,a^{10}\,b^2+4356\,a^8\,b^4-1495\,a^6\,b^6+169\,a^4\,b^8-6\,a^2\,b^{10}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(288\,a^{10}\,b^4-624\,a^8\,b^6+386\,a^6\,b^8-52\,a^4\,b^{10}+2\,a^2\,b^{12}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{11}\,b^4+1056\,a^9\,b^6-1322\,a^7\,b^8+640\,a^5\,b^{10}-89\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(-24\,a^7\,b^{10}+56\,a^5\,b^{12}-36\,a^3\,b^{14}+4\,a\,b^{16}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-48\,a^8\,b^{10}+124\,a^6\,b^{12}-100\,a^4\,b^{14}+24\,a^2\,b^{16}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(8\,a^6\,b^{14}-16\,a^4\,b^{16}+8\,a^2\,b^{18}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{14}+28\,a^5\,b^{16}-32\,a^3\,b^{18}+12\,a\,b^{20}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(288\,a^{10}\,b^4-624\,a^8\,b^6+386\,a^6\,b^8-52\,a^4\,b^{10}+2\,a^2\,b^{12}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{11}\,b^4+1056\,a^9\,b^6-1322\,a^7\,b^8+640\,a^5\,b^{10}-89\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(-24\,a^7\,b^{10}+56\,a^5\,b^{12}-36\,a^3\,b^{14}+4\,a\,b^{16}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-48\,a^8\,b^{10}+124\,a^6\,b^{12}-100\,a^4\,b^{14}+24\,a^2\,b^{16}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,\left(8\,a^6\,b^{14}-16\,a^4\,b^{16}+8\,a^2\,b^{18}\right)}{a^4\,b^{11}-2\,a^2\,b^{13}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{14}+28\,a^5\,b^{16}-32\,a^3\,b^{18}+12\,a\,b^{20}\right)}{a^4\,b^{12}-2\,a^2\,b^{14}+b^{16}}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{d\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}","Not used",1,"- ((12*a^5 - 11*a^3*b^2)/(b^4*(a^2 - b^2)) + (tan(c/2 + (d*x)/2)^7*(6*a^4 - 5*a^2*b^2))/(b^3*(a^2 - b^2)) - (tan(c/2 + (d*x)/2)^5*(4*b^4 - 54*a^4 + 45*a^2*b^2))/(b^3*(a^2 - b^2)) + (tan(c/2 + (d*x)/2)^3*(90*a^4 + 4*b^4 - 87*a^2*b^2))/(b^3*(a^2 - b^2)) + (tan(c/2 + (d*x)/2)^6*(12*a^5 - 14*a*b^4 + 5*a^3*b^2))/(b^4*(a^2 - b^2)) - (tan(c/2 + (d*x)/2)^2*(30*a*b^4 - 36*a^5 + a^3*b^2))/(b^4*(a^2 - b^2)) + (3*tan(c/2 + (d*x)/2)*(14*a^4 - 13*a^2*b^2))/(b^3*(a^2 - b^2)) - (tan(c/2 + (d*x)/2)^4*(11*a*b^2 - 12*a^3)*(3*a^2 + 4*b^2))/(b^4*(a^2 - b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^6*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(6*a^2 + 8*b^2) + a^2*tan(c/2 + (d*x)/2)^8 + a^2 + 12*a*b*tan(c/2 + (d*x)/2)^3 + 12*a*b*tan(c/2 + (d*x)/2)^5 + 4*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2))) - (atan((((a^2*12i - b^2*1i)*((4*(2*a^2*b^12 - 52*a^4*b^10 + 386*a^6*b^8 - 624*a^8*b^6 + 288*a^10*b^4))/(b^15 - 2*a^2*b^13 + a^4*b^11) - ((a^2*12i - b^2*1i)*((4*(4*a*b^16 - 36*a^3*b^14 + 56*a^5*b^12 - 24*a^7*b^10))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(24*a^2*b^16 - 100*a^4*b^14 + 124*a^6*b^12 - 48*a^8*b^10))/(b^16 - 2*a^2*b^14 + a^4*b^12) - ((a^2*12i - b^2*1i)*((4*(8*a^2*b^18 - 16*a^4*b^16 + 8*a^6*b^14))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(12*a*b^20 - 32*a^3*b^18 + 28*a^5*b^16 - 8*a^7*b^14))/(b^16 - 2*a^2*b^14 + a^4*b^12)))/(2*b^5)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(2*a*b^14 - 89*a^3*b^12 + 640*a^5*b^10 - 1322*a^7*b^8 + 1056*a^9*b^6 - 288*a^11*b^4))/(b^16 - 2*a^2*b^14 + a^4*b^12))*1i)/(2*b^5) + ((a^2*12i - b^2*1i)*((4*(2*a^2*b^12 - 52*a^4*b^10 + 386*a^6*b^8 - 624*a^8*b^6 + 288*a^10*b^4))/(b^15 - 2*a^2*b^13 + a^4*b^11) + ((a^2*12i - b^2*1i)*((4*(4*a*b^16 - 36*a^3*b^14 + 56*a^5*b^12 - 24*a^7*b^10))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(24*a^2*b^16 - 100*a^4*b^14 + 124*a^6*b^12 - 48*a^8*b^10))/(b^16 - 2*a^2*b^14 + a^4*b^12) + ((a^2*12i - b^2*1i)*((4*(8*a^2*b^18 - 16*a^4*b^16 + 8*a^6*b^14))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(12*a*b^20 - 32*a^3*b^18 + 28*a^5*b^16 - 8*a^7*b^14))/(b^16 - 2*a^2*b^14 + a^4*b^12)))/(2*b^5)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(2*a*b^14 - 89*a^3*b^12 + 640*a^5*b^10 - 1322*a^7*b^8 + 1056*a^9*b^6 - 288*a^11*b^4))/(b^16 - 2*a^2*b^14 + a^4*b^12))*1i)/(2*b^5))/((8*(864*a^11 + 30*a^3*b^8 - 491*a^5*b^6 + 1746*a^7*b^4 - 2160*a^9*b^2))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (16*tan(c/2 + (d*x)/2)*(1728*a^12 - 6*a^2*b^10 + 169*a^4*b^8 - 1495*a^6*b^6 + 4356*a^8*b^4 - 4752*a^10*b^2))/(b^16 - 2*a^2*b^14 + a^4*b^12) + ((a^2*12i - b^2*1i)*((4*(2*a^2*b^12 - 52*a^4*b^10 + 386*a^6*b^8 - 624*a^8*b^6 + 288*a^10*b^4))/(b^15 - 2*a^2*b^13 + a^4*b^11) - ((a^2*12i - b^2*1i)*((4*(4*a*b^16 - 36*a^3*b^14 + 56*a^5*b^12 - 24*a^7*b^10))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(24*a^2*b^16 - 100*a^4*b^14 + 124*a^6*b^12 - 48*a^8*b^10))/(b^16 - 2*a^2*b^14 + a^4*b^12) - ((a^2*12i - b^2*1i)*((4*(8*a^2*b^18 - 16*a^4*b^16 + 8*a^6*b^14))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(12*a*b^20 - 32*a^3*b^18 + 28*a^5*b^16 - 8*a^7*b^14))/(b^16 - 2*a^2*b^14 + a^4*b^12)))/(2*b^5)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(2*a*b^14 - 89*a^3*b^12 + 640*a^5*b^10 - 1322*a^7*b^8 + 1056*a^9*b^6 - 288*a^11*b^4))/(b^16 - 2*a^2*b^14 + a^4*b^12)))/(2*b^5) - ((a^2*12i - b^2*1i)*((4*(2*a^2*b^12 - 52*a^4*b^10 + 386*a^6*b^8 - 624*a^8*b^6 + 288*a^10*b^4))/(b^15 - 2*a^2*b^13 + a^4*b^11) + ((a^2*12i - b^2*1i)*((4*(4*a*b^16 - 36*a^3*b^14 + 56*a^5*b^12 - 24*a^7*b^10))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(24*a^2*b^16 - 100*a^4*b^14 + 124*a^6*b^12 - 48*a^8*b^10))/(b^16 - 2*a^2*b^14 + a^4*b^12) + ((a^2*12i - b^2*1i)*((4*(8*a^2*b^18 - 16*a^4*b^16 + 8*a^6*b^14))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(12*a*b^20 - 32*a^3*b^18 + 28*a^5*b^16 - 8*a^7*b^14))/(b^16 - 2*a^2*b^14 + a^4*b^12)))/(2*b^5)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(2*a*b^14 - 89*a^3*b^12 + 640*a^5*b^10 - 1322*a^7*b^8 + 1056*a^9*b^6 - 288*a^11*b^4))/(b^16 - 2*a^2*b^14 + a^4*b^12)))/(2*b^5)))*(a^2*12i - b^2*1i)*1i)/(b^5*d) - (a*atan(((a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(2*a^2*b^12 - 52*a^4*b^10 + 386*a^6*b^8 - 624*a^8*b^6 + 288*a^10*b^4))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(2*a*b^14 - 89*a^3*b^12 + 640*a^5*b^10 - 1322*a^7*b^8 + 1056*a^9*b^6 - 288*a^11*b^4))/(b^16 - 2*a^2*b^14 + a^4*b^12) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(4*a*b^16 - 36*a^3*b^14 + 56*a^5*b^12 - 24*a^7*b^10))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(24*a^2*b^16 - 100*a^4*b^14 + 124*a^6*b^12 - 48*a^8*b^10))/(b^16 - 2*a^2*b^14 + a^4*b^12) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(8*a^2*b^18 - 16*a^4*b^16 + 8*a^6*b^14))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(12*a*b^20 - 32*a^3*b^18 + 28*a^5*b^16 - 8*a^7*b^14))/(b^16 - 2*a^2*b^14 + a^4*b^12))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(12*a^4 + 6*b^4 - 19*a^2*b^2)*1i)/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(2*a^2*b^12 - 52*a^4*b^10 + 386*a^6*b^8 - 624*a^8*b^6 + 288*a^10*b^4))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(2*a*b^14 - 89*a^3*b^12 + 640*a^5*b^10 - 1322*a^7*b^8 + 1056*a^9*b^6 - 288*a^11*b^4))/(b^16 - 2*a^2*b^14 + a^4*b^12) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(4*a*b^16 - 36*a^3*b^14 + 56*a^5*b^12 - 24*a^7*b^10))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(24*a^2*b^16 - 100*a^4*b^14 + 124*a^6*b^12 - 48*a^8*b^10))/(b^16 - 2*a^2*b^14 + a^4*b^12) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(8*a^2*b^18 - 16*a^4*b^16 + 8*a^6*b^14))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(12*a*b^20 - 32*a^3*b^18 + 28*a^5*b^16 - 8*a^7*b^14))/(b^16 - 2*a^2*b^14 + a^4*b^12))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(12*a^4 + 6*b^4 - 19*a^2*b^2)*1i)/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))/((8*(864*a^11 + 30*a^3*b^8 - 491*a^5*b^6 + 1746*a^7*b^4 - 2160*a^9*b^2))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (16*tan(c/2 + (d*x)/2)*(1728*a^12 - 6*a^2*b^10 + 169*a^4*b^8 - 1495*a^6*b^6 + 4356*a^8*b^4 - 4752*a^10*b^2))/(b^16 - 2*a^2*b^14 + a^4*b^12) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(2*a^2*b^12 - 52*a^4*b^10 + 386*a^6*b^8 - 624*a^8*b^6 + 288*a^10*b^4))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(2*a*b^14 - 89*a^3*b^12 + 640*a^5*b^10 - 1322*a^7*b^8 + 1056*a^9*b^6 - 288*a^11*b^4))/(b^16 - 2*a^2*b^14 + a^4*b^12) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(4*a*b^16 - 36*a^3*b^14 + 56*a^5*b^12 - 24*a^7*b^10))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(24*a^2*b^16 - 100*a^4*b^14 + 124*a^6*b^12 - 48*a^8*b^10))/(b^16 - 2*a^2*b^14 + a^4*b^12) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(8*a^2*b^18 - 16*a^4*b^16 + 8*a^6*b^14))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(12*a*b^20 - 32*a^3*b^18 + 28*a^5*b^16 - 8*a^7*b^14))/(b^16 - 2*a^2*b^14 + a^4*b^12))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(2*a^2*b^12 - 52*a^4*b^10 + 386*a^6*b^8 - 624*a^8*b^6 + 288*a^10*b^4))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(2*a*b^14 - 89*a^3*b^12 + 640*a^5*b^10 - 1322*a^7*b^8 + 1056*a^9*b^6 - 288*a^11*b^4))/(b^16 - 2*a^2*b^14 + a^4*b^12) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(4*a*b^16 - 36*a^3*b^14 + 56*a^5*b^12 - 24*a^7*b^10))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(24*a^2*b^16 - 100*a^4*b^14 + 124*a^6*b^12 - 48*a^8*b^10))/(b^16 - 2*a^2*b^14 + a^4*b^12) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((4*(8*a^2*b^18 - 16*a^4*b^16 + 8*a^6*b^14))/(b^15 - 2*a^2*b^13 + a^4*b^11) + (8*tan(c/2 + (d*x)/2)*(12*a*b^20 - 32*a^3*b^18 + 28*a^5*b^16 - 8*a^7*b^14))/(b^16 - 2*a^2*b^14 + a^4*b^12))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2)*1i)/(d*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))","B"
1086,1,3031,180,15.787681,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^2)/(a + b*sin(c + d*x))^3,x)","\frac{\frac{6\,a^4-5\,a^2\,b^2}{b^3\,\left(a^2-b^2\right)}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^4+a^2\,b^2-2\,b^4\right)}{b^3\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^4+3\,a^2\,b^2-7\,b^4\right)}{b^3\,\left(a^2-b^2\right)}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-7\,a^3\right)}{b^2\,\left(a^2-b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a\,b^2-3\,a^3\right)}{b^2\,\left(a^2-b^2\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,a\,b^2-6\,a^3\right)}{b^2\,\left(a^2-b^2\right)}}{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{6\,a\,\mathrm{atan}\left(\frac{192\,a^2\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{192\,a^2\,b^{19}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{384\,a^4\,b^{17}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{48\,a^6\,b^{15}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{288\,a^8\,b^{13}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{144\,a^{10}\,b^{11}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}}-\frac{144\,a^6\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{192\,a^2\,b^{19}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{384\,a^4\,b^{17}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{48\,a^6\,b^{15}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{288\,a^8\,b^{13}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{144\,a^{10}\,b^{11}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}}\right)}{b^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(36\,a^8\,b^3-72\,a^6\,b^5+36\,a^4\,b^7\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^9\,b^3-252\,a^7\,b^5+285\,a^5\,b^7-108\,a^3\,b^9+4\,a\,b^{11}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-24\,a^7\,b^8+60\,a^5\,b^{10}-44\,a^3\,b^{12}+8\,a\,b^{14}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{8\,\left(6\,a^6\,b^8-14\,a^4\,b^{10}+8\,a^2\,b^{12}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(36\,a^8\,b^3-72\,a^6\,b^5+36\,a^4\,b^7\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^9\,b^3-252\,a^7\,b^5+285\,a^5\,b^7-108\,a^3\,b^9+4\,a\,b^{11}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(6\,a^6\,b^8-14\,a^4\,b^{10}+8\,a^2\,b^{12}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-24\,a^7\,b^8+60\,a^5\,b^{10}-44\,a^3\,b^{12}+8\,a\,b^{14}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(54\,a^8-117\,a^6\,b^2+72\,a^4\,b^4-12\,a^2\,b^6\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(216\,a^9-540\,a^7\,b^2+396\,a^5\,b^4-72\,a^3\,b^6\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(36\,a^8\,b^3-72\,a^6\,b^5+36\,a^4\,b^7\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^9\,b^3-252\,a^7\,b^5+285\,a^5\,b^7-108\,a^3\,b^9+4\,a\,b^{11}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-24\,a^7\,b^8+60\,a^5\,b^{10}-44\,a^3\,b^{12}+8\,a\,b^{14}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{8\,\left(6\,a^6\,b^8-14\,a^4\,b^{10}+8\,a^2\,b^{12}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(36\,a^8\,b^3-72\,a^6\,b^5+36\,a^4\,b^7\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^9\,b^3-252\,a^7\,b^5+285\,a^5\,b^7-108\,a^3\,b^9+4\,a\,b^{11}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(6\,a^6\,b^8-14\,a^4\,b^{10}+8\,a^2\,b^{12}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-24\,a^7\,b^8+60\,a^5\,b^{10}-44\,a^3\,b^{12}+8\,a\,b^{14}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"((6*a^4 - 5*a^2*b^2)/(b^3*(a^2 - b^2)) + (3*tan(c/2 + (d*x)/2)^4*(2*a^4 - 2*b^4 + a^2*b^2))/(b^3*(a^2 - b^2)) + (2*tan(c/2 + (d*x)/2)^2*(6*a^4 - 7*b^4 + 3*a^2*b^2))/(b^3*(a^2 - b^2)) - (3*tan(c/2 + (d*x)/2)*(6*a*b^2 - 7*a^3))/(b^2*(a^2 - b^2)) - (tan(c/2 + (d*x)/2)^5*(2*a*b^2 - 3*a^3))/(b^2*(a^2 - b^2)) - (4*tan(c/2 + (d*x)/2)^3*(5*a*b^2 - 6*a^3))/(b^2*(a^2 - 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))) + (6*a*atan((192*a^2*b^7*tan(c/2 + (d*x)/2))/((192*a^2*b^19)/(b^12 - 2*a^2*b^10 + a^4*b^8) - (384*a^4*b^17)/(b^12 - 2*a^2*b^10 + a^4*b^8) + (48*a^6*b^15)/(b^12 - 2*a^2*b^10 + a^4*b^8) + (288*a^8*b^13)/(b^12 - 2*a^2*b^10 + a^4*b^8) - (144*a^10*b^11)/(b^12 - 2*a^2*b^10 + a^4*b^8)) - (144*a^6*b^3*tan(c/2 + (d*x)/2))/((192*a^2*b^19)/(b^12 - 2*a^2*b^10 + a^4*b^8) - (384*a^4*b^17)/(b^12 - 2*a^2*b^10 + a^4*b^8) + (48*a^6*b^15)/(b^12 - 2*a^2*b^10 + a^4*b^8) + (288*a^8*b^13)/(b^12 - 2*a^2*b^10 + a^4*b^8) - (144*a^10*b^11)/(b^12 - 2*a^2*b^10 + a^4*b^8))))/(b^4*d) + (atan((((-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*((8*(36*a^4*b^7 - 72*a^6*b^5 + 36*a^8*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (8*tan(c/2 + (d*x)/2)*(4*a*b^11 - 108*a^3*b^9 + 285*a^5*b^7 - 252*a^7*b^5 + 72*a^9*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*((8*tan(c/2 + (d*x)/2)*(8*a*b^14 - 44*a^3*b^12 + 60*a^5*b^10 - 24*a^7*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (8*(8*a^2*b^12 - 14*a^4*b^10 + 6*a^6*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + ((-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + ((-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*((8*(36*a^4*b^7 - 72*a^6*b^5 + 36*a^8*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (8*tan(c/2 + (d*x)/2)*(4*a*b^11 - 108*a^3*b^9 + 285*a^5*b^7 - 252*a^7*b^5 + 72*a^9*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*((8*(8*a^2*b^12 - 14*a^4*b^10 + 6*a^6*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (8*tan(c/2 + (d*x)/2)*(8*a*b^14 - 44*a^3*b^12 + 60*a^5*b^10 - 24*a^7*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(54*a^8 - 12*a^2*b^6 + 72*a^4*b^4 - 117*a^6*b^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (16*tan(c/2 + (d*x)/2)*(216*a^9 - 72*a^3*b^6 + 396*a^5*b^4 - 540*a^7*b^2))/(b^13 - 2*a^2*b^11 + a^4*b^9) - ((-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*((8*(36*a^4*b^7 - 72*a^6*b^5 + 36*a^8*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (8*tan(c/2 + (d*x)/2)*(4*a*b^11 - 108*a^3*b^9 + 285*a^5*b^7 - 252*a^7*b^5 + 72*a^9*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*((8*tan(c/2 + (d*x)/2)*(8*a*b^14 - 44*a^3*b^12 + 60*a^5*b^10 - 24*a^7*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (8*(8*a^2*b^12 - 14*a^4*b^10 + 6*a^6*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + ((-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + ((-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*((8*(36*a^4*b^7 - 72*a^6*b^5 + 36*a^8*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (8*tan(c/2 + (d*x)/2)*(4*a*b^11 - 108*a^3*b^9 + 285*a^5*b^7 - 252*a^7*b^5 + 72*a^9*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*((8*(8*a^2*b^12 - 14*a^4*b^10 + 6*a^6*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (8*tan(c/2 + (d*x)/2)*(8*a*b^14 - 44*a^3*b^12 + 60*a^5*b^10 - 24*a^7*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
1087,1,2709,167,13.929942,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x))/(a + b*sin(c + d*x))^3,x)","\frac{2\,\mathrm{atan}\left(\frac{64\,a\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{176\,a^3\,b^{12}}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{160\,a^5\,b^{10}}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{48\,a^7\,b^8}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{64\,a\,b^{14}}{a^4\,b^5-2\,a^2\,b^7+b^9}}-\frac{48\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{176\,a^3\,b^{12}}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{160\,a^5\,b^{10}}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{48\,a^7\,b^8}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{64\,a\,b^{14}}{a^4\,b^5-2\,a^2\,b^7+b^9}}\right)}{b^3\,d}-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^2-4\,b^2\right)}{b\,\left(a^2-b^2\right)}-\frac{a\,b^2-2\,a^3}{b^2\,\left(a^2-b^2\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)\,\left(2\,a^2-b^2\right)}{a\,b^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{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^2-8\,a^4\,b^4+4\,a^2\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^2+28\,a^5\,b^4-29\,a^3\,b^6+8\,a\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,a^5\,b^6-6\,a^3\,b^8+4\,a\,b^{10}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6\,b^6-20\,a^4\,b^8+12\,a^2\,b^{10}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^8-8\,a^4\,b^{10}+4\,a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^8+28\,a^5\,b^{10}-32\,a^3\,b^{12}+12\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^2-8\,a^4\,b^4+4\,a^2\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^2+28\,a^5\,b^4-29\,a^3\,b^6+8\,a\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,a^5\,b^6-6\,a^3\,b^8+4\,a\,b^{10}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6\,b^6-20\,a^4\,b^8+12\,a^2\,b^{10}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^8-8\,a^4\,b^{10}+4\,a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^8+28\,a^5\,b^{10}-32\,a^3\,b^{12}+12\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}}{\frac{16\,\left(2\,a^5-3\,a^3\,b^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-20\,a^4\,b^2+12\,a^2\,b^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^2-8\,a^4\,b^4+4\,a^2\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^2+28\,a^5\,b^4-29\,a^3\,b^6+8\,a\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,a^5\,b^6-6\,a^3\,b^8+4\,a\,b^{10}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6\,b^6-20\,a^4\,b^8+12\,a^2\,b^{10}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^8-8\,a^4\,b^{10}+4\,a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^8+28\,a^5\,b^{10}-32\,a^3\,b^{12}+12\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^2-8\,a^4\,b^4+4\,a^2\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^2+28\,a^5\,b^4-29\,a^3\,b^6+8\,a\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,a^5\,b^6-6\,a^3\,b^8+4\,a\,b^{10}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6\,b^6-20\,a^4\,b^8+12\,a^2\,b^{10}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^8-8\,a^4\,b^{10}+4\,a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7\,b^8+28\,a^5\,b^{10}-32\,a^3\,b^{12}+12\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"(2*atan((64*a*b^5*tan(c/2 + (d*x)/2))/((176*a^3*b^12)/(b^9 - 2*a^2*b^7 + a^4*b^5) - (160*a^5*b^10)/(b^9 - 2*a^2*b^7 + a^4*b^5) + (48*a^7*b^8)/(b^9 - 2*a^2*b^7 + a^4*b^5) - (64*a*b^14)/(b^9 - 2*a^2*b^7 + a^4*b^5)) - (48*a^3*b^3*tan(c/2 + (d*x)/2))/((176*a^3*b^12)/(b^9 - 2*a^2*b^7 + a^4*b^5) - (160*a^5*b^10)/(b^9 - 2*a^2*b^7 + a^4*b^5) + (48*a^7*b^8)/(b^9 - 2*a^2*b^7 + a^4*b^5) - (64*a*b^14)/(b^9 - 2*a^2*b^7 + a^4*b^5))))/(b^3*d) - ((tan(c/2 + (d*x)/2)*(7*a^2 - 4*b^2))/(b*(a^2 - b^2)) - (a*b^2 - 2*a^3)/(b^2*(a^2 - b^2)) + (a^2*tan(c/2 + (d*x)/2)^3)/(b*(a^2 - b^2)) + (tan(c/2 + (d*x)/2)^2*(a^2 + 2*b^2)*(2*a^2 - b^2))/(a*b^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))) - (a*atan(((a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^6 - 8*a^4*b^4 + 4*a^6*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(8*a*b^8 - 29*a^3*b^6 + 28*a^5*b^4 - 8*a^7*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a*b^10 - 6*a^3*b^8 + 2*a^5*b^6))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(12*a^2*b^10 - 20*a^4*b^8 + 8*a^6*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^12 - 8*a^4*b^10 + 4*a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(12*a*b^14 - 32*a^3*b^12 + 28*a^5*b^10 - 8*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6)))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*1i)/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^6 - 8*a^4*b^4 + 4*a^6*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(8*a*b^8 - 29*a^3*b^6 + 28*a^5*b^4 - 8*a^7*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a*b^10 - 6*a^3*b^8 + 2*a^5*b^6))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(12*a^2*b^10 - 20*a^4*b^8 + 8*a^6*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^12 - 8*a^4*b^10 + 4*a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(12*a*b^14 - 32*a^3*b^12 + 28*a^5*b^10 - 8*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6)))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*1i)/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))/((16*(2*a^5 - 3*a^3*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (16*tan(c/2 + (d*x)/2)*(8*a^6 + 12*a^2*b^4 - 20*a^4*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^6 - 8*a^4*b^4 + 4*a^6*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(8*a*b^8 - 29*a^3*b^6 + 28*a^5*b^4 - 8*a^7*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a*b^10 - 6*a^3*b^8 + 2*a^5*b^6))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(12*a^2*b^10 - 20*a^4*b^8 + 8*a^6*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^12 - 8*a^4*b^10 + 4*a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(12*a*b^14 - 32*a^3*b^12 + 28*a^5*b^10 - 8*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6)))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^6 - 8*a^4*b^4 + 4*a^6*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(8*a*b^8 - 29*a^3*b^6 + 28*a^5*b^4 - 8*a^7*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a*b^10 - 6*a^3*b^8 + 2*a^5*b^6))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(12*a^2*b^10 - 20*a^4*b^8 + 8*a^6*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^12 - 8*a^4*b^10 + 4*a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (8*tan(c/2 + (d*x)/2)*(12*a*b^14 - 32*a^3*b^12 + 28*a^5*b^10 - 8*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6)))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
1088,1,1610,154,12.439323,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)*(a + b*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{\frac{2\,a^2-3\,b^2}{a\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^4+a^2\,b^2-6\,b^4\right)}{a^3\,\left(a^2-b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2\,b-8\,b^3\right)}{a^2\,\left(a^2-b^2\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2-4\,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{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{5\,a^5\,b-4\,a^3\,b^3}{a^6-a^4\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^7+14\,a^5\,b^2-20\,a^3\,b^4+8\,a\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{b\,\left(\frac{2\,a^8\,b-2\,a^6\,b^3}{a^6-a^4\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{10}-20\,a^8\,b^2+22\,a^6\,b^4-8\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}+\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{5\,a^5\,b-4\,a^3\,b^3}{a^6-a^4\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^7+14\,a^5\,b^2-20\,a^3\,b^4+8\,a\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b\,\left(\frac{2\,a^8\,b-2\,a^6\,b^3}{a^6-a^4\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{10}-20\,a^8\,b^2+22\,a^6\,b^4-8\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}}{\frac{2\,\left(3\,a^2\,b-2\,b^3\right)}{a^6-a^4\,b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,b^4-3\,a^2\,b^2\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{5\,a^5\,b-4\,a^3\,b^3}{a^6-a^4\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^7+14\,a^5\,b^2-20\,a^3\,b^4+8\,a\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{b\,\left(\frac{2\,a^8\,b-2\,a^6\,b^3}{a^6-a^4\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{10}-20\,a^8\,b^2+22\,a^6\,b^4-8\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}+\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{5\,a^5\,b-4\,a^3\,b^3}{a^6-a^4\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^7+14\,a^5\,b^2-20\,a^3\,b^4+8\,a\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b\,\left(\frac{2\,a^8\,b-2\,a^6\,b^3}{a^6-a^4\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{10}-20\,a^8\,b^2+22\,a^6\,b^4-8\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) + ((2*a^2 - 3*b^2)/(a*(a^2 - b^2)) + (tan(c/2 + (d*x)/2)^2*(2*a^4 - 6*b^4 + a^2*b^2))/(a^3*(a^2 - b^2)) + (tan(c/2 + (d*x)/2)*(5*a^2*b - 8*b^3))/(a^2*(a^2 - b^2)) + (b*tan(c/2 + (d*x)/2)^3*(3*a^2 - 4*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))) + (b*atan(((b*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((5*a^5*b - 4*a^3*b^3)/(a^6 - a^4*b^2) + (tan(c/2 + (d*x)/2)*(8*a*b^6 - 2*a^7 - 20*a^3*b^4 + 14*a^5*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (b*((2*a^8*b - 2*a^6*b^3)/(a^6 - a^4*b^2) - (tan(c/2 + (d*x)/2)*(6*a^10 - 8*a^4*b^6 + 22*a^6*b^4 - 20*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*1i)/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)) + (b*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((5*a^5*b - 4*a^3*b^3)/(a^6 - a^4*b^2) + (tan(c/2 + (d*x)/2)*(8*a*b^6 - 2*a^7 - 20*a^3*b^4 + 14*a^5*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b*((2*a^8*b - 2*a^6*b^3)/(a^6 - a^4*b^2) - (tan(c/2 + (d*x)/2)*(6*a^10 - 8*a^4*b^6 + 22*a^6*b^4 - 20*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*1i)/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))/((2*(3*a^2*b - 2*b^3))/(a^6 - a^4*b^2) + (2*tan(c/2 + (d*x)/2)*(2*b^4 - 3*a^2*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (b*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((5*a^5*b - 4*a^3*b^3)/(a^6 - a^4*b^2) + (tan(c/2 + (d*x)/2)*(8*a*b^6 - 2*a^7 - 20*a^3*b^4 + 14*a^5*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (b*((2*a^8*b - 2*a^6*b^3)/(a^6 - a^4*b^2) - (tan(c/2 + (d*x)/2)*(6*a^10 - 8*a^4*b^6 + 22*a^6*b^4 - 20*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)) + (b*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((5*a^5*b - 4*a^3*b^3)/(a^6 - a^4*b^2) + (tan(c/2 + (d*x)/2)*(8*a*b^6 - 2*a^7 - 20*a^3*b^4 + 14*a^5*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b*((2*a^8*b - 2*a^6*b^3)/(a^6 - a^4*b^2) - (tan(c/2 + (d*x)/2)*(6*a^10 - 8*a^4*b^6 + 22*a^6*b^4 - 20*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
1089,1,1762,202,10.630622,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{a^2-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a\,b^3-6\,a^3\,b\right)}{a^2-b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^4+9\,a^2\,b^2-12\,b^4\right)}{a^2-b^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^4+12\,a^2\,b^2-16\,b^4\right)}{a^2-b^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^4\,b+a^2\,b^3-10\,b^5\right)}{a\,\left(a^2-b^2\right)}}{d\,\left(2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^5+8\,a^3\,b^2\right)+2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(\frac{2\,a^8-15\,a^6\,b^2+12\,a^4\,b^4}{a^8-a^6\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^8\,b-46\,a^6\,b^3+60\,a^4\,b^5-24\,a^2\,b^7\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}+\frac{\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(\frac{2\,a^8-15\,a^6\,b^2+12\,a^4\,b^4}{a^8-a^6\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^8\,b-46\,a^6\,b^3+60\,a^4\,b^5-24\,a^2\,b^7\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}-\frac{\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{2\,\left(6\,a^4\,b-27\,a^2\,b^3+18\,b^5\right)}{a^8-a^6\,b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-24\,a^4\,b^2+39\,a^2\,b^4-18\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}-\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(\frac{2\,a^8-15\,a^6\,b^2+12\,a^4\,b^4}{a^8-a^6\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^8\,b-46\,a^6\,b^3+60\,a^4\,b^5-24\,a^2\,b^7\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}+\frac{\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(\frac{2\,a^8-15\,a^6\,b^2+12\,a^4\,b^4}{a^8-a^6\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^8\,b-46\,a^6\,b^3+60\,a^4\,b^5-24\,a^2\,b^7\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}-\frac{\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - (a^2 - (2*tan(c/2 + (d*x)/2)*(7*a*b^3 - 6*a^3*b))/(a^2 - b^2) + (tan(c/2 + (d*x)/2)^4*(a^4 - 12*b^4 + 9*a^2*b^2))/(a^2 - b^2) + (2*tan(c/2 + (d*x)/2)^2*(a^4 - 16*b^4 + 12*a^2*b^2))/(a^2 - b^2) + (2*tan(c/2 + (d*x)/2)^3*(6*a^4*b - 10*b^5 + a^2*b^3))/(a*(a^2 - b^2)))/(d*(2*a^5*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^3*(4*a^5 + 8*a^3*b^2) + 2*a^5*tan(c/2 + (d*x)/2) + 8*a^4*b*tan(c/2 + (d*x)/2)^2 + 8*a^4*b*tan(c/2 + (d*x)/2)^4)) - (3*b*log(tan(c/2 + (d*x)/2)))/(a^4*d) - (atan((((-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*((2*a^8 + 12*a^4*b^4 - 15*a^6*b^2)/(a^8 - a^6*b^2) + (tan(c/2 + (d*x)/2)*(10*a^8*b - 24*a^2*b^7 + 60*a^4*b^5 - 46*a^6*b^3))/(a^9 + a^5*b^4 - 2*a^7*b^2) + (((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + ((-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*((2*a^8 + 12*a^4*b^4 - 15*a^6*b^2)/(a^8 - a^6*b^2) + (tan(c/2 + (d*x)/2)*(10*a^8*b - 24*a^2*b^7 + 60*a^4*b^5 - 46*a^6*b^3))/(a^9 + a^5*b^4 - 2*a^7*b^2) - (((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((2*(6*a^4*b + 18*b^5 - 27*a^2*b^3))/(a^8 - a^6*b^2) + (2*tan(c/2 + (d*x)/2)*(4*a^6 - 18*b^6 + 39*a^2*b^4 - 24*a^4*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2) - ((-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*((2*a^8 + 12*a^4*b^4 - 15*a^6*b^2)/(a^8 - a^6*b^2) + (tan(c/2 + (d*x)/2)*(10*a^8*b - 24*a^2*b^7 + 60*a^4*b^5 - 46*a^6*b^3))/(a^9 + a^5*b^4 - 2*a^7*b^2) + (((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + ((-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*((2*a^8 + 12*a^4*b^4 - 15*a^6*b^2)/(a^8 - a^6*b^2) + (tan(c/2 + (d*x)/2)*(10*a^8*b - 24*a^2*b^7 + 60*a^4*b^5 - 46*a^6*b^3))/(a^9 + a^5*b^4 - 2*a^7*b^2) - (((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
1090,1,1906,269,11.006044,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^3*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{\frac{a^3}{2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^4\,b+11\,a^2\,b^3-16\,b^5\right)}{a^2-b^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,a^4\,b+41\,a^2\,b^3-52\,b^5\right)}{a^2-b^2}-4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^5-47\,a^3\,b^2+50\,a\,b^4\right)}{a^2-b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^6-97\,a^4\,b^2+8\,a^2\,b^4+112\,b^6\right)}{2\,a\,\left(a^2-b^2\right)}}{d\,\left(4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^6+16\,a^4\,b^2\right)+16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-12\,b^2\right)}{2\,a^5\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(\frac{7\,a^9\,b-32\,a^7\,b^3+24\,a^5\,b^5}{a^{10}-a^8\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{11}-28\,a^9\,b^2+103\,a^7\,b^4-124\,a^5\,b^6+48\,a^3\,b^8\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}+\frac{b\,\left(\frac{2\,a^{12}\,b-2\,a^{10}\,b^3}{a^{10}-a^8\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{14}-20\,a^{12}\,b^2+22\,a^{10}\,b^4-8\,a^8\,b^6\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{11}-28\,a^9\,b^2+103\,a^7\,b^4-124\,a^5\,b^6+48\,a^3\,b^8\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}-\frac{7\,a^9\,b-32\,a^7\,b^3+24\,a^5\,b^5}{a^{10}-a^8\,b^2}+\frac{b\,\left(\frac{2\,a^{12}\,b-2\,a^{10}\,b^3}{a^{10}-a^8\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{14}-20\,a^{12}\,b^2+22\,a^{10}\,b^4-8\,a^8\,b^6\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}}{\frac{6\,a^6\,b-91\,a^4\,b^3+240\,a^2\,b^5-144\,b^7}{a^{10}-a^8\,b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-30\,a^6\,b^2+131\,a^4\,b^4-174\,a^2\,b^6+72\,b^8\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(\frac{7\,a^9\,b-32\,a^7\,b^3+24\,a^5\,b^5}{a^{10}-a^8\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{11}-28\,a^9\,b^2+103\,a^7\,b^4-124\,a^5\,b^6+48\,a^3\,b^8\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}+\frac{b\,\left(\frac{2\,a^{12}\,b-2\,a^{10}\,b^3}{a^{10}-a^8\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{14}-20\,a^{12}\,b^2+22\,a^{10}\,b^4-8\,a^8\,b^6\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{11}-28\,a^9\,b^2+103\,a^7\,b^4-124\,a^5\,b^6+48\,a^3\,b^8\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}-\frac{7\,a^9\,b-32\,a^7\,b^3+24\,a^5\,b^5}{a^{10}-a^8\,b^2}+\frac{b\,\left(\frac{2\,a^{12}\,b-2\,a^{10}\,b^3}{a^{10}-a^8\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{14}-20\,a^{12}\,b^2+22\,a^{10}\,b^4-8\,a^8\,b^6\right)}{a^{11}-2\,a^9\,b^2+a^7\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{d\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^3*d) - (a^3/2 - (2*tan(c/2 + (d*x)/2)^5*(3*a^4*b - 16*b^5 + 11*a^2*b^3))/(a^2 - b^2) - (2*tan(c/2 + (d*x)/2)^3*(5*a^4*b - 52*b^5 + 41*a^2*b^3))/(a^2 - b^2) - 4*a^2*b*tan(c/2 + (d*x)/2) + (tan(c/2 + (d*x)/2)^2*(50*a*b^4 + a^5 - 47*a^3*b^2))/(a^2 - b^2) + (tan(c/2 + (d*x)/2)^4*(a^6 + 112*b^6 + 8*a^2*b^4 - 97*a^4*b^2))/(2*a*(a^2 - b^2)))/(d*(4*a^6*tan(c/2 + (d*x)/2)^2 + 4*a^6*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^4*(8*a^6 + 16*a^4*b^2) + 16*a^5*b*tan(c/2 + (d*x)/2)^3 + 16*a^5*b*tan(c/2 + (d*x)/2)^5)) - (3*b*tan(c/2 + (d*x)/2))/(2*a^4*d) - (log(tan(c/2 + (d*x)/2))*(a^2 - 12*b^2))/(2*a^5*d) - (b*atan(((b*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*((7*a^9*b + 24*a^5*b^5 - 32*a^7*b^3)/(a^10 - a^8*b^2) - (tan(c/2 + (d*x)/2)*(a^11 + 48*a^3*b^8 - 124*a^5*b^6 + 103*a^7*b^4 - 28*a^9*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2) + (b*((2*a^12*b - 2*a^10*b^3)/(a^10 - a^8*b^2) - (tan(c/2 + (d*x)/2)*(6*a^14 - 8*a^8*b^6 + 22*a^10*b^4 - 20*a^12*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*1i)/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*((tan(c/2 + (d*x)/2)*(a^11 + 48*a^3*b^8 - 124*a^5*b^6 + 103*a^7*b^4 - 28*a^9*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2) - (7*a^9*b + 24*a^5*b^5 - 32*a^7*b^3)/(a^10 - a^8*b^2) + (b*((2*a^12*b - 2*a^10*b^3)/(a^10 - a^8*b^2) - (tan(c/2 + (d*x)/2)*(6*a^14 - 8*a^8*b^6 + 22*a^10*b^4 - 20*a^12*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*1i)/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))/((6*a^6*b - 144*b^7 + 240*a^2*b^5 - 91*a^4*b^3)/(a^10 - a^8*b^2) + (2*tan(c/2 + (d*x)/2)*(72*b^8 - 174*a^2*b^6 + 131*a^4*b^4 - 30*a^6*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*((7*a^9*b + 24*a^5*b^5 - 32*a^7*b^3)/(a^10 - a^8*b^2) - (tan(c/2 + (d*x)/2)*(a^11 + 48*a^3*b^8 - 124*a^5*b^6 + 103*a^7*b^4 - 28*a^9*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2) + (b*((2*a^12*b - 2*a^10*b^3)/(a^10 - a^8*b^2) - (tan(c/2 + (d*x)/2)*(6*a^14 - 8*a^8*b^6 + 22*a^10*b^4 - 20*a^12*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*((tan(c/2 + (d*x)/2)*(a^11 + 48*a^3*b^8 - 124*a^5*b^6 + 103*a^7*b^4 - 28*a^9*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2) - (7*a^9*b + 24*a^5*b^5 - 32*a^7*b^3)/(a^10 - a^8*b^2) + (b*((2*a^12*b - 2*a^10*b^3)/(a^10 - a^8*b^2) - (tan(c/2 + (d*x)/2)*(6*a^14 - 8*a^8*b^6 + 22*a^10*b^4 - 20*a^12*b^2))/(a^11 + a^7*b^4 - 2*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*1i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
1091,0,-1,347,0.000000,"\text{Not used}","int(cos(e + f*x)^2/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(5/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{\sqrt{d\,\sin\left(e+f\,x\right)}\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(e + f*x)^2/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(5/2)), x)","F"
1092,1,223,143,13.316708,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^4*(a + b*sin(c + d*x)),x)","\frac{3\,a\,x}{128}-\frac{-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}-\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{32}+\frac{155\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{32\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}-\frac{169\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}-16\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{112\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{5}+\frac{169\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}-\frac{32\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}-\frac{155\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}+\frac{64\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}+\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}+\frac{16\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{16\,b}{315}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(3*a*x)/128 - ((16*b)/315 + (3*a*tan(c/2 + (d*x)/2))/64 + (13*a*tan(c/2 + (d*x)/2)^3)/32 - (155*a*tan(c/2 + (d*x)/2)^5)/32 + (169*a*tan(c/2 + (d*x)/2)^7)/32 - (169*a*tan(c/2 + (d*x)/2)^11)/32 + (155*a*tan(c/2 + (d*x)/2)^13)/32 - (13*a*tan(c/2 + (d*x)/2)^15)/32 - (3*a*tan(c/2 + (d*x)/2)^17)/64 + (16*b*tan(c/2 + (d*x)/2)^2)/35 + (64*b*tan(c/2 + (d*x)/2)^4)/35 - (32*b*tan(c/2 + (d*x)/2)^6)/5 + (112*b*tan(c/2 + (d*x)/2)^8)/5 - 16*b*tan(c/2 + (d*x)/2)^10 + (32*b*tan(c/2 + (d*x)/2)^12)/3)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
1093,1,209,127,13.166190,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^3*(a + b*sin(c + d*x)),x)","\frac{3\,b\,x}{128}-\frac{-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}-\frac{23\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\frac{333\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}-\frac{671\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{671\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{64}+\frac{32\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}-\frac{333\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64}-\frac{4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{23\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}+\frac{32\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{4\,a}{35}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"(3*b*x)/128 - ((4*a)/35 + (3*b*tan(c/2 + (d*x)/2))/64 + (32*a*tan(c/2 + (d*x)/2)^2)/35 - (4*a*tan(c/2 + (d*x)/2)^4)/5 + (32*a*tan(c/2 + (d*x)/2)^6)/5 + 4*a*tan(c/2 + (d*x)/2)^8 + 4*a*tan(c/2 + (d*x)/2)^12 + (23*b*tan(c/2 + (d*x)/2)^3)/64 - (333*b*tan(c/2 + (d*x)/2)^5)/64 + (671*b*tan(c/2 + (d*x)/2)^7)/64 - (671*b*tan(c/2 + (d*x)/2)^9)/64 + (333*b*tan(c/2 + (d*x)/2)^11)/64 - (23*b*tan(c/2 + (d*x)/2)^13)/64 - (3*b*tan(c/2 + (d*x)/2)^15)/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
1094,1,181,103,13.024667,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + b*sin(c + d*x)),x)","\frac{a\,x}{16}-\frac{-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{6}+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{31\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}-4\,b\,{\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)}^6+\frac{31\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{24}-\frac{8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{4\,b}{35}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(a*x)/16 - ((4*b)/35 + (a*tan(c/2 + (d*x)/2))/8 - (11*a*tan(c/2 + (d*x)/2)^3)/6 + (31*a*tan(c/2 + (d*x)/2)^5)/24 - (31*a*tan(c/2 + (d*x)/2)^9)/24 + (11*a*tan(c/2 + (d*x)/2)^11)/6 - (a*tan(c/2 + (d*x)/2)^13)/8 + (4*b*tan(c/2 + (d*x)/2)^2)/5 - (8*b*tan(c/2 + (d*x)/2)^4)/5 + 8*b*tan(c/2 + (d*x)/2)^6 - 4*b*tan(c/2 + (d*x)/2)^8 + 4*b*tan(c/2 + (d*x)/2)^10)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
1095,1,181,87,12.860007,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x)),x)","\frac{b\,x}{16}-\frac{-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{47\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{13\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{13\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{47\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{2\,a}{5}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(b*x)/16 - ((2*a)/5 + (b*tan(c/2 + (d*x)/2))/8 + (2*a*tan(c/2 + (d*x)/2)^2)/5 + 4*a*tan(c/2 + (d*x)/2)^4 + 4*a*tan(c/2 + (d*x)/2)^6 + 2*a*tan(c/2 + (d*x)/2)^8 + 2*a*tan(c/2 + (d*x)/2)^10 - (47*b*tan(c/2 + (d*x)/2)^3)/24 + (13*b*tan(c/2 + (d*x)/2)^5)/4 - (13*b*tan(c/2 + (d*x)/2)^7)/4 + (47*b*tan(c/2 + (d*x)/2)^9)/24 - (b*tan(c/2 + (d*x)/2)^11)/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
1096,1,242,89,10.823873,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x),x)","\frac{3\,b\,\mathrm{atan}\left(\frac{9\,b^2}{16\,\left(\frac{3\,a\,b}{2}-\frac{9\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{3\,a\,b}{2}-\frac{9\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}+\frac{-\frac{5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{8\,a}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(3*b*atan((9*b^2)/(16*((3*a*b)/2 - (9*b^2*tan(c/2 + (d*x)/2))/16)) + (3*a*b*tan(c/2 + (d*x)/2))/(2*((3*a*b)/2 - (9*b^2*tan(c/2 + (d*x)/2))/16))))/(4*d) + ((8*a)/3 + (5*b*tan(c/2 + (d*x)/2))/4 + (20*a*tan(c/2 + (d*x)/2)^2)/3 + 8*a*tan(c/2 + (d*x)/2)^4 + 4*a*tan(c/2 + (d*x)/2)^6 - (3*b*tan(c/2 + (d*x)/2)^3)/4 + (3*b*tan(c/2 + (d*x)/2)^5)/4 - (5*b*tan(c/2 + (d*x)/2)^7)/4)/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*log(tan(c/2 + (d*x)/2)))/d","B"
1097,1,241,83,9.388422,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,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+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+\frac{16\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-a}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{3\,a\,\mathrm{atan}\left(\frac{9\,a^2}{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,b\,a}-\frac{6\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,b\,a}\right)}{d}","Not used",1,"((16*b*tan(c/2 + (d*x)/2))/3 - a - 5*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 + 8*b*tan(c/2 + (d*x)/2)^3 + 8*b*tan(c/2 + (d*x)/2)^5)/(d*(2*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^3 + 6*tan(c/2 + (d*x)/2)^5 + 2*tan(c/2 + (d*x)/2)^7)) + (a*tan(c/2 + (d*x)/2))/(2*d) + (b*log(tan(c/2 + (d*x)/2)))/d + (3*a*atan((9*a^2)/(6*a*b + 9*a^2*tan(c/2 + (d*x)/2)) - (6*a*b*tan(c/2 + (d*x)/2))/(6*a*b + 9*a^2*tan(c/2 + (d*x)/2))))/d","B"
1098,1,236,94,9.373072,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+9\,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)+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{3\,b\,\mathrm{atan}\left(\frac{9\,b^2}{9\,a\,b-9\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{9\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,a\,b-9\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + 2*b*tan(c/2 + (d*x)/2) + 9*a*tan(c/2 + (d*x)/2)^2 + (17*a*tan(c/2 + (d*x)/2)^4)/2 + 8*b*tan(c/2 + (d*x)/2)^3 - 2*b*tan(c/2 + (d*x)/2)^5)/(d*(4*tan(c/2 + (d*x)/2)^2 + 8*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6)) - (3*b*atan((9*b^2)/(9*a*b - 9*b^2*tan(c/2 + (d*x)/2)) + (9*a*b*tan(c/2 + (d*x)/2))/(9*a*b - 9*b^2*tan(c/2 + (d*x)/2))))/d + (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*a*log(tan(c/2 + (d*x)/2)))/(2*d)","B"
1099,1,225,82,9.445602,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x)^4,x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+17\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,b\,a}-\frac{6\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,b\,a}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a/3 + b*tan(c/2 + (d*x)/2) - (14*a*tan(c/2 + (d*x)/2)^2)/3 - 5*a*tan(c/2 + (d*x)/2)^4 + 17*b*tan(c/2 + (d*x)/2)^3)/(d*(8*tan(c/2 + (d*x)/2)^3 + 8*tan(c/2 + (d*x)/2)^5)) - (5*a*tan(c/2 + (d*x)/2))/(8*d) + (b*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*b*log(tan(c/2 + (d*x)/2)))/(2*d) - (2*a*atan((4*a^2)/(6*a*b + 4*a^2*tan(c/2 + (d*x)/2)) - (6*a*b*tan(c/2 + (d*x)/2))/(6*a*b + 4*a^2*tan(c/2 + (d*x)/2))))/d","B"
1100,1,221,88,9.674241,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x)^5,x)","\frac{3\,a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8\,d}+\frac{5\,b\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{2\,b\,\mathrm{atan}\left(\frac{8\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{b\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}","Not used",1,"(3*a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(8*d) + (5*b*cot(c/2 + (d*x)/2))/(8*d) - (5*b*tan(c/2 + (d*x)/2))/(8*d) + (2*b*atan((8*b*cos(c/2 + (d*x)/2) + 3*a*sin(c/2 + (d*x)/2))/(3*a*cos(c/2 + (d*x)/2) - 8*b*sin(c/2 + (d*x)/2))))/d + (a*cot(c/2 + (d*x)/2)^2)/(8*d) - (a*cot(c/2 + (d*x)/2)^4)/(64*d) - (b*cot(c/2 + (d*x)/2)^3)/(24*d) - (a*tan(c/2 + (d*x)/2)^2)/(8*d) + (a*tan(c/2 + (d*x)/2)^4)/(64*d) + (b*tan(c/2 + (d*x)/2)^3)/(24*d)","B"
1101,1,174,74,9.559219,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x)^6,x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,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-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}\right)}{32\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(16*d) - (a*tan(c/2 + (d*x)/2)^3)/(32*d) + (a*tan(c/2 + (d*x)/2)^5)/(160*d) - (b*tan(c/2 + (d*x)/2)^2)/(8*d) + (b*tan(c/2 + (d*x)/2)^4)/(64*d) + (3*b*log(tan(c/2 + (d*x)/2)))/(8*d) - (cot(c/2 + (d*x)/2)^5*(a/5 + (b*tan(c/2 + (d*x)/2))/2 - a*tan(c/2 + (d*x)/2)^2 + 2*a*tan(c/2 + (d*x)/2)^4 - 4*b*tan(c/2 + (d*x)/2)^3))/(32*d)","B"
1102,1,205,98,9.521794,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x)^7,x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{a}{6}\right)}{64\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{16\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(16*d) - (a*tan(c/2 + (d*x)/2)^2)/(128*d) - (a*tan(c/2 + (d*x)/2)^4)/(128*d) + (a*tan(c/2 + (d*x)/2)^6)/(384*d) - (b*tan(c/2 + (d*x)/2)^3)/(32*d) + (b*tan(c/2 + (d*x)/2)^5)/(160*d) - (cot(c/2 + (d*x)/2)^6*(a/6 + (2*b*tan(c/2 + (d*x)/2))/5 - (a*tan(c/2 + (d*x)/2)^2)/2 - (a*tan(c/2 + (d*x)/2)^4)/2 - 2*b*tan(c/2 + (d*x)/2)^3 + 4*b*tan(c/2 + (d*x)/2)^5))/(64*d) + (a*log(tan(c/2 + (d*x)/2)))/(16*d)","B"
1103,1,399,114,10.994802,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x)^8,x)","\frac{15\,a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-15\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-21\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-105\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+315\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-315\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+105\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+21\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-105\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-105\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+105\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+105\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+35\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-35\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+840\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{13440\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(15*a*sin(c/2 + (d*x)/2)^14 - 15*a*cos(c/2 + (d*x)/2)^14 - 21*a*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 105*a*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 + 315*a*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 - 315*a*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 105*a*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 + 21*a*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 - 105*b*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 - 105*b*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 + 105*b*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 + 105*b*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 + 35*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 - 35*b*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) + 840*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)/(13440*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)","B"
1104,1,205,136,9.876996,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x)))/sin(c + d*x)^9,x)","\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}+\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{7}+\frac{a}{8}\right)}{256\,d}+\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,d}","Not used",1,"(3*b*tan(c/2 + (d*x)/2))/(128*d) - (a*tan(c/2 + (d*x)/2)^4)/(256*d) + (a*tan(c/2 + (d*x)/2)^8)/(2048*d) - (b*tan(c/2 + (d*x)/2)^3)/(128*d) - (b*tan(c/2 + (d*x)/2)^5)/(640*d) + (b*tan(c/2 + (d*x)/2)^7)/(896*d) - (cot(c/2 + (d*x)/2)^8*(a/8 + (2*b*tan(c/2 + (d*x)/2))/7 - a*tan(c/2 + (d*x)/2)^4 - (2*b*tan(c/2 + (d*x)/2)^3)/5 - 2*b*tan(c/2 + (d*x)/2)^5 + 6*b*tan(c/2 + (d*x)/2)^7))/(256*d) + (3*a*log(tan(c/2 + (d*x)/2)))/(128*d)","B"
1105,1,309,301,12.923954,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^3*(a + b*sin(c + d*x))^2,x)","\frac{3\,a\,b\,x}{64}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(4\,a^2-16\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(4\,a^2+\frac{32\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{28\,a^2}{5}-\frac{32\,b^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{36\,a^2}{35}+\frac{16\,b^2}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{4\,a^2}{35}+\frac{64\,b^2}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{52\,a^2}{5}+\frac{112\,b^2}{5}\right)+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\frac{4\,a^2}{35}+\frac{16\,b^2}{315}+\frac{13\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{16}-\frac{155\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{16}+\frac{169\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}-\frac{169\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{16}+\frac{155\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{16}-\frac{13\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{16}-\frac{3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{32}+\frac{3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(3*a*b*x)/64 - (tan(c/2 + (d*x)/2)^10*(4*a^2 - 16*b^2) + tan(c/2 + (d*x)/2)^12*(4*a^2 + (32*b^2)/3) + tan(c/2 + (d*x)/2)^6*((28*a^2)/5 - (32*b^2)/5) + tan(c/2 + (d*x)/2)^2*((36*a^2)/35 + (16*b^2)/35) + tan(c/2 + (d*x)/2)^4*((4*a^2)/35 + (64*b^2)/35) + tan(c/2 + (d*x)/2)^8*((52*a^2)/5 + (112*b^2)/5) + 4*a^2*tan(c/2 + (d*x)/2)^14 + (4*a^2)/35 + (16*b^2)/315 + (13*a*b*tan(c/2 + (d*x)/2)^3)/16 - (155*a*b*tan(c/2 + (d*x)/2)^5)/16 + (169*a*b*tan(c/2 + (d*x)/2)^7)/16 - (169*a*b*tan(c/2 + (d*x)/2)^11)/16 + (155*a*b*tan(c/2 + (d*x)/2)^13)/16 - (13*a*b*tan(c/2 + (d*x)/2)^15)/16 - (3*a*b*tan(c/2 + (d*x)/2)^17)/32 + (3*a*b*tan(c/2 + (d*x)/2))/32)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
1106,1,139,278,9.942763,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + b*sin(c + d*x))^2,x)","\frac{210\,a^2\,\sin\left(2\,c+2\,d\,x\right)-210\,a^2\,\sin\left(4\,c+4\,d\,x\right)-70\,a^2\,\sin\left(6\,c+6\,d\,x\right)-105\,b^2\,\sin\left(4\,c+4\,d\,x\right)+\frac{105\,b^2\,\sin\left(8\,c+8\,d\,x\right)}{8}-1260\,a\,b\,\cos\left(c+d\,x\right)-420\,a\,b\,\cos\left(3\,c+3\,d\,x\right)+84\,a\,b\,\cos\left(5\,c+5\,d\,x\right)+60\,a\,b\,\cos\left(7\,c+7\,d\,x\right)+840\,a^2\,d\,x+315\,b^2\,d\,x}{13440\,d}","Not used",1,"(210*a^2*sin(2*c + 2*d*x) - 210*a^2*sin(4*c + 4*d*x) - 70*a^2*sin(6*c + 6*d*x) - 105*b^2*sin(4*c + 4*d*x) + (105*b^2*sin(8*c + 8*d*x))/8 - 1260*a*b*cos(c + d*x) - 420*a*b*cos(3*c + 3*d*x) + 84*a*b*cos(5*c + 5*d*x) + 60*a*b*cos(7*c + 7*d*x) + 840*a^2*d*x + 315*b^2*d*x)/(13440*d)","B"
1107,1,256,129,13.013047,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))^2,x)","\frac{a\,b\,x}{8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(6\,a^2-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{4\,a^2}{5}+\frac{4\,b^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(8\,a^2+8\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{22\,a^2}{5}-\frac{8\,b^2}{5}\right)+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\frac{2\,a^2}{5}+\frac{4\,b^2}{35}-\frac{11\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{31\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}-\frac{31\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}+\frac{11\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+\frac{a\,b\,\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)}^7}","Not used",1,"(a*b*x)/8 - (tan(c/2 + (d*x)/2)^8*(6*a^2 - 4*b^2) + tan(c/2 + (d*x)/2)^10*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^2*((4*a^2)/5 + (4*b^2)/5) + tan(c/2 + (d*x)/2)^6*(8*a^2 + 8*b^2) + tan(c/2 + (d*x)/2)^4*((22*a^2)/5 - (8*b^2)/5) + 2*a^2*tan(c/2 + (d*x)/2)^12 + (2*a^2)/5 + (4*b^2)/35 - (11*a*b*tan(c/2 + (d*x)/2)^3)/3 + (31*a*b*tan(c/2 + (d*x)/2)^5)/12 - (31*a*b*tan(c/2 + (d*x)/2)^9)/12 + (11*a*b*tan(c/2 + (d*x)/2)^11)/3 - (a*b*tan(c/2 + (d*x)/2)^13)/4 + (a*b*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
1108,1,319,116,11.123484,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(4\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{44\,a^2}{3}-4\,b^2\right)+\frac{28\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{8\,a^2}{3}-\frac{2\,b^2}{5}+a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{5\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}+\frac{5\,a\,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)}^{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{3\,a\,b\,\mathrm{atan}\left(\frac{9\,a^2\,b^2}{4\,\left(3\,a^3\,b-\frac{9\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)}+\frac{3\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,a^3\,b-\frac{9\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}\right)}{2\,d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (tan(c/2 + (d*x)/2)^8*(4*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*((44*a^2)/3 - 4*b^2) + (28*a^2*tan(c/2 + (d*x)/2)^2)/3 + 12*a^2*tan(c/2 + (d*x)/2)^6 + (8*a^2)/3 - (2*b^2)/5 + a*b*tan(c/2 + (d*x)/2)^3 - a*b*tan(c/2 + (d*x)/2)^7 - (5*a*b*tan(c/2 + (d*x)/2)^9)/2 + (5*a*b*tan(c/2 + (d*x)/2))/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)) + (3*a*b*atan((9*a^2*b^2)/(4*(3*a^3*b - (9*a^2*b^2*tan(c/2 + (d*x)/2))/4)) + (3*a^3*b*tan(c/2 + (d*x)/2))/(3*a^3*b - (9*a^2*b^2*tan(c/2 + (d*x)/2))/4)))/(2*d)","B"
1109,1,578,181,9.544831,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-\frac{5\,b^2}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^2-\frac{5\,b^2}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^2+\frac{3\,b^2}{2}\right)-a^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2-\frac{3\,b^2}{2}\right)+\frac{80\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+32\,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+\frac{32\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{\mathrm{atan}\left(\frac{\left(\frac{a^2\,3{}\mathrm{i}}{2}-\frac{b^2\,3{}\mathrm{i}}{8}\right)\,\left(\frac{3\,b^2}{4}-3\,a^2+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,3{}\mathrm{i}}{2}-\frac{b^2\,3{}\mathrm{i}}{8}\right)+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,1{}\mathrm{i}-\left(\frac{a^2\,3{}\mathrm{i}}{2}-\frac{b^2\,3{}\mathrm{i}}{8}\right)\,\left(3\,a^2-\frac{3\,b^2}{4}+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,3{}\mathrm{i}}{2}-\frac{b^2\,3{}\mathrm{i}}{8}\right)-4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,1{}\mathrm{i}}{\left(\frac{a^2\,3{}\mathrm{i}}{2}-\frac{b^2\,3{}\mathrm{i}}{8}\right)\,\left(\frac{3\,b^2}{4}-3\,a^2+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,3{}\mathrm{i}}{2}-\frac{b^2\,3{}\mathrm{i}}{8}\right)+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\left(\frac{a^2\,3{}\mathrm{i}}{2}-\frac{b^2\,3{}\mathrm{i}}{8}\right)\,\left(3\,a^2-\frac{3\,b^2}{4}+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,3{}\mathrm{i}}{2}-\frac{b^2\,3{}\mathrm{i}}{8}\right)-4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+3\,a\,b^3-12\,a^3\,b+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^4-\frac{9\,a^2\,b^2}{2}+\frac{9\,b^4}{16}\right)}\right)\,\left(3\,a^2-\frac{3\,b^2}{4}\right)}{d}+\frac{2\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^8*(a^2 - (5*b^2)/2) - tan(c/2 + (d*x)/2)^2*(6*a^2 - (5*b^2)/2) - tan(c/2 + (d*x)/2)^4*(8*a^2 + (3*b^2)/2) - a^2 - tan(c/2 + (d*x)/2)^6*(2*a^2 - (3*b^2)/2) + (80*a*b*tan(c/2 + (d*x)/2)^3)/3 + 32*a*b*tan(c/2 + (d*x)/2)^5 + 16*a*b*tan(c/2 + (d*x)/2)^7 + (32*a*b*tan(c/2 + (d*x)/2))/3)/(d*(2*tan(c/2 + (d*x)/2) + 8*tan(c/2 + (d*x)/2)^3 + 12*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^7 + 2*tan(c/2 + (d*x)/2)^9)) + (a^2*tan(c/2 + (d*x)/2))/(2*d) - (atan((((a^2*3i)/2 - (b^2*3i)/8)*((3*b^2)/4 - 3*a^2 + 6*tan(c/2 + (d*x)/2)*((a^2*3i)/2 - (b^2*3i)/8) + 4*a*b*tan(c/2 + (d*x)/2))*1i - ((a^2*3i)/2 - (b^2*3i)/8)*(3*a^2 - (3*b^2)/4 + 6*tan(c/2 + (d*x)/2)*((a^2*3i)/2 - (b^2*3i)/8) - 4*a*b*tan(c/2 + (d*x)/2))*1i)/(((a^2*3i)/2 - (b^2*3i)/8)*((3*b^2)/4 - 3*a^2 + 6*tan(c/2 + (d*x)/2)*((a^2*3i)/2 - (b^2*3i)/8) + 4*a*b*tan(c/2 + (d*x)/2)) + ((a^2*3i)/2 - (b^2*3i)/8)*(3*a^2 - (3*b^2)/4 + 6*tan(c/2 + (d*x)/2)*((a^2*3i)/2 - (b^2*3i)/8) - 4*a*b*tan(c/2 + (d*x)/2)) + 3*a*b^3 - 12*a^3*b + 2*tan(c/2 + (d*x)/2)*(9*a^4 + (9*b^4)/16 - (9*a^2*b^2)/2)))*(3*a^2 - (3*b^2)/4))/d + (2*a*b*log(tan(c/2 + (d*x)/2)))/d","B"
1110,1,397,189,9.443903,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^2}{2}-b^2\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{17\,a^2}{2}-16\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{35\,a^2}{2}-16\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{19\,a^2}{2}-\frac{32\,b^2}{3}\right)+\frac{a^2}{2}+20\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,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)}^7+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{6\,a\,b\,\mathrm{atan}\left(\frac{36\,a^2\,b^2}{-18\,a^3\,b+36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+12\,a\,b^3}-\frac{12\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-18\,a^3\,b+36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+12\,a\,b^3}+\frac{18\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-18\,a^3\,b+36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+12\,a\,b^3}\right)}{d}+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (log(tan(c/2 + (d*x)/2))*((3*a^2)/2 - b^2))/d - (tan(c/2 + (d*x)/2)^6*((17*a^2)/2 - 16*b^2) + tan(c/2 + (d*x)/2)^4*((35*a^2)/2 - 16*b^2) + tan(c/2 + (d*x)/2)^2*((19*a^2)/2 - (32*b^2)/3) + a^2/2 + 20*a*b*tan(c/2 + (d*x)/2)^3 + 12*a*b*tan(c/2 + (d*x)/2)^5 - 4*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^4 + 12*tan(c/2 + (d*x)/2)^6 + 4*tan(c/2 + (d*x)/2)^8)) + (6*a*b*atan((36*a^2*b^2)/(12*a*b^3 - 18*a^3*b + 36*a^2*b^2*tan(c/2 + (d*x)/2)) - (12*a*b^3*tan(c/2 + (d*x)/2))/(12*a*b^3 - 18*a^3*b + 36*a^2*b^2*tan(c/2 + (d*x)/2)) + (18*a^3*b*tan(c/2 + (d*x)/2))/(12*a*b^3 - 18*a^3*b + 36*a^2*b^2*tan(c/2 + (d*x)/2))))/d + (a*b*tan(c/2 + (d*x)/2))/d","B"
1111,1,584,133,11.747302,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^2)/sin(c + d*x)^4,x)","-\frac{\frac{5\,b^2\,\cos\left(c+d\,x\right)}{16}+\frac{a^2\,\cos\left(3\,c+3\,d\,x\right)}{3}-\frac{11\,b^2\,\cos\left(3\,c+3\,d\,x\right)}{32}+\frac{b^2\,\cos\left(5\,c+5\,d\,x\right)}{32}+\frac{a^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{2}-\frac{3\,b^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,a\,b\,\sin\left(c+d\,x\right)}{2}-\frac{3\,a^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{2}+\frac{9\,b^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{4}+a\,b\,\sin\left(2\,c+2\,d\,x\right)-\frac{a\,b\,\sin\left(3\,c+3\,d\,x\right)}{2}-\frac{a\,b\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{9\,a\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}-\frac{3\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{4}}{d\,{\sin\left(c+d\,x\right)}^3}","Not used",1,"-((5*b^2*cos(c + d*x))/16 + (a^2*cos(3*c + 3*d*x))/3 - (11*b^2*cos(3*c + 3*d*x))/32 + (b^2*cos(5*c + 5*d*x))/32 + (a^2*atan((3*b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - 3*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/2 - (3*b^2*atan((3*b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - 3*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/4 + (3*a*b*sin(c + d*x))/2 - (3*a^2*atan((3*b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - 3*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2)))*sin(c + d*x))/2 + (9*b^2*atan((3*b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - 3*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2)))*sin(c + d*x))/4 + a*b*sin(2*c + 2*d*x) - (a*b*sin(3*c + 3*d*x))/2 - (a*b*sin(4*c + 4*d*x))/4 + (9*a*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 - (3*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/4)/(d*sin(c + d*x)^3)","B"
1112,1,825,178,10.893696,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^2)/sin(c + d*x)^5,x)","-\frac{3\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,a^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+21\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-24\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-21\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-24\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-24\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+408\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+24\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-16\,a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+16\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-72\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-72\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+288\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+288\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+224\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-224\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+768\,a\,b\,\mathrm{atan}\left(\frac{3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+16\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+12\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+768\,a\,b\,\mathrm{atan}\left(\frac{3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+16\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+12\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{192\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}","Not used",1,"-(3*a^2*cos(c/2 + (d*x)/2)^10 - 3*a^2*sin(c/2 + (d*x)/2)^10 + 21*a^2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 + 24*a^2*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 - 24*a^2*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 - 21*a^2*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 - 24*b^2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 - 24*b^2*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + 408*b^2*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 24*b^2*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 - 16*a*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 + 16*a*b*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - 72*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 - 72*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 288*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + 288*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 224*a*b*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7 - 224*a*b*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3 + 768*a*b*atan((3*a^2*sin(c/2 + (d*x)/2) - 12*b^2*sin(c/2 + (d*x)/2) + 16*a*b*cos(c/2 + (d*x)/2))/(12*b^2*cos(c/2 + (d*x)/2) - 3*a^2*cos(c/2 + (d*x)/2) + 16*a*b*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + 768*a*b*atan((3*a^2*sin(c/2 + (d*x)/2) - 12*b^2*sin(c/2 + (d*x)/2) + 16*a*b*cos(c/2 + (d*x)/2))/(12*b^2*cos(c/2 + (d*x)/2) - 3*a^2*cos(c/2 + (d*x)/2) + 16*a*b*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4)/(192*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4*(cos(c/2 + (d*x)/2)^2 + sin(c/2 + (d*x)/2)^2))","B"
1113,1,346,209,10.102747,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^2)/sin(c + d*x)^6,x)","\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,d}-\frac{a^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{b^2\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{5\,b^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{2\,b^2\,\mathrm{atan}\left(\frac{4\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a\,b\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{a\,b\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}+\frac{3\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}","Not used",1,"(a^2*cot(c/2 + (d*x)/2)^3)/(32*d) - (a^2*cot(c/2 + (d*x)/2)^5)/(160*d) - (b^2*cot(c/2 + (d*x)/2)^3)/(24*d) - (a^2*tan(c/2 + (d*x)/2)^3)/(32*d) + (a^2*tan(c/2 + (d*x)/2)^5)/(160*d) + (b^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (a^2*cot(c/2 + (d*x)/2))/(16*d) + (5*b^2*cot(c/2 + (d*x)/2))/(8*d) + (a^2*tan(c/2 + (d*x)/2))/(16*d) - (5*b^2*tan(c/2 + (d*x)/2))/(8*d) + (2*b^2*atan((4*b*cos(c/2 + (d*x)/2) + 3*a*sin(c/2 + (d*x)/2))/(3*a*cos(c/2 + (d*x)/2) - 4*b*sin(c/2 + (d*x)/2))))/d + (a*b*cot(c/2 + (d*x)/2)^2)/(4*d) - (a*b*cot(c/2 + (d*x)/2)^4)/(32*d) - (a*b*tan(c/2 + (d*x)/2)^2)/(4*d) + (a*b*tan(c/2 + (d*x)/2)^4)/(32*d) + (3*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d)","B"
1114,1,262,236,9.669208,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^2)/sin(c + d*x)^7,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{a^2}{16}+\frac{3\,b^2}{8}\right)}{d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{2}-b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{2}+8\,b^2\right)-\frac{a^2}{6}+4\,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)}^5-\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}\right)}{64\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{128}+\frac{b^2}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{128}-\frac{b^2}{64}\right)}{d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{16\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{80\,d}+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2))*(a^2/16 + (3*b^2)/8))/d + (a^2*tan(c/2 + (d*x)/2)^6)/(384*d) + (cot(c/2 + (d*x)/2)^6*(tan(c/2 + (d*x)/2)^2*(a^2/2 - b^2) + tan(c/2 + (d*x)/2)^4*(a^2/2 + 8*b^2) - a^2/6 + 4*a*b*tan(c/2 + (d*x)/2)^3 - 8*a*b*tan(c/2 + (d*x)/2)^5 - (4*a*b*tan(c/2 + (d*x)/2))/5))/(64*d) - (tan(c/2 + (d*x)/2)^2*(a^2/128 + b^2/8))/d - (tan(c/2 + (d*x)/2)^4*(a^2/128 - b^2/64))/d - (a*b*tan(c/2 + (d*x)/2)^3)/(16*d) + (a*b*tan(c/2 + (d*x)/2)^5)/(80*d) + (a*b*tan(c/2 + (d*x)/2))/(8*d)","B"
1115,1,302,261,9.921139,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^2)/sin(c + d*x)^8,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{5}-\frac{4\,b^2}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a^2+8\,b^2\right)-\frac{a^2}{7}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+4\,b^2\right)+2\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}\right)}{128\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a^2}{128}+\frac{b^2}{16}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2}{128}+\frac{b^2}{32}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{a^2}{640}-\frac{b^2}{160}\right)}{d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}+\frac{a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^7)/(896*d) + (cot(c/2 + (d*x)/2)^7*(tan(c/2 + (d*x)/2)^2*(a^2/5 - (4*b^2)/5) - tan(c/2 + (d*x)/2)^6*(3*a^2 + 8*b^2) - a^2/7 + tan(c/2 + (d*x)/2)^4*(a^2 + 4*b^2) + 2*a*b*tan(c/2 + (d*x)/2)^3 + 2*a*b*tan(c/2 + (d*x)/2)^5 - (2*a*b*tan(c/2 + (d*x)/2))/3))/(128*d) + (tan(c/2 + (d*x)/2)*((3*a^2)/128 + b^2/16))/d - (tan(c/2 + (d*x)/2)^3*(a^2/128 + b^2/32))/d - (tan(c/2 + (d*x)/2)^5*(a^2/640 - b^2/160))/d - (a*b*tan(c/2 + (d*x)/2)^2)/(64*d) - (a*b*tan(c/2 + (d*x)/2)^4)/(64*d) + (a*b*tan(c/2 + (d*x)/2)^6)/(192*d) + (a*b*log(tan(c/2 + (d*x)/2)))/(8*d)","B"
1116,1,578,354,10.773416,"\text{Not used}","int(cos(c + d*x)^4*sin(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(8\,a^2+9\,b^2\right)}{64\,\left(\frac{a^3}{8}+\frac{9\,a\,b^2}{64}\right)}\right)\,\left(8\,a^2+9\,b^2\right)}{64\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^3}{8}+\frac{9\,a\,b^2}{64}\right)+\frac{12\,a^2\,b}{35}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{a^3}{8}+\frac{9\,a\,b^2}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{39\,a\,b^2}{32}-\frac{19\,a^3}{12}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{39\,a\,b^2}{32}-\frac{19\,a^3}{12}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{9\,a^3}{4}+\frac{465\,a\,b^2}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{9\,a^3}{4}+\frac{465\,a\,b^2}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{3\,a^3}{4}+\frac{507\,a\,b^2}{32}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{3\,a^3}{4}+\frac{507\,a\,b^2}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(12\,a^2\,b-16\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(12\,a^2\,b+\frac{32\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{84\,a^2\,b}{5}-\frac{32\,b^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{12\,a^2\,b}{35}+\frac{64\,b^3}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{108\,a^2\,b}{35}+\frac{16\,b^3}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{156\,a^2\,b}{5}+\frac{112\,b^3}{5}\right)+\frac{16\,b^3}{315}+12\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\left(8\,a^2+9\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{64\,d}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(8*a^2 + 9*b^2))/(64*((9*a*b^2)/64 + a^3/8)))*(8*a^2 + 9*b^2))/(64*d) - (tan(c/2 + (d*x)/2)*((9*a*b^2)/64 + a^3/8) + (12*a^2*b)/35 - tan(c/2 + (d*x)/2)^17*((9*a*b^2)/64 + a^3/8) + tan(c/2 + (d*x)/2)^3*((39*a*b^2)/32 - (19*a^3)/12) - tan(c/2 + (d*x)/2)^15*((39*a*b^2)/32 - (19*a^3)/12) - tan(c/2 + (d*x)/2)^5*((465*a*b^2)/32 + (9*a^3)/4) + tan(c/2 + (d*x)/2)^13*((465*a*b^2)/32 + (9*a^3)/4) + tan(c/2 + (d*x)/2)^7*((507*a*b^2)/32 + (3*a^3)/4) - tan(c/2 + (d*x)/2)^11*((507*a*b^2)/32 + (3*a^3)/4) + tan(c/2 + (d*x)/2)^10*(12*a^2*b - 16*b^3) + tan(c/2 + (d*x)/2)^12*(12*a^2*b + (32*b^3)/3) + tan(c/2 + (d*x)/2)^6*((84*a^2*b)/5 - (32*b^3)/5) + tan(c/2 + (d*x)/2)^4*((12*a^2*b)/35 + (64*b^3)/35) + tan(c/2 + (d*x)/2)^2*((108*a^2*b)/35 + (16*b^3)/35) + tan(c/2 + (d*x)/2)^8*((156*a^2*b)/5 + (112*b^3)/5) + (16*b^3)/315 + 12*a^2*b*tan(c/2 + (d*x)/2)^14)/(d*(9*tan(c/2 + (d*x)/2)^2 + 36*tan(c/2 + (d*x)/2)^4 + 84*tan(c/2 + (d*x)/2)^6 + 126*tan(c/2 + (d*x)/2)^8 + 126*tan(c/2 + (d*x)/2)^10 + 84*tan(c/2 + (d*x)/2)^12 + 36*tan(c/2 + (d*x)/2)^14 + 9*tan(c/2 + (d*x)/2)^16 + tan(c/2 + (d*x)/2)^18 + 1)) - (a*(8*a^2 + 9*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(64*d)","B"
1117,1,552,194,10.920645,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))^3,x)","\frac{3\,b\,\mathrm{atan}\left(\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^2+b^2\right)}{64\,\left(\frac{3\,a^2\,b}{8}+\frac{3\,b^3}{64}\right)}\right)\,\left(8\,a^2+b^2\right)}{64\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a^2\,b}{8}+\frac{3\,b^3}{64}\right)+10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\frac{12\,a\,b^2}{35}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(6\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(14\,a^3+12\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{12\,a\,b^2}{5}-\frac{26\,a^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{6\,a^3}{5}+\frac{96\,a\,b^2}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{62\,a^3}{5}+\frac{96\,a\,b^2}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{3\,a^2\,b}{8}+\frac{3\,b^3}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{41\,a^2\,b}{8}-\frac{23\,b^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{41\,a^2\,b}{8}-\frac{23\,b^3}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{13\,a^2\,b}{8}+\frac{333\,b^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{13\,a^2\,b}{8}+\frac{333\,b^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{31\,a^2\,b}{8}+\frac{671\,b^3}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{31\,a^2\,b}{8}+\frac{671\,b^3}{64}\right)+\frac{2\,a^3}{5}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{3\,b\,\left(8\,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)}{64\,d}","Not used",1,"(3*b*atan((3*b*tan(c/2 + (d*x)/2)*(8*a^2 + b^2))/(64*((3*a^2*b)/8 + (3*b^3)/64)))*(8*a^2 + b^2))/(64*d) - (tan(c/2 + (d*x)/2)*((3*a^2*b)/8 + (3*b^3)/64) + 10*a^3*tan(c/2 + (d*x)/2)^10 + 2*a^3*tan(c/2 + (d*x)/2)^14 + (12*a*b^2)/35 + tan(c/2 + (d*x)/2)^12*(12*a*b^2 + 6*a^3) + tan(c/2 + (d*x)/2)^8*(12*a*b^2 + 14*a^3) - tan(c/2 + (d*x)/2)^4*((12*a*b^2)/5 - (26*a^3)/5) + tan(c/2 + (d*x)/2)^2*((96*a*b^2)/35 + (6*a^3)/5) + tan(c/2 + (d*x)/2)^6*((96*a*b^2)/5 + (62*a^3)/5) - tan(c/2 + (d*x)/2)^15*((3*a^2*b)/8 + (3*b^3)/64) - tan(c/2 + (d*x)/2)^3*((41*a^2*b)/8 - (23*b^3)/64) + tan(c/2 + (d*x)/2)^13*((41*a^2*b)/8 - (23*b^3)/64) - tan(c/2 + (d*x)/2)^5*((13*a^2*b)/8 + (333*b^3)/64) + tan(c/2 + (d*x)/2)^11*((13*a^2*b)/8 + (333*b^3)/64) + tan(c/2 + (d*x)/2)^7*((31*a^2*b)/8 + (671*b^3)/64) - tan(c/2 + (d*x)/2)^9*((31*a^2*b)/8 + (671*b^3)/64) + (2*a^3)/5)/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) - (3*b*(8*a^2 + b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(64*d)","B"
1118,1,690,250,11.573704,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x),x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\frac{6\,a\,b^2}{5}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{15\,a^2\,b}{4}-\frac{b^3}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(6\,a\,b^2-4\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{6\,a\,b^2}{5}-12\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(6\,a\,b^2-16\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a\,b^2-24\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(12\,a\,b^2-\frac{80\,a^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,a^2\,b}{2}-\frac{13\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{3\,a^2\,b}{2}-\frac{13\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{15\,a^2\,b}{4}-\frac{b^3}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{21\,a^2\,b}{4}+\frac{47\,b^3}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{21\,a^2\,b}{4}+\frac{47\,b^3}{24}\right)-\frac{8\,a^3}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(18\,a^2+b^2\right)\,\left(\frac{9\,a^2\,b}{4}+\frac{b^3}{8}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,a^2+b^2\right)\,3{}\mathrm{i}}{8}\right)}{16}+\frac{b\,\left(18\,a^2+b^2\right)\,\left(\frac{9\,a^2\,b}{4}+\frac{b^3}{8}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,a^2+b^2\right)\,3{}\mathrm{i}}{8}\right)}{16}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{81\,a^4\,b^2}{16}+\frac{9\,a^2\,b^4}{16}+\frac{b^6}{64}\right)+\frac{9\,a^5\,b}{2}+\frac{a^3\,b^3}{4}-\frac{b\,\left(18\,a^2+b^2\right)\,\left(\frac{9\,a^2\,b}{4}+\frac{b^3}{8}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,a^2+b^2\right)\,3{}\mathrm{i}}{8}\right)\,1{}\mathrm{i}}{16}+\frac{b\,\left(18\,a^2+b^2\right)\,\left(\frac{9\,a^2\,b}{4}+\frac{b^3}{8}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,a^2+b^2\right)\,3{}\mathrm{i}}{8}\right)\,1{}\mathrm{i}}{16}}\right)\,\left(18\,a^2+b^2\right)}{8\,d}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d - ((6*a*b^2)/5 - tan(c/2 + (d*x)/2)*((15*a^2*b)/4 - b^3/8) + tan(c/2 + (d*x)/2)^10*(6*a*b^2 - 4*a^3) + tan(c/2 + (d*x)/2)^2*((6*a*b^2)/5 - 12*a^3) + tan(c/2 + (d*x)/2)^8*(6*a*b^2 - 16*a^3) + tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 24*a^3) + tan(c/2 + (d*x)/2)^6*(12*a*b^2 - (80*a^3)/3) - tan(c/2 + (d*x)/2)^5*((3*a^2*b)/2 - (13*b^3)/4) + tan(c/2 + (d*x)/2)^7*((3*a^2*b)/2 - (13*b^3)/4) + tan(c/2 + (d*x)/2)^11*((15*a^2*b)/4 - b^3/8) - tan(c/2 + (d*x)/2)^3*((21*a^2*b)/4 + (47*b^3)/24) + tan(c/2 + (d*x)/2)^9*((21*a^2*b)/4 + (47*b^3)/24) - (8*a^3)/3)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (b*atan(((b*(18*a^2 + b^2)*((9*a^2*b)/4 + b^3/8 + 2*a^3*tan(c/2 + (d*x)/2) - (b*tan(c/2 + (d*x)/2)*(18*a^2 + b^2)*3i)/8))/16 + (b*(18*a^2 + b^2)*((9*a^2*b)/4 + b^3/8 + 2*a^3*tan(c/2 + (d*x)/2) + (b*tan(c/2 + (d*x)/2)*(18*a^2 + b^2)*3i)/8))/16)/(2*tan(c/2 + (d*x)/2)*(b^6/64 + (9*a^2*b^4)/16 + (81*a^4*b^2)/16) + (9*a^5*b)/2 + (a^3*b^3)/4 - (b*(18*a^2 + b^2)*((9*a^2*b)/4 + b^3/8 + 2*a^3*tan(c/2 + (d*x)/2) - (b*tan(c/2 + (d*x)/2)*(18*a^2 + b^2)*3i)/8)*1i)/16 + (b*(18*a^2 + b^2)*((9*a^2*b)/4 + b^3/8 + 2*a^3*tan(c/2 + (d*x)/2) + (b*tan(c/2 + (d*x)/2)*(18*a^2 + b^2)*3i)/8)*1i)/16))*(18*a^2 + b^2))/(8*d)","B"
1119,1,674,229,9.592205,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x)^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^2\,b-\frac{4\,b^3}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3+3\,a\,b^2\right)-10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a\,b^2-14\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{15\,a\,b^2}{2}-7\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{15\,a\,b^2}{2}-a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(24\,a^2\,b-4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(88\,a^2\,b-8\,b^3\right)-a^3+56\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+72\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{3\,a\,\mathrm{atan}\left(\frac{\frac{3\,a\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{9\,a\,b^2}{4}-3\,a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-3\,b^2\right)\,9{}\mathrm{i}}{4}\right)}{8}+\frac{3\,a\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{9\,a\,b^2}{4}-3\,a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-3\,b^2\right)\,9{}\mathrm{i}}{4}\right)}{8}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^6-\frac{27\,a^4\,b^2}{2}+\frac{81\,a^2\,b^4}{16}\right)-18\,a^5\,b+\frac{27\,a^3\,b^3}{2}-\frac{a\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{9\,a\,b^2}{4}-3\,a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-3\,b^2\right)\,9{}\mathrm{i}}{4}\right)\,3{}\mathrm{i}}{8}+\frac{a\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{9\,a\,b^2}{4}-3\,a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-3\,b^2\right)\,9{}\mathrm{i}}{4}\right)\,3{}\mathrm{i}}{8}}\right)\,\left(4\,a^2-3\,b^2\right)}{4\,d}+\frac{3\,a^2\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(16*a^2*b - (4*b^3)/5) - tan(c/2 + (d*x)/2)^8*(3*a*b^2 + a^3) - 10*a^3*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^4*(3*a*b^2 - 14*a^3) + tan(c/2 + (d*x)/2)^2*((15*a*b^2)/2 - 7*a^3) - tan(c/2 + (d*x)/2)^10*((15*a*b^2)/2 - a^3) + tan(c/2 + (d*x)/2)^9*(24*a^2*b - 4*b^3) + tan(c/2 + (d*x)/2)^5*(88*a^2*b - 8*b^3) - a^3 + 56*a^2*b*tan(c/2 + (d*x)/2)^3 + 72*a^2*b*tan(c/2 + (d*x)/2)^7)/(d*(2*tan(c/2 + (d*x)/2) + 10*tan(c/2 + (d*x)/2)^3 + 20*tan(c/2 + (d*x)/2)^5 + 20*tan(c/2 + (d*x)/2)^7 + 10*tan(c/2 + (d*x)/2)^9 + 2*tan(c/2 + (d*x)/2)^11)) + (a^3*tan(c/2 + (d*x)/2))/(2*d) + (3*a*atan(((3*a*(4*a^2 - 3*b^2)*((9*a*b^2)/4 - 3*a^3 - (a*tan(c/2 + (d*x)/2)*(4*a^2 - 3*b^2)*9i)/4 + 6*a^2*b*tan(c/2 + (d*x)/2)))/8 + (3*a*(4*a^2 - 3*b^2)*((9*a*b^2)/4 - 3*a^3 + (a*tan(c/2 + (d*x)/2)*(4*a^2 - 3*b^2)*9i)/4 + 6*a^2*b*tan(c/2 + (d*x)/2)))/8)/(2*tan(c/2 + (d*x)/2)*(9*a^6 + (81*a^2*b^4)/16 - (27*a^4*b^2)/2) - 18*a^5*b + (27*a^3*b^3)/2 - (a*(4*a^2 - 3*b^2)*((9*a*b^2)/4 - 3*a^3 - (a*tan(c/2 + (d*x)/2)*(4*a^2 - 3*b^2)*9i)/4 + 6*a^2*b*tan(c/2 + (d*x)/2))*3i)/8 + (a*(4*a^2 - 3*b^2)*((9*a*b^2)/4 - 3*a^3 + (a*tan(c/2 + (d*x)/2)*(4*a^2 - 3*b^2)*9i)/4 + 6*a^2*b*tan(c/2 + (d*x)/2))*3i)/8))*(4*a^2 - 3*b^2))/(4*d) + (3*a^2*b*log(tan(c/2 + (d*x)/2)))/d","B"
1120,1,718,231,9.594701,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x)^3,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(32\,a\,b^2-10\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(48\,a\,b^2-\frac{17\,a^3}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(80\,a\,b^2-27\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(96\,a\,b^2-26\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(6\,a^2\,b-5\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(12\,a^2\,b-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,a^2\,b-5\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(48\,a^2\,b+3\,b^3\right)-\frac{a^3}{2}-6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a\,b^2-\frac{3\,a^3}{2}\right)}{d}+\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{3\,b\,\mathrm{atan}\left(\frac{\frac{3\,b\,\left(12\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-3\,a^3\right)-9\,a^2\,b+\frac{3\,b^3}{4}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2-b^2\right)\,9{}\mathrm{i}}{4}\right)}{8}+\frac{3\,b\,\left(12\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-3\,a^3\right)-9\,a^2\,b+\frac{3\,b^3}{4}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2-b^2\right)\,9{}\mathrm{i}}{4}\right)}{8}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(81\,a^4\,b^2-\frac{27\,a^2\,b^4}{2}+\frac{9\,b^6}{16}\right)+\frac{9\,a\,b^5}{2}+27\,a^5\,b-\frac{225\,a^3\,b^3}{4}-\frac{b\,\left(12\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-3\,a^3\right)-9\,a^2\,b+\frac{3\,b^3}{4}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2-b^2\right)\,9{}\mathrm{i}}{4}\right)\,3{}\mathrm{i}}{8}+\frac{b\,\left(12\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-3\,a^3\right)-9\,a^2\,b+\frac{3\,b^3}{4}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2-b^2\right)\,9{}\mathrm{i}}{4}\right)\,3{}\mathrm{i}}{8}}\right)\,\left(12\,a^2-b^2\right)}{4\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (tan(c/2 + (d*x)/2)^2*(32*a*b^2 - 10*a^3) + tan(c/2 + (d*x)/2)^8*(48*a*b^2 - (17*a^3)/2) + tan(c/2 + (d*x)/2)^4*(80*a*b^2 - 27*a^3) + tan(c/2 + (d*x)/2)^6*(96*a*b^2 - 26*a^3) + tan(c/2 + (d*x)/2)^9*(6*a^2*b - 5*b^3) - tan(c/2 + (d*x)/2)^7*(12*a^2*b - 3*b^3) - tan(c/2 + (d*x)/2)^3*(36*a^2*b - 5*b^3) - tan(c/2 + (d*x)/2)^5*(48*a^2*b + 3*b^3) - a^3/2 - 6*a^2*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 16*tan(c/2 + (d*x)/2)^4 + 24*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8 + 4*tan(c/2 + (d*x)/2)^10)) + (log(tan(c/2 + (d*x)/2))*(3*a*b^2 - (3*a^3)/2))/d + (3*a^2*b*tan(c/2 + (d*x)/2))/(2*d) + (3*b*atan(((3*b*(12*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(6*a*b^2 - 3*a^3) - 9*a^2*b + (3*b^3)/4 - (b*tan(c/2 + (d*x)/2)*(12*a^2 - b^2)*9i)/4))/8 + (3*b*(12*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(6*a*b^2 - 3*a^3) - 9*a^2*b + (3*b^3)/4 + (b*tan(c/2 + (d*x)/2)*(12*a^2 - b^2)*9i)/4))/8)/(2*tan(c/2 + (d*x)/2)*((9*b^6)/16 - (27*a^2*b^4)/2 + 81*a^4*b^2) + (9*a*b^5)/2 + 27*a^5*b - (225*a^3*b^3)/4 - (b*(12*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(6*a*b^2 - 3*a^3) - 9*a^2*b + (3*b^3)/4 - (b*tan(c/2 + (d*x)/2)*(12*a^2 - b^2)*9i)/4)*3i)/8 + (b*(12*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(6*a*b^2 - 3*a^3) - 9*a^2*b + (3*b^3)/4 + (b*tan(c/2 + (d*x)/2)*(12*a^2 - b^2)*9i)/4)*3i)/8))*(12*a^2 - b^2))/(4*d)","B"
1121,1,405,194,9.648511,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x)^4,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{9\,a^2\,b}{2}-b^3\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(\frac{a\,b^2\,9{}\mathrm{i}}{2}-a^3\,1{}\mathrm{i}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a\,b^2}{2}-\frac{5\,a^3}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-4\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(60\,a\,b^2-14\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(36\,a\,b^2-\frac{44\,a^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(51\,a^2\,b-32\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(57\,a^2\,b-\frac{64\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(105\,a^2\,b-32\,b^3\right)+\frac{a^3}{3}+3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(2\,a^2-9\,b^2\right)\,1{}\mathrm{i}}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (log(tan(c/2 + (d*x)/2))*((9*a^2*b)/2 - b^3))/d - (log(tan(c/2 + (d*x)/2) + 1i)*((a*b^2*9i)/2 - a^3*1i))/d + (tan(c/2 + (d*x)/2)*((3*a*b^2)/2 - (5*a^3)/8))/d - (tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 4*a^3) - tan(c/2 + (d*x)/2)^8*(12*a*b^2 + 5*a^3) + tan(c/2 + (d*x)/2)^4*(60*a*b^2 - 14*a^3) + tan(c/2 + (d*x)/2)^6*(36*a*b^2 - (44*a^3)/3) + tan(c/2 + (d*x)/2)^7*(51*a^2*b - 32*b^3) + tan(c/2 + (d*x)/2)^3*(57*a^2*b - (64*b^3)/3) + tan(c/2 + (d*x)/2)^5*(105*a^2*b - 32*b^3) + a^3/3 + 3*a^2*b*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 24*tan(c/2 + (d*x)/2)^5 + 24*tan(c/2 + (d*x)/2)^7 + 8*tan(c/2 + (d*x)/2)^9)) + (3*a^2*b*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*log(tan(c/2 + (d*x)/2) - 1i)*(2*a^2 - 9*b^2)*1i)/(2*d)","B"
1122,1,699,187,9.499968,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x)^5,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a\,b^2}{8}-\frac{a^3}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a\,b^2-\frac{3\,a^3}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(102\,a\,b^2-2\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(108\,a\,b^2-\frac{15\,a^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(26\,a^2\,b-8\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(30\,a^2\,b+8\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(58\,a^2\,b-32\,b^3\right)+\frac{a^3}{4}+2\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{15\,a^2\,b}{8}-\frac{b^3}{2}\right)}{d}+\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-12\,b^2\right)}{8\,d}+\frac{a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}-\frac{3\,b\,\mathrm{atan}\left(\frac{\frac{3\,b\,\left(2\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a\,b^2-\frac{3\,a^3}{4}\right)-6\,a^2\,b+3\,b^3-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-b^2\right)\,9{}\mathrm{i}\right)}{2}+\frac{3\,b\,\left(2\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a\,b^2-\frac{3\,a^3}{4}\right)-6\,a^2\,b+3\,b^3+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-b^2\right)\,9{}\mathrm{i}\right)}{2}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^4\,b^2-36\,a^2\,b^4+9\,b^6\right)+27\,a\,b^5+\frac{9\,a^5\,b}{2}-\frac{225\,a^3\,b^3}{4}-\frac{b\,\left(2\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a\,b^2-\frac{3\,a^3}{4}\right)-6\,a^2\,b+3\,b^3-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-b^2\right)\,9{}\mathrm{i}\right)\,3{}\mathrm{i}}{2}+\frac{b\,\left(2\,a^2-b^2\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a\,b^2-\frac{3\,a^3}{4}\right)-6\,a^2\,b+3\,b^3+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-b^2\right)\,9{}\mathrm{i}\right)\,3{}\mathrm{i}}{2}}\right)\,\left(2\,a^2-b^2\right)}{d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^4)/(64*d) + (tan(c/2 + (d*x)/2)^2*((3*a*b^2)/8 - a^3/8))/d - (tan(c/2 + (d*x)/2)^2*(6*a*b^2 - (3*a^3)/2) + tan(c/2 + (d*x)/2)^6*(102*a*b^2 - 2*a^3) + tan(c/2 + (d*x)/2)^4*(108*a*b^2 - (15*a^3)/4) - tan(c/2 + (d*x)/2)^3*(26*a^2*b - 8*b^3) - tan(c/2 + (d*x)/2)^7*(30*a^2*b + 8*b^3) - tan(c/2 + (d*x)/2)^5*(58*a^2*b - 32*b^3) + a^3/4 + 2*a^2*b*tan(c/2 + (d*x)/2))/(d*(16*tan(c/2 + (d*x)/2)^4 + 32*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8)) - (tan(c/2 + (d*x)/2)*((15*a^2*b)/8 - b^3/2))/d + (3*a*log(tan(c/2 + (d*x)/2))*(a^2 - 12*b^2))/(8*d) + (a^2*b*tan(c/2 + (d*x)/2)^3)/(8*d) - (3*b*atan(((3*b*(2*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(9*a*b^2 - (3*a^3)/4) - 6*a^2*b + 3*b^3 - b*tan(c/2 + (d*x)/2)*(2*a^2 - b^2)*9i))/2 + (3*b*(2*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(9*a*b^2 - (3*a^3)/4) - 6*a^2*b + 3*b^3 + b*tan(c/2 + (d*x)/2)*(2*a^2 - b^2)*9i))/2)/(2*tan(c/2 + (d*x)/2)*(9*b^6 - 36*a^2*b^4 + 36*a^4*b^2) + 27*a*b^5 + (9*a^5*b)/2 - (225*a^3*b^3)/4 - (b*(2*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(9*a*b^2 - (3*a^3)/4) - 6*a^2*b + 3*b^3 - b*tan(c/2 + (d*x)/2)*(2*a^2 - b^2)*9i)*3i)/2 + (b*(2*a^2 - b^2)*(tan(c/2 + (d*x)/2)*(9*a*b^2 - (3*a^3)/4) - 6*a^2*b + 3*b^3 + b*tan(c/2 + (d*x)/2)*(2*a^2 - b^2)*9i)*3i)/2))*(2*a^2 - b^2))/d","B"
1123,1,1007,227,12.284324,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x)^6,x)","-\frac{2\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-2\,a^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+8\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-10\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-40\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-40\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+680\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+40\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+480\,b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+480\,b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-15\,a^2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+15\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-40\,a\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+560\,a\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-560\,a\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+40\,a\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+105\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+120\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-120\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-105\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+1920\,a\,b^2\,\mathrm{atan}\left(\frac{3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+1920\,a\,b^2\,\mathrm{atan}\left(\frac{3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-360\,a^2\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-360\,a^2\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}","Not used",1,"-(2*a^3*cos(c/2 + (d*x)/2)^12 - 2*a^3*sin(c/2 + (d*x)/2)^12 + 8*a^3*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 - 10*a^3*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 10*a^3*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 8*a^3*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 - 40*b^3*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 - 40*b^3*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 680*b^3*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 + 40*b^3*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 480*b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 480*b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 15*a^2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 + 15*a^2*b*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 40*a*b^2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 560*a*b^2*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 560*a*b^2*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 40*a*b^2*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 105*a^2*b*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 120*a^2*b*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 - 120*a^2*b*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 105*a^2*b*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 1920*a*b^2*atan((3*a^2*sin(c/2 + (d*x)/2) - 4*b^2*sin(c/2 + (d*x)/2) + 8*a*b*cos(c/2 + (d*x)/2))/(4*b^2*cos(c/2 + (d*x)/2) - 3*a^2*cos(c/2 + (d*x)/2) + 8*a*b*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 + 1920*a*b^2*atan((3*a^2*sin(c/2 + (d*x)/2) - 4*b^2*sin(c/2 + (d*x)/2) + 8*a*b*cos(c/2 + (d*x)/2))/(4*b^2*cos(c/2 + (d*x)/2) - 3*a^2*cos(c/2 + (d*x)/2) + 8*a*b*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 360*a^2*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 - 360*a^2*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)/(320*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5*(cos(c/2 + (d*x)/2)^2 + sin(c/2 + (d*x)/2)^2))","B"
1124,1,446,275,9.934371,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x)^7,x)","\frac{2\,b^3\,\mathrm{atan}\left(\frac{4\,b^6}{\frac{a^3\,b^3}{4}+\frac{9\,a\,b^5}{2}-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6}+\frac{9\,a\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{a^3\,b^3}{4}+\frac{9\,a\,b^5}{2}-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6\right)}+\frac{a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{a^3\,b^3}{4}+\frac{9\,a\,b^5}{2}-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6\right)}\right)}{d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3}{128}+\frac{3\,a\,b^2}{8}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{3\,a\,b^2}{64}-\frac{a^3}{128}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{3\,a^2\,b}{32}-\frac{b^3}{24}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a\,b^2-\frac{a^3}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3}{2}+24\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^2\,b-\frac{8\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(12\,a^2\,b-40\,b^3\right)+\frac{a^3}{6}+\frac{6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}}{64\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a^2\,b}{16}-\frac{5\,b^3}{8}\right)}{d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+18\,b^2\right)}{16\,d}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}","Not used",1,"(2*b^3*atan((4*b^6)/((9*a*b^5)/2 + (a^3*b^3)/4 - 4*b^6*tan(c/2 + (d*x)/2)) + (9*a*b^5*tan(c/2 + (d*x)/2))/(2*((9*a*b^5)/2 + (a^3*b^3)/4 - 4*b^6*tan(c/2 + (d*x)/2))) + (a^3*b^3*tan(c/2 + (d*x)/2))/(4*((9*a*b^5)/2 + (a^3*b^3)/4 - 4*b^6*tan(c/2 + (d*x)/2)))))/d + (a^3*tan(c/2 + (d*x)/2)^6)/(384*d) - (tan(c/2 + (d*x)/2)^2*((3*a*b^2)/8 + a^3/128))/d + (tan(c/2 + (d*x)/2)^4*((3*a*b^2)/64 - a^3/128))/d - (tan(c/2 + (d*x)/2)^3*((3*a^2*b)/32 - b^3/24))/d - (tan(c/2 + (d*x)/2)^2*(3*a*b^2 - a^3/2) - tan(c/2 + (d*x)/2)^4*(24*a*b^2 + a^3/2) - tan(c/2 + (d*x)/2)^3*(6*a^2*b - (8*b^3)/3) + tan(c/2 + (d*x)/2)^5*(12*a^2*b - 40*b^3) + a^3/6 + (6*a^2*b*tan(c/2 + (d*x)/2))/5)/(64*d*tan(c/2 + (d*x)/2)^6) + (tan(c/2 + (d*x)/2)*((3*a^2*b)/16 - (5*b^3)/8))/d + (a*log(tan(c/2 + (d*x)/2))*(a^2 + 18*b^2))/(16*d) + (3*a^2*b*tan(c/2 + (d*x)/2)^5)/(160*d)","B"
1125,1,359,303,9.905940,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x)^8,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^3}{128}+\frac{3\,a\,b^2}{32}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,a\,b^2}{160}-\frac{a^3}{640}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a^2\,b}{128}+\frac{b^3}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{3\,a^2\,b}{128}-\frac{b^3}{64}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^2\,b}{16}+\frac{3\,b^3}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{12\,a\,b^2}{5}-\frac{a^3}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a^3+24\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2\,b-2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^2\,b+16\,b^3\right)+\frac{a^3}{7}+a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a^3}{128}+\frac{3\,a\,b^2}{16}\right)}{d}+\frac{a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^7)/(896*d) - (tan(c/2 + (d*x)/2)^3*((3*a*b^2)/32 + a^3/128))/d + (tan(c/2 + (d*x)/2)^5*((3*a*b^2)/160 - a^3/640))/d - (tan(c/2 + (d*x)/2)^2*((3*a^2*b)/128 + b^3/8))/d - (tan(c/2 + (d*x)/2)^4*((3*a^2*b)/128 - b^3/64))/d + (log(tan(c/2 + (d*x)/2))*((3*a^2*b)/16 + (3*b^3)/8))/d - (tan(c/2 + (d*x)/2)^2*((12*a*b^2)/5 - a^3/5) - tan(c/2 + (d*x)/2)^4*(12*a*b^2 + a^3) + tan(c/2 + (d*x)/2)^6*(24*a*b^2 + 3*a^3) - tan(c/2 + (d*x)/2)^3*(3*a^2*b - 2*b^3) - tan(c/2 + (d*x)/2)^5*(3*a^2*b + 16*b^3) + a^3/7 + a^2*b*tan(c/2 + (d*x)/2))/(128*d*tan(c/2 + (d*x)/2)^7) + (tan(c/2 + (d*x)/2)*((3*a*b^2)/16 + (3*a^3)/128))/d + (a^2*b*tan(c/2 + (d*x)/2)^6)/(128*d)","B"
1126,1,381,334,9.951339,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^3)/sin(c + d*x)^9,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3}{256}+\frac{3\,a\,b^2}{128}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{3\,a^2\,b}{128}+\frac{b^3}{32}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,a^2\,b}{640}-\frac{b^3}{160}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^3}{128}+\frac{3\,a\,b^2}{16}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^3+6\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^2\,b+8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{6\,a^2\,b}{5}-\frac{8\,b^3}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(18\,a^2\,b+16\,b^3\right)-\frac{a^3}{8}-\frac{6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{7}-2\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{256\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,a^2\,b}{128}+\frac{b^3}{16}\right)}{d}-\frac{3\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}+\frac{a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128\,d}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^8)/(2048*d) - (tan(c/2 + (d*x)/2)^4*((3*a*b^2)/128 + a^3/256))/d - (tan(c/2 + (d*x)/2)^3*((3*a^2*b)/128 + b^3/32))/d - (tan(c/2 + (d*x)/2)^5*((3*a^2*b)/640 - b^3/160))/d + (log(tan(c/2 + (d*x)/2))*((3*a*b^2)/16 + (3*a^3)/128))/d + (tan(c/2 + (d*x)/2)^4*(6*a*b^2 + a^3) + tan(c/2 + (d*x)/2)^5*(6*a^2*b + 8*b^3) + tan(c/2 + (d*x)/2)^3*((6*a^2*b)/5 - (8*b^3)/5) - tan(c/2 + (d*x)/2)^7*(18*a^2*b + 16*b^3) - a^3/8 - (6*a^2*b*tan(c/2 + (d*x)/2))/7 - 2*a*b^2*tan(c/2 + (d*x)/2)^2 + 6*a*b^2*tan(c/2 + (d*x)/2)^6)/(256*d*tan(c/2 + (d*x)/2)^8) + (tan(c/2 + (d*x)/2)*((9*a^2*b)/128 + b^3/16))/d - (3*a*b^2*tan(c/2 + (d*x)/2)^2)/(128*d) + (a*b^2*tan(c/2 + (d*x)/2)^6)/(128*d) + (3*a^2*b*tan(c/2 + (d*x)/2)^7)/(896*d)","B"
1127,1,2390,307,12.320840,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x))^2,x)","-\frac{\frac{2\,\left(30\,a^5-25\,a^3\,b^2+a\,b^4\right)}{5\,b^6}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(-4\,a^5+2\,a^3\,b^2+a\,b^4\right)}{b^6}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(20\,a^5-18\,a^3\,b^2+a\,b^4\right)}{b^6}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(30\,a^5-25\,a^3\,b^2+a\,b^4\right)}{b^6}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(100\,a^5-90\,a^3\,b^2+9\,a\,b^4\right)}{5\,b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(180\,a^4-155\,a^2\,b^2+8\,b^4\right)}{10\,b^5}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(4\,a^4-3\,a^2\,b^2\right)}{2\,b^5}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(10\,a^5-7\,a^3\,b^2\right)}{b^6}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(36\,a^4-31\,a^2\,b^2\right)}{b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(156\,a^4-125\,a^2\,b^2\right)}{2\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(84\,a^4-75\,a^2\,b^2+8\,b^4\right)}{2\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(132\,a^4-107\,a^2\,b^2+8\,b^4\right)}{b^5}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+10\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+20\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+10\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,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{2\,\mathrm{atanh}\left(\frac{108\,a^6\,\sqrt{b^2-a^2}}{108\,a^6\,b-\frac{324\,a^8}{b}+\frac{216\,a^{10}}{b^3}-648\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+216\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{432\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}-\frac{216\,a^8\,\sqrt{b^2-a^2}}{108\,a^6\,b^3-324\,a^8\,b+\frac{216\,a^{10}}{b}+432\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+216\,a^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-648\,a^7\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{216\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{108\,a^6-\frac{324\,a^8}{b^2}+\frac{216\,a^{10}}{b^4}+216\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{648\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{432\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}}-\frac{540\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{108\,a^6\,b^2-324\,a^8+\frac{216\,a^{10}}{b^2}-648\,a^7\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+216\,a^5\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{432\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{216\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{216\,a^{10}+432\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b-324\,a^8\,b^2-648\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^3+108\,a^6\,b^4+216\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^5}\right)\,\left(6\,a^4\,\sqrt{b^2-a^2}-3\,a^2\,b^2\,\sqrt{b^2-a^2}\right)}{b^7\,d}-\frac{3\,a\,\mathrm{atan}\left(\frac{\frac{3\,a\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,\left(\frac{2\,\left(576\,a^{12}\,b^6-1152\,a^{10}\,b^8+720\,a^8\,b^{10}-144\,a^6\,b^{12}+9\,a^4\,b^{14}\right)}{b^{17}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-1152\,a^{13}\,b^6+4032\,a^{11}\,b^8-4896\,a^9\,b^{10}+2448\,a^7\,b^{12}-441\,a^5\,b^{14}+18\,a^3\,b^{16}\right)}{b^{18}}-\frac{a\,\left(\frac{2\,\left(48\,a^6\,b^{14}-60\,a^4\,b^{16}+12\,a^2\,b^{18}\right)}{b^{17}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a^7\,b^{14}-288\,a^5\,b^{16}+96\,a^3\,b^{18}\right)}{b^{18}}-\frac{a\,\left(32\,a^2\,b^3+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a\,b^{22}-32\,a^3\,b^{20}\right)}{b^{18}}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,3{}\mathrm{i}}{4\,b^7}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,3{}\mathrm{i}}{4\,b^7}\right)}{4\,b^7}+\frac{3\,a\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,\left(\frac{2\,\left(576\,a^{12}\,b^6-1152\,a^{10}\,b^8+720\,a^8\,b^{10}-144\,a^6\,b^{12}+9\,a^4\,b^{14}\right)}{b^{17}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-1152\,a^{13}\,b^6+4032\,a^{11}\,b^8-4896\,a^9\,b^{10}+2448\,a^7\,b^{12}-441\,a^5\,b^{14}+18\,a^3\,b^{16}\right)}{b^{18}}+\frac{a\,\left(\frac{2\,\left(48\,a^6\,b^{14}-60\,a^4\,b^{16}+12\,a^2\,b^{18}\right)}{b^{17}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a^7\,b^{14}-288\,a^5\,b^{16}+96\,a^3\,b^{18}\right)}{b^{18}}+\frac{a\,\left(32\,a^2\,b^3+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a\,b^{22}-32\,a^3\,b^{20}\right)}{b^{18}}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,3{}\mathrm{i}}{4\,b^7}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,3{}\mathrm{i}}{4\,b^7}\right)}{4\,b^7}}{\frac{4\,\left(1728\,a^{16}-5616\,a^{14}\,b^2+6912\,a^{12}\,b^4-3942\,a^{10}\,b^6+999\,a^8\,b^8-81\,a^6\,b^{10}\right)}{b^{17}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6912\,a^{17}-24192\,a^{15}\,b^2+32832\,a^{13}\,b^4-21600\,a^{11}\,b^6+7020\,a^9\,b^8-1026\,a^7\,b^{10}+54\,a^5\,b^{12}\right)}{b^{18}}-\frac{a\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,\left(\frac{2\,\left(576\,a^{12}\,b^6-1152\,a^{10}\,b^8+720\,a^8\,b^{10}-144\,a^6\,b^{12}+9\,a^4\,b^{14}\right)}{b^{17}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-1152\,a^{13}\,b^6+4032\,a^{11}\,b^8-4896\,a^9\,b^{10}+2448\,a^7\,b^{12}-441\,a^5\,b^{14}+18\,a^3\,b^{16}\right)}{b^{18}}-\frac{a\,\left(\frac{2\,\left(48\,a^6\,b^{14}-60\,a^4\,b^{16}+12\,a^2\,b^{18}\right)}{b^{17}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a^7\,b^{14}-288\,a^5\,b^{16}+96\,a^3\,b^{18}\right)}{b^{18}}-\frac{a\,\left(32\,a^2\,b^3+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a\,b^{22}-32\,a^3\,b^{20}\right)}{b^{18}}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,3{}\mathrm{i}}{4\,b^7}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,3{}\mathrm{i}}{4\,b^7}\right)\,3{}\mathrm{i}}{4\,b^7}+\frac{a\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,\left(\frac{2\,\left(576\,a^{12}\,b^6-1152\,a^{10}\,b^8+720\,a^8\,b^{10}-144\,a^6\,b^{12}+9\,a^4\,b^{14}\right)}{b^{17}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-1152\,a^{13}\,b^6+4032\,a^{11}\,b^8-4896\,a^9\,b^{10}+2448\,a^7\,b^{12}-441\,a^5\,b^{14}+18\,a^3\,b^{16}\right)}{b^{18}}+\frac{a\,\left(\frac{2\,\left(48\,a^6\,b^{14}-60\,a^4\,b^{16}+12\,a^2\,b^{18}\right)}{b^{17}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a^7\,b^{14}-288\,a^5\,b^{16}+96\,a^3\,b^{18}\right)}{b^{18}}+\frac{a\,\left(32\,a^2\,b^3+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a\,b^{22}-32\,a^3\,b^{20}\right)}{b^{18}}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,3{}\mathrm{i}}{4\,b^7}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)\,3{}\mathrm{i}}{4\,b^7}\right)\,3{}\mathrm{i}}{4\,b^7}}\right)\,\left(8\,a^4-8\,a^2\,b^2+b^4\right)}{2\,b^7\,d}","Not used",1,"- ((2*(a*b^4 + 30*a^5 - 25*a^3*b^2))/(5*b^6) - (3*tan(c/2 + (d*x)/2)^10*(a*b^4 - 4*a^5 + 2*a^3*b^2))/b^6 + (6*tan(c/2 + (d*x)/2)^4*(a*b^4 + 20*a^5 - 18*a^3*b^2))/b^6 + (4*tan(c/2 + (d*x)/2)^6*(a*b^4 + 30*a^5 - 25*a^3*b^2))/b^6 + (3*tan(c/2 + (d*x)/2)^2*(9*a*b^4 + 100*a^5 - 90*a^3*b^2))/(5*b^6) + (tan(c/2 + (d*x)/2)*(180*a^4 + 8*b^4 - 155*a^2*b^2))/(10*b^5) + (3*tan(c/2 + (d*x)/2)^11*(4*a^4 - 3*a^2*b^2))/(2*b^5) + (6*tan(c/2 + (d*x)/2)^8*(10*a^5 - 7*a^3*b^2))/b^6 + (3*tan(c/2 + (d*x)/2)^7*(36*a^4 - 31*a^2*b^2))/b^5 + (tan(c/2 + (d*x)/2)^3*(156*a^4 - 125*a^2*b^2))/(2*b^5) + (tan(c/2 + (d*x)/2)^9*(84*a^4 + 8*b^4 - 75*a^2*b^2))/(2*b^5) + (tan(c/2 + (d*x)/2)^5*(132*a^4 + 8*b^4 - 107*a^2*b^2))/b^5)/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 6*a*tan(c/2 + (d*x)/2)^2 + 15*a*tan(c/2 + (d*x)/2)^4 + 20*a*tan(c/2 + (d*x)/2)^6 + 15*a*tan(c/2 + (d*x)/2)^8 + 6*a*tan(c/2 + (d*x)/2)^10 + a*tan(c/2 + (d*x)/2)^12 + 10*b*tan(c/2 + (d*x)/2)^3 + 20*b*tan(c/2 + (d*x)/2)^5 + 20*b*tan(c/2 + (d*x)/2)^7 + 10*b*tan(c/2 + (d*x)/2)^9 + 2*b*tan(c/2 + (d*x)/2)^11)) - (2*atanh((108*a^6*(b^2 - a^2)^(1/2))/(108*a^6*b - (324*a^8)/b + (216*a^10)/b^3 - 648*a^7*tan(c/2 + (d*x)/2) + 216*a^5*b^2*tan(c/2 + (d*x)/2) + (432*a^9*tan(c/2 + (d*x)/2))/b^2) - (216*a^8*(b^2 - a^2)^(1/2))/(108*a^6*b^3 - 324*a^8*b + (216*a^10)/b + 432*a^9*tan(c/2 + (d*x)/2) + 216*a^5*b^4*tan(c/2 + (d*x)/2) - 648*a^7*b^2*tan(c/2 + (d*x)/2)) + (216*a^5*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(108*a^6 - (324*a^8)/b^2 + (216*a^10)/b^4 + 216*a^5*b*tan(c/2 + (d*x)/2) - (648*a^7*tan(c/2 + (d*x)/2))/b + (432*a^9*tan(c/2 + (d*x)/2))/b^3) - (540*a^7*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(108*a^6*b^2 - 324*a^8 + (216*a^10)/b^2 - 648*a^7*b*tan(c/2 + (d*x)/2) + 216*a^5*b^3*tan(c/2 + (d*x)/2) + (432*a^9*tan(c/2 + (d*x)/2))/b) + (216*a^9*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(216*a^10 + 108*a^6*b^4 - 324*a^8*b^2 + 432*a^9*b*tan(c/2 + (d*x)/2) + 216*a^5*b^5*tan(c/2 + (d*x)/2) - 648*a^7*b^3*tan(c/2 + (d*x)/2)))*(6*a^4*(b^2 - a^2)^(1/2) - 3*a^2*b^2*(b^2 - a^2)^(1/2)))/(b^7*d) - (3*a*atan(((3*a*(8*a^4 + b^4 - 8*a^2*b^2)*((2*(9*a^4*b^14 - 144*a^6*b^12 + 720*a^8*b^10 - 1152*a^10*b^8 + 576*a^12*b^6))/b^17 + (2*tan(c/2 + (d*x)/2)*(18*a^3*b^16 - 441*a^5*b^14 + 2448*a^7*b^12 - 4896*a^9*b^10 + 4032*a^11*b^8 - 1152*a^13*b^6))/b^18 - (a*((2*(12*a^2*b^18 - 60*a^4*b^16 + 48*a^6*b^14))/b^17 + (2*tan(c/2 + (d*x)/2)*(96*a^3*b^18 - 288*a^5*b^16 + 192*a^7*b^14))/b^18 - (a*(32*a^2*b^3 + (2*tan(c/2 + (d*x)/2)*(48*a*b^22 - 32*a^3*b^20))/b^18)*(8*a^4 + b^4 - 8*a^2*b^2)*3i)/(4*b^7))*(8*a^4 + b^4 - 8*a^2*b^2)*3i)/(4*b^7)))/(4*b^7) + (3*a*(8*a^4 + b^4 - 8*a^2*b^2)*((2*(9*a^4*b^14 - 144*a^6*b^12 + 720*a^8*b^10 - 1152*a^10*b^8 + 576*a^12*b^6))/b^17 + (2*tan(c/2 + (d*x)/2)*(18*a^3*b^16 - 441*a^5*b^14 + 2448*a^7*b^12 - 4896*a^9*b^10 + 4032*a^11*b^8 - 1152*a^13*b^6))/b^18 + (a*((2*(12*a^2*b^18 - 60*a^4*b^16 + 48*a^6*b^14))/b^17 + (2*tan(c/2 + (d*x)/2)*(96*a^3*b^18 - 288*a^5*b^16 + 192*a^7*b^14))/b^18 + (a*(32*a^2*b^3 + (2*tan(c/2 + (d*x)/2)*(48*a*b^22 - 32*a^3*b^20))/b^18)*(8*a^4 + b^4 - 8*a^2*b^2)*3i)/(4*b^7))*(8*a^4 + b^4 - 8*a^2*b^2)*3i)/(4*b^7)))/(4*b^7))/((4*(1728*a^16 - 81*a^6*b^10 + 999*a^8*b^8 - 3942*a^10*b^6 + 6912*a^12*b^4 - 5616*a^14*b^2))/b^17 + (4*tan(c/2 + (d*x)/2)*(6912*a^17 + 54*a^5*b^12 - 1026*a^7*b^10 + 7020*a^9*b^8 - 21600*a^11*b^6 + 32832*a^13*b^4 - 24192*a^15*b^2))/b^18 - (a*(8*a^4 + b^4 - 8*a^2*b^2)*((2*(9*a^4*b^14 - 144*a^6*b^12 + 720*a^8*b^10 - 1152*a^10*b^8 + 576*a^12*b^6))/b^17 + (2*tan(c/2 + (d*x)/2)*(18*a^3*b^16 - 441*a^5*b^14 + 2448*a^7*b^12 - 4896*a^9*b^10 + 4032*a^11*b^8 - 1152*a^13*b^6))/b^18 - (a*((2*(12*a^2*b^18 - 60*a^4*b^16 + 48*a^6*b^14))/b^17 + (2*tan(c/2 + (d*x)/2)*(96*a^3*b^18 - 288*a^5*b^16 + 192*a^7*b^14))/b^18 - (a*(32*a^2*b^3 + (2*tan(c/2 + (d*x)/2)*(48*a*b^22 - 32*a^3*b^20))/b^18)*(8*a^4 + b^4 - 8*a^2*b^2)*3i)/(4*b^7))*(8*a^4 + b^4 - 8*a^2*b^2)*3i)/(4*b^7))*3i)/(4*b^7) + (a*(8*a^4 + b^4 - 8*a^2*b^2)*((2*(9*a^4*b^14 - 144*a^6*b^12 + 720*a^8*b^10 - 1152*a^10*b^8 + 576*a^12*b^6))/b^17 + (2*tan(c/2 + (d*x)/2)*(18*a^3*b^16 - 441*a^5*b^14 + 2448*a^7*b^12 - 4896*a^9*b^10 + 4032*a^11*b^8 - 1152*a^13*b^6))/b^18 + (a*((2*(12*a^2*b^18 - 60*a^4*b^16 + 48*a^6*b^14))/b^17 + (2*tan(c/2 + (d*x)/2)*(96*a^3*b^18 - 288*a^5*b^16 + 192*a^7*b^14))/b^18 + (a*(32*a^2*b^3 + (2*tan(c/2 + (d*x)/2)*(48*a*b^22 - 32*a^3*b^20))/b^18)*(8*a^4 + b^4 - 8*a^2*b^2)*3i)/(4*b^7))*(8*a^4 + b^4 - 8*a^2*b^2)*3i)/(4*b^7))*3i)/(4*b^7)))*(8*a^4 + b^4 - 8*a^2*b^2))/(2*b^7*d)","B"
1128,1,1003,267,11.794617,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x))^2,x)","\frac{60\,a^4\,b+\frac{3\,b^5\,\cos\left(c+d\,x\right)}{2}+120\,a^5\,\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)-44\,a^2\,b^3-\frac{21\,b^5\,\cos\left(3\,c+3\,d\,x\right)}{16}-\frac{3\,b^5\,\cos\left(5\,c+5\,d\,x\right)}{16}+9\,a\,b^4\,\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{93\,a^2\,b^3\,\cos\left(c+d\,x\right)}{2}+9\,b^5\,\sin\left(c+d\,x\right)\,\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)-11\,a\,b^4\,\sin\left(2\,c+2\,d\,x\right)-\frac{5\,a\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+60\,a^3\,b^2\,\sin\left(c+d\,x\right)-108\,a^3\,b^2\,\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{5\,a^2\,b^3\,\cos\left(3\,c+3\,d\,x\right)}{2}-120\,a^4\,\mathrm{atanh}\left(\frac{2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\sqrt{b^2-a^2}+15\,a^3\,b^2\,\sin\left(2\,c+2\,d\,x\right)+60\,a^4\,b\,\cos\left(c+d\,x\right)-44\,a\,b^4\,\sin\left(c+d\,x\right)-108\,a^2\,b^3\,\sin\left(c+d\,x\right)\,\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)+48\,a^2\,b^2\,\mathrm{atanh}\left(\frac{2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\sqrt{b^2-a^2}+120\,a^4\,b\,\sin\left(c+d\,x\right)\,\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)+48\,a\,b^3\,\sin\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\sqrt{b^2-a^2}-120\,a^3\,b\,\sin\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\sqrt{b^2-a^2}}{12\,b^6\,d\,\left(a+b\,\sin\left(c+d\,x\right)\right)}","Not used",1,"(60*a^4*b + (3*b^5*cos(c + d*x))/2 + 120*a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - 44*a^2*b^3 - (21*b^5*cos(3*c + 3*d*x))/16 - (3*b^5*cos(5*c + 5*d*x))/16 + 9*a*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (93*a^2*b^3*cos(c + d*x))/2 + 9*b^5*sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - 11*a*b^4*sin(2*c + 2*d*x) - (5*a*b^4*sin(4*c + 4*d*x))/8 + 60*a^3*b^2*sin(c + d*x) - 108*a^3*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (5*a^2*b^3*cos(3*c + 3*d*x))/2 - 120*a^4*atanh((2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + a*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*cos(c/2 + (d*x)/2) - 2*b^3*sin(c/2 + (d*x)/2) - a*b^2*cos(c/2 + (d*x)/2) + 2*a^2*b*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2) + 15*a^3*b^2*sin(2*c + 2*d*x) + 60*a^4*b*cos(c + d*x) - 44*a*b^4*sin(c + d*x) - 108*a^2*b^3*sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 48*a^2*b^2*atanh((2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + a*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*cos(c/2 + (d*x)/2) - 2*b^3*sin(c/2 + (d*x)/2) - a*b^2*cos(c/2 + (d*x)/2) + 2*a^2*b*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2) + 120*a^4*b*sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 48*a*b^3*sin(c + d*x)*atanh((2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + a*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*cos(c/2 + (d*x)/2) - 2*b^3*sin(c/2 + (d*x)/2) - a*b^2*cos(c/2 + (d*x)/2) + 2*a^2*b*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2) - 120*a^3*b*sin(c + d*x)*atanh((2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + a*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*cos(c/2 + (d*x)/2) - 2*b^3*sin(c/2 + (d*x)/2) - a*b^2*cos(c/2 + (d*x)/2) + 2*a^2*b*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(12*b^6*d*(a + b*sin(c + d*x)))","B"
1129,1,964,163,11.525526,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x))^2,x)","\frac{\frac{2\,\left(7\,a\,b^2-12\,a^3\right)}{3\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a\,b^2-4\,a^3\right)}{b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(7\,a\,b^2-12\,a^3\right)}{b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(25\,a\,b^2-36\,a^3\right)}{3\,b^4}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,a^2-11\,b^2\right)}{3\,b^3}-\frac{14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^2-b^2\right)}{b^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^2-b^2\right)}{b^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(10\,a^2-7\,b^2\right)}{b^3}}{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+4\,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\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,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{2\,\mathrm{atanh}\left(\frac{64\,a^2\,\sqrt{b^2-a^2}}{64\,a^2\,b-\frac{320\,a^4}{b}+\frac{256\,a^6}{b^3}-640\,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{512\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}-\frac{256\,a^4\,\sqrt{b^2-a^2}}{64\,a^2\,b^3-320\,a^4\,b+\frac{256\,a^6}{b}+512\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+128\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-640\,a^3\,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{320\,a^4}{b^2}+\frac{256\,a^6}{b^4}-\frac{640\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{512\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+128\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{576\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{64\,a^2\,b^2-320\,a^4+\frac{256\,a^6}{b^2}+128\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-640\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{512\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{256\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{256\,a^6+512\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b-320\,a^4\,b^2-640\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^3+64\,a^2\,b^4+128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^5}\right)\,\left(4\,a^2\,\sqrt{b^2-a^2}-b^2\,\sqrt{b^2-a^2}\right)}{b^5\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{192\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{192\,a^2-\frac{448\,a^4}{b^2}+\frac{256\,a^6}{b^4}}-\frac{448\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{192\,a^2\,b^2-448\,a^4+\frac{256\,a^6}{b^2}}+\frac{256\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,a^6-448\,a^4\,b^2+192\,a^2\,b^4}\right)\,\left(4\,a^2-3\,b^2\right)}{b^5\,d}","Not used",1,"((2*(7*a*b^2 - 12*a^3))/(3*b^4) + (2*tan(c/2 + (d*x)/2)^6*(a*b^2 - 4*a^3))/b^4 + (2*tan(c/2 + (d*x)/2)^4*(7*a*b^2 - 12*a^3))/b^4 + (2*tan(c/2 + (d*x)/2)^2*(25*a*b^2 - 36*a^3))/(3*b^4) - (2*tan(c/2 + (d*x)/2)*(18*a^2 - 11*b^2))/(3*b^3) - (14*tan(c/2 + (d*x)/2)^3*(2*a^2 - b^2))/b^3 - (2*tan(c/2 + (d*x)/2)^7*(2*a^2 - b^2))/b^3 - (2*tan(c/2 + (d*x)/2)^5*(10*a^2 - 7*b^2))/b^3)/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 + 4*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)) - (2*atanh((64*a^2*(b^2 - a^2)^(1/2))/(64*a^2*b - (320*a^4)/b + (256*a^6)/b^3 - 640*a^3*tan(c/2 + (d*x)/2) + 128*a*b^2*tan(c/2 + (d*x)/2) + (512*a^5*tan(c/2 + (d*x)/2))/b^2) - (256*a^4*(b^2 - a^2)^(1/2))/(64*a^2*b^3 - 320*a^4*b + (256*a^6)/b + 512*a^5*tan(c/2 + (d*x)/2) + 128*a*b^4*tan(c/2 + (d*x)/2) - 640*a^3*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 - (320*a^4)/b^2 + (256*a^6)/b^4 - (640*a^3*tan(c/2 + (d*x)/2))/b + (512*a^5*tan(c/2 + (d*x)/2))/b^3 + 128*a*b*tan(c/2 + (d*x)/2)) - (576*a^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(64*a^2*b^2 - 320*a^4 + (256*a^6)/b^2 + 128*a*b^3*tan(c/2 + (d*x)/2) - 640*a^3*b*tan(c/2 + (d*x)/2) + (512*a^5*tan(c/2 + (d*x)/2))/b) + (256*a^5*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(256*a^6 + 64*a^2*b^4 - 320*a^4*b^2 + 128*a*b^5*tan(c/2 + (d*x)/2) + 512*a^5*b*tan(c/2 + (d*x)/2) - 640*a^3*b^3*tan(c/2 + (d*x)/2)))*(4*a^2*(b^2 - a^2)^(1/2) - b^2*(b^2 - a^2)^(1/2)))/(b^5*d) - (2*a*atan((192*a^2*tan(c/2 + (d*x)/2))/(192*a^2 - (448*a^4)/b^2 + (256*a^6)/b^4) - (448*a^4*tan(c/2 + (d*x)/2))/(192*a^2*b^2 - 448*a^4 + (256*a^6)/b^2) + (256*a^6*tan(c/2 + (d*x)/2))/(256*a^6 + 192*a^2*b^4 - 448*a^4*b^2))*(4*a^2 - 3*b^2))/(b^5*d)","B"
1130,1,2773,137,11.152666,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + b*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{\mathrm{atan}\left(\frac{\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\left(\frac{32\,\left(4\,a^4\,b^{10}-3\,a^6\,b^8\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{10}-17\,a^6\,b^{12}+16\,a^4\,b^{14}\right)}{a^3\,b^8}\right)\,\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)+\frac{32\,\left(8\,a^2\,b^{10}-7\,a^6\,b^6\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^8-18\,a^6\,b^{10}-5\,a^4\,b^{12}+16\,a^2\,b^{14}\right)}{a^3\,b^8}\right)+\frac{32\,\left(-12\,a^8\,b^2+16\,a^6\,b^4-7\,a^4\,b^6+3\,a^2\,b^8+4\,b^{10}\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b^4-100\,a^8\,b^6+101\,a^6\,b^8+6\,a^4\,b^{10}-11\,a^2\,b^{12}\right)}{a^3\,b^8}\right)-\frac{32\,\left(28\,a^8-6\,a^6\,b^2-28\,a^4\,b^4+2\,a^2\,b^6\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{10}\,b^2-72\,a^8\,b^4-20\,a^6\,b^6+61\,a^4\,b^8+2\,a^2\,b^{10}+b^{12}\right)}{a^3\,b^8}\right)\,1{}\mathrm{i}-\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\frac{32\,\left(-12\,a^8\,b^2+16\,a^6\,b^4-7\,a^4\,b^6+3\,a^2\,b^8+4\,b^{10}\right)}{a^2\,b^5}-\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\frac{32\,\left(8\,a^2\,b^{10}-7\,a^6\,b^6\right)}{a^2\,b^5}-\left(\frac{32\,\left(4\,a^4\,b^{10}-3\,a^6\,b^8\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{10}-17\,a^6\,b^{12}+16\,a^4\,b^{14}\right)}{a^3\,b^8}\right)\,\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^8-18\,a^6\,b^{10}-5\,a^4\,b^{12}+16\,a^2\,b^{14}\right)}{a^3\,b^8}\right)+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b^4-100\,a^8\,b^6+101\,a^6\,b^8+6\,a^4\,b^{10}-11\,a^2\,b^{12}\right)}{a^3\,b^8}\right)+\frac{32\,\left(28\,a^8-6\,a^6\,b^2-28\,a^4\,b^4+2\,a^2\,b^6\right)}{a^2\,b^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{10}\,b^2-72\,a^8\,b^4-20\,a^6\,b^6+61\,a^4\,b^8+2\,a^2\,b^{10}+b^{12}\right)}{a^3\,b^8}\right)\,1{}\mathrm{i}}{\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\left(\frac{32\,\left(4\,a^4\,b^{10}-3\,a^6\,b^8\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{10}-17\,a^6\,b^{12}+16\,a^4\,b^{14}\right)}{a^3\,b^8}\right)\,\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)+\frac{32\,\left(8\,a^2\,b^{10}-7\,a^6\,b^6\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^8-18\,a^6\,b^{10}-5\,a^4\,b^{12}+16\,a^2\,b^{14}\right)}{a^3\,b^8}\right)+\frac{32\,\left(-12\,a^8\,b^2+16\,a^6\,b^4-7\,a^4\,b^6+3\,a^2\,b^8+4\,b^{10}\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b^4-100\,a^8\,b^6+101\,a^6\,b^8+6\,a^4\,b^{10}-11\,a^2\,b^{12}\right)}{a^3\,b^8}\right)-\frac{32\,\left(28\,a^8-6\,a^6\,b^2-28\,a^4\,b^4+2\,a^2\,b^6\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{10}\,b^2-72\,a^8\,b^4-20\,a^6\,b^6+61\,a^4\,b^8+2\,a^2\,b^{10}+b^{12}\right)}{a^3\,b^8}\right)+\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\frac{32\,\left(-12\,a^8\,b^2+16\,a^6\,b^4-7\,a^4\,b^6+3\,a^2\,b^8+4\,b^{10}\right)}{a^2\,b^5}-\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)\,\left(\frac{32\,\left(8\,a^2\,b^{10}-7\,a^6\,b^6\right)}{a^2\,b^5}-\left(\frac{32\,\left(4\,a^4\,b^{10}-3\,a^6\,b^8\right)}{a^2\,b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{10}-17\,a^6\,b^{12}+16\,a^4\,b^{14}\right)}{a^3\,b^8}\right)\,\left(\frac{2\,\sqrt{b^2-a^2}}{b^3}+\frac{\sqrt{b^2-a^2}}{a^2\,b}\right)+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^8-18\,a^6\,b^{10}-5\,a^4\,b^{12}+16\,a^2\,b^{14}\right)}{a^3\,b^8}\right)+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b^4-100\,a^8\,b^6+101\,a^6\,b^8+6\,a^4\,b^{10}-11\,a^2\,b^{12}\right)}{a^3\,b^8}\right)+\frac{32\,\left(28\,a^8-6\,a^6\,b^2-28\,a^4\,b^4+2\,a^2\,b^6\right)}{a^2\,b^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{10}\,b^2-72\,a^8\,b^4-20\,a^6\,b^6+61\,a^4\,b^8+2\,a^2\,b^{10}+b^{12}\right)}{a^3\,b^8}\right)-\frac{64\,\left(28\,a^6-18\,a^4\,b^2-12\,a^2\,b^4+2\,b^6\right)}{a^2\,b^5}-\frac{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{10}-160\,a^8\,b^2-16\,a^6\,b^4+48\,a^4\,b^6\right)}{a^3\,b^8}}\right)\,\left(\frac{\sqrt{b^2-a^2}\,4{}\mathrm{i}}{b^3}+\frac{\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^2\,b}\right)}{d}-\frac{\frac{2\,\left(2\,a^2-b^2\right)}{a\,b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-b^2\right)}{a^2\,b}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2-b^2\right)}{a^2\,b}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-b^2\right)}{a\,b^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\,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{4\,a\,\mathrm{atan}\left(\frac{256\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{128\,b^2}{a^2}-\frac{384\,a^2}{b^2}+\frac{256\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{512\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}-\frac{768\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}+256}-\frac{512\,a^3}{256\,b^3-384\,a^2\,b+\frac{128\,b^5}{a^2}+512\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+256\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{768\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}+\frac{768\,a^5}{256\,b^5-384\,a^2\,b^3+\frac{128\,b^7}{a^2}-768\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+256\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+512\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{256\,a}{256\,b+256\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{384\,a^2}{b}+\frac{128\,b^3}{a^2}+\frac{512\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{768\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}}-\frac{384\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,b^2-384\,a^2+\frac{128\,b^4}{a^2}+\frac{512\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{768\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+256\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{128\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,b+\frac{256\,a^2}{b}-\frac{384\,a^4}{b^3}+\frac{256\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{512\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}-\frac{768\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}\right)}{b^3\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) + (atan((((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*(((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*(((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*(((32*(4*a^4*b^10 - 3*a^6*b^8))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^14 - 17*a^6*b^12 + 2*a^8*b^10))/(a^3*b^8))*((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b)) + (32*(8*a^2*b^10 - 7*a^6*b^6))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^14 - 5*a^4*b^12 - 18*a^6*b^10 + 8*a^8*b^8))/(a^3*b^8)) + (32*(4*b^10 + 3*a^2*b^8 - 7*a^4*b^6 + 16*a^6*b^4 - 12*a^8*b^2))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(6*a^4*b^10 - 11*a^2*b^12 + 101*a^6*b^8 - 100*a^8*b^6 + 8*a^10*b^4))/(a^3*b^8)) - (32*(28*a^8 + 2*a^2*b^6 - 28*a^4*b^4 - 6*a^6*b^2))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(b^12 + 2*a^2*b^10 + 61*a^4*b^8 - 20*a^6*b^6 - 72*a^8*b^4 + 32*a^10*b^2))/(a^3*b^8))*1i - ((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*(((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*((32*(4*b^10 + 3*a^2*b^8 - 7*a^4*b^6 + 16*a^6*b^4 - 12*a^8*b^2))/(a^2*b^5) - ((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*((32*(8*a^2*b^10 - 7*a^6*b^6))/(a^2*b^5) - ((32*(4*a^4*b^10 - 3*a^6*b^8))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^14 - 17*a^6*b^12 + 2*a^8*b^10))/(a^3*b^8))*((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b)) + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^14 - 5*a^4*b^12 - 18*a^6*b^10 + 8*a^8*b^8))/(a^3*b^8)) + (32*tan(c/2 + (d*x)/2)*(6*a^4*b^10 - 11*a^2*b^12 + 101*a^6*b^8 - 100*a^8*b^6 + 8*a^10*b^4))/(a^3*b^8)) + (32*(28*a^8 + 2*a^2*b^6 - 28*a^4*b^4 - 6*a^6*b^2))/(a^2*b^5) - (32*tan(c/2 + (d*x)/2)*(b^12 + 2*a^2*b^10 + 61*a^4*b^8 - 20*a^6*b^6 - 72*a^8*b^4 + 32*a^10*b^2))/(a^3*b^8))*1i)/(((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*(((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*(((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*(((32*(4*a^4*b^10 - 3*a^6*b^8))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^14 - 17*a^6*b^12 + 2*a^8*b^10))/(a^3*b^8))*((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b)) + (32*(8*a^2*b^10 - 7*a^6*b^6))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^14 - 5*a^4*b^12 - 18*a^6*b^10 + 8*a^8*b^8))/(a^3*b^8)) + (32*(4*b^10 + 3*a^2*b^8 - 7*a^4*b^6 + 16*a^6*b^4 - 12*a^8*b^2))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(6*a^4*b^10 - 11*a^2*b^12 + 101*a^6*b^8 - 100*a^8*b^6 + 8*a^10*b^4))/(a^3*b^8)) - (32*(28*a^8 + 2*a^2*b^6 - 28*a^4*b^4 - 6*a^6*b^2))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(b^12 + 2*a^2*b^10 + 61*a^4*b^8 - 20*a^6*b^6 - 72*a^8*b^4 + 32*a^10*b^2))/(a^3*b^8)) + ((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*(((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*((32*(4*b^10 + 3*a^2*b^8 - 7*a^4*b^6 + 16*a^6*b^4 - 12*a^8*b^2))/(a^2*b^5) - ((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b))*((32*(8*a^2*b^10 - 7*a^6*b^6))/(a^2*b^5) - ((32*(4*a^4*b^10 - 3*a^6*b^8))/(a^2*b^5) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^14 - 17*a^6*b^12 + 2*a^8*b^10))/(a^3*b^8))*((2*(b^2 - a^2)^(1/2))/b^3 + (b^2 - a^2)^(1/2)/(a^2*b)) + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^14 - 5*a^4*b^12 - 18*a^6*b^10 + 8*a^8*b^8))/(a^3*b^8)) + (32*tan(c/2 + (d*x)/2)*(6*a^4*b^10 - 11*a^2*b^12 + 101*a^6*b^8 - 100*a^8*b^6 + 8*a^10*b^4))/(a^3*b^8)) + (32*(28*a^8 + 2*a^2*b^6 - 28*a^4*b^4 - 6*a^6*b^2))/(a^2*b^5) - (32*tan(c/2 + (d*x)/2)*(b^12 + 2*a^2*b^10 + 61*a^4*b^8 - 20*a^6*b^6 - 72*a^8*b^4 + 32*a^10*b^2))/(a^3*b^8)) - (64*(28*a^6 + 2*b^6 - 12*a^2*b^4 - 18*a^4*b^2))/(a^2*b^5) - (64*tan(c/2 + (d*x)/2)*(128*a^10 + 48*a^4*b^6 - 16*a^6*b^4 - 160*a^8*b^2))/(a^3*b^8)))*(((b^2 - a^2)^(1/2)*4i)/b^3 + ((b^2 - a^2)^(1/2)*2i)/(a^2*b)))/d - ((2*(2*a^2 - b^2))/(a*b^2) + (2*tan(c/2 + (d*x)/2)*(3*a^2 - b^2))/(a^2*b) + (2*tan(c/2 + (d*x)/2)^3*(a^2 - b^2))/(a^2*b) + (2*tan(c/2 + (d*x)/2)^2*(2*a^2 - b^2))/(a*b^2))/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4 + 2*b*tan(c/2 + (d*x)/2)^3)) - (4*a*atan((256*tan(c/2 + (d*x)/2))/((128*b^2)/a^2 - (384*a^2)/b^2 + (256*a*tan(c/2 + (d*x)/2))/b + (512*a^3*tan(c/2 + (d*x)/2))/b^3 - (768*a^5*tan(c/2 + (d*x)/2))/b^5 + 256) - (512*a^3)/(256*b^3 - 384*a^2*b + (128*b^5)/a^2 + 512*a^3*tan(c/2 + (d*x)/2) + 256*a*b^2*tan(c/2 + (d*x)/2) - (768*a^5*tan(c/2 + (d*x)/2))/b^2) + (768*a^5)/(256*b^5 - 384*a^2*b^3 + (128*b^7)/a^2 - 768*a^5*tan(c/2 + (d*x)/2) + 256*a*b^4*tan(c/2 + (d*x)/2) + 512*a^3*b^2*tan(c/2 + (d*x)/2)) - (256*a)/(256*b + 256*a*tan(c/2 + (d*x)/2) - (384*a^2)/b + (128*b^3)/a^2 + (512*a^3*tan(c/2 + (d*x)/2))/b^2 - (768*a^5*tan(c/2 + (d*x)/2))/b^4) - (384*a^2*tan(c/2 + (d*x)/2))/(256*b^2 - 384*a^2 + (128*b^4)/a^2 + (512*a^3*tan(c/2 + (d*x)/2))/b - (768*a^5*tan(c/2 + (d*x)/2))/b^3 + 256*a*b*tan(c/2 + (d*x)/2)) + (128*b*tan(c/2 + (d*x)/2))/(128*b + (256*a^2)/b - (384*a^4)/b^3 + (256*a^3*tan(c/2 + (d*x)/2))/b^2 + (512*a^5*tan(c/2 + (d*x)/2))/b^4 - (768*a^7*tan(c/2 + (d*x)/2))/b^6)))/(b^3*d)","B"
1131,1,6377,154,12.090664,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","\frac{2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2\,a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2\,a\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{3\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{b\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\mathrm{atan}\left(\frac{40\,a^5\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-128\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,a^3\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+4\,a^5\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,a^7\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-20\,a^7\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+9\,a^9\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,a^2\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,a^2\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+104\,a^4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+8\,a^4\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+18\,a^6\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-26\,a^6\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,a^8\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+28\,a^8\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-64\,a\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+2\,a^9\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+5\,a^{11}\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{-3{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+34{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-72{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-172{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+44{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+56{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+80{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+192{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-64{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-128{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{a^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\mathrm{atan}\left(\frac{40\,a^5\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-128\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,a^3\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+4\,a^5\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,a^7\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-20\,a^7\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+9\,a^9\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,a^2\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,a^2\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+104\,a^4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+8\,a^4\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+18\,a^6\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-26\,a^6\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,a^8\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+28\,a^8\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-64\,a\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+2\,a^9\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+5\,a^{11}\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{-3{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+34{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-72{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-172{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+44{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+56{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+80{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+192{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-64{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-128{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{b^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\mathrm{atan}\left(\frac{40\,a^5\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-128\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,a^3\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+4\,a^5\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,a^7\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-20\,a^7\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+9\,a^9\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,a^2\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,a^2\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+104\,a^4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+8\,a^4\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+18\,a^6\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-26\,a^6\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,a^8\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+28\,a^8\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-64\,a\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+2\,a^9\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+5\,a^{11}\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{-3{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+34{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-72{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-172{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+44{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+56{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+80{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+192{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-64{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-128{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{a^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\mathrm{atan}\left(\frac{40\,a^5\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-128\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,a^3\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+4\,a^5\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,a^7\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-20\,a^7\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+9\,a^9\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,a^2\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,a^2\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+104\,a^4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+8\,a^4\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+18\,a^6\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-26\,a^6\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,a^8\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+28\,a^8\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-64\,a\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+2\,a^9\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+5\,a^{11}\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{-3{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+34{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-72{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-172{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+44{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+56{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+80{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+192{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-64{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-128{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{b^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,a\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,a\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{4\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{4\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\mathrm{atan}\left(\frac{40\,a^5\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-128\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,a^3\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+4\,a^5\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,a^7\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-20\,a^7\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+9\,a^9\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,a^2\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,a^2\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+104\,a^4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+8\,a^4\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+18\,a^6\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-26\,a^6\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,a^8\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+28\,a^8\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-64\,a\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+2\,a^9\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+5\,a^{11}\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{-3{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+34{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-72{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-172{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+44{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+56{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+80{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+192{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-64{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-128{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{a\,b\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{b\,\mathrm{atan}\left(\frac{40\,a^5\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-128\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,a^3\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-4\,a^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+4\,a^5\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,a^7\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-20\,a^7\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+9\,a^9\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,a^2\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,a^2\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+104\,a^4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+8\,a^4\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+18\,a^6\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-26\,a^6\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,a^8\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+28\,a^8\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-64\,a\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+2\,a^9\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+5\,a^{11}\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{-3{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+34{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-72{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-172{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+44{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+56{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+80{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+192{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-64{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-128{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}}{a^3\,d\,\left(a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}","Not used",1,"(2*cos(c/2 + (d*x)/2)^2)/(b*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + sin(c/2 + (d*x)/2)^3/(2*a*d*cos(c/2 + (d*x)/2)*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - cos(c/2 + (d*x)/2)^3/(2*a*d*sin(c/2 + (d*x)/2)*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - (3*b*cos(c/2 + (d*x)/2)^2)/(a^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + (2*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + (b*sin(c/2 + (d*x)/2)^2)/(a^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - (2*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^2)/(a^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + (atan((40*a^5*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^12*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 128*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*a^3*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 4*a^5*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*a^7*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 20*a^7*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 9*a^9*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*a^2*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*a^2*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 104*a^4*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 8*a^4*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 18*a^6*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 26*a^6*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*a^8*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 28*a^8*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 64*a*b^9*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 2*a^9*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 5*a^11*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*b^10*cos(c/2 + (d*x)/2)*80i - a*b^12*cos(c/2 + (d*x)/2)*64i - a^12*b*sin(c/2 + (d*x)/2)*3i - b^13*sin(c/2 + (d*x)/2)*128i + a^5*b^8*cos(c/2 + (d*x)/2)*44i - a^7*b^6*cos(c/2 + (d*x)/2)*72i + a^9*b^4*cos(c/2 + (d*x)/2)*3i + a^11*b^2*cos(c/2 + (d*x)/2)*9i + a^2*b^11*sin(c/2 + (d*x)/2)*192i + a^4*b^9*sin(c/2 + (d*x)/2)*56i - a^6*b^7*sin(c/2 + (d*x)/2)*172i + a^8*b^5*sin(c/2 + (d*x)/2)*34i + a^10*b^3*sin(c/2 + (d*x)/2)*21i))*cos(c/2 + (d*x)/2)^2*(b^2 - a^2)^(1/2)*4i)/(a^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + (atan((40*a^5*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^12*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 128*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*a^3*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 4*a^5*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*a^7*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 20*a^7*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 9*a^9*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*a^2*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*a^2*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 104*a^4*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 8*a^4*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 18*a^6*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 26*a^6*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*a^8*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 28*a^8*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 64*a*b^9*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 2*a^9*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 5*a^11*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*b^10*cos(c/2 + (d*x)/2)*80i - a*b^12*cos(c/2 + (d*x)/2)*64i - a^12*b*sin(c/2 + (d*x)/2)*3i - b^13*sin(c/2 + (d*x)/2)*128i + a^5*b^8*cos(c/2 + (d*x)/2)*44i - a^7*b^6*cos(c/2 + (d*x)/2)*72i + a^9*b^4*cos(c/2 + (d*x)/2)*3i + a^11*b^2*cos(c/2 + (d*x)/2)*9i + a^2*b^11*sin(c/2 + (d*x)/2)*192i + a^4*b^9*sin(c/2 + (d*x)/2)*56i - a^6*b^7*sin(c/2 + (d*x)/2)*172i + a^8*b^5*sin(c/2 + (d*x)/2)*34i + a^10*b^3*sin(c/2 + (d*x)/2)*21i))*cos(c/2 + (d*x)/2)^2*(b^2 - a^2)^(1/2)*2i)/(b^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - (2*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(c/2 + (d*x)/2)^2)/(a^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - (2*b^2*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^3*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + (atan((40*a^5*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^12*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 128*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*a^3*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 4*a^5*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*a^7*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 20*a^7*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 9*a^9*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*a^2*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*a^2*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 104*a^4*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 8*a^4*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 18*a^6*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 26*a^6*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*a^8*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 28*a^8*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 64*a*b^9*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 2*a^9*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 5*a^11*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*b^10*cos(c/2 + (d*x)/2)*80i - a*b^12*cos(c/2 + (d*x)/2)*64i - a^12*b*sin(c/2 + (d*x)/2)*3i - b^13*sin(c/2 + (d*x)/2)*128i + a^5*b^8*cos(c/2 + (d*x)/2)*44i - a^7*b^6*cos(c/2 + (d*x)/2)*72i + a^9*b^4*cos(c/2 + (d*x)/2)*3i + a^11*b^2*cos(c/2 + (d*x)/2)*9i + a^2*b^11*sin(c/2 + (d*x)/2)*192i + a^4*b^9*sin(c/2 + (d*x)/2)*56i - a^6*b^7*sin(c/2 + (d*x)/2)*172i + a^8*b^5*sin(c/2 + (d*x)/2)*34i + a^10*b^3*sin(c/2 + (d*x)/2)*21i))*sin(c/2 + (d*x)/2)^2*(b^2 - a^2)^(1/2)*4i)/(a^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + (atan((40*a^5*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^12*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 128*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*a^3*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 4*a^5*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*a^7*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 20*a^7*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 9*a^9*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*a^2*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*a^2*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 104*a^4*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 8*a^4*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 18*a^6*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 26*a^6*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*a^8*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 28*a^8*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 64*a*b^9*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 2*a^9*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 5*a^11*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*b^10*cos(c/2 + (d*x)/2)*80i - a*b^12*cos(c/2 + (d*x)/2)*64i - a^12*b*sin(c/2 + (d*x)/2)*3i - b^13*sin(c/2 + (d*x)/2)*128i + a^5*b^8*cos(c/2 + (d*x)/2)*44i - a^7*b^6*cos(c/2 + (d*x)/2)*72i + a^9*b^4*cos(c/2 + (d*x)/2)*3i + a^11*b^2*cos(c/2 + (d*x)/2)*9i + a^2*b^11*sin(c/2 + (d*x)/2)*192i + a^4*b^9*sin(c/2 + (d*x)/2)*56i - a^6*b^7*sin(c/2 + (d*x)/2)*172i + a^8*b^5*sin(c/2 + (d*x)/2)*34i + a^10*b^3*sin(c/2 + (d*x)/2)*21i))*sin(c/2 + (d*x)/2)^2*(b^2 - a^2)^(1/2)*2i)/(b^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - (2*a*atan((a^3*cos(c/2 + (d*x)/2) - 2*b^3*sin(c/2 + (d*x)/2))/(2*b^3*cos(c/2 + (d*x)/2) + a^3*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^2)/(b^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - (2*a*atan((a^3*cos(c/2 + (d*x)/2) - 2*b^3*sin(c/2 + (d*x)/2))/(2*b^3*cos(c/2 + (d*x)/2) + a^3*sin(c/2 + (d*x)/2)))*sin(c/2 + (d*x)/2)^2)/(b^2*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - (4*atan((a^3*cos(c/2 + (d*x)/2) - 2*b^3*sin(c/2 + (d*x)/2))/(2*b^3*cos(c/2 + (d*x)/2) + a^3*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(b*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) - (4*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^3*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + (atan((40*a^5*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^12*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 128*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*a^3*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 4*a^5*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*a^7*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 20*a^7*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 9*a^9*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*a^2*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*a^2*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 104*a^4*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 8*a^4*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 18*a^6*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 26*a^6*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*a^8*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 28*a^8*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 64*a*b^9*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 2*a^9*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 5*a^11*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*b^10*cos(c/2 + (d*x)/2)*80i - a*b^12*cos(c/2 + (d*x)/2)*64i - a^12*b*sin(c/2 + (d*x)/2)*3i - b^13*sin(c/2 + (d*x)/2)*128i + a^5*b^8*cos(c/2 + (d*x)/2)*44i - a^7*b^6*cos(c/2 + (d*x)/2)*72i + a^9*b^4*cos(c/2 + (d*x)/2)*3i + a^11*b^2*cos(c/2 + (d*x)/2)*9i + a^2*b^11*sin(c/2 + (d*x)/2)*192i + a^4*b^9*sin(c/2 + (d*x)/2)*56i - a^6*b^7*sin(c/2 + (d*x)/2)*172i + a^8*b^5*sin(c/2 + (d*x)/2)*34i + a^10*b^3*sin(c/2 + (d*x)/2)*21i))*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a*b*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))) + (b*atan((40*a^5*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^12*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 128*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*a^3*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 4*a^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 4*a^5*b^7*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*a^7*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 20*a^7*b^5*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 9*a^9*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*a^2*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*a^2*b^10*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 104*a^4*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 8*a^4*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 18*a^6*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 26*a^6*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*a^8*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 28*a^8*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 64*a*b^9*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 2*a^9*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 5*a^11*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*b^10*cos(c/2 + (d*x)/2)*80i - a*b^12*cos(c/2 + (d*x)/2)*64i - a^12*b*sin(c/2 + (d*x)/2)*3i - b^13*sin(c/2 + (d*x)/2)*128i + a^5*b^8*cos(c/2 + (d*x)/2)*44i - a^7*b^6*cos(c/2 + (d*x)/2)*72i + a^9*b^4*cos(c/2 + (d*x)/2)*3i + a^11*b^2*cos(c/2 + (d*x)/2)*9i + a^2*b^11*sin(c/2 + (d*x)/2)*192i + a^4*b^9*sin(c/2 + (d*x)/2)*56i - a^6*b^7*sin(c/2 + (d*x)/2)*172i + a^8*b^5*sin(c/2 + (d*x)/2)*34i + a^10*b^3*sin(c/2 + (d*x)/2)*21i))*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i)/(a^3*d*(a*cos(c/2 + (d*x)/2)^2 + a*sin(c/2 + (d*x)/2)^2 + 2*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)))","B"
1132,1,675,158,9.729049,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{17\,a^2}{2}-16\,b^2\right)+\frac{a^2}{2}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2\,b-2\,b^3\right)}{a}-3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,b\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^2-6\,b^2\right)}{2\,a^4\,d}-\frac{6\,b\,\mathrm{atanh}\left(\frac{72\,b^4\,\sqrt{b^2-a^2}}{18\,a^4\,b+72\,b^5-90\,a^2\,b^3-216\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+72\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{144\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}}-\frac{54\,b^2\,\sqrt{b^2-a^2}}{18\,a^2\,b-90\,b^3+\frac{72\,b^5}{a^2}+72\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{216\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{144\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}+\frac{18\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{18\,a\,b-\frac{90\,b^3}{a}+\frac{72\,b^5}{a^3}+72\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{216\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}+\frac{144\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4}}-\frac{144\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{18\,a^3\,b-90\,a\,b^3+\frac{72\,b^5}{a}-216\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+72\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{144\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}}+\frac{144\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{18\,a^5\,b+72\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^2-90\,a^3\,b^3-216\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^4+72\,a\,b^5+144\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6}\right)\,\sqrt{b^2-a^2}}{a^4\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) - (tan(c/2 + (d*x)/2)^2*((17*a^2)/2 - 16*b^2) + a^2/2 + (4*tan(c/2 + (d*x)/2)^3*(a^2*b - 2*b^3))/a - 3*a*b*tan(c/2 + (d*x)/2))/(d*(4*a^4*tan(c/2 + (d*x)/2)^2 + 4*a^4*tan(c/2 + (d*x)/2)^4 + 8*a^3*b*tan(c/2 + (d*x)/2)^3)) - (b*tan(c/2 + (d*x)/2))/(a^3*d) - (log(tan(c/2 + (d*x)/2))*(3*a^2 - 6*b^2))/(2*a^4*d) - (6*b*atanh((72*b^4*(b^2 - a^2)^(1/2))/(18*a^4*b + 72*b^5 - 90*a^2*b^3 - 216*a*b^4*tan(c/2 + (d*x)/2) + 72*a^3*b^2*tan(c/2 + (d*x)/2) + (144*b^6*tan(c/2 + (d*x)/2))/a) - (54*b^2*(b^2 - a^2)^(1/2))/(18*a^2*b - 90*b^3 + (72*b^5)/a^2 + 72*a*b^2*tan(c/2 + (d*x)/2) - (216*b^4*tan(c/2 + (d*x)/2))/a + (144*b^6*tan(c/2 + (d*x)/2))/a^3) + (18*b*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(18*a*b - (90*b^3)/a + (72*b^5)/a^3 + 72*b^2*tan(c/2 + (d*x)/2) - (216*b^4*tan(c/2 + (d*x)/2))/a^2 + (144*b^6*tan(c/2 + (d*x)/2))/a^4) - (144*b^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(18*a^3*b - 90*a*b^3 + (72*b^5)/a - 216*b^4*tan(c/2 + (d*x)/2) + 72*a^2*b^2*tan(c/2 + (d*x)/2) + (144*b^6*tan(c/2 + (d*x)/2))/a^2) + (144*b^5*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(72*a*b^5 + 18*a^5*b - 90*a^3*b^3 + 144*b^6*tan(c/2 + (d*x)/2) - 216*a^2*b^4*tan(c/2 + (d*x)/2) + 72*a^4*b^2*tan(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(a^4*d)","B"
1133,1,973,238,9.800873,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(28\,a^2\,b-40\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a\,b^2-\frac{14\,a^3}{3}\right)-\frac{a^3}{3}+\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(5\,a^4+4\,a^2\,b^2-16\,b^4\right)}{a}}{d\,\left(8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,b\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{16\,a^2+32\,b^2}{64\,a^4}+\frac{3}{8\,a^2}-\frac{2\,b^2}{a^4}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^3\,d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^2-4\,b^2\right)}{a^5\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{2\,\left(a^9-8\,a^7\,b^2+8\,a^5\,b^4\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^7\,b-20\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}+\frac{\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{a^5}\right)\,1{}\mathrm{i}}{a^5}+\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{2\,\left(a^9-8\,a^7\,b^2+8\,a^5\,b^4\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^7\,b-20\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}-\frac{\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{a^5}\right)\,1{}\mathrm{i}}{a^5}}{\frac{4\,\left(3\,a^6\,b-19\,a^4\,b^3+32\,a^2\,b^5-16\,b^7\right)}{a^8}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-14\,a^4\,b^2+28\,a^2\,b^4-16\,b^6\right)}{a^7}-\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{2\,\left(a^9-8\,a^7\,b^2+8\,a^5\,b^4\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^7\,b-20\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}+\frac{\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{a^5}\right)}{a^5}+\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{2\,\left(a^9-8\,a^7\,b^2+8\,a^5\,b^4\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^7\,b-20\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}-\frac{\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{a^5}\right)}{a^5}}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,2{}\mathrm{i}}{a^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(28*a^2*b - 40*b^3) - tan(c/2 + (d*x)/2)^2*(8*a*b^2 - (14*a^3)/3) - a^3/3 + (4*a^2*b*tan(c/2 + (d*x)/2))/3 + (tan(c/2 + (d*x)/2)^4*(5*a^4 - 16*b^4 + 4*a^2*b^2))/a)/(d*(8*a^5*tan(c/2 + (d*x)/2)^3 + 8*a^5*tan(c/2 + (d*x)/2)^5 + 16*a^4*b*tan(c/2 + (d*x)/2)^4)) + tan(c/2 + (d*x)/2)^3/(24*a^2*d) - (tan(c/2 + (d*x)/2)*((16*a^2 + 32*b^2)/(64*a^4) + 3/(8*a^2) - (2*b^2)/a^4))/d - (b*tan(c/2 + (d*x)/2)^2)/(4*a^3*d) + (b*log(tan(c/2 + (d*x)/2))*(3*a^2 - 4*b^2))/(a^5*d) + (atan((((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((2*(a^9 + 8*a^5*b^4 - 8*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(5*a^7*b + 16*a^3*b^5 - 20*a^5*b^3))/a^7 + ((2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/a^5)*1i)/a^5 + ((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((2*(a^9 + 8*a^5*b^4 - 8*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(5*a^7*b + 16*a^3*b^5 - 20*a^5*b^3))/a^7 - ((2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/a^5)*1i)/a^5)/((4*(3*a^6*b - 16*b^7 + 32*a^2*b^5 - 19*a^4*b^3))/a^8 + (4*tan(c/2 + (d*x)/2)*(2*a^6 - 16*b^6 + 28*a^2*b^4 - 14*a^4*b^2))/a^7 - ((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((2*(a^9 + 8*a^5*b^4 - 8*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(5*a^7*b + 16*a^3*b^5 - 20*a^5*b^3))/a^7 + ((2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/a^5))/a^5 + ((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((2*(a^9 + 8*a^5*b^4 - 8*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(5*a^7*b + 16*a^3*b^5 - 20*a^5*b^3))/a^7 - ((2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/a^5))/a^5))*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*2i)/(a^5*d)","B"
1134,1,1158,292,9.828975,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^4-78\,a^2\,b^2+96\,b^4\right)-\frac{a^4}{4}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{7\,a^4}{4}-\frac{10\,a^2\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(20\,a\,b^3-\frac{44\,a^3\,b}{3}\right)-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(5\,a^4\,b-8\,b^5\right)}{a}+\frac{5\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6}}{d\,\left(16\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+32\,b\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{32\,a^2+64\,b^2}{512\,a^4}+\frac{1}{16\,a^2}-\frac{b^2}{2\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b\,\left(32\,a^2+64\,b^2\right)}{64\,a^5}-\frac{b}{4\,a^3}+\frac{4\,b\,\left(\frac{32\,a^2+64\,b^2}{256\,a^4}+\frac{1}{8\,a^2}-\frac{b^2}{a^4}\right)}{a}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,a^3\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^4-36\,a^2\,b^2+40\,b^4\right)}{8\,a^6\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-74\,a^8\,b^2+224\,a^6\,b^4-160\,a^4\,b^6\right)}{4\,a^9}-\frac{19\,a^{10}\,b-92\,a^8\,b^3+80\,a^6\,b^5}{4\,a^{10}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)}{a^6}\right)\,1{}\mathrm{i}}{a^6}-\frac{b\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{19\,a^{10}\,b-92\,a^8\,b^3+80\,a^6\,b^5}{4\,a^{10}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-74\,a^8\,b^2+224\,a^6\,b^4-160\,a^4\,b^6\right)}{4\,a^9}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)}{a^6}\right)\,1{}\mathrm{i}}{a^6}}{\frac{6\,a^8\,b-93\,a^6\,b^3+347\,a^4\,b^5-460\,a^2\,b^7+200\,b^9}{2\,a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-52\,a^6\,b^2+262\,a^4\,b^4-410\,a^2\,b^6+200\,b^8\right)}{2\,a^9}+\frac{b\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-74\,a^8\,b^2+224\,a^6\,b^4-160\,a^4\,b^6\right)}{4\,a^9}-\frac{19\,a^{10}\,b-92\,a^8\,b^3+80\,a^6\,b^5}{4\,a^{10}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)}{a^6}\right)}{a^6}+\frac{b\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{19\,a^{10}\,b-92\,a^8\,b^3+80\,a^6\,b^5}{4\,a^{10}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-74\,a^8\,b^2+224\,a^6\,b^4-160\,a^4\,b^6\right)}{4\,a^9}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)}{a^6}\right)}{a^6}}\right)\,\sqrt{b^2-a^2}\,\left(2\,a^2-5\,b^2\right)\,2{}\mathrm{i}}{a^6\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a^2*d) + (tan(c/2 + (d*x)/2)^4*(2*a^4 + 96*b^4 - 78*a^2*b^2) - a^4/4 + tan(c/2 + (d*x)/2)^2*((7*a^4)/4 - (10*a^2*b^2)/3) + tan(c/2 + (d*x)/2)^3*(20*a*b^3 - (44*a^3*b)/3) - (4*tan(c/2 + (d*x)/2)^5*(5*a^4*b - 8*b^5))/a + (5*a^3*b*tan(c/2 + (d*x)/2))/6)/(d*(16*a^6*tan(c/2 + (d*x)/2)^4 + 16*a^6*tan(c/2 + (d*x)/2)^6 + 32*a^5*b*tan(c/2 + (d*x)/2)^5)) - (tan(c/2 + (d*x)/2)^2*((32*a^2 + 64*b^2)/(512*a^4) + 1/(16*a^2) - b^2/(2*a^4)))/d + (tan(c/2 + (d*x)/2)*((b*(32*a^2 + 64*b^2))/(64*a^5) - b/(4*a^3) + (4*b*((32*a^2 + 64*b^2)/(256*a^4) + 1/(8*a^2) - b^2/a^4))/a))/d - (b*tan(c/2 + (d*x)/2)^3)/(12*a^3*d) + (log(tan(c/2 + (d*x)/2))*(3*a^4 + 40*b^4 - 36*a^2*b^2))/(8*a^6*d) - (b*atan(((b*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2)*((tan(c/2 + (d*x)/2)*(3*a^10 - 160*a^4*b^6 + 224*a^6*b^4 - 74*a^8*b^2))/(4*a^9) - (19*a^10*b + 80*a^6*b^5 - 92*a^8*b^3)/(4*a^10) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2))/a^6)*1i)/a^6 - (b*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2)*((19*a^10*b + 80*a^6*b^5 - 92*a^8*b^3)/(4*a^10) - (tan(c/2 + (d*x)/2)*(3*a^10 - 160*a^4*b^6 + 224*a^6*b^4 - 74*a^8*b^2))/(4*a^9) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2))/a^6)*1i)/a^6)/((6*a^8*b + 200*b^9 - 460*a^2*b^7 + 347*a^4*b^5 - 93*a^6*b^3)/(2*a^10) + (tan(c/2 + (d*x)/2)*(200*b^8 - 410*a^2*b^6 + 262*a^4*b^4 - 52*a^6*b^2))/(2*a^9) + (b*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2)*((tan(c/2 + (d*x)/2)*(3*a^10 - 160*a^4*b^6 + 224*a^6*b^4 - 74*a^8*b^2))/(4*a^9) - (19*a^10*b + 80*a^6*b^5 - 92*a^8*b^3)/(4*a^10) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2))/a^6))/a^6 + (b*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2)*((19*a^10*b + 80*a^6*b^5 - 92*a^8*b^3)/(4*a^10) - (tan(c/2 + (d*x)/2)*(3*a^10 - 160*a^4*b^6 + 224*a^6*b^4 - 74*a^8*b^2))/(4*a^9) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2))/a^6))/a^6))*(b^2 - a^2)^(1/2)*(2*a^2 - 5*b^2)*2i)/(a^6*d)","B"
1135,1,3581,331,16.595687,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x))^3,x)","\frac{\frac{30\,a^5-13\,a^3\,b^2}{b^6}+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(10\,a^5+9\,a^3\,b^2-6\,a\,b^4\right)}{b^6}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(10\,a^5+9\,a^3\,b^2-5\,a\,b^4\right)}{b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(150\,a^5+15\,a^3\,b^2-37\,a\,b^4\right)}{b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(150\,a^5+75\,a^3\,b^2-59\,a\,b^4\right)}{b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(420\,a^4-187\,a^2\,b^2\right)}{4\,b^5}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(20\,a^4-7\,a^2\,b^2\right)}{4\,b^5}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(340\,a^4-139\,a^2\,b^2+2\,b^4\right)}{2\,b^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-660\,a^4+231\,a^2\,b^2+20\,b^4\right)}{4\,b^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-1380\,a^4+623\,a^2\,b^2+6\,b^4\right)}{2\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(1740\,a^4-809\,a^2\,b^2+20\,b^4\right)}{4\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(13\,a\,b^2-30\,a^3\right)\,\left(5\,a^2+6\,b^2\right)}{b^6}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(6\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(15\,a^2+16\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(15\,a^2+16\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(20\,a^2+24\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+a^2+20\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+40\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+40\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,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)}^{11}+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{7200\,a^{10}\,b^6-8640\,a^8\,b^8+2952\,a^6\,b^{10}-216\,a^4\,b^{12}+\frac{9\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+77760\,a^9\,b^8-63648\,a^7\,b^{10}+18576\,a^5\,b^{12}-1449\,a^3\,b^{14}+18\,a\,b^{16}\right)}{2\,b^{18}}-\frac{3\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{240\,a^5\,b^{14}-204\,a^3\,b^{16}+12\,a\,b^{18}}{b^{17}}-\frac{3\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2112\,a^4\,b^{16}+384\,a^2\,b^{18}\right)}{2\,b^{18}}\right)}{8\,b^7}\right)\,3{}\mathrm{i}}{8\,b^7}+\frac{\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{7200\,a^{10}\,b^6-8640\,a^8\,b^8+2952\,a^6\,b^{10}-216\,a^4\,b^{12}+\frac{9\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+77760\,a^9\,b^8-63648\,a^7\,b^{10}+18576\,a^5\,b^{12}-1449\,a^3\,b^{14}+18\,a\,b^{16}\right)}{2\,b^{18}}+\frac{3\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{240\,a^5\,b^{14}-204\,a^3\,b^{16}+12\,a\,b^{18}}{b^{17}}+\frac{3\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2112\,a^4\,b^{16}+384\,a^2\,b^{18}\right)}{2\,b^{18}}\right)}{8\,b^7}\right)\,3{}\mathrm{i}}{8\,b^7}}{\frac{108000\,a^{13}-221400\,a^{11}\,b^2+159840\,a^9\,b^4-49383\,a^7\,b^6+\frac{12231\,a^5\,b^8}{2}-189\,a^3\,b^{10}}{b^{17}}-\frac{3\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{7200\,a^{10}\,b^6-8640\,a^8\,b^8+2952\,a^6\,b^{10}-216\,a^4\,b^{12}+\frac{9\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+77760\,a^9\,b^8-63648\,a^7\,b^{10}+18576\,a^5\,b^{12}-1449\,a^3\,b^{14}+18\,a\,b^{16}\right)}{2\,b^{18}}-\frac{3\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{240\,a^5\,b^{14}-204\,a^3\,b^{16}+12\,a\,b^{18}}{b^{17}}-\frac{3\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2112\,a^4\,b^{16}+384\,a^2\,b^{18}\right)}{2\,b^{18}}\right)}{8\,b^7}\right)}{8\,b^7}+\frac{3\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{7200\,a^{10}\,b^6-8640\,a^8\,b^8+2952\,a^6\,b^{10}-216\,a^4\,b^{12}+\frac{9\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+77760\,a^9\,b^8-63648\,a^7\,b^{10}+18576\,a^5\,b^{12}-1449\,a^3\,b^{14}+18\,a\,b^{16}\right)}{2\,b^{18}}+\frac{3\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{240\,a^5\,b^{14}-204\,a^3\,b^{16}+12\,a\,b^{18}}{b^{17}}+\frac{3\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2112\,a^4\,b^{16}+384\,a^2\,b^{18}\right)}{2\,b^{18}}\right)}{8\,b^7}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(432000\,a^{14}-993600\,a^{12}\,b^2+833760\,a^{10}\,b^4-311472\,a^8\,b^6+49950\,a^6\,b^8-2889\,a^4\,b^{10}+54\,a^2\,b^{12}\right)}{b^{18}}}\right)\,\left(a^4\,40{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,3{}\mathrm{i}}{4\,b^7\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)\,\left(\frac{7200\,a^{10}\,b^6-8640\,a^8\,b^8+2952\,a^6\,b^{10}-216\,a^4\,b^{12}+\frac{9\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+77760\,a^9\,b^8-63648\,a^7\,b^{10}+18576\,a^5\,b^{12}-1449\,a^3\,b^{14}+18\,a\,b^{16}\right)}{2\,b^{18}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{240\,a^5\,b^{14}-204\,a^3\,b^{16}+12\,a\,b^{18}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2112\,a^4\,b^{16}+384\,a^2\,b^{18}\right)}{2\,b^{18}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)}{2\,\left(b^9-a^2\,b^7\right)}\right)\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)}{2\,\left(b^9-a^2\,b^7\right)}\right)\,3{}\mathrm{i}}{2\,\left(b^9-a^2\,b^7\right)}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)\,\left(\frac{7200\,a^{10}\,b^6-8640\,a^8\,b^8+2952\,a^6\,b^{10}-216\,a^4\,b^{12}+\frac{9\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+77760\,a^9\,b^8-63648\,a^7\,b^{10}+18576\,a^5\,b^{12}-1449\,a^3\,b^{14}+18\,a\,b^{16}\right)}{2\,b^{18}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{240\,a^5\,b^{14}-204\,a^3\,b^{16}+12\,a\,b^{18}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2112\,a^4\,b^{16}+384\,a^2\,b^{18}\right)}{2\,b^{18}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)}{2\,\left(b^9-a^2\,b^7\right)}\right)\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)}{2\,\left(b^9-a^2\,b^7\right)}\right)\,3{}\mathrm{i}}{2\,\left(b^9-a^2\,b^7\right)}}{\frac{108000\,a^{13}-221400\,a^{11}\,b^2+159840\,a^9\,b^4-49383\,a^7\,b^6+\frac{12231\,a^5\,b^8}{2}-189\,a^3\,b^{10}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(432000\,a^{14}-993600\,a^{12}\,b^2+833760\,a^{10}\,b^4-311472\,a^8\,b^6+49950\,a^6\,b^8-2889\,a^4\,b^{10}+54\,a^2\,b^{12}\right)}{b^{18}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)\,\left(\frac{7200\,a^{10}\,b^6-8640\,a^8\,b^8+2952\,a^6\,b^{10}-216\,a^4\,b^{12}+\frac{9\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+77760\,a^9\,b^8-63648\,a^7\,b^{10}+18576\,a^5\,b^{12}-1449\,a^3\,b^{14}+18\,a\,b^{16}\right)}{2\,b^{18}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{240\,a^5\,b^{14}-204\,a^3\,b^{16}+12\,a\,b^{18}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2112\,a^4\,b^{16}+384\,a^2\,b^{18}\right)}{2\,b^{18}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)}{2\,\left(b^9-a^2\,b^7\right)}\right)\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)}{2\,\left(b^9-a^2\,b^7\right)}\right)}{2\,\left(b^9-a^2\,b^7\right)}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)\,\left(\frac{7200\,a^{10}\,b^6-8640\,a^8\,b^8+2952\,a^6\,b^{10}-216\,a^4\,b^{12}+\frac{9\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+77760\,a^9\,b^8-63648\,a^7\,b^{10}+18576\,a^5\,b^{12}-1449\,a^3\,b^{14}+18\,a\,b^{16}\right)}{2\,b^{18}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{240\,a^5\,b^{14}-204\,a^3\,b^{16}+12\,a\,b^{18}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2112\,a^4\,b^{16}+384\,a^2\,b^{18}\right)}{2\,b^{18}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)}{2\,\left(b^9-a^2\,b^7\right)}\right)\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)}{2\,\left(b^9-a^2\,b^7\right)}\right)}{2\,\left(b^9-a^2\,b^7\right)}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-11\,a^2\,b^2+2\,b^4\right)\,3{}\mathrm{i}}{d\,\left(b^9-a^2\,b^7\right)}","Not used",1,"((30*a^5 - 13*a^3*b^2)/b^6 + (15*tan(c/2 + (d*x)/2)^8*(10*a^5 - 6*a*b^4 + 9*a^3*b^2))/b^6 + (3*tan(c/2 + (d*x)/2)^10*(10*a^5 - 5*a*b^4 + 9*a^3*b^2))/b^6 + (tan(c/2 + (d*x)/2)^2*(150*a^5 - 37*a*b^4 + 15*a^3*b^2))/b^6 + (2*tan(c/2 + (d*x)/2)^4*(150*a^5 - 59*a*b^4 + 75*a^3*b^2))/b^6 + (tan(c/2 + (d*x)/2)*(420*a^4 - 187*a^2*b^2))/(4*b^5) + (3*tan(c/2 + (d*x)/2)^11*(20*a^4 - 7*a^2*b^2))/(4*b^5) + (3*tan(c/2 + (d*x)/2)^7*(340*a^4 + 2*b^4 - 139*a^2*b^2))/(2*b^5) - (tan(c/2 + (d*x)/2)^9*(20*b^4 - 660*a^4 + 231*a^2*b^2))/(4*b^5) - (tan(c/2 + (d*x)/2)^5*(6*b^4 - 1380*a^4 + 623*a^2*b^2))/(2*b^5) + (tan(c/2 + (d*x)/2)^3*(1740*a^4 + 20*b^4 - 809*a^2*b^2))/(4*b^5) - (2*tan(c/2 + (d*x)/2)^6*(13*a*b^2 - 30*a^3)*(5*a^2 + 6*b^2))/b^6)/(d*(tan(c/2 + (d*x)/2)^2*(6*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^10*(6*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(15*a^2 + 16*b^2) + tan(c/2 + (d*x)/2)^8*(15*a^2 + 16*b^2) + tan(c/2 + (d*x)/2)^6*(20*a^2 + 24*b^2) + a^2*tan(c/2 + (d*x)/2)^12 + a^2 + 20*a*b*tan(c/2 + (d*x)/2)^3 + 40*a*b*tan(c/2 + (d*x)/2)^5 + 40*a*b*tan(c/2 + (d*x)/2)^7 + 20*a*b*tan(c/2 + (d*x)/2)^9 + 4*a*b*tan(c/2 + (d*x)/2)^11 + 4*a*b*tan(c/2 + (d*x)/2))) + (atan((((a^4*40i + b^4*1i - a^2*b^2*24i)*(((9*a^2*b^14)/2 - 216*a^4*b^12 + 2952*a^6*b^10 - 8640*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(18*a*b^16 - 1449*a^3*b^14 + 18576*a^5*b^12 - 63648*a^7*b^10 + 77760*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) - (3*(a^4*40i + b^4*1i - a^2*b^2*24i)*((12*a*b^18 - 204*a^3*b^16 + 240*a^5*b^14)/b^17 - (3*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(a^4*40i + b^4*1i - a^2*b^2*24i))/(8*b^7) + (tan(c/2 + (d*x)/2)*(384*a^2*b^18 - 2112*a^4*b^16 + 1920*a^6*b^14))/(2*b^18)))/(8*b^7))*3i)/(8*b^7) + ((a^4*40i + b^4*1i - a^2*b^2*24i)*(((9*a^2*b^14)/2 - 216*a^4*b^12 + 2952*a^6*b^10 - 8640*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(18*a*b^16 - 1449*a^3*b^14 + 18576*a^5*b^12 - 63648*a^7*b^10 + 77760*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) + (3*(a^4*40i + b^4*1i - a^2*b^2*24i)*((12*a*b^18 - 204*a^3*b^16 + 240*a^5*b^14)/b^17 + (3*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(a^4*40i + b^4*1i - a^2*b^2*24i))/(8*b^7) + (tan(c/2 + (d*x)/2)*(384*a^2*b^18 - 2112*a^4*b^16 + 1920*a^6*b^14))/(2*b^18)))/(8*b^7))*3i)/(8*b^7))/((108000*a^13 - 189*a^3*b^10 + (12231*a^5*b^8)/2 - 49383*a^7*b^6 + 159840*a^9*b^4 - 221400*a^11*b^2)/b^17 - (3*(a^4*40i + b^4*1i - a^2*b^2*24i)*(((9*a^2*b^14)/2 - 216*a^4*b^12 + 2952*a^6*b^10 - 8640*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(18*a*b^16 - 1449*a^3*b^14 + 18576*a^5*b^12 - 63648*a^7*b^10 + 77760*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) - (3*(a^4*40i + b^4*1i - a^2*b^2*24i)*((12*a*b^18 - 204*a^3*b^16 + 240*a^5*b^14)/b^17 - (3*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(a^4*40i + b^4*1i - a^2*b^2*24i))/(8*b^7) + (tan(c/2 + (d*x)/2)*(384*a^2*b^18 - 2112*a^4*b^16 + 1920*a^6*b^14))/(2*b^18)))/(8*b^7)))/(8*b^7) + (3*(a^4*40i + b^4*1i - a^2*b^2*24i)*(((9*a^2*b^14)/2 - 216*a^4*b^12 + 2952*a^6*b^10 - 8640*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(18*a*b^16 - 1449*a^3*b^14 + 18576*a^5*b^12 - 63648*a^7*b^10 + 77760*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) + (3*(a^4*40i + b^4*1i - a^2*b^2*24i)*((12*a*b^18 - 204*a^3*b^16 + 240*a^5*b^14)/b^17 + (3*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(a^4*40i + b^4*1i - a^2*b^2*24i))/(8*b^7) + (tan(c/2 + (d*x)/2)*(384*a^2*b^18 - 2112*a^4*b^16 + 1920*a^6*b^14))/(2*b^18)))/(8*b^7)))/(8*b^7) + (tan(c/2 + (d*x)/2)*(432000*a^14 + 54*a^2*b^12 - 2889*a^4*b^10 + 49950*a^6*b^8 - 311472*a^8*b^6 + 833760*a^10*b^4 - 993600*a^12*b^2))/b^18))*(a^4*40i + b^4*1i - a^2*b^2*24i)*3i)/(4*b^7*d) + (a*atan(((a*(-(a + b)*(a - b))^(1/2)*(10*a^4 + 2*b^4 - 11*a^2*b^2)*(((9*a^2*b^14)/2 - 216*a^4*b^12 + 2952*a^6*b^10 - 8640*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(18*a*b^16 - 1449*a^3*b^14 + 18576*a^5*b^12 - 63648*a^7*b^10 + 77760*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) - (3*a*(-(a + b)*(a - b))^(1/2)*((12*a*b^18 - 204*a^3*b^16 + 240*a^5*b^14)/b^17 + (tan(c/2 + (d*x)/2)*(384*a^2*b^18 - 2112*a^4*b^16 + 1920*a^6*b^14))/(2*b^18) - (3*a*(-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(10*a^4 + 2*b^4 - 11*a^2*b^2))/(2*(b^9 - a^2*b^7)))*(10*a^4 + 2*b^4 - 11*a^2*b^2))/(2*(b^9 - a^2*b^7)))*3i)/(2*(b^9 - a^2*b^7)) + (a*(-(a + b)*(a - b))^(1/2)*(10*a^4 + 2*b^4 - 11*a^2*b^2)*(((9*a^2*b^14)/2 - 216*a^4*b^12 + 2952*a^6*b^10 - 8640*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(18*a*b^16 - 1449*a^3*b^14 + 18576*a^5*b^12 - 63648*a^7*b^10 + 77760*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) + (3*a*(-(a + b)*(a - b))^(1/2)*((12*a*b^18 - 204*a^3*b^16 + 240*a^5*b^14)/b^17 + (tan(c/2 + (d*x)/2)*(384*a^2*b^18 - 2112*a^4*b^16 + 1920*a^6*b^14))/(2*b^18) + (3*a*(-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(10*a^4 + 2*b^4 - 11*a^2*b^2))/(2*(b^9 - a^2*b^7)))*(10*a^4 + 2*b^4 - 11*a^2*b^2))/(2*(b^9 - a^2*b^7)))*3i)/(2*(b^9 - a^2*b^7)))/((108000*a^13 - 189*a^3*b^10 + (12231*a^5*b^8)/2 - 49383*a^7*b^6 + 159840*a^9*b^4 - 221400*a^11*b^2)/b^17 + (tan(c/2 + (d*x)/2)*(432000*a^14 + 54*a^2*b^12 - 2889*a^4*b^10 + 49950*a^6*b^8 - 311472*a^8*b^6 + 833760*a^10*b^4 - 993600*a^12*b^2))/b^18 - (3*a*(-(a + b)*(a - b))^(1/2)*(10*a^4 + 2*b^4 - 11*a^2*b^2)*(((9*a^2*b^14)/2 - 216*a^4*b^12 + 2952*a^6*b^10 - 8640*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(18*a*b^16 - 1449*a^3*b^14 + 18576*a^5*b^12 - 63648*a^7*b^10 + 77760*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) - (3*a*(-(a + b)*(a - b))^(1/2)*((12*a*b^18 - 204*a^3*b^16 + 240*a^5*b^14)/b^17 + (tan(c/2 + (d*x)/2)*(384*a^2*b^18 - 2112*a^4*b^16 + 1920*a^6*b^14))/(2*b^18) - (3*a*(-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(10*a^4 + 2*b^4 - 11*a^2*b^2))/(2*(b^9 - a^2*b^7)))*(10*a^4 + 2*b^4 - 11*a^2*b^2))/(2*(b^9 - a^2*b^7))))/(2*(b^9 - a^2*b^7)) + (3*a*(-(a + b)*(a - b))^(1/2)*(10*a^4 + 2*b^4 - 11*a^2*b^2)*(((9*a^2*b^14)/2 - 216*a^4*b^12 + 2952*a^6*b^10 - 8640*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(18*a*b^16 - 1449*a^3*b^14 + 18576*a^5*b^12 - 63648*a^7*b^10 + 77760*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) + (3*a*(-(a + b)*(a - b))^(1/2)*((12*a*b^18 - 204*a^3*b^16 + 240*a^5*b^14)/b^17 + (tan(c/2 + (d*x)/2)*(384*a^2*b^18 - 2112*a^4*b^16 + 1920*a^6*b^14))/(2*b^18) + (3*a*(-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(10*a^4 + 2*b^4 - 11*a^2*b^2))/(2*(b^9 - a^2*b^7)))*(10*a^4 + 2*b^4 - 11*a^2*b^2))/(2*(b^9 - a^2*b^7))))/(2*(b^9 - a^2*b^7))))*(-(a + b)*(a - b))^(1/2)*(10*a^4 + 2*b^4 - 11*a^2*b^2)*3i)/(d*(b^9 - a^2*b^7))","B"
1136,1,2034,284,14.338422,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x))^3,x)","-\frac{\frac{60\,a^4-17\,a^2\,b^2}{3\,b^5}-\frac{20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a\,b^2-5\,a^3\right)}{b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(a\,b^2-5\,a^3\right)}{b^4}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(17\,a\,b^2-60\,a^3\right)}{b^4}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(53\,a\,b^2-165\,a^3\right)}{3\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(20\,a^4+21\,a^2\,b^2-6\,b^4\right)}{b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(40\,a^4+42\,a^2\,b^2-17\,b^4\right)}{b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(120\,a^4+46\,a^2\,b^2-25\,b^4\right)}{3\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(180\,a^4+149\,a^2\,b^2-51\,b^4\right)}{3\,b^5}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a\,b^2-105\,a^3\right)}{3\,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{a\,\mathrm{atan}\left(\frac{280\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{280\,a^4-288\,a^2\,b^2+\frac{800\,a^6}{b^2}}-\frac{288\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{280\,a^4}{b^2}-288\,a^2+\frac{800\,a^6}{b^4}}+\frac{800\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{800\,a^6+280\,a^4\,b^2-288\,a^2\,b^4}\right)\,\left(20\,a^2-9\,b^2\right)}{b^6\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(400\,a^8\,b^5-360\,a^6\,b^7+81\,a^4\,b^9\right)}{b^{14}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^9\,b^5-1920\,a^7\,b^7+1242\,a^5\,b^9-238\,a^3\,b^{11}+4\,a\,b^{13}\right)}{b^{15}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(80\,a^5\,b^{12}-76\,a^3\,b^{14}+8\,a\,b^{16}\right)}{b^{15}}-\frac{8\,\left(14\,a^2\,b^{14}-20\,a^4\,b^{12}\right)}{b^{14}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{19}-8\,a^3\,b^{17}\right)}{b^{15}}\right)\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)}{b^8-a^2\,b^6}\right)}{b^8-a^2\,b^6}\right)\,1{}\mathrm{i}}{b^8-a^2\,b^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(400\,a^8\,b^5-360\,a^6\,b^7+81\,a^4\,b^9\right)}{b^{14}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^9\,b^5-1920\,a^7\,b^7+1242\,a^5\,b^9-238\,a^3\,b^{11}+4\,a\,b^{13}\right)}{b^{15}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(14\,a^2\,b^{14}-20\,a^4\,b^{12}\right)}{b^{14}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(80\,a^5\,b^{12}-76\,a^3\,b^{14}+8\,a\,b^{16}\right)}{b^{15}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{19}-8\,a^3\,b^{17}\right)}{b^{15}}\right)\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)}{b^8-a^2\,b^6}\right)}{b^8-a^2\,b^6}\right)\,1{}\mathrm{i}}{b^8-a^2\,b^6}}{\frac{16\,\left(2000\,a^{10}-3200\,a^8\,b^2+1615\,a^6\,b^4-301\,a^4\,b^6+18\,a^2\,b^8\right)}{b^{14}}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8000\,a^{11}-14800\,a^9\,b^2+9260\,a^7\,b^4-2259\,a^5\,b^6+162\,a^3\,b^8\right)}{b^{15}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(400\,a^8\,b^5-360\,a^6\,b^7+81\,a^4\,b^9\right)}{b^{14}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^9\,b^5-1920\,a^7\,b^7+1242\,a^5\,b^9-238\,a^3\,b^{11}+4\,a\,b^{13}\right)}{b^{15}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(80\,a^5\,b^{12}-76\,a^3\,b^{14}+8\,a\,b^{16}\right)}{b^{15}}-\frac{8\,\left(14\,a^2\,b^{14}-20\,a^4\,b^{12}\right)}{b^{14}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{19}-8\,a^3\,b^{17}\right)}{b^{15}}\right)\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)}{b^8-a^2\,b^6}\right)}{b^8-a^2\,b^6}\right)}{b^8-a^2\,b^6}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(400\,a^8\,b^5-360\,a^6\,b^7+81\,a^4\,b^9\right)}{b^{14}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^9\,b^5-1920\,a^7\,b^7+1242\,a^5\,b^9-238\,a^3\,b^{11}+4\,a\,b^{13}\right)}{b^{15}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(14\,a^2\,b^{14}-20\,a^4\,b^{12}\right)}{b^{14}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(80\,a^5\,b^{12}-76\,a^3\,b^{14}+8\,a\,b^{16}\right)}{b^{15}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{19}-8\,a^3\,b^{17}\right)}{b^{15}}\right)\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)}{b^8-a^2\,b^6}\right)}{b^8-a^2\,b^6}\right)}{b^8-a^2\,b^6}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(10\,a^4-\frac{19\,a^2\,b^2}{2}+b^4\right)\,2{}\mathrm{i}}{d\,\left(b^8-a^2\,b^6\right)}","Not used",1,"- ((60*a^4 - 17*a^2*b^2)/(3*b^5) - (20*tan(c/2 + (d*x)/2)^7*(a*b^2 - 5*a^3))/b^4 - (2*tan(c/2 + (d*x)/2)^9*(a*b^2 - 5*a^3))/b^4 - (4*tan(c/2 + (d*x)/2)^5*(17*a*b^2 - 60*a^3))/b^4 - (4*tan(c/2 + (d*x)/2)^3*(53*a*b^2 - 165*a^3))/(3*b^4) + (tan(c/2 + (d*x)/2)^8*(20*a^4 - 6*b^4 + 21*a^2*b^2))/b^5 + (2*tan(c/2 + (d*x)/2)^6*(40*a^4 - 17*b^4 + 42*a^2*b^2))/b^5 + (2*tan(c/2 + (d*x)/2)^2*(120*a^4 - 25*b^4 + 46*a^2*b^2))/(3*b^5) + (2*tan(c/2 + (d*x)/2)^4*(180*a^4 - 51*b^4 + 149*a^2*b^2))/(3*b^5) - (2*tan(c/2 + (d*x)/2)*(31*a*b^2 - 105*a^3))/(3*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))) - (a*atan((280*a^4*tan(c/2 + (d*x)/2))/(280*a^4 - 288*a^2*b^2 + (800*a^6)/b^2) - (288*a^2*tan(c/2 + (d*x)/2))/((280*a^4)/b^2 - 288*a^2 + (800*a^6)/b^4) + (800*a^6*tan(c/2 + (d*x)/2))/(800*a^6 - 288*a^2*b^4 + 280*a^4*b^2))*(20*a^2 - 9*b^2))/(b^6*d) - (atan((((-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*((8*(81*a^4*b^9 - 360*a^6*b^7 + 400*a^8*b^5))/b^14 - (8*tan(c/2 + (d*x)/2)*(4*a*b^13 - 238*a^3*b^11 + 1242*a^5*b^9 - 1920*a^7*b^7 + 800*a^9*b^5))/b^15 + ((-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*((8*tan(c/2 + (d*x)/2)*(8*a*b^16 - 76*a^3*b^14 + 80*a^5*b^12))/b^15 - (8*(14*a^2*b^14 - 20*a^4*b^12))/b^14 + ((-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^19 - 8*a^3*b^17))/b^15)*(10*a^4 + b^4 - (19*a^2*b^2)/2))/(b^8 - a^2*b^6)))/(b^8 - a^2*b^6))*1i)/(b^8 - a^2*b^6) + ((-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*((8*(81*a^4*b^9 - 360*a^6*b^7 + 400*a^8*b^5))/b^14 - (8*tan(c/2 + (d*x)/2)*(4*a*b^13 - 238*a^3*b^11 + 1242*a^5*b^9 - 1920*a^7*b^7 + 800*a^9*b^5))/b^15 + ((-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*((8*(14*a^2*b^14 - 20*a^4*b^12))/b^14 - (8*tan(c/2 + (d*x)/2)*(8*a*b^16 - 76*a^3*b^14 + 80*a^5*b^12))/b^15 + ((-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^19 - 8*a^3*b^17))/b^15)*(10*a^4 + b^4 - (19*a^2*b^2)/2))/(b^8 - a^2*b^6)))/(b^8 - a^2*b^6))*1i)/(b^8 - a^2*b^6))/((16*(2000*a^10 + 18*a^2*b^8 - 301*a^4*b^6 + 1615*a^6*b^4 - 3200*a^8*b^2))/b^14 + (16*tan(c/2 + (d*x)/2)*(8000*a^11 + 162*a^3*b^8 - 2259*a^5*b^6 + 9260*a^7*b^4 - 14800*a^9*b^2))/b^15 + ((-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*((8*(81*a^4*b^9 - 360*a^6*b^7 + 400*a^8*b^5))/b^14 - (8*tan(c/2 + (d*x)/2)*(4*a*b^13 - 238*a^3*b^11 + 1242*a^5*b^9 - 1920*a^7*b^7 + 800*a^9*b^5))/b^15 + ((-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*((8*tan(c/2 + (d*x)/2)*(8*a*b^16 - 76*a^3*b^14 + 80*a^5*b^12))/b^15 - (8*(14*a^2*b^14 - 20*a^4*b^12))/b^14 + ((-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^19 - 8*a^3*b^17))/b^15)*(10*a^4 + b^4 - (19*a^2*b^2)/2))/(b^8 - a^2*b^6)))/(b^8 - a^2*b^6)))/(b^8 - a^2*b^6) - ((-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*((8*(81*a^4*b^9 - 360*a^6*b^7 + 400*a^8*b^5))/b^14 - (8*tan(c/2 + (d*x)/2)*(4*a*b^13 - 238*a^3*b^11 + 1242*a^5*b^9 - 1920*a^7*b^7 + 800*a^9*b^5))/b^15 + ((-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*((8*(14*a^2*b^14 - 20*a^4*b^12))/b^14 - (8*tan(c/2 + (d*x)/2)*(8*a*b^16 - 76*a^3*b^14 + 80*a^5*b^12))/b^15 + ((-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^19 - 8*a^3*b^17))/b^15)*(10*a^4 + b^4 - (19*a^2*b^2)/2))/(b^8 - a^2*b^6)))/(b^8 - a^2*b^6)))/(b^8 - a^2*b^6)))*(-(a + b)*(a - b))^(1/2)*(10*a^4 + b^4 - (19*a^2*b^2)/2)*2i)/(d*(b^8 - a^2*b^6))","B"
1137,1,1743,173,12.408011,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x))^3,x)","\frac{\frac{54\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{b^3}-\frac{a\,b^2-12\,a^3}{b^4}+\frac{6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{b^3}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(21\,a^2-2\,b^2\right)}{b^3}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(15\,a^2-2\,b^2\right)}{b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(12\,a^4+15\,a^2\,b^2-2\,b^4\right)}{a\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(36\,a^4+29\,a^2\,b^2-2\,b^4\right)}{a\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^2+4\,b^2\right)\,\left(12\,a^2-b^2\right)}{a\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2+8\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+a^2+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,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)}^7+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{atan}\left(\frac{864\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{216\,a\,b^2-864\,a^3}-\frac{216\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{216\,a-\frac{864\,a^3}{b^2}}\right)\,\left(a^2\,6{}\mathrm{i}-\frac{b^2\,3{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{b^5\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{8\,\left(144\,a^6\,b^4-72\,a^4\,b^6+9\,a^2\,b^8\right)}{b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^7\,b^4+576\,a^5\,b^6-234\,a^3\,b^8+18\,a\,b^{10}\right)}{b^{12}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{8\,\left(6\,a\,b^{12}-12\,a^3\,b^{10}\right)}{b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^2\,b^{12}-48\,a^4\,b^{10}\right)}{b^{12}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,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^{16}-8\,a^3\,b^{14}\right)}{b^{12}}\right)}{2\,\left(b^7-a^2\,b^5\right)}\right)}{2\,\left(b^7-a^2\,b^5\right)}\right)\,3{}\mathrm{i}}{2\,\left(b^7-a^2\,b^5\right)}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{8\,\left(144\,a^6\,b^4-72\,a^4\,b^6+9\,a^2\,b^8\right)}{b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^7\,b^4+576\,a^5\,b^6-234\,a^3\,b^8+18\,a\,b^{10}\right)}{b^{12}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{8\,\left(6\,a\,b^{12}-12\,a^3\,b^{10}\right)}{b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^2\,b^{12}-48\,a^4\,b^{10}\right)}{b^{12}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,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^{16}-8\,a^3\,b^{14}\right)}{b^{12}}\right)}{2\,\left(b^7-a^2\,b^5\right)}\right)}{2\,\left(b^7-a^2\,b^5\right)}\right)\,3{}\mathrm{i}}{2\,\left(b^7-a^2\,b^5\right)}}{\frac{16\,\left(432\,a^7-432\,a^5\,b^2+81\,a^3\,b^4\right)}{b^{11}}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1728\,a^8-2160\,a^6\,b^2+756\,a^4\,b^4-81\,a^2\,b^6\right)}{b^{12}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{8\,\left(144\,a^6\,b^4-72\,a^4\,b^6+9\,a^2\,b^8\right)}{b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^7\,b^4+576\,a^5\,b^6-234\,a^3\,b^8+18\,a\,b^{10}\right)}{b^{12}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{8\,\left(6\,a\,b^{12}-12\,a^3\,b^{10}\right)}{b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^2\,b^{12}-48\,a^4\,b^{10}\right)}{b^{12}}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,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^{16}-8\,a^3\,b^{14}\right)}{b^{12}}\right)}{2\,\left(b^7-a^2\,b^5\right)}\right)}{2\,\left(b^7-a^2\,b^5\right)}\right)}{2\,\left(b^7-a^2\,b^5\right)}-\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{8\,\left(144\,a^6\,b^4-72\,a^4\,b^6+9\,a^2\,b^8\right)}{b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^7\,b^4+576\,a^5\,b^6-234\,a^3\,b^8+18\,a\,b^{10}\right)}{b^{12}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{8\,\left(6\,a\,b^{12}-12\,a^3\,b^{10}\right)}{b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^2\,b^{12}-48\,a^4\,b^{10}\right)}{b^{12}}+\frac{3\,a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,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^{16}-8\,a^3\,b^{14}\right)}{b^{12}}\right)}{2\,\left(b^7-a^2\,b^5\right)}\right)}{2\,\left(b^7-a^2\,b^5\right)}\right)}{2\,\left(b^7-a^2\,b^5\right)}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,3{}\mathrm{i}}{d\,\left(b^7-a^2\,b^5\right)}","Not used",1,"((54*a^2*tan(c/2 + (d*x)/2)^5)/b^3 - (a*b^2 - 12*a^3)/b^4 + (6*a^2*tan(c/2 + (d*x)/2)^7)/b^3 + (2*tan(c/2 + (d*x)/2)*(21*a^2 - 2*b^2))/b^3 + (6*tan(c/2 + (d*x)/2)^3*(15*a^2 - 2*b^2))/b^3 + (tan(c/2 + (d*x)/2)^6*(12*a^4 - 2*b^4 + 15*a^2*b^2))/(a*b^4) + (tan(c/2 + (d*x)/2)^2*(36*a^4 - 2*b^4 + 29*a^2*b^2))/(a*b^4) + (tan(c/2 + (d*x)/2)^4*(3*a^2 + 4*b^2)*(12*a^2 - b^2))/(a*b^4))/(d*(tan(c/2 + (d*x)/2)^2*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^6*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(6*a^2 + 8*b^2) + a^2*tan(c/2 + (d*x)/2)^8 + a^2 + 12*a*b*tan(c/2 + (d*x)/2)^3 + 12*a*b*tan(c/2 + (d*x)/2)^5 + 4*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2))) + (atan((864*a^3*tan(c/2 + (d*x)/2))/(216*a*b^2 - 864*a^3) - (216*a*tan(c/2 + (d*x)/2))/(216*a - (864*a^3)/b^2))*(a^2*6i - (b^2*3i)/2)*2i)/(b^5*d) + (a*atan(((a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((8*(9*a^2*b^8 - 72*a^4*b^6 + 144*a^6*b^4))/b^11 + (8*tan(c/2 + (d*x)/2)*(18*a*b^10 - 234*a^3*b^8 + 576*a^5*b^6 - 288*a^7*b^4))/b^12 - (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((8*(6*a*b^12 - 12*a^3*b^10))/b^11 + (8*tan(c/2 + (d*x)/2)*(36*a^2*b^12 - 48*a^4*b^10))/b^12 - (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^16 - 8*a^3*b^14))/b^12))/(2*(b^7 - a^2*b^5))))/(2*(b^7 - a^2*b^5)))*3i)/(2*(b^7 - a^2*b^5)) + (a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((8*(9*a^2*b^8 - 72*a^4*b^6 + 144*a^6*b^4))/b^11 + (8*tan(c/2 + (d*x)/2)*(18*a*b^10 - 234*a^3*b^8 + 576*a^5*b^6 - 288*a^7*b^4))/b^12 + (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((8*(6*a*b^12 - 12*a^3*b^10))/b^11 + (8*tan(c/2 + (d*x)/2)*(36*a^2*b^12 - 48*a^4*b^10))/b^12 + (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^16 - 8*a^3*b^14))/b^12))/(2*(b^7 - a^2*b^5))))/(2*(b^7 - a^2*b^5)))*3i)/(2*(b^7 - a^2*b^5)))/((16*(432*a^7 + 81*a^3*b^4 - 432*a^5*b^2))/b^11 + (16*tan(c/2 + (d*x)/2)*(1728*a^8 - 81*a^2*b^6 + 756*a^4*b^4 - 2160*a^6*b^2))/b^12 + (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((8*(9*a^2*b^8 - 72*a^4*b^6 + 144*a^6*b^4))/b^11 + (8*tan(c/2 + (d*x)/2)*(18*a*b^10 - 234*a^3*b^8 + 576*a^5*b^6 - 288*a^7*b^4))/b^12 - (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((8*(6*a*b^12 - 12*a^3*b^10))/b^11 + (8*tan(c/2 + (d*x)/2)*(36*a^2*b^12 - 48*a^4*b^10))/b^12 - (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^16 - 8*a^3*b^14))/b^12))/(2*(b^7 - a^2*b^5))))/(2*(b^7 - a^2*b^5))))/(2*(b^7 - a^2*b^5)) - (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((8*(9*a^2*b^8 - 72*a^4*b^6 + 144*a^6*b^4))/b^11 + (8*tan(c/2 + (d*x)/2)*(18*a*b^10 - 234*a^3*b^8 + 576*a^5*b^6 - 288*a^7*b^4))/b^12 + (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((8*(6*a*b^12 - 12*a^3*b^10))/b^11 + (8*tan(c/2 + (d*x)/2)*(36*a^2*b^12 - 48*a^4*b^10))/b^12 + (3*a*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^16 - 8*a^3*b^14))/b^12))/(2*(b^7 - a^2*b^5))))/(2*(b^7 - a^2*b^5))))/(2*(b^7 - a^2*b^5))))*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*3i)/(d*(b^7 - a^2*b^5))","B"
1138,1,3001,175,13.504670,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + b*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{\frac{2\,a^2+3\,b^2}{a\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^2+8\,b^2\right)}{a^2\,b}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+4\,b^2\right)}{a^2\,b}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^4+7\,a^2\,b^2+6\,b^4\right)}{a^3\,b^2}}{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{2\,\mathrm{atan}\left(\frac{144\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{64\,b^2}{a^2}-\frac{64\,b^4}{a^4}-\frac{64\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{64\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{144\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}-144}+\frac{144\,a}{144\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{144\,b^3}{a^2}+\frac{64\,b^5}{a^4}-\frac{64\,b^7}{a^6}-\frac{64\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{64\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}+\frac{64}{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{144\,a}{b}+\frac{64\,b}{a}-\frac{64\,b^3}{a^3}-\frac{64\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{144\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}}+\frac{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{64\,b^2}{a^2}+\frac{144\,a^2}{b^2}-\frac{64\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}-\frac{144\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}-64}+\frac{64}{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{144\,b}{a}-\frac{64\,b^3}{a^3}+\frac{64\,b^5}{a^5}-\frac{64\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}-\frac{144\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}-\frac{64\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,b-\frac{64\,a^2}{b}+\frac{144\,a^4}{b^3}-\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{64\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}-\frac{144\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}\right)}{b^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(14\,a^9-15\,a^7\,b^2+28\,a^5\,b^4+4\,a^3\,b^6\right)}{a^6\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-12\,a^{10}\,b^2+16\,a^8\,b^4+14\,a^6\,b^6-12\,a^4\,b^8+16\,a^2\,b^{10}\right)}{a^6\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(14\,a^9\,b^6-24\,a^7\,b^8+32\,a^5\,b^{10}\right)}{a^6\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(16\,a^8\,b^{10}-12\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{10}-68\,a^9\,b^{12}+64\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^8+48\,a^8\,b^{10}-68\,a^6\,b^{12}+64\,a^4\,b^{14}\right)}{a^6\,b^8}\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^4-100\,a^9\,b^6+89\,a^7\,b^8-36\,a^5\,b^{10}+4\,a^3\,b^{12}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^2+48\,a^8\,b^4-68\,a^6\,b^6+73\,a^4\,b^8-4\,a^2\,b^{10}+4\,b^{12}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)\,1{}\mathrm{i}}{a^3\,b^5-a^5\,b^3}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(14\,a^9-15\,a^7\,b^2+28\,a^5\,b^4+4\,a^3\,b^6\right)}{a^6\,b^5}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-12\,a^{10}\,b^2+16\,a^8\,b^4+14\,a^6\,b^6-12\,a^4\,b^8+16\,a^2\,b^{10}\right)}{a^6\,b^5}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(14\,a^9\,b^6-24\,a^7\,b^8+32\,a^5\,b^{10}\right)}{a^6\,b^5}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(16\,a^8\,b^{10}-12\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{10}-68\,a^9\,b^{12}+64\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^8+48\,a^8\,b^{10}-68\,a^6\,b^{12}+64\,a^4\,b^{14}\right)}{a^6\,b^8}\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^4-100\,a^9\,b^6+89\,a^7\,b^8-36\,a^5\,b^{10}+4\,a^3\,b^{12}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^2+48\,a^8\,b^4-68\,a^6\,b^6+73\,a^4\,b^8-4\,a^2\,b^{10}+4\,b^{12}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)\,1{}\mathrm{i}}{a^3\,b^5-a^5\,b^3}}{\frac{16\,\left(14\,a^6-3\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}{a^6\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(14\,a^9-15\,a^7\,b^2+28\,a^5\,b^4+4\,a^3\,b^6\right)}{a^6\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-12\,a^{10}\,b^2+16\,a^8\,b^4+14\,a^6\,b^6-12\,a^4\,b^8+16\,a^2\,b^{10}\right)}{a^6\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(14\,a^9\,b^6-24\,a^7\,b^8+32\,a^5\,b^{10}\right)}{a^6\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(16\,a^8\,b^{10}-12\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{10}-68\,a^9\,b^{12}+64\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^8+48\,a^8\,b^{10}-68\,a^6\,b^{12}+64\,a^4\,b^{14}\right)}{a^6\,b^8}\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^4-100\,a^9\,b^6+89\,a^7\,b^8-36\,a^5\,b^{10}+4\,a^3\,b^{12}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^2+48\,a^8\,b^4-68\,a^6\,b^6+73\,a^4\,b^8-4\,a^2\,b^{10}+4\,b^{12}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(14\,a^9-15\,a^7\,b^2+28\,a^5\,b^4+4\,a^3\,b^6\right)}{a^6\,b^5}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-12\,a^{10}\,b^2+16\,a^8\,b^4+14\,a^6\,b^6-12\,a^4\,b^8+16\,a^2\,b^{10}\right)}{a^6\,b^5}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{8\,\left(14\,a^9\,b^6-24\,a^7\,b^8+32\,a^5\,b^{10}\right)}{a^6\,b^5}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(16\,a^8\,b^{10}-12\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{10}-68\,a^9\,b^{12}+64\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^8+48\,a^8\,b^{10}-68\,a^6\,b^{12}+64\,a^4\,b^{14}\right)}{a^6\,b^8}\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^4-100\,a^9\,b^6+89\,a^7\,b^8-36\,a^5\,b^{10}+4\,a^3\,b^{12}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^2+48\,a^8\,b^4-68\,a^6\,b^6+73\,a^4\,b^8-4\,a^2\,b^{10}+4\,b^{12}\right)}{a^6\,b^8}\right)\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5-a^5\,b^3}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^9-16\,a^7\,b^2+32\,a^5\,b^4\right)}{a^6\,b^8}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{a^2\,b^2}{2}+b^4\right)\,2{}\mathrm{i}}{d\,\left(a^3\,b^5-a^5\,b^3\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) + ((2*a^2 + 3*b^2)/(a*b^2) + (tan(c/2 + (d*x)/2)*(7*a^2 + 8*b^2))/(a^2*b) + (tan(c/2 + (d*x)/2)^3*(a^2 + 4*b^2))/(a^2*b) + (tan(c/2 + (d*x)/2)^2*(2*a^4 + 6*b^4 + 7*a^2*b^2))/(a^3*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))) - (2*atan((144*tan(c/2 + (d*x)/2))/((64*b^2)/a^2 - (64*b^4)/a^4 - (64*a*tan(c/2 + (d*x)/2))/b + (64*b*tan(c/2 + (d*x)/2))/a + (144*a^3*tan(c/2 + (d*x)/2))/b^3 - 144) + (144*a)/(144*a*tan(c/2 + (d*x)/2) - (144*b^3)/a^2 + (64*b^5)/a^4 - (64*b^7)/a^6 - (64*b^2*tan(c/2 + (d*x)/2))/a + (64*b^4*tan(c/2 + (d*x)/2))/a^3) + 64/(64*tan(c/2 + (d*x)/2) - (144*a)/b + (64*b)/a - (64*b^3)/a^3 - (64*a^2*tan(c/2 + (d*x)/2))/b^2 + (144*a^4*tan(c/2 + (d*x)/2))/b^4) + (64*tan(c/2 + (d*x)/2))/((64*b^2)/a^2 + (144*a^2)/b^2 - (64*a*tan(c/2 + (d*x)/2))/b + (64*a^3*tan(c/2 + (d*x)/2))/b^3 - (144*a^5*tan(c/2 + (d*x)/2))/b^5 - 64) + 64/(64*tan(c/2 + (d*x)/2) + (144*b)/a - (64*b^3)/a^3 + (64*b^5)/a^5 - (64*b^2*tan(c/2 + (d*x)/2))/a^2 - (144*a^2*tan(c/2 + (d*x)/2))/b^2) - (64*b*tan(c/2 + (d*x)/2))/(64*b - (64*a^2)/b + (144*a^4)/b^3 - (64*a^3*tan(c/2 + (d*x)/2))/b^2 + (64*a^5*tan(c/2 + (d*x)/2))/b^4 - (144*a^7*tan(c/2 + (d*x)/2))/b^6)))/(b^3*d) + (atan((((-(a + b)*(a - b))^(1/2)*((8*(14*a^9 + 4*a^3*b^6 + 28*a^5*b^4 - 15*a^7*b^2))/(a^6*b^5) + ((-(a + b)*(a - b))^(1/2)*((8*(16*a^2*b^10 - 12*a^4*b^8 + 14*a^6*b^6 + 16*a^8*b^4 - 12*a^10*b^2))/(a^6*b^5) + ((-(a + b)*(a - b))^(1/2)*(a^4 + b^4 - (a^2*b^2)/2)*((8*(32*a^5*b^10 - 24*a^7*b^8 + 14*a^9*b^6))/(a^6*b^5) + ((-(a + b)*(a - b))^(1/2)*((8*(16*a^8*b^10 - 12*a^10*b^8))/(a^6*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^14 - 68*a^9*b^12 + 8*a^11*b^10))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^14 - 68*a^6*b^12 + 48*a^8*b^10 - 16*a^10*b^8))/(a^6*b^8)))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^12 - 36*a^5*b^10 + 89*a^7*b^8 - 100*a^9*b^6 + 8*a^11*b^4))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(4*b^12 - 4*a^2*b^10 + 73*a^4*b^8 - 68*a^6*b^6 + 48*a^8*b^4 - 16*a^10*b^2))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2)*1i)/(a^3*b^5 - a^5*b^3) + ((-(a + b)*(a - b))^(1/2)*((8*(14*a^9 + 4*a^3*b^6 + 28*a^5*b^4 - 15*a^7*b^2))/(a^6*b^5) - ((-(a + b)*(a - b))^(1/2)*((8*(16*a^2*b^10 - 12*a^4*b^8 + 14*a^6*b^6 + 16*a^8*b^4 - 12*a^10*b^2))/(a^6*b^5) - ((-(a + b)*(a - b))^(1/2)*(a^4 + b^4 - (a^2*b^2)/2)*((8*(32*a^5*b^10 - 24*a^7*b^8 + 14*a^9*b^6))/(a^6*b^5) - ((-(a + b)*(a - b))^(1/2)*((8*(16*a^8*b^10 - 12*a^10*b^8))/(a^6*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^14 - 68*a^9*b^12 + 8*a^11*b^10))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^14 - 68*a^6*b^12 + 48*a^8*b^10 - 16*a^10*b^8))/(a^6*b^8)))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^12 - 36*a^5*b^10 + 89*a^7*b^8 - 100*a^9*b^6 + 8*a^11*b^4))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(4*b^12 - 4*a^2*b^10 + 73*a^4*b^8 - 68*a^6*b^6 + 48*a^8*b^4 - 16*a^10*b^2))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2)*1i)/(a^3*b^5 - a^5*b^3))/((16*(14*a^6 + 4*b^6 + 12*a^2*b^4 - 3*a^4*b^2))/(a^6*b^5) + ((-(a + b)*(a - b))^(1/2)*((8*(14*a^9 + 4*a^3*b^6 + 28*a^5*b^4 - 15*a^7*b^2))/(a^6*b^5) + ((-(a + b)*(a - b))^(1/2)*((8*(16*a^2*b^10 - 12*a^4*b^8 + 14*a^6*b^6 + 16*a^8*b^4 - 12*a^10*b^2))/(a^6*b^5) + ((-(a + b)*(a - b))^(1/2)*(a^4 + b^4 - (a^2*b^2)/2)*((8*(32*a^5*b^10 - 24*a^7*b^8 + 14*a^9*b^6))/(a^6*b^5) + ((-(a + b)*(a - b))^(1/2)*((8*(16*a^8*b^10 - 12*a^10*b^8))/(a^6*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^14 - 68*a^9*b^12 + 8*a^11*b^10))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^14 - 68*a^6*b^12 + 48*a^8*b^10 - 16*a^10*b^8))/(a^6*b^8)))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^12 - 36*a^5*b^10 + 89*a^7*b^8 - 100*a^9*b^6 + 8*a^11*b^4))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(4*b^12 - 4*a^2*b^10 + 73*a^4*b^8 - 68*a^6*b^6 + 48*a^8*b^4 - 16*a^10*b^2))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) - ((-(a + b)*(a - b))^(1/2)*((8*(14*a^9 + 4*a^3*b^6 + 28*a^5*b^4 - 15*a^7*b^2))/(a^6*b^5) - ((-(a + b)*(a - b))^(1/2)*((8*(16*a^2*b^10 - 12*a^4*b^8 + 14*a^6*b^6 + 16*a^8*b^4 - 12*a^10*b^2))/(a^6*b^5) - ((-(a + b)*(a - b))^(1/2)*(a^4 + b^4 - (a^2*b^2)/2)*((8*(32*a^5*b^10 - 24*a^7*b^8 + 14*a^9*b^6))/(a^6*b^5) - ((-(a + b)*(a - b))^(1/2)*((8*(16*a^8*b^10 - 12*a^10*b^8))/(a^6*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^14 - 68*a^9*b^12 + 8*a^11*b^10))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^14 - 68*a^6*b^12 + 48*a^8*b^10 - 16*a^10*b^8))/(a^6*b^8)))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^12 - 36*a^5*b^10 + 89*a^7*b^8 - 100*a^9*b^6 + 8*a^11*b^4))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) + (8*tan(c/2 + (d*x)/2)*(4*b^12 - 4*a^2*b^10 + 73*a^4*b^8 - 68*a^6*b^6 + 48*a^8*b^4 - 16*a^10*b^2))/(a^6*b^8))*(a^4 + b^4 - (a^2*b^2)/2))/(a^3*b^5 - a^5*b^3) - (16*tan(c/2 + (d*x)/2)*(32*a^9 + 32*a^5*b^4 - 16*a^7*b^2))/(a^6*b^8)))*(-(a + b)*(a - b))^(1/2)*(a^4 + b^4 - (a^2*b^2)/2)*2i)/(d*(a^3*b^5 - a^5*b^3))","B"
1139,1,956,182,9.877708,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+32\,b^2\right)+a^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-12\,b^2\right)+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(7\,a^2\,b+10\,b^3\right)}{a}+14\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^5+8\,a^3\,b^2\right)+2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(\frac{3\,a^6-12\,a^4\,b^2}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^4\,b-24\,a^2\,b^3\right)}{a^5}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-8\,a^6\,b^2\right)}{a^5}\right)\,\left(a^2-2\,b^2\right)}{2\,\left(a^6-a^4\,b^2\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^6-a^4\,b^2\right)}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(\frac{3\,a^6-12\,a^4\,b^2}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^4\,b-24\,a^2\,b^3\right)}{a^5}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-8\,a^6\,b^2\right)}{a^5}\right)\,\left(a^2-2\,b^2\right)}{2\,\left(a^6-a^4\,b^2\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^6-a^4\,b^2\right)}}{\frac{2\,\left(9\,a^2\,b-18\,b^3\right)}{a^6}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^2-18\,b^2\right)}{a^5}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(\frac{3\,a^6-12\,a^4\,b^2}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^4\,b-24\,a^2\,b^3\right)}{a^5}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-8\,a^6\,b^2\right)}{a^5}\right)\,\left(a^2-2\,b^2\right)}{2\,\left(a^6-a^4\,b^2\right)}\right)}{2\,\left(a^6-a^4\,b^2\right)}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(\frac{3\,a^6-12\,a^4\,b^2}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^4\,b-24\,a^2\,b^3\right)}{a^5}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-8\,a^6\,b^2\right)}{a^5}\right)\,\left(a^2-2\,b^2\right)}{2\,\left(a^6-a^4\,b^2\right)}\right)}{2\,\left(a^6-a^4\,b^2\right)}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,3{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - (tan(c/2 + (d*x)/2)^2*(4*a^2 + 32*b^2) + a^2 - tan(c/2 + (d*x)/2)^4*(a^2 - 12*b^2) + (2*tan(c/2 + (d*x)/2)^3*(7*a^2*b + 10*b^3))/a + 14*a*b*tan(c/2 + (d*x)/2))/(d*(2*a^5*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^3*(4*a^5 + 8*a^3*b^2) + 2*a^5*tan(c/2 + (d*x)/2) + 8*a^4*b*tan(c/2 + (d*x)/2)^2 + 8*a^4*b*tan(c/2 + (d*x)/2)^4)) - (3*b*log(tan(c/2 + (d*x)/2)))/(a^4*d) - (atan((((-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*((3*a^6 - 12*a^4*b^2)/a^6 + (tan(c/2 + (d*x)/2)*(12*a^4*b - 24*a^2*b^3))/a^5 - (3*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^8 - 8*a^6*b^2))/a^5)*(a^2 - 2*b^2))/(2*(a^6 - a^4*b^2)))*3i)/(2*(a^6 - a^4*b^2)) + ((-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*((3*a^6 - 12*a^4*b^2)/a^6 + (tan(c/2 + (d*x)/2)*(12*a^4*b - 24*a^2*b^3))/a^5 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^8 - 8*a^6*b^2))/a^5)*(a^2 - 2*b^2))/(2*(a^6 - a^4*b^2)))*3i)/(2*(a^6 - a^4*b^2)))/((2*(9*a^2*b - 18*b^3))/a^6 + (2*tan(c/2 + (d*x)/2)*(9*a^2 - 18*b^2))/a^5 + (3*(-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*((3*a^6 - 12*a^4*b^2)/a^6 + (tan(c/2 + (d*x)/2)*(12*a^4*b - 24*a^2*b^3))/a^5 - (3*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^8 - 8*a^6*b^2))/a^5)*(a^2 - 2*b^2))/(2*(a^6 - a^4*b^2))))/(2*(a^6 - a^4*b^2)) - (3*(-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*((3*a^6 - 12*a^4*b^2)/a^6 + (tan(c/2 + (d*x)/2)*(12*a^4*b - 24*a^2*b^3))/a^5 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^8 - 8*a^6*b^2))/a^5)*(a^2 - 2*b^2))/(2*(a^6 - a^4*b^2))))/(2*(a^6 - a^4*b^2))))*(-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*3i)/(d*(a^6 - a^4*b^2))","B"
1140,1,1100,218,9.904475,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(50\,a\,b^2-9\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^2\,b-32\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(10\,a^2\,b-104\,b^3\right)-\frac{a^3}{2}+4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-17\,a^4+72\,a^2\,b^2+112\,b^4\right)}{2\,a}}{d\,\left(4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^6+16\,a^4\,b^2\right)+16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^2-12\,b^2\right)}{2\,a^5\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{12\,a^7\,b-24\,a^5\,b^3}{a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^7-36\,a^5\,b^2+48\,a^3\,b^4\right)}{a^7}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{10}-8\,a^8\,b^2\right)}{a^7}\right)\,\left(3\,a^2-4\,b^2\right)}{2\,\left(a^7-a^5\,b^2\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^7-a^5\,b^2\right)}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^7-36\,a^5\,b^2+48\,a^3\,b^4\right)}{a^7}-\frac{12\,a^7\,b-24\,a^5\,b^3}{a^8}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{10}-8\,a^8\,b^2\right)}{a^7}\right)\,\left(3\,a^2-4\,b^2\right)}{2\,\left(a^7-a^5\,b^2\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^7-a^5\,b^2\right)}}{\frac{27\,a^4\,b-144\,a^2\,b^3+144\,b^5}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,b^4-54\,a^2\,b^2\right)}{a^7}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{12\,a^7\,b-24\,a^5\,b^3}{a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^7-36\,a^5\,b^2+48\,a^3\,b^4\right)}{a^7}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{10}-8\,a^8\,b^2\right)}{a^7}\right)\,\left(3\,a^2-4\,b^2\right)}{2\,\left(a^7-a^5\,b^2\right)}\right)}{2\,\left(a^7-a^5\,b^2\right)}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^7-36\,a^5\,b^2+48\,a^3\,b^4\right)}{a^7}-\frac{12\,a^7\,b-24\,a^5\,b^3}{a^8}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{10}-8\,a^8\,b^2\right)}{a^7}\right)\,\left(3\,a^2-4\,b^2\right)}{2\,\left(a^7-a^5\,b^2\right)}\right)}{2\,\left(a^7-a^5\,b^2\right)}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,3{}\mathrm{i}}{d\,\left(a^7-a^5\,b^2\right)}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^3*d) + (tan(c/2 + (d*x)/2)^2*(50*a*b^2 - 9*a^3) - tan(c/2 + (d*x)/2)^5*(6*a^2*b - 32*b^3) - tan(c/2 + (d*x)/2)^3*(10*a^2*b - 104*b^3) - a^3/2 + 4*a^2*b*tan(c/2 + (d*x)/2) + (tan(c/2 + (d*x)/2)^4*(112*b^4 - 17*a^4 + 72*a^2*b^2))/(2*a))/(d*(4*a^6*tan(c/2 + (d*x)/2)^2 + 4*a^6*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^4*(8*a^6 + 16*a^4*b^2) + 16*a^5*b*tan(c/2 + (d*x)/2)^3 + 16*a^5*b*tan(c/2 + (d*x)/2)^5)) - (3*b*tan(c/2 + (d*x)/2))/(2*a^4*d) - (log(tan(c/2 + (d*x)/2))*(3*a^2 - 12*b^2))/(2*a^5*d) - (b*atan(((b*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((12*a^7*b - 24*a^5*b^3)/a^8 - (tan(c/2 + (d*x)/2)*(3*a^7 + 48*a^3*b^4 - 36*a^5*b^2))/a^7 + (3*b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^10 - 8*a^8*b^2))/a^7)*(3*a^2 - 4*b^2))/(2*(a^7 - a^5*b^2)))*3i)/(2*(a^7 - a^5*b^2)) - (b*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((tan(c/2 + (d*x)/2)*(3*a^7 + 48*a^3*b^4 - 36*a^5*b^2))/a^7 - (12*a^7*b - 24*a^5*b^3)/a^8 + (3*b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^10 - 8*a^8*b^2))/a^7)*(3*a^2 - 4*b^2))/(2*(a^7 - a^5*b^2)))*3i)/(2*(a^7 - a^5*b^2)))/((27*a^4*b + 144*b^5 - 144*a^2*b^3)/a^8 + (2*tan(c/2 + (d*x)/2)*(72*b^4 - 54*a^2*b^2))/a^7 + (3*b*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((12*a^7*b - 24*a^5*b^3)/a^8 - (tan(c/2 + (d*x)/2)*(3*a^7 + 48*a^3*b^4 - 36*a^5*b^2))/a^7 + (3*b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^10 - 8*a^8*b^2))/a^7)*(3*a^2 - 4*b^2))/(2*(a^7 - a^5*b^2))))/(2*(a^7 - a^5*b^2)) + (3*b*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((tan(c/2 + (d*x)/2)*(3*a^7 + 48*a^3*b^4 - 36*a^5*b^2))/a^7 - (12*a^7*b - 24*a^5*b^3)/a^8 + (3*b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^10 - 8*a^8*b^2))/a^7)*(3*a^2 - 4*b^2))/(2*(a^7 - a^5*b^2))))/(2*(a^7 - a^5*b^2))))*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*3i)/(d*(a^7 - a^5*b^2))","B"
1141,1,1261,289,10.044035,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{8\,a^5}+\frac{1}{4\,a^3}-\frac{9\,b^2}{2\,a^5}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5\,a^4+16\,a^2\,b^2-80\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{29\,a^4}{3}+72\,a^2\,b^2-304\,b^4\right)-\frac{a^4}{3}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{13\,a^4}{3}-\frac{40\,a^2\,b^2}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(156\,a\,b^3-\frac{170\,a^3\,b}{3}\right)-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-55\,a^4\,b+104\,a^2\,b^3+144\,b^5\right)}{a}+\frac{5\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{d\,\left(8\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(16\,a^7+32\,a^5\,b^2\right)+32\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+32\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(9\,a^2\,b-20\,b^3\right)}{2\,a^6\,d}-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,\left(\frac{2\,a^{10}-28\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,a^8\,b-76\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)}{a^8-a^6\,b^2}\right)\,1{}\mathrm{i}}{a^8-a^6\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,\left(\frac{2\,a^{10}-28\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,a^8\,b-76\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)}{a^8-a^6\,b^2}\right)\,1{}\mathrm{i}}{a^8-a^6\,b^2}}{\frac{18\,a^6\,b-211\,a^4\,b^3+560\,a^2\,b^5-400\,b^7}{a^{10}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-58\,a^4\,b^2+230\,a^2\,b^4-200\,b^6\right)}{a^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,\left(\frac{2\,a^{10}-28\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,a^8\,b-76\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)}{a^8-a^6\,b^2}\right)}{a^8-a^6\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,\left(\frac{2\,a^{10}-28\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,a^8\,b-76\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)}{a^8-a^6\,b^2}\right)}{a^8-a^6\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^8-a^6\,b^2\right)}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^3*d) - (tan(c/2 + (d*x)/2)*((3*(a^2 + 4*b^2))/(8*a^5) + 1/(4*a^3) - (9*b^2)/(2*a^5)))/d + (tan(c/2 + (d*x)/2)^6*(5*a^4 - 80*b^4 + 16*a^2*b^2) + tan(c/2 + (d*x)/2)^4*((29*a^4)/3 - 304*b^4 + 72*a^2*b^2) - a^4/3 + tan(c/2 + (d*x)/2)^2*((13*a^4)/3 - (40*a^2*b^2)/3) - tan(c/2 + (d*x)/2)^3*(156*a*b^3 - (170*a^3*b)/3) - (tan(c/2 + (d*x)/2)^5*(144*b^5 - 55*a^4*b + 104*a^2*b^3))/a + (5*a^3*b*tan(c/2 + (d*x)/2))/3)/(d*(8*a^7*tan(c/2 + (d*x)/2)^3 + 8*a^7*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^5*(16*a^7 + 32*a^5*b^2) + 32*a^6*b*tan(c/2 + (d*x)/2)^4 + 32*a^6*b*tan(c/2 + (d*x)/2)^6)) + (log(tan(c/2 + (d*x)/2))*(9*a^2*b - 20*b^3))/(2*a^6*d) - (3*b*tan(c/2 + (d*x)/2)^2)/(8*a^4*d) + (atan((((-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*((2*a^10 + 40*a^6*b^4 - 28*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(13*a^8*b + 80*a^4*b^5 - 76*a^6*b^3))/a^9 + ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(a^4 + 10*b^4 - (19*a^2*b^2)/2))/(a^8 - a^6*b^2))*1i)/(a^8 - a^6*b^2) + ((-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*((2*a^10 + 40*a^6*b^4 - 28*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(13*a^8*b + 80*a^4*b^5 - 76*a^6*b^3))/a^9 - ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(a^4 + 10*b^4 - (19*a^2*b^2)/2))/(a^8 - a^6*b^2))*1i)/(a^8 - a^6*b^2))/((18*a^6*b - 400*b^7 + 560*a^2*b^5 - 211*a^4*b^3)/a^10 + (2*tan(c/2 + (d*x)/2)*(4*a^6 - 200*b^6 + 230*a^2*b^4 - 58*a^4*b^2))/a^9 - ((-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*((2*a^10 + 40*a^6*b^4 - 28*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(13*a^8*b + 80*a^4*b^5 - 76*a^6*b^3))/a^9 + ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(a^4 + 10*b^4 - (19*a^2*b^2)/2))/(a^8 - a^6*b^2)))/(a^8 - a^6*b^2) + ((-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*((2*a^10 + 40*a^6*b^4 - 28*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(13*a^8*b + 80*a^4*b^5 - 76*a^6*b^3))/a^9 - ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(a^4 + 10*b^4 - (19*a^2*b^2)/2))/(a^8 - a^6*b^2)))/(a^8 - a^6*b^2)))*(-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*2i)/(d*(a^8 - a^6*b^2))","B"
1142,1,1487,340,10.214504,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{1}{32\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{16\,a^5}+\frac{1}{16\,a^3}-\frac{9\,b^2}{4\,a^5}\right)}{a}-\frac{192\,a^2\,b+128\,b^3}{256\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{8\,a^6}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(19\,a^4\,b-40\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{15\,a^5}{4}-224\,a^3\,b^2+448\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(30\,a^4\,b+32\,a^2\,b^3-192\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(50\,a^4\,b+280\,a^2\,b^3-832\,b^5\right)+\frac{a^5}{4}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a^5}{2}-5\,a^3\,b^2\right)-a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^6-114\,a^4\,b^2+152\,a^2\,b^4+176\,b^6\right)}{a}}{d\,\left(16\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+16\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(32\,a^8+64\,a^6\,b^2\right)+64\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+64\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^4\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^4}{8}-9\,a^2\,b^2+15\,b^4\right)}{a^7\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\frac{27\,a^{11}\,b}{4}-51\,a^9\,b^3+60\,a^7\,b^5}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{11}-126\,a^9\,b^2+528\,a^7\,b^4-480\,a^5\,b^6\right)}{4\,a^{11}}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}-32\,a^{12}\,b^2\right)}{4\,a^{11}}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,3{}\mathrm{i}}{2\,\left(a^9-a^7\,b^2\right)}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{11}-126\,a^9\,b^2+528\,a^7\,b^4-480\,a^5\,b^6\right)}{4\,a^{11}}-\frac{\frac{27\,a^{11}\,b}{4}-51\,a^9\,b^3+60\,a^7\,b^5}{a^{12}}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}-32\,a^{12}\,b^2\right)}{4\,a^{11}}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,3{}\mathrm{i}}{2\,\left(a^9-a^7\,b^2\right)}}{\frac{\frac{9\,a^8\,b}{2}-\frac{531\,a^6\,b^3}{4}+\frac{1593\,a^4\,b^5}{2}-1530\,a^2\,b^7+900\,b^9}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-126\,a^6\,b^2+1053\,a^4\,b^4-2610\,a^2\,b^6+1800\,b^8\right)}{2\,a^{11}}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\frac{27\,a^{11}\,b}{4}-51\,a^9\,b^3+60\,a^7\,b^5}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{11}-126\,a^9\,b^2+528\,a^7\,b^4-480\,a^5\,b^6\right)}{4\,a^{11}}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}-32\,a^{12}\,b^2\right)}{4\,a^{11}}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{11}-126\,a^9\,b^2+528\,a^7\,b^4-480\,a^5\,b^6\right)}{4\,a^{11}}-\frac{\frac{27\,a^{11}\,b}{4}-51\,a^9\,b^3+60\,a^7\,b^5}{a^{12}}+\frac{3\,b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}-32\,a^{12}\,b^2\right)}{4\,a^{11}}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,3{}\mathrm{i}}{d\,\left(a^9-a^7\,b^2\right)}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a^3*d) - (tan(c/2 + (d*x)/2)^2*((3*(a^2 + 4*b^2))/(32*a^5) + 1/(32*a^3) - (9*b^2)/(8*a^5)))/d + (tan(c/2 + (d*x)/2)*((6*b*((3*(a^2 + 4*b^2))/(16*a^5) + 1/(16*a^3) - (9*b^2)/(4*a^5)))/a - (192*a^2*b + 128*b^3)/(256*a^6) + (9*b*(a^2 + 4*b^2))/(8*a^6)))/d - (tan(c/2 + (d*x)/2)^3*(19*a^4*b - 40*a^2*b^3) - tan(c/2 + (d*x)/2)^4*(448*a*b^4 + (15*a^5)/4 - 224*a^3*b^2) + tan(c/2 + (d*x)/2)^7*(30*a^4*b - 192*b^5 + 32*a^2*b^3) + tan(c/2 + (d*x)/2)^5*(50*a^4*b - 832*b^5 + 280*a^2*b^3) + a^5/4 - tan(c/2 + (d*x)/2)^2*((3*a^5)/2 - 5*a^3*b^2) - a^4*b*tan(c/2 + (d*x)/2) - (2*tan(c/2 + (d*x)/2)^6*(a^6 + 176*b^6 + 152*a^2*b^4 - 114*a^4*b^2))/a)/(d*(16*a^8*tan(c/2 + (d*x)/2)^4 + 16*a^8*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^6*(32*a^8 + 64*a^6*b^2) + 64*a^7*b*tan(c/2 + (d*x)/2)^5 + 64*a^7*b*tan(c/2 + (d*x)/2)^7)) - (b*tan(c/2 + (d*x)/2)^3)/(8*a^4*d) + (log(tan(c/2 + (d*x)/2))*((3*a^4)/8 + 15*b^4 - 9*a^2*b^2))/(a^7*d) + (b*atan(((b*(-(a + b)*(a - b))^(1/2)*(((27*a^11*b)/4 + 60*a^7*b^5 - 51*a^9*b^3)/a^12 - (tan(c/2 + (d*x)/2)*(3*a^11 - 480*a^5*b^6 + 528*a^7*b^4 - 126*a^9*b^2))/(4*a^11) + (3*b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^14 - 32*a^12*b^2))/(4*a^11))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2)*3i)/(2*(a^9 - a^7*b^2)) - (b*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(3*a^11 - 480*a^5*b^6 + 528*a^7*b^4 - 126*a^9*b^2))/(4*a^11) - ((27*a^11*b)/4 + 60*a^7*b^5 - 51*a^9*b^3)/a^12 + (3*b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^14 - 32*a^12*b^2))/(4*a^11))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2)*3i)/(2*(a^9 - a^7*b^2)))/(((9*a^8*b)/2 + 900*b^9 - 1530*a^2*b^7 + (1593*a^4*b^5)/2 - (531*a^6*b^3)/4)/a^12 + (tan(c/2 + (d*x)/2)*(1800*b^8 - 2610*a^2*b^6 + 1053*a^4*b^4 - 126*a^6*b^2))/(2*a^11) + (3*b*(-(a + b)*(a - b))^(1/2)*(((27*a^11*b)/4 + 60*a^7*b^5 - 51*a^9*b^3)/a^12 - (tan(c/2 + (d*x)/2)*(3*a^11 - 480*a^5*b^6 + 528*a^7*b^4 - 126*a^9*b^2))/(4*a^11) + (3*b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^14 - 32*a^12*b^2))/(4*a^11))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)) + (3*b*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(3*a^11 - 480*a^5*b^6 + 528*a^7*b^4 - 126*a^9*b^2))/(4*a^11) - ((27*a^11*b)/4 + 60*a^7*b^5 - 51*a^9*b^3)/a^12 + (3*b*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^14 - 32*a^12*b^2))/(4*a^11))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2))))*(-(a + b)*(a - b))^(1/2)*(2*a^4 + 10*b^4 - 11*a^2*b^2)*3i)/(d*(a^9 - a^7*b^2))","B"
1143,0,-1,463,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + b*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2*(a + b*sin(c + d*x))^(1/2), x)","F"
1144,0,-1,332,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))^(1/2), x)","F"
1145,0,-1,338,0.000000,"\text{Not used}","int(cos(c + d*x)^3*cot(c + d*x)*(a + b*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\mathrm{cot}\left(c+d\,x\right)\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^3*cot(c + d*x)*(a + b*sin(c + d*x))^(1/2), x)","F"
1146,0,-1,323,0.000000,"\text{Not used}","int(cos(c + d*x)^2*cot(c + d*x)^2*(a + b*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\mathrm{cot}\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*cot(c + d*x)^2*(a + b*sin(c + d*x))^(1/2), x)","F"
1147,0,-1,345,0.000000,"\text{Not used}","int(cos(c + d*x)*cot(c + d*x)^3*(a + b*sin(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,{\mathrm{cot}\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)*cot(c + d*x)^3*(a + b*sin(c + d*x))^(1/2), x)","F"
1148,0,-1,351,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x))^(1/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cot(c + d*x)^4*(a + b*sin(c + d*x))^(1/2), x)","F"
1149,0,-1,412,0.000000,"\text{Not used}","int((cot(c + d*x)^4*(a + b*sin(c + d*x))^(1/2))/sin(c + d*x),x)","\int \frac{{\left({\sin\left(c+d\,x\right)}^2-1\right)}^2\,\sqrt{a+b\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((sin(c + d*x)^2 - 1)^2*(a + b*sin(c + d*x))^(1/2))/sin(c + d*x)^5, x)","F"
1150,0,-1,484,0.000000,"\text{Not used}","int((cot(c + d*x)^4*(a + b*sin(c + d*x))^(1/2))/sin(c + d*x)^2,x)","\int \frac{{\left({\sin\left(c+d\,x\right)}^2-1\right)}^2\,\sqrt{a+b\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^6} \,d x","Not used",1,"int(((sin(c + d*x)^2 - 1)^2*(a + b*sin(c + d*x))^(1/2))/sin(c + d*x)^6, x)","F"
1151,0,-1,528,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^2*(a + b*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2*(a + b*sin(c + d*x))^(3/2), x)","F"
1152,0,-1,394,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))^(3/2), x)","F"
1153,0,-1,390,0.000000,"\text{Not used}","int(cos(c + d*x)^3*cot(c + d*x)*(a + b*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\mathrm{cot}\left(c+d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^3*cot(c + d*x)*(a + b*sin(c + d*x))^(3/2), x)","F"
1154,0,-1,374,0.000000,"\text{Not used}","int(cos(c + d*x)^2*cot(c + d*x)^2*(a + b*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\mathrm{cot}\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*cot(c + d*x)^2*(a + b*sin(c + d*x))^(3/2), x)","F"
1155,0,-1,383,0.000000,"\text{Not used}","int(cos(c + d*x)*cot(c + d*x)^3*(a + b*sin(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,{\mathrm{cot}\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)*cot(c + d*x)^3*(a + b*sin(c + d*x))^(3/2), x)","F"
1156,0,-1,386,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x))^(3/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cot(c + d*x)^4*(a + b*sin(c + d*x))^(3/2), x)","F"
1157,0,-1,408,0.000000,"\text{Not used}","int((cot(c + d*x)^4*(a + b*sin(c + d*x))^(3/2))/sin(c + d*x),x)","\int \frac{{\left({\sin\left(c+d\,x\right)}^2-1\right)}^2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((sin(c + d*x)^2 - 1)^2*(a + b*sin(c + d*x))^(3/2))/sin(c + d*x)^5, x)","F"
1158,-1,-1,484,0.000000,"\text{Not used}","int((cot(c + d*x)^4*(a + b*sin(c + d*x))^(3/2))/sin(c + d*x)^2,x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
1159,-1,-1,551,0.000000,"\text{Not used}","int((cot(c + d*x)^4*(a + b*sin(c + d*x))^(3/2))/sin(c + d*x)^3,x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
1160,0,-1,451,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))^(5/2), x)","F"
1161,0,-1,447,0.000000,"\text{Not used}","int(cos(c + d*x)^3*cot(c + d*x)*(a + b*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\mathrm{cot}\left(c+d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^3*cot(c + d*x)*(a + b*sin(c + d*x))^(5/2), x)","F"
1162,0,-1,426,0.000000,"\text{Not used}","int(cos(c + d*x)^2*cot(c + d*x)^2*(a + b*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\mathrm{cot}\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*cot(c + d*x)^2*(a + b*sin(c + d*x))^(5/2), x)","F"
1163,0,-1,430,0.000000,"\text{Not used}","int(cos(c + d*x)*cot(c + d*x)^3*(a + b*sin(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,{\mathrm{cot}\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)*cot(c + d*x)^3*(a + b*sin(c + d*x))^(5/2), x)","F"
1164,0,-1,429,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x))^(5/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cot(c + d*x)^4*(a + b*sin(c + d*x))^(5/2), x)","F"
1165,-1,-1,449,0.000000,"\text{Not used}","int((cot(c + d*x)^4*(a + b*sin(c + d*x))^(5/2))/sin(c + d*x),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
1166,-1,-1,482,0.000000,"\text{Not used}","int((cot(c + d*x)^4*(a + b*sin(c + d*x))^(5/2))/sin(c + d*x)^2,x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
1167,-1,-1,551,0.000000,"\text{Not used}","int((cot(c + d*x)^4*(a + b*sin(c + d*x))^(5/2))/sin(c + d*x)^3,x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
1168,0,-1,471,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x))^(1/2), x)","F"
1169,0,-1,405,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x))^(1/2), x)","F"
1170,0,-1,283,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x))^(1/2), x)","F"
1171,0,-1,288,0.000000,"\text{Not used}","int((cos(c + d*x)^3*cot(c + d*x))/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\mathrm{cot}\left(c+d\,x\right)}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^3*cot(c + d*x))/(a + b*sin(c + d*x))^(1/2), x)","F"
1172,0,-1,285,0.000000,"\text{Not used}","int((cos(c + d*x)^2*cot(c + d*x)^2)/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\mathrm{cot}\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*cot(c + d*x)^2)/(a + b*sin(c + d*x))^(1/2), x)","F"
1173,0,-1,307,0.000000,"\text{Not used}","int((cos(c + d*x)*cot(c + d*x)^3)/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,{\mathrm{cot}\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)*cot(c + d*x)^3)/(a + b*sin(c + d*x))^(1/2), x)","F"
1174,0,-1,353,0.000000,"\text{Not used}","int(cot(c + d*x)^4/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^4}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)^4/(a + b*sin(c + d*x))^(1/2), x)","F"
1175,0,-1,412,0.000000,"\text{Not used}","int(cot(c + d*x)^4/(sin(c + d*x)*(a + b*sin(c + d*x))^(1/2)),x)","\int \frac{{\left({\sin\left(c+d\,x\right)}^2-1\right)}^2}{{\sin\left(c+d\,x\right)}^5\,\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((sin(c + d*x)^2 - 1)^2/(sin(c + d*x)^5*(a + b*sin(c + d*x))^(1/2)), x)","F"
1176,0,-1,466,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x))^(3/2), x)","F"
1177,0,-1,401,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x))^(3/2), x)","F"
1178,0,-1,261,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x))^(3/2), x)","F"
1179,0,-1,296,0.000000,"\text{Not used}","int((cos(c + d*x)^3*cot(c + d*x))/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\mathrm{cot}\left(c+d\,x\right)}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*cot(c + d*x))/(a + b*sin(c + d*x))^(3/2), x)","F"
1180,0,-1,294,0.000000,"\text{Not used}","int((cos(c + d*x)^2*cot(c + d*x)^2)/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\mathrm{cot}\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*cot(c + d*x)^2)/(a + b*sin(c + d*x))^(3/2), x)","F"
1181,0,-1,366,0.000000,"\text{Not used}","int((cos(c + d*x)*cot(c + d*x)^3)/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,{\mathrm{cot}\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)*cot(c + d*x)^3)/(a + b*sin(c + d*x))^(3/2), x)","F"
1182,0,-1,416,0.000000,"\text{Not used}","int(cot(c + d*x)^4/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^4}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cot(c + d*x)^4/(a + b*sin(c + d*x))^(3/2), x)","F"
1183,0,-1,469,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x))^(5/2), x)","F"
1184,0,-1,411,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\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)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x))^(5/2), x)","F"
1185,0,-1,254,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x))^(5/2), x)","F"
1186,0,-1,313,0.000000,"\text{Not used}","int((cos(c + d*x)^3*cot(c + d*x))/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\mathrm{cot}\left(c+d\,x\right)}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*cot(c + d*x))/(a + b*sin(c + d*x))^(5/2), x)","F"
1187,0,-1,346,0.000000,"\text{Not used}","int((cos(c + d*x)^2*cot(c + d*x)^2)/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\mathrm{cot}\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*cot(c + d*x)^2)/(a + b*sin(c + d*x))^(5/2), x)","F"
1188,0,-1,407,0.000000,"\text{Not used}","int((cos(c + d*x)*cot(c + d*x)^3)/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,{\mathrm{cot}\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)*cot(c + d*x)^3)/(a + b*sin(c + d*x))^(5/2), x)","F"
1189,-1,-1,458,0.000000,"\text{Not used}","int(cot(c + d*x)^4/(a + b*sin(c + d*x))^(5/2),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
1190,0,-1,510,0.000000,"\text{Not used}","int(cos(e + f*x)^4/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(9/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^4}{\sqrt{d\,\sin\left(e+f\,x\right)}\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(cos(e + f*x)^4/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(9/2)), x)","F"
1191,0,-1,36,0.000000,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^(1/3))/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^{1/3}}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",0,"int((cos(c + d*x)^4*sin(c + d*x)^(1/3))/(a + b*sin(c + d*x))^(1/2), x)","F"
1192,0,-1,32,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^n*(a + b*sin(c + d*x))^p,x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^n\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^p \,d x","Not used",0,"int(cos(c + d*x)^4*sin(c + d*x)^n*(a + b*sin(c + d*x))^p, x)","F"
1193,0,-1,36,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^p)/sin(c + d*x)^(p + 3),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^p}{{\sin\left(c+d\,x\right)}^{p+3}} \,d x","Not used",0,"int((cos(c + d*x)^4*(a + b*sin(c + d*x))^p)/sin(c + d*x)^(p + 3), x)","F"
1194,0,-1,36,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(a + b*sin(c + d*x))^p)/sin(c + d*x)^(p + 4),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^p}{{\sin\left(c+d\,x\right)}^{p+4}} \,d x","Not used",0,"int((cos(c + d*x)^4*(a + b*sin(c + d*x))^p)/sin(c + d*x)^(p + 4), x)","F"
1195,0,-1,623,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^n*(a + b*sin(c + d*x))^3,x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^n\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)^n*(a + b*sin(c + d*x))^3, x)","F"
1196,0,-1,487,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^n*(a + b*sin(c + d*x))^2,x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^n\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)^n*(a + b*sin(c + d*x))^2, x)","F"
1197,0,-1,129,0.000000,"\text{Not used}","int(cos(c + d*x)^4*sin(c + d*x)^n*(a + b*sin(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^4\,{\sin\left(c+d\,x\right)}^n\,\left(a+b\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^4*sin(c + d*x)^n*(a + b*sin(c + d*x)), x)","F"
1198,1,71,97,0.082704,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^5*(a + b*sin(c + d*x)),x)","\frac{\frac{b\,{\sin\left(c+d\,x\right)}^{11}}{11}+\frac{a\,{\sin\left(c+d\,x\right)}^{10}}{10}-\frac{2\,b\,{\sin\left(c+d\,x\right)}^9}{9}-\frac{a\,{\sin\left(c+d\,x\right)}^8}{4}+\frac{b\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a\,{\sin\left(c+d\,x\right)}^6}{6}}{d}","Not used",1,"((a*sin(c + d*x)^6)/6 - (a*sin(c + d*x)^8)/4 + (a*sin(c + d*x)^10)/10 + (b*sin(c + d*x)^7)/7 - (2*b*sin(c + d*x)^9)/9 + (b*sin(c + d*x)^11)/11)/d","B"
1199,1,71,97,0.058087,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^4*(a + b*sin(c + d*x)),x)","\frac{\frac{b\,{\sin\left(c+d\,x\right)}^{10}}{10}+\frac{a\,{\sin\left(c+d\,x\right)}^9}{9}-\frac{b\,{\sin\left(c+d\,x\right)}^8}{4}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{b\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{5}}{d}","Not used",1,"((a*sin(c + d*x)^5)/5 - (2*a*sin(c + d*x)^7)/7 + (a*sin(c + d*x)^9)/9 + (b*sin(c + d*x)^6)/6 - (b*sin(c + d*x)^8)/4 + (b*sin(c + d*x)^10)/10)/d","B"
1200,1,71,81,0.056598,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^3*(a + b*sin(c + d*x)),x)","\frac{\frac{b\,{\sin\left(c+d\,x\right)}^9}{9}+\frac{a\,{\sin\left(c+d\,x\right)}^8}{8}-\frac{2\,b\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{a\,{\sin\left(c+d\,x\right)}^6}{3}+\frac{b\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{4}}{d}","Not used",1,"((a*sin(c + d*x)^4)/4 - (a*sin(c + d*x)^6)/3 + (a*sin(c + d*x)^8)/8 + (b*sin(c + d*x)^5)/5 - (2*b*sin(c + d*x)^7)/7 + (b*sin(c + d*x)^9)/9)/d","B"
1201,1,71,81,0.055046,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^2*(a + b*sin(c + d*x)),x)","\frac{\frac{b\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{a\,{\sin\left(c+d\,x\right)}^7}{7}-\frac{b\,{\sin\left(c+d\,x\right)}^6}{3}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{b\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"((a*sin(c + d*x)^3)/3 - (2*a*sin(c + d*x)^5)/5 + (a*sin(c + d*x)^7)/7 + (b*sin(c + d*x)^4)/4 - (b*sin(c + d*x)^6)/3 + (b*sin(c + d*x)^8)/8)/d","B"
1202,1,71,65,11.593556,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)*(a + b*sin(c + d*x)),x)","\frac{\frac{b\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a\,{\sin\left(c+d\,x\right)}^6}{6}-\frac{2\,b\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{a\,{\sin\left(c+d\,x\right)}^4}{2}+\frac{b\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"((a*sin(c + d*x)^2)/2 - (a*sin(c + d*x)^4)/2 + (a*sin(c + d*x)^6)/6 + (b*sin(c + d*x)^3)/3 - (2*b*sin(c + d*x)^5)/5 + (b*sin(c + d*x)^7)/7)/d","B"
1203,1,126,86,12.003136,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x),x)","\frac{a\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a\,{\cos\left(c+d\,x\right)}^2}{2\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^4}{4\,d}+\frac{8\,b\,\sin\left(c+d\,x\right)}{15\,d}+\frac{4\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{15\,d}+\frac{b\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{5\,d}","Not used",1,"(a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*log(1/cos(c/2 + (d*x)/2)^2))/d + (a*cos(c + d*x)^2)/(2*d) + (a*cos(c + d*x)^4)/(4*d) + (8*b*sin(c + d*x))/(15*d) + (4*b*cos(c + d*x)^2*sin(c + d*x))/(15*d) + (b*cos(c + d*x)^4*sin(c + d*x))/(5*d)","B"
1204,1,250,83,11.927346,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^2,x)","\frac{b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}-\frac{4\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d}+\frac{8\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}-\frac{8\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d}+\frac{4\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d}-\frac{9\,a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{20\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{16\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{8\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (b*log(1/cos(c/2 + (d*x)/2)^2))/d - (4*b*cos(c/2 + (d*x)/2)^2)/d + (8*b*cos(c/2 + (d*x)/2)^4)/d - (8*b*cos(c/2 + (d*x)/2)^6)/d + (4*b*cos(c/2 + (d*x)/2)^8)/d - (9*a*cos(c/2 + (d*x)/2))/(2*d*sin(c/2 + (d*x)/2)) - (a*sin(c/2 + (d*x)/2))/(2*d*cos(c/2 + (d*x)/2)) + (20*a*cos(c/2 + (d*x)/2)^3)/(3*d*sin(c/2 + (d*x)/2)) - (16*a*cos(c/2 + (d*x)/2)^5)/(3*d*sin(c/2 + (d*x)/2)) + (8*a*cos(c/2 + (d*x)/2)^7)/(3*d*sin(c/2 + (d*x)/2))","B"
1205,1,229,86,11.885270,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^3,x)","\frac{2\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{18\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{82\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+22\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{2\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(2*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (b*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + 2*b*tan(c/2 + (d*x)/2) + (3*a*tan(c/2 + (d*x)/2)^2)/2 - (13*a*tan(c/2 + (d*x)/2)^4)/2 - (15*a*tan(c/2 + (d*x)/2)^6)/2 + 22*b*tan(c/2 + (d*x)/2)^3 + (82*b*tan(c/2 + (d*x)/2)^5)/3 + 18*b*tan(c/2 + (d*x)/2)^7)/(d*(4*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^4 + 12*tan(c/2 + (d*x)/2)^6 + 4*tan(c/2 + (d*x)/2)^8)) - (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (2*a*log(tan(c/2 + (d*x)/2)))/d","B"
1206,1,218,85,11.911062,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^4,x)","\frac{23\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{89\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{19\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{7\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{2\,b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{2\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"((19*a*tan(c/2 + (d*x)/2)^2)/3 - b*tan(c/2 + (d*x)/2) - a/3 + (89*a*tan(c/2 + (d*x)/2)^4)/3 + 23*a*tan(c/2 + (d*x)/2)^6 - 2*b*tan(c/2 + (d*x)/2)^3 + 15*b*tan(c/2 + (d*x)/2)^5)/(d*(8*tan(c/2 + (d*x)/2)^3 + 16*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^7)) + (7*a*tan(c/2 + (d*x)/2))/(8*d) + (2*b*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (b*tan(c/2 + (d*x)/2)^2)/(8*d) - (2*b*log(tan(c/2 + (d*x)/2)))/d","B"
1207,1,207,81,12.261305,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^5,x)","\frac{7\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{46\,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+\frac{40\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{a}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(7*b*tan(c/2 + (d*x)/2))/(8*d) + ((11*a*tan(c/2 + (d*x)/2)^2)/4 - (2*b*tan(c/2 + (d*x)/2))/3 - a/4 + 3*a*tan(c/2 + (d*x)/2)^4 + (40*b*tan(c/2 + (d*x)/2)^3)/3 + 46*b*tan(c/2 + (d*x)/2)^5)/(d*(16*tan(c/2 + (d*x)/2)^4 + 16*tan(c/2 + (d*x)/2)^6)) - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d + (3*a*tan(c/2 + (d*x)/2)^2)/(16*d) - (a*tan(c/2 + (d*x)/2)^4)/(64*d) - (b*tan(c/2 + (d*x)/2)^3)/(24*d) + (a*log(tan(c/2 + (d*x)/2)))/d","B"
1208,1,193,86,11.802598,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^6,x)","\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}\right)}{32\,d}","Not used",1,"(5*a*tan(c/2 + (d*x)/2)^3)/(96*d) - (b*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (5*a*tan(c/2 + (d*x)/2))/(16*d) - (a*tan(c/2 + (d*x)/2)^5)/(160*d) + (3*b*tan(c/2 + (d*x)/2)^2)/(16*d) - (b*tan(c/2 + (d*x)/2)^4)/(64*d) + (b*log(tan(c/2 + (d*x)/2)))/d - (cot(c/2 + (d*x)/2)^5*(a/5 + (b*tan(c/2 + (d*x)/2))/2 - (5*a*tan(c/2 + (d*x)/2)^2)/3 + 10*a*tan(c/2 + (d*x)/2)^4 - 6*b*tan(c/2 + (d*x)/2)^3))/(32*d)","B"
1209,1,69,61,11.791457,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^7,x)","-\frac{b\,{\sin\left(c+d\,x\right)}^5+\frac{a\,{\sin\left(c+d\,x\right)}^4}{2}-\frac{2\,b\,{\sin\left(c+d\,x\right)}^3}{3}-\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{b\,\sin\left(c+d\,x\right)}{5}+\frac{a}{6}}{d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"-(a/6 + (b*sin(c + d*x))/5 - (a*sin(c + d*x)^2)/2 + (a*sin(c + d*x)^4)/2 - (2*b*sin(c + d*x)^3)/3 + b*sin(c + d*x)^5)/(d*sin(c + d*x)^6)","B"
1210,1,70,65,11.605794,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^8,x)","-\frac{105\,b\,{\sin\left(c+d\,x\right)}^5+70\,a\,{\sin\left(c+d\,x\right)}^4-105\,b\,{\sin\left(c+d\,x\right)}^3-84\,a\,{\sin\left(c+d\,x\right)}^2+35\,b\,\sin\left(c+d\,x\right)+30\,a}{210\,d\,{\sin\left(c+d\,x\right)}^7}","Not used",1,"-(30*a + 35*b*sin(c + d*x) - 84*a*sin(c + d*x)^2 + 70*a*sin(c + d*x)^4 - 105*b*sin(c + d*x)^3 + 105*b*sin(c + d*x)^5)/(210*d*sin(c + d*x)^7)","B"
1211,1,70,81,11.641872,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^9,x)","-\frac{280\,b\,{\sin\left(c+d\,x\right)}^5+210\,a\,{\sin\left(c+d\,x\right)}^4-336\,b\,{\sin\left(c+d\,x\right)}^3-280\,a\,{\sin\left(c+d\,x\right)}^2+120\,b\,\sin\left(c+d\,x\right)+105\,a}{840\,d\,{\sin\left(c+d\,x\right)}^8}","Not used",1,"-(105*a + 120*b*sin(c + d*x) - 280*a*sin(c + d*x)^2 + 210*a*sin(c + d*x)^4 - 336*b*sin(c + d*x)^3 + 280*b*sin(c + d*x)^5)/(840*d*sin(c + d*x)^8)","B"
1212,1,70,81,11.669274,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^10,x)","-\frac{\frac{b\,{\sin\left(c+d\,x\right)}^5}{4}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{5}-\frac{b\,{\sin\left(c+d\,x\right)}^3}{3}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^2}{7}+\frac{b\,\sin\left(c+d\,x\right)}{8}+\frac{a}{9}}{d\,{\sin\left(c+d\,x\right)}^9}","Not used",1,"-(a/9 + (b*sin(c + d*x))/8 - (2*a*sin(c + d*x)^2)/7 + (a*sin(c + d*x)^4)/5 - (b*sin(c + d*x)^3)/3 + (b*sin(c + d*x)^5)/4)/(d*sin(c + d*x)^9)","B"
1213,1,70,97,11.641224,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^11,x)","-\frac{252\,b\,{\sin\left(c+d\,x\right)}^5+210\,a\,{\sin\left(c+d\,x\right)}^4-360\,b\,{\sin\left(c+d\,x\right)}^3-315\,a\,{\sin\left(c+d\,x\right)}^2+140\,b\,\sin\left(c+d\,x\right)+126\,a}{1260\,d\,{\sin\left(c+d\,x\right)}^{10}}","Not used",1,"-(126*a + 140*b*sin(c + d*x) - 315*a*sin(c + d*x)^2 + 210*a*sin(c + d*x)^4 - 360*b*sin(c + d*x)^3 + 252*b*sin(c + d*x)^5)/(1260*d*sin(c + d*x)^10)","B"
1214,1,70,97,11.685713,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x)))/sin(c + d*x)^12,x)","-\frac{\frac{b\,{\sin\left(c+d\,x\right)}^5}{6}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{7}-\frac{b\,{\sin\left(c+d\,x\right)}^3}{4}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^2}{9}+\frac{b\,\sin\left(c+d\,x\right)}{10}+\frac{a}{11}}{d\,{\sin\left(c+d\,x\right)}^{11}}","Not used",1,"-(a/11 + (b*sin(c + d*x))/10 - (2*a*sin(c + d*x)^2)/9 + (a*sin(c + d*x)^4)/7 - (b*sin(c + d*x)^3)/4 + (b*sin(c + d*x)^5)/6)/(d*sin(c + d*x)^11)","B"
1215,1,108,138,11.438480,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^2*(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^7\,\left(\frac{a^2}{7}-\frac{2\,b^2}{7}\right)-{\sin\left(c+d\,x\right)}^5\,\left(\frac{2\,a^2}{5}-\frac{b^2}{5}\right)+\frac{a^2\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{b^2\,{\sin\left(c+d\,x\right)}^9}{9}+\frac{a\,b\,{\sin\left(c+d\,x\right)}^4}{2}-\frac{2\,a\,b\,{\sin\left(c+d\,x\right)}^6}{3}+\frac{a\,b\,{\sin\left(c+d\,x\right)}^8}{4}}{d}","Not used",1,"(sin(c + d*x)^7*(a^2/7 - (2*b^2)/7) - sin(c + d*x)^5*((2*a^2)/5 - b^2/5) + (a^2*sin(c + d*x)^3)/3 + (b^2*sin(c + d*x)^9)/9 + (a*b*sin(c + d*x)^4)/2 - (2*a*b*sin(c + d*x)^6)/3 + (a*b*sin(c + d*x)^8)/4)/d","B"
1216,1,108,138,11.467813,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)*(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^6\,\left(\frac{a^2}{6}-\frac{b^2}{3}\right)-{\sin\left(c+d\,x\right)}^4\,\left(\frac{a^2}{2}-\frac{b^2}{4}\right)+\frac{a^2\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{b^2\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{2\,a\,b\,{\sin\left(c+d\,x\right)}^3}{3}-\frac{4\,a\,b\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{2\,a\,b\,{\sin\left(c+d\,x\right)}^7}{7}}{d}","Not used",1,"(sin(c + d*x)^6*(a^2/6 - b^2/3) - sin(c + d*x)^4*(a^2/2 - b^2/4) + (a^2*sin(c + d*x)^2)/2 + (b^2*sin(c + d*x)^8)/8 + (2*a*b*sin(c + d*x)^3)/3 - (4*a*b*sin(c + d*x)^5)/5 + (2*a*b*sin(c + d*x)^7)/7)/d","B"
1217,1,153,130,11.735538,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a^2\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a^2\,{\cos\left(c+d\,x\right)}^2}{2\,d}+\frac{a^2\,{\cos\left(c+d\,x\right)}^4}{4\,d}-\frac{b^2\,{\cos\left(c+d\,x\right)}^6}{6\,d}+\frac{16\,a\,b\,\sin\left(c+d\,x\right)}{15\,d}+\frac{8\,a\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{15\,d}+\frac{2\,a\,b\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{5\,d}","Not used",1,"(a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a^2*log(1/cos(c/2 + (d*x)/2)^2))/d + (a^2*cos(c + d*x)^2)/(2*d) + (a^2*cos(c + d*x)^4)/(4*d) - (b^2*cos(c + d*x)^6)/(6*d) + (16*a*b*sin(c + d*x))/(15*d) + (8*a*b*cos(c + d*x)^2*sin(c + d*x))/(15*d) + (2*a*b*cos(c + d*x)^4*sin(c + d*x))/(5*d)","B"
1218,1,445,125,12.015575,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{16\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}-\frac{8\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d}-\frac{16\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d}+\frac{8\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d}+\frac{20\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{16\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{8\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{22\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{256\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{368\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{15\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{96\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{32\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{5\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{2\,a\,b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{2\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{9\,a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{2\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(16*a*b*cos(c/2 + (d*x)/2)^4)/d - (8*a*b*cos(c/2 + (d*x)/2)^2)/d - (16*a*b*cos(c/2 + (d*x)/2)^6)/d + (8*a*b*cos(c/2 + (d*x)/2)^8)/d + (20*a^2*cos(c/2 + (d*x)/2)^3)/(3*d*sin(c/2 + (d*x)/2)) - (16*a^2*cos(c/2 + (d*x)/2)^5)/(3*d*sin(c/2 + (d*x)/2)) + (8*a^2*cos(c/2 + (d*x)/2)^7)/(3*d*sin(c/2 + (d*x)/2)) - (22*b^2*cos(c/2 + (d*x)/2)^3)/(3*d*sin(c/2 + (d*x)/2)) + (256*b^2*cos(c/2 + (d*x)/2)^5)/(15*d*sin(c/2 + (d*x)/2)) - (368*b^2*cos(c/2 + (d*x)/2)^7)/(15*d*sin(c/2 + (d*x)/2)) + (96*b^2*cos(c/2 + (d*x)/2)^9)/(5*d*sin(c/2 + (d*x)/2)) - (32*b^2*cos(c/2 + (d*x)/2)^11)/(5*d*sin(c/2 + (d*x)/2)) - (2*a*b*log(1/cos(c/2 + (d*x)/2)^2))/d + (2*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (9*a^2*cos(c/2 + (d*x)/2))/(2*d*sin(c/2 + (d*x)/2)) - (a^2*sin(c/2 + (d*x)/2))/(2*d*cos(c/2 + (d*x)/2)) + (2*b^2*cos(c/2 + (d*x)/2))/(d*sin(c/2 + (d*x)/2))","B"
1219,1,331,127,11.683567,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(2\,a^2-b^2\right)}{d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(14\,a^2-16\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{15\,a^2}{2}-16\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(5\,a^2-16\,b^2\right)+\frac{a^2}{2}+48\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{296\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{272\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+36\,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)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2-b^2\right)}{d}-\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1)*(2*a^2 - b^2))/d - (a^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (2*a^2*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^6*(14*a^2 - 16*b^2) - tan(c/2 + (d*x)/2)^8*((15*a^2)/2 - 16*b^2) - tan(c/2 + (d*x)/2)^4*(5*a^2 - 16*b^2) + a^2/2 + 48*a*b*tan(c/2 + (d*x)/2)^3 + (296*a*b*tan(c/2 + (d*x)/2)^5)/3 + (272*a*b*tan(c/2 + (d*x)/2)^7)/3 + 36*a*b*tan(c/2 + (d*x)/2)^9 + 4*a*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 16*tan(c/2 + (d*x)/2)^4 + 24*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8 + 4*tan(c/2 + (d*x)/2)^10)) - (log(tan(c/2 + (d*x)/2))*(2*a^2 - b^2))/d - (a*b*tan(c/2 + (d*x)/2))/d","B"
1220,1,315,120,11.712010,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x)^4,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^2-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(23\,a^2-36\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(36\,a^2-44\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{158\,a^2}{3}-\frac{164\,b^2}{3}\right)-\frac{a^2}{3}-6\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+26\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+30\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7\,a^2}{8}-\frac{b^2}{2}\right)}{d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{4\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{4\,a\,b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(6*a^2 - 4*b^2) + tan(c/2 + (d*x)/2)^8*(23*a^2 - 36*b^2) + tan(c/2 + (d*x)/2)^4*(36*a^2 - 44*b^2) + tan(c/2 + (d*x)/2)^6*((158*a^2)/3 - (164*b^2)/3) - a^2/3 - 6*a*b*tan(c/2 + (d*x)/2)^3 + 26*a*b*tan(c/2 + (d*x)/2)^5 + 30*a*b*tan(c/2 + (d*x)/2)^7 - 2*a*b*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 24*tan(c/2 + (d*x)/2)^5 + 24*tan(c/2 + (d*x)/2)^7 + 8*tan(c/2 + (d*x)/2)^9)) - (a^2*tan(c/2 + (d*x)/2)^3)/(24*d) + (tan(c/2 + (d*x)/2)*((7*a^2)/8 - b^2/2))/d - (a*b*tan(c/2 + (d*x)/2)^2)/(4*d) - (4*a*b*log(tan(c/2 + (d*x)/2)))/d + (4*a*b*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
1221,1,310,126,11.688016,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x)^5,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{5\,a^2}{2}-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{23\,a^2}{4}-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a^2+30\,b^2\right)-\frac{a^2}{4}+\frac{76\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{356\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+92\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2-2\,b^2\right)}{d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-2\,b^2\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a^2}{16}-\frac{b^2}{8}\right)}{d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,d}+\frac{7\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*((5*a^2)/2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*((23*a^2)/4 - 4*b^2) + tan(c/2 + (d*x)/2)^6*(3*a^2 + 30*b^2) - a^2/4 + (76*a*b*tan(c/2 + (d*x)/2)^3)/3 + (356*a*b*tan(c/2 + (d*x)/2)^5)/3 + 92*a*b*tan(c/2 + (d*x)/2)^7 - (4*a*b*tan(c/2 + (d*x)/2))/3)/(d*(16*tan(c/2 + (d*x)/2)^4 + 32*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8)) - (log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 - 2*b^2))/d - (a^2*tan(c/2 + (d*x)/2)^4)/(64*d) + (log(tan(c/2 + (d*x)/2))*(a^2 - 2*b^2))/d + (tan(c/2 + (d*x)/2)^2*((3*a^2)/16 - b^2/8))/d - (a*b*tan(c/2 + (d*x)/2)^3)/(12*d) + (7*a*b*tan(c/2 + (d*x)/2))/(4*d)","B"
1222,1,297,124,11.712837,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x)^6,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,a^2}{96}-\frac{b^2}{24}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,a^2}{16}-\frac{7\,b^2}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(10\,a^2-92\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{22\,a^2}{15}-\frac{4\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{25\,a^2}{3}-\frac{80\,b^2}{3}\right)+\frac{a^2}{5}-11\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}+\frac{2\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a\,b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((5*a^2)/96 - b^2/24))/d - (tan(c/2 + (d*x)/2)*((5*a^2)/16 - (7*b^2)/8))/d - (tan(c/2 + (d*x)/2)^6*(10*a^2 - 92*b^2) - tan(c/2 + (d*x)/2)^2*((22*a^2)/15 - (4*b^2)/3) + tan(c/2 + (d*x)/2)^4*((25*a^2)/3 - (80*b^2)/3) + a^2/5 - 11*a*b*tan(c/2 + (d*x)/2)^3 - 12*a*b*tan(c/2 + (d*x)/2)^5 + a*b*tan(c/2 + (d*x)/2))/(d*(32*tan(c/2 + (d*x)/2)^5 + 32*tan(c/2 + (d*x)/2)^7)) - (a^2*tan(c/2 + (d*x)/2)^5)/(160*d) + (3*a*b*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*b*tan(c/2 + (d*x)/2)^4)/(32*d) + (2*a*b*log(tan(c/2 + (d*x)/2)))/d - (2*a*b*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
1223,1,274,130,11.865093,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x)^7,x)","\frac{b^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{5\,a^2}{2}-12\,b^2\right)+\frac{a^2}{6}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2-b^2\right)-\frac{20\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+40\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}\right)}{64\,d}-\frac{b^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{64}-\frac{b^2}{64}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{5\,a^2}{128}-\frac{3\,b^2}{16}\right)}{d}+\frac{5\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{48\,d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{80\,d}-\frac{5\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(b^2*log(tan(c/2 + (d*x)/2)))/d - (a^2*tan(c/2 + (d*x)/2)^6)/(384*d) - (cot(c/2 + (d*x)/2)^6*(tan(c/2 + (d*x)/2)^4*((5*a^2)/2 - 12*b^2) + a^2/6 - tan(c/2 + (d*x)/2)^2*(a^2 - b^2) - (20*a*b*tan(c/2 + (d*x)/2)^3)/3 + 40*a*b*tan(c/2 + (d*x)/2)^5 + (4*a*b*tan(c/2 + (d*x)/2))/5))/(64*d) - (b^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d + (tan(c/2 + (d*x)/2)^4*(a^2/64 - b^2/64))/d - (tan(c/2 + (d*x)/2)^2*((5*a^2)/128 - (3*b^2)/16))/d + (5*a*b*tan(c/2 + (d*x)/2)^3)/(48*d) - (a*b*tan(c/2 + (d*x)/2)^5)/(80*d) - (5*a*b*tan(c/2 + (d*x)/2))/(8*d)","B"
1224,1,105,129,11.794438,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x)^8,x)","-\frac{\frac{a^2}{7}+{\sin\left(c+d\,x\right)}^4\,\left(\frac{a^2}{3}-\frac{2\,b^2}{3}\right)-{\sin\left(c+d\,x\right)}^2\,\left(\frac{2\,a^2}{5}-\frac{b^2}{5}\right)+b^2\,{\sin\left(c+d\,x\right)}^6+\frac{a\,b\,\sin\left(c+d\,x\right)}{3}-a\,b\,{\sin\left(c+d\,x\right)}^3+a\,b\,{\sin\left(c+d\,x\right)}^5}{d\,{\sin\left(c+d\,x\right)}^7}","Not used",1,"-(a^2/7 + sin(c + d*x)^4*(a^2/3 - (2*b^2)/3) - sin(c + d*x)^2*((2*a^2)/5 - b^2/5) + b^2*sin(c + d*x)^6 + (a*b*sin(c + d*x))/3 - a*b*sin(c + d*x)^3 + a*b*sin(c + d*x)^5)/(d*sin(c + d*x)^7)","B"
1225,1,107,138,11.776003,"\text{Not used}","int((cos(c + d*x)^5*(a + b*sin(c + d*x))^2)/sin(c + d*x)^9,x)","-\frac{\frac{a^2}{8}+{\sin\left(c+d\,x\right)}^4\,\left(\frac{a^2}{4}-\frac{b^2}{2}\right)-{\sin\left(c+d\,x\right)}^2\,\left(\frac{a^2}{3}-\frac{b^2}{6}\right)+\frac{b^2\,{\sin\left(c+d\,x\right)}^6}{2}+\frac{2\,a\,b\,\sin\left(c+d\,x\right)}{7}-\frac{4\,a\,b\,{\sin\left(c+d\,x\right)}^3}{5}+\frac{2\,a\,b\,{\sin\left(c+d\,x\right)}^5}{3}}{d\,{\sin\left(c+d\,x\right)}^8}","Not used",1,"-(a^2/8 + sin(c + d*x)^4*(a^2/4 - b^2/2) - sin(c + d*x)^2*(a^2/3 - b^2/6) + (b^2*sin(c + d*x)^6)/2 + (2*a*b*sin(c + d*x))/7 - (4*a*b*sin(c + d*x)^3)/5 + (2*a*b*sin(c + d*x)^5)/3)/(d*sin(c + d*x)^8)","B"
1226,1,375,235,0.135070,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^3)/(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{2\,a^3}{3\,b^5}+\frac{2\,a\,\left(\frac{2}{b^2}-\frac{3\,a^2}{b^4}\right)}{3\,b}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^4\,\left(\frac{1}{2\,b^2}-\frac{3\,a^2}{4\,b^4}\right)}{d}+\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{1}{2\,b^2}+\frac{a^2\,\left(\frac{2}{b^2}-\frac{3\,a^2}{b^4}\right)}{2\,b^2}-\frac{a\,\left(\frac{2\,a^3}{b^5}+\frac{2\,a\,\left(\frac{2}{b^2}-\frac{3\,a^2}{b^4}\right)}{b}\right)}{b}\right)}{d}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{a^2\,\left(\frac{2\,a^3}{b^5}+\frac{2\,a\,\left(\frac{2}{b^2}-\frac{3\,a^2}{b^4}\right)}{b}\right)}{b^2}+\frac{2\,a\,\left(\frac{1}{b^2}+\frac{a^2\,\left(\frac{2}{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{2}{b^2}-\frac{3\,a^2}{b^4}\right)}{b}\right)}{b}\right)}{b}\right)}{d}+\frac{{\sin\left(c+d\,x\right)}^6}{6\,b^2\,d}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^5}{5\,b^3\,d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(7\,a^6-10\,a^4\,b^2+3\,a^2\,b^4\right)}{b^8\,d}+\frac{a^7-2\,a^5\,b^2+a^3\,b^4}{b\,d\,\left(\sin\left(c+d\,x\right)\,b^8+a\,b^7\right)}","Not used",1,"(sin(c + d*x)^3*((2*a^3)/(3*b^5) + (2*a*(2/b^2 - (3*a^2)/b^4))/(3*b)))/d - (sin(c + d*x)^4*(1/(2*b^2) - (3*a^2)/(4*b^4)))/d + (sin(c + d*x)^2*(1/(2*b^2) + (a^2*(2/b^2 - (3*a^2)/b^4))/(2*b^2) - (a*((2*a^3)/b^5 + (2*a*(2/b^2 - (3*a^2)/b^4))/b))/b))/d - (sin(c + d*x)*((a^2*((2*a^3)/b^5 + (2*a*(2/b^2 - (3*a^2)/b^4))/b))/b^2 + (2*a*(1/b^2 + (a^2*(2/b^2 - (3*a^2)/b^4))/b^2 - (2*a*((2*a^3)/b^5 + (2*a*(2/b^2 - (3*a^2)/b^4))/b))/b))/b))/d + sin(c + d*x)^6/(6*b^2*d) - (2*a*sin(c + d*x)^5)/(5*b^3*d) + (log(a + b*sin(c + d*x))*(7*a^6 + 3*a^2*b^4 - 10*a^4*b^2))/(b^8*d) + (a^7 + a^3*b^4 - 2*a^5*b^2)/(b*d*(a*b^7 + b^8*sin(c + d*x)))","B"
1227,1,254,193,11.458348,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^2)/(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{a^3}{b^5}+\frac{a\,\left(\frac{2}{b^2}-\frac{3\,a^2}{b^4}\right)}{b}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{2}{3\,b^2}-\frac{a^2}{b^4}\right)}{d}+\frac{\sin\left(c+d\,x\right)\,\left(\frac{1}{b^2}+\frac{a^2\,\left(\frac{2}{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{2}{b^2}-\frac{3\,a^2}{b^4}\right)}{b}\right)}{b}\right)}{d}+\frac{{\sin\left(c+d\,x\right)}^5}{5\,b^2\,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^5-8\,a^3\,b^2+2\,a\,b^4\right)}{b^7\,d}-\frac{a^6-2\,a^4\,b^2+a^2\,b^4}{b\,d\,\left(\sin\left(c+d\,x\right)\,b^7+a\,b^6\right)}","Not used",1,"(sin(c + d*x)^2*(a^3/b^5 + (a*(2/b^2 - (3*a^2)/b^4))/b))/d - (sin(c + d*x)^3*(2/(3*b^2) - a^2/b^4))/d + (sin(c + d*x)*(1/b^2 + (a^2*(2/b^2 - (3*a^2)/b^4))/b^2 - (2*a*((2*a^3)/b^5 + (2*a*(2/b^2 - (3*a^2)/b^4))/b))/b))/d + sin(c + d*x)^5/(5*b^2*d) - (a*sin(c + d*x)^4)/(2*b^3*d) - (log(a + b*sin(c + d*x))*(2*a*b^4 + 6*a^5 - 8*a^3*b^2))/(b^7*d) - (a^6 + a^2*b^4 - 2*a^4*b^2)/(b*d*(a*b^6 + b^7*sin(c + d*x)))","B"
1228,1,161,157,0.088450,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x))/(a + b*sin(c + d*x))^2,x)","\frac{\frac{{\sin\left(c+d\,x\right)}^4}{4\,b^2}-{\sin\left(c+d\,x\right)}^2\,\left(\frac{1}{b^2}-\frac{3\,a^2}{2\,b^4}\right)+\sin\left(c+d\,x\right)\,\left(\frac{2\,a^3}{b^5}+\frac{2\,a\,\left(\frac{2}{b^2}-\frac{3\,a^2}{b^4}\right)}{b}\right)-\frac{2\,a\,{\sin\left(c+d\,x\right)}^3}{3\,b^3}+\frac{a^5-2\,a^3\,b^2+a\,b^4}{b\,\left(\sin\left(c+d\,x\right)\,b^6+a\,b^5\right)}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(5\,a^4-6\,a^2\,b^2+b^4\right)}{b^6}}{d}","Not used",1,"(sin(c + d*x)^4/(4*b^2) - sin(c + d*x)^2*(1/b^2 - (3*a^2)/(2*b^4)) + sin(c + d*x)*((2*a^3)/b^5 + (2*a*(2/b^2 - (3*a^2)/b^4))/b) - (2*a*sin(c + d*x)^3)/(3*b^3) + (a*b^4 + a^5 - 2*a^3*b^2)/(b*(a*b^5 + b^6*sin(c + d*x))) + (log(a + b*sin(c + d*x))*(5*a^4 + b^4 - 6*a^2*b^2))/b^6)/d","B"
1229,1,338,120,12.075735,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)*(a + b*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\frac{6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2}+\frac{6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{b^2}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^4-3\,a^2\,b^2+b^4\right)}{a^2\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^4-2\,a^2\,b^2+b^4\right)}{a^2\,b^3}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^4-2\,a^2\,b^2+b^4\right)}{a^2\,b^3}}{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{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(3\,a^2-2\,b^2\right)}{b^4\,d}-\frac{\ln\left(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)\,\left(-3\,a^4+2\,a^2\,b^2+b^4\right)}{a^2\,b^4\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) - ((6*a*tan(c/2 + (d*x)/2)^2)/b^2 + (6*a*tan(c/2 + (d*x)/2)^4)/b^2 + (4*tan(c/2 + (d*x)/2)^3*(3*a^4 + b^4 - 3*a^2*b^2))/(a^2*b^3) + (2*tan(c/2 + (d*x)/2)^5*(3*a^4 + b^4 - 2*a^2*b^2))/(a^2*b^3) + (2*tan(c/2 + (d*x)/2)*(3*a^4 + b^4 - 2*a^2*b^2))/(a^2*b^3))/(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)) - (log(tan(c/2 + (d*x)/2)^2 + 1)*(3*a^2 - 2*b^2))/(b^4*d) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(b^4 - 3*a^4 + 2*a^2*b^2))/(a^2*b^4*d)","B"
1230,1,313,109,12.101391,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^2-b^2\right)}{b}-2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{a\,b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^4-9\,a^2\,b^2+4\,b^4\right)}{a\,b^2}}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,b\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}+\frac{2\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b^3\,d}-\frac{2\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{2\,\ln\left(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)\,\left(a^4-b^4\right)}{a^3\,b^3\,d}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(4*a^2 - b^2))/b - 2*b*tan(c/2 + (d*x)/2) - a + (2*tan(c/2 + (d*x)/2)^2*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(a*b^2) + (tan(c/2 + (d*x)/2)^4*(8*a^4 + 4*b^4 - 9*a^2*b^2))/(a*b^2))/(d*(4*a^3*tan(c/2 + (d*x)/2)^3 + 2*a^3*tan(c/2 + (d*x)/2)^5 + 2*a^3*tan(c/2 + (d*x)/2) + 4*a^2*b*tan(c/2 + (d*x)/2)^2 + 4*a^2*b*tan(c/2 + (d*x)/2)^4)) - tan(c/2 + (d*x)/2)/(2*a^2*d) + (2*a*log(tan(c/2 + (d*x)/2)^2 + 1))/(b^3*d) - (2*b*log(tan(c/2 + (d*x)/2)))/(a^3*d) - (2*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 - b^4))/(a^3*b^3*d)","B"
1231,1,280,131,11.923356,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^3*(a + b*sin(c + d*x))^2),x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{2}-8\,b^2\right)+\frac{a^2}{2}-3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^4-5\,a^2\,b^2+2\,b^4\right)}{a\,b}}{d\,\left(4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,b\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2-3\,b^2\right)}{a^4\,d}+\frac{\ln\left(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)\,\left(a^4+2\,a^2\,b^2-3\,b^4\right)}{a^4\,b^2\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(a^3*d) - (tan(c/2 + (d*x)/2)^2*(a^2/2 - 8*b^2) + a^2/2 - 3*a*b*tan(c/2 + (d*x)/2) + (4*tan(c/2 + (d*x)/2)^3*(2*a^4 + 2*b^4 - 5*a^2*b^2))/(a*b))/(d*(4*a^4*tan(c/2 + (d*x)/2)^2 + 4*a^4*tan(c/2 + (d*x)/2)^4 + 8*a^3*b*tan(c/2 + (d*x)/2)^3)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(b^2*d) - tan(c/2 + (d*x)/2)^2/(8*a^2*d) - (log(tan(c/2 + (d*x)/2))*(2*a^2 - 3*b^2))/(a^4*d) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 - 3*b^4 + 2*a^2*b^2))/(a^4*b^2*d)","B"
1232,1,319,147,11.716712,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^4*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(16\,a^2\,b-24\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a\,b^2-\frac{20\,a^3}{3}\right)-\frac{a^3}{3}+\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(23\,a^4-44\,a^2\,b^2+16\,b^4\right)}{a}}{d\,\left(8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,b\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{\frac{a^2}{4}+\frac{b^2}{2}}{a^4}+\frac{5}{8\,a^2}-\frac{2\,b^2}{a^4}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,a^2\,b-4\,b^3\right)}{a^5\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^3\,d}-\frac{\ln\left(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)\,\left(4\,a^2\,b-4\,b^3\right)}{a^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(16*a^2*b - 24*b^3) - tan(c/2 + (d*x)/2)^2*(8*a*b^2 - (20*a^3)/3) - a^3/3 + (4*a^2*b*tan(c/2 + (d*x)/2))/3 + (tan(c/2 + (d*x)/2)^4*(23*a^4 + 16*b^4 - 44*a^2*b^2))/a)/(d*(8*a^5*tan(c/2 + (d*x)/2)^3 + 8*a^5*tan(c/2 + (d*x)/2)^5 + 16*a^4*b*tan(c/2 + (d*x)/2)^4)) - tan(c/2 + (d*x)/2)^3/(24*a^2*d) + (tan(c/2 + (d*x)/2)*((a^2/4 + b^2/2)/a^4 + 5/(8*a^2) - (2*b^2)/a^4))/d + (log(tan(c/2 + (d*x)/2))*(4*a^2*b - 4*b^3))/(a^5*d) + (b*tan(c/2 + (d*x)/2)^2)/(4*a^3*d) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(4*a^2*b - 4*b^3))/(a^5*d)","B"
1233,1,439,188,11.805119,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^5*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^4-62\,a^2\,b^2+64\,b^4\right)-\frac{a^4}{4}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{11\,a^4}{4}-\frac{10\,a^2\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(20\,a\,b^3-\frac{62\,a^3\,b}{3}\right)-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(60\,a^4\,b-96\,a^2\,b^3+32\,b^5\right)}{a}+\frac{5\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6}}{d\,\left(16\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+32\,b\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{\frac{a^2}{16}+\frac{b^2}{8}}{a^4}+\frac{1}{8\,a^2}-\frac{b^2}{2\,a^4}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b\,\left(32\,a^2+64\,b^2\right)}{64\,a^5}-\frac{b}{4\,a^3}+\frac{4\,b\,\left(\frac{\frac{a^2}{8}+\frac{b^2}{4}}{a^4}+\frac{1}{4\,a^2}-\frac{b^2}{a^4}\right)}{a}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4-6\,a^2\,b^2+5\,b^4\right)}{a^6\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,a^3\,d}-\frac{\ln\left(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)\,\left(a^4-6\,a^2\,b^2+5\,b^4\right)}{a^6\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^4*(3*a^4 + 64*b^4 - 62*a^2*b^2) - a^4/4 + tan(c/2 + (d*x)/2)^2*((11*a^4)/4 - (10*a^2*b^2)/3) + tan(c/2 + (d*x)/2)^3*(20*a*b^3 - (62*a^3*b)/3) - (tan(c/2 + (d*x)/2)^5*(60*a^4*b + 32*b^5 - 96*a^2*b^3))/a + (5*a^3*b*tan(c/2 + (d*x)/2))/6)/(d*(16*a^6*tan(c/2 + (d*x)/2)^4 + 16*a^6*tan(c/2 + (d*x)/2)^6 + 32*a^5*b*tan(c/2 + (d*x)/2)^5)) - tan(c/2 + (d*x)/2)^4/(64*a^2*d) + (tan(c/2 + (d*x)/2)^2*((a^2/16 + b^2/8)/a^4 + 1/(8*a^2) - b^2/(2*a^4)))/d - (tan(c/2 + (d*x)/2)*((b*(32*a^2 + 64*b^2))/(64*a^5) - b/(4*a^3) + (4*b*((a^2/8 + b^2/4)/a^4 + 1/(4*a^2) - b^2/a^4))/a))/d + (log(tan(c/2 + (d*x)/2))*(a^4 + 5*b^4 - 6*a^2*b^2))/(a^6*d) + (b*tan(c/2 + (d*x)/2)^3)/(12*a^3*d) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 + 5*b^4 - 6*a^2*b^2))/(a^6*d)","B"
1234,1,628,226,11.901855,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^6*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{64\,a^2+128\,b^2}{3072\,a^4}+\frac{1}{32\,a^2}-\frac{b^2}{6\,a^4}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b^2}{2\,a^4}-\frac{4\,b\,\left(\frac{b\,\left(64\,a^2+128\,b^2\right)}{256\,a^5}-\frac{b}{8\,a^3}+\frac{4\,b\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{3}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{a}\right)}{a}+\frac{\left(64\,a^2+128\,b^2\right)\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{3}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{32\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{23\,a^4\,b}{3}-8\,a^2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{25\,a^5}{3}-56\,a^3\,b^2+48\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(32\,a^4\,b-184\,a^2\,b^3+160\,b^5\right)+\frac{a^5}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{22\,a^5}{15}-2\,a^3\,b^2\right)-\frac{3\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5\,a^6-74\,a^4\,b^2+104\,a^2\,b^4-32\,b^6\right)}{a}}{d\,\left(32\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+64\,b\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b\,\left(64\,a^2+128\,b^2\right)}{512\,a^5}-\frac{b}{16\,a^3}+\frac{2\,b\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{3}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{a}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^4\,b-8\,a^2\,b^3+6\,b^5\right)}{a^7\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,a^3\,d}+\frac{\ln\left(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)\,\left(2\,a^4\,b-8\,a^2\,b^3+6\,b^5\right)}{a^7\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((64*a^2 + 128*b^2)/(3072*a^4) + 1/(32*a^2) - b^2/(6*a^4)))/d - (tan(c/2 + (d*x)/2)*(b^2/(2*a^4) - (4*b*((b*(64*a^2 + 128*b^2))/(256*a^5) - b/(8*a^3) + (4*b*((64*a^2 + 128*b^2)/(1024*a^4) + 3/(32*a^2) - b^2/(2*a^4)))/a))/a + ((64*a^2 + 128*b^2)*((64*a^2 + 128*b^2)/(1024*a^4) + 3/(32*a^2) - b^2/(2*a^4)))/(32*a^2)))/d - tan(c/2 + (d*x)/2)^5/(160*a^2*d) - (tan(c/2 + (d*x)/2)^3*((23*a^4*b)/3 - 8*a^2*b^3) + tan(c/2 + (d*x)/2)^4*(48*a*b^4 + (25*a^5)/3 - 56*a^3*b^2) + tan(c/2 + (d*x)/2)^5*(32*a^4*b + 160*b^5 - 184*a^2*b^3) + a^5/5 - tan(c/2 + (d*x)/2)^2*((22*a^5)/15 - 2*a^3*b^2) - (3*a^4*b*tan(c/2 + (d*x)/2))/5 + (2*tan(c/2 + (d*x)/2)^6*(5*a^6 - 32*b^6 + 104*a^2*b^4 - 74*a^4*b^2))/a)/(d*(32*a^7*tan(c/2 + (d*x)/2)^5 + 32*a^7*tan(c/2 + (d*x)/2)^7 + 64*a^6*b*tan(c/2 + (d*x)/2)^6)) - (tan(c/2 + (d*x)/2)^2*((b*(64*a^2 + 128*b^2))/(512*a^5) - b/(16*a^3) + (2*b*((64*a^2 + 128*b^2)/(1024*a^4) + 3/(32*a^2) - b^2/(2*a^4)))/a))/d - (log(tan(c/2 + (d*x)/2))*(2*a^4*b + 6*b^5 - 8*a^2*b^3))/(a^7*d) + (b*tan(c/2 + (d*x)/2)^4)/(32*a^3*d) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(2*a^4*b + 6*b^5 - 8*a^2*b^3))/(a^7*d)","B"
1235,1,887,170,18.920862,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^n*(a + b*sin(c + d*x))^2,x)","\frac{\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(n^3+12\,n^2+44\,n+48\right)\,\left(8\,a^2\,n^3+152\,a^2\,n^2+1272\,a^2\,n+4200\,a^2+3\,b^2\,n^3+59\,b^2\,n^2+581\,b^2\,n+525\,b^2\right)\,1{}\mathrm{i}}{64\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(4\,a^2\,n-b^2\,n+28\,a^2-21\,b^2\right)\,\left(n^5+16\,n^4+95\,n^3+260\,n^2+324\,n+144\right)\,1{}\mathrm{i}}{64\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}-\frac{b^2\,{\sin\left(c+d\,x\right)}^n\,\sin\left(7\,c+7\,d\,x\right)\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)\,1{}\mathrm{i}}{64\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(n^4+13\,n^3+56\,n^2+92\,n+48\right)\,\left(12\,a^2\,n^2+184\,a^2\,n+700\,a^2+3\,b^2\,n^2+40\,b^2\,n-35\,b^2\right)\,1{}\mathrm{i}}{64\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{a\,b\,{\sin\left(c+d\,x\right)}^n\,\left(n^6\,1{}\mathrm{i}+n^5\,30{}\mathrm{i}+n^4\,398{}\mathrm{i}+n^3\,2788{}\mathrm{i}+n^2\,10137{}\mathrm{i}+n\,16958{}\mathrm{i}+9240{}\mathrm{i}\right)}{8\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}-\frac{a\,b\,{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(n^6\,1{}\mathrm{i}+n^5\,22{}\mathrm{i}+n^4\,190{}\mathrm{i}+n^3\,820{}\mathrm{i}+n^2\,1849{}\mathrm{i}+n\,2038{}\mathrm{i}+840{}\mathrm{i}\right)}{16\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}-\frac{a\,b\,{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(n^6\,1{}\mathrm{i}+n^5\,30{}\mathrm{i}+n^4\,334{}\mathrm{i}+n^3\,1764{}\mathrm{i}+n^2\,4633{}\mathrm{i}+n\,5694{}\mathrm{i}+2520{}\mathrm{i}\right)}{8\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}-\frac{a\,b\,{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(-n^6\,1{}\mathrm{i}-n^5\,22{}\mathrm{i}-n^4\,62{}\mathrm{i}+n^3\,1228{}\mathrm{i}+n^2\,9159{}\mathrm{i}+n\,20490{}\mathrm{i}+12600{}\mathrm{i}\right)}{16\,d\,\left(n^7\,1{}\mathrm{i}+n^6\,28{}\mathrm{i}+n^5\,322{}\mathrm{i}+n^4\,1960{}\mathrm{i}+n^3\,6769{}\mathrm{i}+n^2\,13132{}\mathrm{i}+n\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}","Not used",1,"(sin(c + d*x)*sin(c + d*x)^n*(44*n + 12*n^2 + n^3 + 48)*(1272*a^2*n + 581*b^2*n + 4200*a^2 + 525*b^2 + 152*a^2*n^2 + 8*a^2*n^3 + 59*b^2*n^2 + 3*b^2*n^3)*1i)/(64*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) + (sin(c + d*x)^n*sin(5*c + 5*d*x)*(4*a^2*n - b^2*n + 28*a^2 - 21*b^2)*(324*n + 260*n^2 + 95*n^3 + 16*n^4 + n^5 + 144)*1i)/(64*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) - (b^2*sin(c + d*x)^n*sin(7*c + 7*d*x)*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)*1i)/(64*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) + (sin(c + d*x)^n*sin(3*c + 3*d*x)*(92*n + 56*n^2 + 13*n^3 + n^4 + 48)*(184*a^2*n + 40*b^2*n + 700*a^2 - 35*b^2 + 12*a^2*n^2 + 3*b^2*n^2)*1i)/(64*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) + (a*b*sin(c + d*x)^n*(n*16958i + n^2*10137i + n^3*2788i + n^4*398i + n^5*30i + n^6*1i + 9240i))/(8*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) - (a*b*sin(c + d*x)^n*cos(6*c + 6*d*x)*(n*2038i + n^2*1849i + n^3*820i + n^4*190i + n^5*22i + n^6*1i + 840i))/(16*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) - (a*b*sin(c + d*x)^n*cos(4*c + 4*d*x)*(n*5694i + n^2*4633i + n^3*1764i + n^4*334i + n^5*30i + n^6*1i + 2520i))/(8*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i)) - (a*b*sin(c + d*x)^n*cos(2*c + 2*d*x)*(n*20490i + n^2*9159i + n^3*1228i - n^4*62i - n^5*22i - n^6*1i + 12600i))/(16*d*(n*13068i + n^2*13132i + n^3*6769i + n^4*1960i + n^5*322i + n^6*28i + n^7*1i + 5040i))","B"
1236,1,550,123,16.337110,"\text{Not used}","int(cos(c + d*x)^5*sin(c + d*x)^n*(a + b*sin(c + d*x)),x)","\frac{b\,{\sin\left(c+d\,x\right)}^n\,\left(n^5+23\,n^4+237\,n^3+1129\,n^2+2234\,n+1320\right)}{16\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{b\,{\sin\left(c+d\,x\right)}^n\,\cos\left(6\,c+6\,d\,x\right)\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{32\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{b\,{\sin\left(c+d\,x\right)}^n\,\cos\left(4\,c+4\,d\,x\right)\,\left(n^5+23\,n^4+173\,n^3+553\,n^2+762\,n+360\right)}{16\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,\sin\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^n\,\left(n^5\,1{}\mathrm{i}+n^4\,24{}\mathrm{i}+n^3\,263{}\mathrm{i}+n^2\,1476{}\mathrm{i}+n\,3876{}\mathrm{i}+3600{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{b\,{\sin\left(c+d\,x\right)}^n\,\cos\left(2\,c+2\,d\,x\right)\,\left(-n^5-15\,n^4+43\,n^3+927\,n^2+2670\,n+1800\right)}{32\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\sin\left(5\,c+5\,d\,x\right)\,\left(n^5\,1{}\mathrm{i}+n^4\,16{}\mathrm{i}+n^3\,95{}\mathrm{i}+n^2\,260{}\mathrm{i}+n\,324{}\mathrm{i}+144{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{a\,{\sin\left(c+d\,x\right)}^n\,\sin\left(3\,c+3\,d\,x\right)\,\left(n^5\,3{}\mathrm{i}+n^4\,64{}\mathrm{i}+n^3\,493{}\mathrm{i}+n^2\,1676{}\mathrm{i}+n\,2444{}\mathrm{i}+1200{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,d\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}","Not used",1,"(b*sin(c + d*x)^n*(2234*n + 1129*n^2 + 237*n^3 + 23*n^4 + n^5 + 1320))/(16*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (b*sin(c + d*x)^n*cos(6*c + 6*d*x)*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(32*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (b*sin(c + d*x)^n*cos(4*c + 4*d*x)*(762*n + 553*n^2 + 173*n^3 + 23*n^4 + n^5 + 360))/(16*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)*sin(c + d*x)^n*(n*3876i + n^2*1476i + n^3*263i + n^4*24i + n^5*1i + 3600i)*1i)/(8*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (b*sin(c + d*x)^n*cos(2*c + 2*d*x)*(2670*n + 927*n^2 + 43*n^3 - 15*n^4 - n^5 + 1800))/(32*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)^n*sin(5*c + 5*d*x)*(n*324i + n^2*260i + n^3*95i + n^4*16i + n^5*1i + 144i)*1i)/(16*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (a*sin(c + d*x)^n*sin(3*c + 3*d*x)*(n*2444i + n^2*1676i + n^3*493i + n^4*64i + n^5*3i + 1200i)*1i)/(16*d*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))","B"
1237,0,-1,167,0.000000,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + b*sin(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^5\,{\sin\left(c+d\,x\right)}^n}{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + b*sin(c + d*x)), x)","F"
1238,0,-1,191,0.000000,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + b*sin(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^5\,{\sin\left(c+d\,x\right)}^n}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^5*sin(c + d*x)^n)/(a + b*sin(c + d*x))^2, x)","F"
1239,1,441,238,15.014194,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^5*(a + b*sin(c + d*x))^2,x)","\frac{5\,a\,b\,x}{512}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(16\,a^2-96\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(\frac{16\,a^2}{3}-32\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{128\,a^2}{3}+192\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{256\,a^2}{63}-\frac{64\,b^2}{21}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{416\,a^2}{231}+\frac{64\,b^2}{77}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{96\,a^2}{7}+\frac{768\,b^2}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{208\,a^2}{693}+\frac{32\,b^2}{231}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{64\,a^2}{21}+\frac{1216\,b^2}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{1376\,a^2}{63}-\frac{512\,b^2}{21}\right)+\frac{32\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}}{3}+\frac{16\,a^2}{693}+\frac{32\,b^2}{3003}+\frac{95\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384}+\frac{277\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}-\frac{4025\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{128}+\frac{59435\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{768}-\frac{16813\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{192}+\frac{16813\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{192}-\frac{59435\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{768}+\frac{4025\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}-\frac{277\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{192}-\frac{95\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{23}}{384}-\frac{5\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{25}}{256}+\frac{5\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{13}}","Not used",1,"(5*a*b*x)/512 - (tan(c/2 + (d*x)/2)^16*(16*a^2 - 96*b^2) - tan(c/2 + (d*x)/2)^18*((16*a^2)/3 - 32*b^2) + tan(c/2 + (d*x)/2)^14*((128*a^2)/3 + 192*b^2) - tan(c/2 + (d*x)/2)^6*((256*a^2)/63 - (64*b^2)/21) + tan(c/2 + (d*x)/2)^4*((416*a^2)/231 + (64*b^2)/77) + tan(c/2 + (d*x)/2)^10*((96*a^2)/7 + (768*b^2)/7) + tan(c/2 + (d*x)/2)^2*((208*a^2)/693 + (32*b^2)/231) - tan(c/2 + (d*x)/2)^12*((64*a^2)/21 + (1216*b^2)/7) + tan(c/2 + (d*x)/2)^8*((1376*a^2)/63 - (512*b^2)/21) + (32*a^2*tan(c/2 + (d*x)/2)^20)/3 + (16*a^2)/693 + (32*b^2)/3003 + (95*a*b*tan(c/2 + (d*x)/2)^3)/384 + (277*a*b*tan(c/2 + (d*x)/2)^5)/192 - (4025*a*b*tan(c/2 + (d*x)/2)^7)/128 + (59435*a*b*tan(c/2 + (d*x)/2)^9)/768 - (16813*a*b*tan(c/2 + (d*x)/2)^11)/192 + (16813*a*b*tan(c/2 + (d*x)/2)^15)/192 - (59435*a*b*tan(c/2 + (d*x)/2)^17)/768 + (4025*a*b*tan(c/2 + (d*x)/2)^19)/128 - (277*a*b*tan(c/2 + (d*x)/2)^21)/192 - (95*a*b*tan(c/2 + (d*x)/2)^23)/384 - (5*a*b*tan(c/2 + (d*x)/2)^25)/256 + (5*a*b*tan(c/2 + (d*x)/2))/256)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^13)","B"
1240,1,207,250,13.554908,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^4*(a + b*sin(c + d*x))^2,x)","\frac{6930\,a^2\,\sin\left(2\,c+2\,d\,x\right)-13860\,a^2\,\sin\left(4\,c+4\,d\,x\right)-3465\,a^2\,\sin\left(6\,c+6\,d\,x\right)+\frac{3465\,a^2\,\sin\left(8\,c+8\,d\,x\right)}{2}+693\,a^2\,\sin\left(10\,c+10\,d\,x\right)-\frac{51975\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{10395\,b^2\,\sin\left(8\,c+8\,d\,x\right)}{8}-\frac{1155\,b^2\,\sin\left(12\,c+12\,d\,x\right)}{8}-69300\,a\,b\,\cos\left(c+d\,x\right)-23100\,a\,b\,\cos\left(3\,c+3\,d\,x\right)+6930\,a\,b\,\cos\left(5\,c+5\,d\,x\right)+4950\,a\,b\,\cos\left(7\,c+7\,d\,x\right)-770\,a\,b\,\cos\left(9\,c+9\,d\,x\right)-630\,a\,b\,\cos\left(11\,c+11\,d\,x\right)+41580\,a^2\,d\,x+17325\,b^2\,d\,x}{3548160\,d}","Not used",1,"(6930*a^2*sin(2*c + 2*d*x) - 13860*a^2*sin(4*c + 4*d*x) - 3465*a^2*sin(6*c + 6*d*x) + (3465*a^2*sin(8*c + 8*d*x))/2 + 693*a^2*sin(10*c + 10*d*x) - (51975*b^2*sin(4*c + 4*d*x))/8 + (10395*b^2*sin(8*c + 8*d*x))/8 - (1155*b^2*sin(12*c + 12*d*x))/8 - 69300*a*b*cos(c + d*x) - 23100*a*b*cos(3*c + 3*d*x) + 6930*a*b*cos(5*c + 5*d*x) + 4950*a*b*cos(7*c + 7*d*x) - 770*a*b*cos(9*c + 9*d*x) - 630*a*b*cos(11*c + 11*d*x) + 41580*a^2*d*x + 17325*b^2*d*x)/(3548160*d)","B"
1241,1,386,187,14.943922,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^3*(a + b*sin(c + d*x))^2,x)","\frac{3\,a\,b\,x}{128}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{4\,a^2}{3}+\frac{32\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(8\,a^2-48\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{64\,a^2}{7}-\frac{48\,b^2}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{32\,a^2}{3}-\frac{80\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{44\,a^2}{63}+\frac{16\,b^2}{63}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{32\,a^2}{63}-\frac{80\,b^2}{63}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{64\,a^2}{3}+\frac{176\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{72\,a^2}{7}+\frac{240\,b^2}{7}\right)+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+\frac{4\,a^2}{63}+\frac{16\,b^2}{693}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{3323\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320}+\frac{108\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}-\frac{841\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{32}+\frac{841\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}-\frac{108\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{5}+\frac{3323\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{320}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{2}-\frac{3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{64}+\frac{3\,a\,b\,\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)}^{11}}","Not used",1,"(3*a*b*x)/128 - (tan(c/2 + (d*x)/2)^16*((4*a^2)/3 + (32*b^2)/3) + tan(c/2 + (d*x)/2)^10*(8*a^2 - 48*b^2) + tan(c/2 + (d*x)/2)^6*((64*a^2)/7 - (48*b^2)/7) + tan(c/2 + (d*x)/2)^14*((32*a^2)/3 - (80*b^2)/3) + tan(c/2 + (d*x)/2)^2*((44*a^2)/63 + (16*b^2)/63) - tan(c/2 + (d*x)/2)^4*((32*a^2)/63 - (80*b^2)/63) + tan(c/2 + (d*x)/2)^12*((64*a^2)/3 + (176*b^2)/3) + tan(c/2 + (d*x)/2)^8*((72*a^2)/7 + (240*b^2)/7) + 4*a^2*tan(c/2 + (d*x)/2)^18 + (4*a^2)/63 + (16*b^2)/693 + (a*b*tan(c/2 + (d*x)/2)^3)/2 - (3323*a*b*tan(c/2 + (d*x)/2)^5)/320 + (108*a*b*tan(c/2 + (d*x)/2)^7)/5 - (841*a*b*tan(c/2 + (d*x)/2)^9)/32 + (841*a*b*tan(c/2 + (d*x)/2)^13)/32 - (108*a*b*tan(c/2 + (d*x)/2)^15)/5 + (3323*a*b*tan(c/2 + (d*x)/2)^17)/320 - (a*b*tan(c/2 + (d*x)/2)^19)/2 - (3*a*b*tan(c/2 + (d*x)/2)^21)/64 + (3*a*b*tan(c/2 + (d*x)/2))/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^11)","B"
1242,1,237,201,11.927603,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)^2*(a + b*sin(c + d*x))^2,x)","\frac{5\,a^2\,x}{128}+\frac{3\,b^2\,x}{256}+\frac{5\,a^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{192\,d}+\frac{a^2\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{48\,d}-\frac{a^2\,{\cos\left(c+d\,x\right)}^7\,\sin\left(c+d\,x\right)}{8\,d}+\frac{b^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{128\,d}+\frac{b^2\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{160\,d}-\frac{11\,b^2\,{\cos\left(c+d\,x\right)}^7\,\sin\left(c+d\,x\right)}{80\,d}+\frac{b^2\,{\cos\left(c+d\,x\right)}^9\,\sin\left(c+d\,x\right)}{10\,d}-\frac{2\,a\,b\,{\cos\left(c+d\,x\right)}^7}{7\,d}+\frac{2\,a\,b\,{\cos\left(c+d\,x\right)}^9}{9\,d}+\frac{5\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{128\,d}+\frac{3\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{256\,d}","Not used",1,"(5*a^2*x)/128 + (3*b^2*x)/256 + (5*a^2*cos(c + d*x)^3*sin(c + d*x))/(192*d) + (a^2*cos(c + d*x)^5*sin(c + d*x))/(48*d) - (a^2*cos(c + d*x)^7*sin(c + d*x))/(8*d) + (b^2*cos(c + d*x)^3*sin(c + d*x))/(128*d) + (b^2*cos(c + d*x)^5*sin(c + d*x))/(160*d) - (11*b^2*cos(c + d*x)^7*sin(c + d*x))/(80*d) + (b^2*cos(c + d*x)^9*sin(c + d*x))/(10*d) - (2*a*b*cos(c + d*x)^7)/(7*d) + (2*a*b*cos(c + d*x)^9)/(9*d) + (5*a^2*cos(c + d*x)*sin(c + d*x))/(128*d) + (3*b^2*cos(c + d*x)*sin(c + d*x))/(256*d)","B"
1243,1,332,152,15.045398,"\text{Not used}","int(cos(c + d*x)^6*sin(c + d*x)*(a + b*sin(c + d*x))^2,x)","\frac{5\,a\,b\,x}{64}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{4\,a^2}{7}+\frac{4\,b^2}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(12\,a^2+12\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(16\,a^2-12\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(12\,a^2-\frac{20\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(20\,a^2+20\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{44\,a^2}{7}-\frac{12\,b^2}{7}\right)+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+\frac{2\,a^2}{7}+\frac{4\,b^2}{63}-\frac{191\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{48}+\frac{83\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{16}-\frac{145\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{145\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{16}-\frac{83\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{16}+\frac{191\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{48}-\frac{5\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{32}+\frac{5\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(5*a*b*x)/64 - (tan(c/2 + (d*x)/2)^14*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^2*((4*a^2)/7 + (4*b^2)/7) + tan(c/2 + (d*x)/2)^6*(12*a^2 + 12*b^2) + tan(c/2 + (d*x)/2)^8*(16*a^2 - 12*b^2) + tan(c/2 + (d*x)/2)^12*(12*a^2 - (20*b^2)/3) + tan(c/2 + (d*x)/2)^10*(20*a^2 + 20*b^2) + tan(c/2 + (d*x)/2)^4*((44*a^2)/7 - (12*b^2)/7) + 2*a^2*tan(c/2 + (d*x)/2)^16 + (2*a^2)/7 + (4*b^2)/63 - (191*a*b*tan(c/2 + (d*x)/2)^3)/48 + (83*a*b*tan(c/2 + (d*x)/2)^5)/16 - (145*a*b*tan(c/2 + (d*x)/2)^7)/16 + (145*a*b*tan(c/2 + (d*x)/2)^11)/16 - (83*a*b*tan(c/2 + (d*x)/2)^13)/16 + (191*a*b*tan(c/2 + (d*x)/2)^15)/48 - (5*a*b*tan(c/2 + (d*x)/2)^17)/32 + (5*a*b*tan(c/2 + (d*x)/2))/32)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
1244,1,415,157,13.710496,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(6\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{146\,a^2}{3}-10\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{202\,a^2}{5}-6\,b^2\right)+\frac{232\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{176\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+24\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{46\,a^2}{15}-\frac{2\,b^2}{7}+\frac{7\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{85\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}-\frac{85\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}-\frac{7\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}-\frac{11\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+\frac{11\,a\,b\,\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)}^{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{5\,a\,b\,\mathrm{atan}\left(\frac{25\,a^2\,b^2}{16\,\left(\frac{5\,a^3\,b}{2}-\frac{25\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{5\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{5\,a^3\,b}{2}-\frac{25\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (tan(c/2 + (d*x)/2)^12*(6*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^8*((146*a^2)/3 - 10*b^2) + tan(c/2 + (d*x)/2)^4*((202*a^2)/5 - 6*b^2) + (232*a^2*tan(c/2 + (d*x)/2)^2)/15 + (176*a^2*tan(c/2 + (d*x)/2)^6)/3 + 24*a^2*tan(c/2 + (d*x)/2)^10 + (46*a^2)/15 - (2*b^2)/7 + (7*a*b*tan(c/2 + (d*x)/2)^3)/3 + (85*a*b*tan(c/2 + (d*x)/2)^5)/12 - (85*a*b*tan(c/2 + (d*x)/2)^9)/12 - (7*a*b*tan(c/2 + (d*x)/2)^11)/3 - (11*a*b*tan(c/2 + (d*x)/2)^13)/4 + (11*a*b*tan(c/2 + (d*x)/2))/4)/(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)) + (5*a*b*atan((25*a^2*b^2)/(16*((5*a^3*b)/2 - (25*a^2*b^2*tan(c/2 + (d*x)/2))/16)) + (5*a^3*b*tan(c/2 + (d*x)/2))/(2*((5*a^3*b)/2 - (25*a^2*b^2*tan(c/2 + (d*x)/2))/16))))/(4*d)","B"
1245,1,683,178,11.894070,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{7\,a^2}{2}+\frac{5\,b^2}{12}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(10\,a^2+\frac{15\,b^2}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{7\,a^2}{2}-\frac{11\,b^2}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{21\,a^2}{2}-\frac{11\,b^2}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(25\,a^2-\frac{15\,b^2}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{49\,a^2}{2}+\frac{5\,b^2}{12}\right)-a^2+\frac{248\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{5}+112\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{368\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+72\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\frac{184\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+30\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+30\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{\mathrm{atan}\left(\frac{\left(\frac{a^2\,15{}\mathrm{i}}{8}-\frac{b^2\,5{}\mathrm{i}}{16}\right)\,\left(\frac{5\,b^2}{8}-\frac{15\,a^2}{4}+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,15{}\mathrm{i}}{8}-\frac{b^2\,5{}\mathrm{i}}{16}\right)+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,1{}\mathrm{i}-\left(\frac{a^2\,15{}\mathrm{i}}{8}-\frac{b^2\,5{}\mathrm{i}}{16}\right)\,\left(\frac{15\,a^2}{4}-\frac{5\,b^2}{8}+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,15{}\mathrm{i}}{8}-\frac{b^2\,5{}\mathrm{i}}{16}\right)-4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,1{}\mathrm{i}}{\left(\frac{a^2\,15{}\mathrm{i}}{8}-\frac{b^2\,5{}\mathrm{i}}{16}\right)\,\left(\frac{5\,b^2}{8}-\frac{15\,a^2}{4}+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,15{}\mathrm{i}}{8}-\frac{b^2\,5{}\mathrm{i}}{16}\right)+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\left(\frac{a^2\,15{}\mathrm{i}}{8}-\frac{b^2\,5{}\mathrm{i}}{16}\right)\,\left(\frac{15\,a^2}{4}-\frac{5\,b^2}{8}+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,15{}\mathrm{i}}{8}-\frac{b^2\,5{}\mathrm{i}}{16}\right)-4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\frac{5\,a\,b^3}{2}-15\,a^3\,b+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{225\,a^4}{16}-\frac{75\,a^2\,b^2}{16}+\frac{25\,b^4}{64}\right)}\right)\,\left(\frac{15\,a^2}{4}-\frac{5\,b^2}{8}\right)}{d}+\frac{2\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^10*((7*a^2)/2 + (5*b^2)/12) - tan(c/2 + (d*x)/2)^8*(10*a^2 + (15*b^2)/2) + tan(c/2 + (d*x)/2)^12*((7*a^2)/2 - (11*b^2)/4) - tan(c/2 + (d*x)/2)^2*((21*a^2)/2 - (11*b^2)/4) - tan(c/2 + (d*x)/2)^6*(25*a^2 - (15*b^2)/2) - tan(c/2 + (d*x)/2)^4*((49*a^2)/2 + (5*b^2)/12) - a^2 + (248*a*b*tan(c/2 + (d*x)/2)^3)/5 + 112*a*b*tan(c/2 + (d*x)/2)^5 + (368*a*b*tan(c/2 + (d*x)/2)^7)/3 + 72*a*b*tan(c/2 + (d*x)/2)^9 + 24*a*b*tan(c/2 + (d*x)/2)^11 + (184*a*b*tan(c/2 + (d*x)/2))/15)/(d*(2*tan(c/2 + (d*x)/2) + 12*tan(c/2 + (d*x)/2)^3 + 30*tan(c/2 + (d*x)/2)^5 + 40*tan(c/2 + (d*x)/2)^7 + 30*tan(c/2 + (d*x)/2)^9 + 12*tan(c/2 + (d*x)/2)^11 + 2*tan(c/2 + (d*x)/2)^13)) + (a^2*tan(c/2 + (d*x)/2))/(2*d) - (atan((((a^2*15i)/8 - (b^2*5i)/16)*((5*b^2)/8 - (15*a^2)/4 + 6*tan(c/2 + (d*x)/2)*((a^2*15i)/8 - (b^2*5i)/16) + 4*a*b*tan(c/2 + (d*x)/2))*1i - ((a^2*15i)/8 - (b^2*5i)/16)*((15*a^2)/4 - (5*b^2)/8 + 6*tan(c/2 + (d*x)/2)*((a^2*15i)/8 - (b^2*5i)/16) - 4*a*b*tan(c/2 + (d*x)/2))*1i)/(((a^2*15i)/8 - (b^2*5i)/16)*((5*b^2)/8 - (15*a^2)/4 + 6*tan(c/2 + (d*x)/2)*((a^2*15i)/8 - (b^2*5i)/16) + 4*a*b*tan(c/2 + (d*x)/2)) + ((a^2*15i)/8 - (b^2*5i)/16)*((15*a^2)/4 - (5*b^2)/8 + 6*tan(c/2 + (d*x)/2)*((a^2*15i)/8 - (b^2*5i)/16) - 4*a*b*tan(c/2 + (d*x)/2)) + (5*a*b^3)/2 - 15*a^3*b + 2*tan(c/2 + (d*x)/2)*((225*a^4)/16 + (25*b^4)/64 - (75*a^2*b^2)/16)))*((15*a^2)/4 - (5*b^2)/8))/d + (2*a*b*log(tan(c/2 + (d*x)/2)))/d","B"
1246,1,484,180,11.756609,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^3,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{5\,a^2}{2}-b^2\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{49\,a^2}{2}-24\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{165\,a^2}{2}-48\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{127\,a^2}{6}-\frac{184\,b^2}{15}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{223\,a^2}{3}-\frac{112\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{335\,a^2}{3}-\frac{224\,b^2}{3}\right)+\frac{a^2}{2}+38\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+60\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+40\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-14\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{15\,a\,b\,\mathrm{atan}\left(\frac{225\,a^2\,b^2}{4\,\left(-\frac{75\,a^3\,b}{2}+\frac{225\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2}{4}+15\,a\,b^3\right)}-\frac{15\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-\frac{75\,a^3\,b}{2}+\frac{225\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2}{4}+15\,a\,b^3}+\frac{75\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(-\frac{75\,a^3\,b}{2}+\frac{225\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2}{4}+15\,a\,b^3\right)}\right)}{2\,d}+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (log(tan(c/2 + (d*x)/2))*((5*a^2)/2 - b^2))/d - (tan(c/2 + (d*x)/2)^10*((49*a^2)/2 - 24*b^2) + tan(c/2 + (d*x)/2)^8*((165*a^2)/2 - 48*b^2) + tan(c/2 + (d*x)/2)^2*((127*a^2)/6 - (184*b^2)/15) + tan(c/2 + (d*x)/2)^4*((223*a^2)/3 - (112*b^2)/3) + tan(c/2 + (d*x)/2)^6*((335*a^2)/3 - (224*b^2)/3) + a^2/2 + 38*a*b*tan(c/2 + (d*x)/2)^3 + 60*a*b*tan(c/2 + (d*x)/2)^5 + 40*a*b*tan(c/2 + (d*x)/2)^7 - 14*a*b*tan(c/2 + (d*x)/2)^11 + 4*a*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 20*tan(c/2 + (d*x)/2)^4 + 40*tan(c/2 + (d*x)/2)^6 + 40*tan(c/2 + (d*x)/2)^8 + 20*tan(c/2 + (d*x)/2)^10 + 4*tan(c/2 + (d*x)/2)^12)) + (15*a*b*atan((225*a^2*b^2)/(4*(15*a*b^3 - (75*a^3*b)/2 + (225*a^2*b^2*tan(c/2 + (d*x)/2))/4)) - (15*a*b^3*tan(c/2 + (d*x)/2))/(15*a*b^3 - (75*a^3*b)/2 + (225*a^2*b^2*tan(c/2 + (d*x)/2))/4) + (75*a^3*b*tan(c/2 + (d*x)/2))/(2*(15*a*b^3 - (75*a^3*b)/2 + (225*a^2*b^2*tan(c/2 + (d*x)/2))/4))))/(2*d) + (a*b*tan(c/2 + (d*x)/2))/d","B"
1247,1,665,177,12.095928,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^4,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{\frac{a^2}{3}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(42\,a^2-34\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{83\,a^2}{3}-14\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{182\,a^2}{3}-26\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{23\,a^2}{3}-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^2+14\,b^2\right)+\frac{248\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{644\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+232\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+98\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,a^2}{8}-\frac{b^2}{2}\right)}{d}+\frac{\mathrm{atan}\left(\frac{\left(\frac{a^2\,5{}\mathrm{i}}{2}-\frac{b^2\,15{}\mathrm{i}}{8}\right)\,\left(\frac{15\,b^2}{4}-5\,a^2+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,5{}\mathrm{i}}{2}-\frac{b^2\,15{}\mathrm{i}}{8}\right)+10\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,1{}\mathrm{i}-\left(\frac{a^2\,5{}\mathrm{i}}{2}-\frac{b^2\,15{}\mathrm{i}}{8}\right)\,\left(5\,a^2-\frac{15\,b^2}{4}+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,5{}\mathrm{i}}{2}-\frac{b^2\,15{}\mathrm{i}}{8}\right)-10\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,1{}\mathrm{i}}{\left(\frac{a^2\,5{}\mathrm{i}}{2}-\frac{b^2\,15{}\mathrm{i}}{8}\right)\,\left(\frac{15\,b^2}{4}-5\,a^2+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,5{}\mathrm{i}}{2}-\frac{b^2\,15{}\mathrm{i}}{8}\right)+10\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\left(\frac{a^2\,5{}\mathrm{i}}{2}-\frac{b^2\,15{}\mathrm{i}}{8}\right)\,\left(5\,a^2-\frac{15\,b^2}{4}+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2\,5{}\mathrm{i}}{2}-\frac{b^2\,15{}\mathrm{i}}{8}\right)-10\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\frac{75\,a\,b^3}{2}-50\,a^3\,b+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^4-\frac{75\,a^2\,b^2}{2}+\frac{225\,b^4}{16}\right)}\right)\,\left(5\,a^2-\frac{15\,b^2}{4}\right)}{d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{5\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (a^2/3 - tan(c/2 + (d*x)/2)^4*(42*a^2 - 34*b^2) - tan(c/2 + (d*x)/2)^8*((83*a^2)/3 - 14*b^2) - tan(c/2 + (d*x)/2)^6*((182*a^2)/3 - 26*b^2) - tan(c/2 + (d*x)/2)^2*((23*a^2)/3 - 4*b^2) - tan(c/2 + (d*x)/2)^10*(a^2 + 14*b^2) + (248*a*b*tan(c/2 + (d*x)/2)^3)/3 + (644*a*b*tan(c/2 + (d*x)/2)^5)/3 + 232*a*b*tan(c/2 + (d*x)/2)^7 + 98*a*b*tan(c/2 + (d*x)/2)^9 + 2*a*b*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 32*tan(c/2 + (d*x)/2)^5 + 48*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9 + 8*tan(c/2 + (d*x)/2)^11)) - (tan(c/2 + (d*x)/2)*((9*a^2)/8 - b^2/2))/d + (atan((((a^2*5i)/2 - (b^2*15i)/8)*((15*b^2)/4 - 5*a^2 + 6*tan(c/2 + (d*x)/2)*((a^2*5i)/2 - (b^2*15i)/8) + 10*a*b*tan(c/2 + (d*x)/2))*1i - ((a^2*5i)/2 - (b^2*15i)/8)*(5*a^2 - (15*b^2)/4 + 6*tan(c/2 + (d*x)/2)*((a^2*5i)/2 - (b^2*15i)/8) - 10*a*b*tan(c/2 + (d*x)/2))*1i)/(((a^2*5i)/2 - (b^2*15i)/8)*((15*b^2)/4 - 5*a^2 + 6*tan(c/2 + (d*x)/2)*((a^2*5i)/2 - (b^2*15i)/8) + 10*a*b*tan(c/2 + (d*x)/2)) + ((a^2*5i)/2 - (b^2*15i)/8)*(5*a^2 - (15*b^2)/4 + 6*tan(c/2 + (d*x)/2)*((a^2*5i)/2 - (b^2*15i)/8) - 10*a*b*tan(c/2 + (d*x)/2)) + (75*a*b^3)/2 - 50*a^3*b + 2*tan(c/2 + (d*x)/2)*(25*a^4 + (225*b^4)/16 - (75*a^2*b^2)/2)))*(5*a^2 - (15*b^2)/4))/d + (a*b*tan(c/2 + (d*x)/2)^2)/(4*d) - (5*a*b*log(tan(c/2 + (d*x)/2)))/d","B"
1248,1,479,174,11.742878,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^5,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{15\,a^2}{8}-\frac{5\,b^2}{2}\right)}{d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{13\,a^2}{4}-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(36\,a^2-98\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{173\,a^2}{4}-\frac{242\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{303\,a^2}{4}-134\,b^2\right)-\frac{a^2}{4}+32\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+136\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{320\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{4}-\frac{b^2}{8}\right)}{d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,d}-\frac{10\,a\,b\,\mathrm{atan}\left(\frac{100\,a^2\,b^2}{-\frac{75\,a^3\,b}{2}+100\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+50\,a\,b^3}-\frac{50\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-\frac{75\,a^3\,b}{2}+100\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+50\,a\,b^3}+\frac{75\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(-\frac{75\,a^3\,b}{2}+100\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+50\,a\,b^3\right)}\right)}{d}-\frac{9\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2))*((15*a^2)/8 - (5*b^2)/2))/d + (a^2*tan(c/2 + (d*x)/2)^4)/(64*d) + (tan(c/2 + (d*x)/2)^2*((13*a^2)/4 - 2*b^2) + tan(c/2 + (d*x)/2)^8*(36*a^2 - 98*b^2) + tan(c/2 + (d*x)/2)^4*((173*a^2)/4 - (242*b^2)/3) + tan(c/2 + (d*x)/2)^6*((303*a^2)/4 - 134*b^2) - a^2/4 + 32*a*b*tan(c/2 + (d*x)/2)^3 + 136*a*b*tan(c/2 + (d*x)/2)^5 + (320*a*b*tan(c/2 + (d*x)/2)^7)/3 + 4*a*b*tan(c/2 + (d*x)/2)^9 - (4*a*b*tan(c/2 + (d*x)/2))/3)/(d*(16*tan(c/2 + (d*x)/2)^4 + 48*tan(c/2 + (d*x)/2)^6 + 48*tan(c/2 + (d*x)/2)^8 + 16*tan(c/2 + (d*x)/2)^10)) - (tan(c/2 + (d*x)/2)^2*(a^2/4 - b^2/8))/d + (a*b*tan(c/2 + (d*x)/2)^3)/(12*d) - (10*a*b*atan((100*a^2*b^2)/(50*a*b^3 - (75*a^3*b)/2 + 100*a^2*b^2*tan(c/2 + (d*x)/2)) - (50*a*b^3*tan(c/2 + (d*x)/2))/(50*a*b^3 - (75*a^3*b)/2 + 100*a^2*b^2*tan(c/2 + (d*x)/2)) + (75*a^3*b*tan(c/2 + (d*x)/2))/(2*(50*a*b^3 - (75*a^3*b)/2 + 100*a^2*b^2*tan(c/2 + (d*x)/2)))))/d - (9*a*b*tan(c/2 + (d*x)/2))/(4*d)","B"
1249,1,888,202,16.040125,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^6,x)","\frac{\frac{95\,b^2\,\cos\left(c+d\,x\right)}{384}-\frac{5\,a^2\,\cos\left(c+d\,x\right)}{24}+\frac{5\,a^2\,\cos\left(3\,c+3\,d\,x\right)}{48}-\frac{23\,a^2\,\cos\left(5\,c+5\,d\,x\right)}{240}-\frac{163\,b^2\,\cos\left(3\,c+3\,d\,x\right)}{384}+\frac{71\,b^2\,\cos\left(5\,c+5\,d\,x\right)}{384}-\frac{b^2\,\cos\left(7\,c+7\,d\,x\right)}{128}+\frac{5\,a^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{8}-\frac{a^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(5\,c+5\,d\,x\right)}{8}-\frac{25\,b^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{16}+\frac{5\,b^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(5\,c+5\,d\,x\right)}{16}+\frac{5\,a\,b\,\sin\left(c+d\,x\right)}{4}-\frac{5\,a^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{4}+\frac{25\,b^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{8}+\frac{5\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{8}-\frac{5\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{8}-\frac{17\,a\,b\,\sin\left(4\,c+4\,d\,x\right)}{32}+\frac{a\,b\,\sin\left(5\,c+5\,d\,x\right)}{8}+\frac{a\,b\,\sin\left(6\,c+6\,d\,x\right)}{16}+\frac{75\,a\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{32}-\frac{75\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{64}+\frac{15\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(5\,c+5\,d\,x\right)}{64}}{d\,{\sin\left(c+d\,x\right)}^5}","Not used",1,"((95*b^2*cos(c + d*x))/384 - (5*a^2*cos(c + d*x))/24 + (5*a^2*cos(3*c + 3*d*x))/48 - (23*a^2*cos(5*c + 5*d*x))/240 - (163*b^2*cos(3*c + 3*d*x))/384 + (71*b^2*cos(5*c + 5*d*x))/384 - (b^2*cos(7*c + 7*d*x))/128 + (5*a^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/8 - (a^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(5*c + 5*d*x))/8 - (25*b^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/16 + (5*b^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(5*c + 5*d*x))/16 + (5*a*b*sin(c + d*x))/4 - (5*a^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(c + d*x))/4 + (25*b^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(c + d*x))/8 + (5*a*b*sin(2*c + 2*d*x))/8 - (5*a*b*sin(3*c + 3*d*x))/8 - (17*a*b*sin(4*c + 4*d*x))/32 + (a*b*sin(5*c + 5*d*x))/8 + (a*b*sin(6*c + 6*d*x))/16 + (75*a*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/32 - (75*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/64 + (15*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(5*c + 5*d*x))/64)/(d*sin(c + d*x)^5)","B"
1250,1,985,175,15.062353,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^7,x)","\frac{5\,a^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-5\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-40\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+180\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+225\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-225\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-180\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+40\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+30\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-450\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-480\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4320\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+450\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-30\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+24\,a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-24\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-600\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-600\,a^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3600\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+3600\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-256\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+2360\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-2360\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+256\,a\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+7680\,a\,b\,\mathrm{atan}\left(\frac{5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+32\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-30\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+32\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+30\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+7680\,a\,b\,\mathrm{atan}\left(\frac{5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+32\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-30\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+32\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+30\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{1920\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}","Not used",1,"(5*a^2*sin(c/2 + (d*x)/2)^14 - 5*a^2*cos(c/2 + (d*x)/2)^14 - 40*a^2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 + 180*a^2*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 + 225*a^2*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 - 225*a^2*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 - 180*a^2*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 + 40*a^2*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 30*b^2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 450*b^2*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 - 480*b^2*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 4320*b^2*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 450*b^2*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 - 30*b^2*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 24*a*b*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 - 24*a*b*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) - 600*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 - 600*a^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 3600*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 3600*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 - 256*a*b*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 + 2360*a*b*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 - 2360*a*b*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 + 256*a*b*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 + 7680*a*b*atan((5*a^2*sin(c/2 + (d*x)/2) - 30*b^2*sin(c/2 + (d*x)/2) + 32*a*b*cos(c/2 + (d*x)/2))/(30*b^2*cos(c/2 + (d*x)/2) - 5*a^2*cos(c/2 + (d*x)/2) + 32*a*b*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 7680*a*b*atan((5*a^2*sin(c/2 + (d*x)/2) - 30*b^2*sin(c/2 + (d*x)/2) + 32*a*b*cos(c/2 + (d*x)/2))/(30*b^2*cos(c/2 + (d*x)/2) - 5*a^2*cos(c/2 + (d*x)/2) + 32*a*b*sin(c/2 + (d*x)/2)))*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6)/(1920*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6*(cos(c/2 + (d*x)/2)^2 + sin(c/2 + (d*x)/2)^2))","B"
1251,1,379,158,11.871304,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^8,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,d}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{4\,b^4}{\frac{5\,a\,b^3}{2}-4\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{5\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{5\,a\,b^3}{2}-4\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,a^2}{128}-\frac{11\,b^2}{16}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^2-\frac{28\,b^2}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5\,a^2-88\,b^2\right)+\frac{a^2}{7}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2-\frac{4\,b^2}{5}\right)-6\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+30\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{128\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{3\,a^2}{128}-\frac{7\,b^2}{96}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{a^2}{128}-\frac{b^2}{160}\right)}{d}+\frac{15\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}-\frac{3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}-\frac{5\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^7)/(896*d) - (2*b^2*atan((4*b^4)/((5*a*b^3)/2 - 4*b^4*tan(c/2 + (d*x)/2)) + (5*a*b^3*tan(c/2 + (d*x)/2))/(2*((5*a*b^3)/2 - 4*b^4*tan(c/2 + (d*x)/2)))))/d - (tan(c/2 + (d*x)/2)*((5*a^2)/128 - (11*b^2)/16))/d - (tan(c/2 + (d*x)/2)^4*(3*a^2 - (28*b^2)/3) - tan(c/2 + (d*x)/2)^6*(5*a^2 - 88*b^2) + a^2/7 - tan(c/2 + (d*x)/2)^2*(a^2 - (4*b^2)/5) - 6*a*b*tan(c/2 + (d*x)/2)^3 + 30*a*b*tan(c/2 + (d*x)/2)^5 + (2*a*b*tan(c/2 + (d*x)/2))/3)/(128*d*tan(c/2 + (d*x)/2)^7) + (tan(c/2 + (d*x)/2)^3*((3*a^2)/128 - (7*b^2)/96))/d - (tan(c/2 + (d*x)/2)^5*(a^2/128 - b^2/160))/d + (15*a*b*tan(c/2 + (d*x)/2)^2)/(64*d) - (3*a*b*tan(c/2 + (d*x)/2)^4)/(64*d) + (a*b*tan(c/2 + (d*x)/2)^6)/(192*d) - (5*a*b*log(tan(c/2 + (d*x)/2)))/(8*d)","B"
1252,1,343,159,12.689298,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^9,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{5\,a^2}{128}+\frac{5\,b^2}{16}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2+30\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{2\,a^2}{3}-\frac{2\,b^2}{3}\right)+\frac{a^2}{8}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-6\,b^2\right)-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-20\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{7}\right)}{256\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{128}+\frac{15\,b^2}{128}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{256}-\frac{3\,b^2}{128}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^2}{384}-\frac{b^2}{384}\right)}{d}+\frac{3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64\,d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{448\,d}-\frac{5\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^8)/(2048*d) - (log(tan(c/2 + (d*x)/2))*((5*a^2)/128 + (5*b^2)/16))/d - (cot(c/2 + (d*x)/2)^8*(tan(c/2 + (d*x)/2)^6*(2*a^2 + 30*b^2) - tan(c/2 + (d*x)/2)^2*((2*a^2)/3 - (2*b^2)/3) + a^2/8 + tan(c/2 + (d*x)/2)^4*(a^2 - 6*b^2) - 4*a*b*tan(c/2 + (d*x)/2)^3 + 12*a*b*tan(c/2 + (d*x)/2)^5 - 20*a*b*tan(c/2 + (d*x)/2)^7 + (4*a*b*tan(c/2 + (d*x)/2))/7))/(256*d) + (tan(c/2 + (d*x)/2)^2*(a^2/128 + (15*b^2)/128))/d + (tan(c/2 + (d*x)/2)^4*(a^2/256 - (3*b^2)/128))/d - (tan(c/2 + (d*x)/2)^6*(a^2/384 - b^2/384))/d + (3*a*b*tan(c/2 + (d*x)/2)^3)/(64*d) - (a*b*tan(c/2 + (d*x)/2)^5)/(64*d) + (a*b*tan(c/2 + (d*x)/2)^7)/(448*d) - (5*a*b*tan(c/2 + (d*x)/2))/(64*d)","B"
1253,1,373,151,11.863935,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^10,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4608\,d}-\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a^2}{256}+\frac{5\,b^2}{128}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{8\,a^2}{3}+12\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a^2}{7}-\frac{4\,b^2}{7}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(6\,a^2+20\,b^2\right)-4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{a^2}{9}-\frac{8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{512\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2}{192}+\frac{3\,b^2}{128}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{3\,a^2}{3584}-\frac{b^2}{896}\right)}{d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{1024\,d}-\frac{5\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^9)/(4608*d) - (b^2*tan(c/2 + (d*x)/2)^5)/(128*d) - (tan(c/2 + (d*x)/2)*((3*a^2)/256 + (5*b^2)/128))/d - (cot(c/2 + (d*x)/2)^9*(tan(c/2 + (d*x)/2)^6*((8*a^2)/3 + 12*b^2) - tan(c/2 + (d*x)/2)^2*((3*a^2)/7 - (4*b^2)/7) - tan(c/2 + (d*x)/2)^8*(6*a^2 + 20*b^2) - 4*b^2*tan(c/2 + (d*x)/2)^4 + a^2/9 - (8*a*b*tan(c/2 + (d*x)/2)^3)/3 + 4*a*b*tan(c/2 + (d*x)/2)^5 + 8*a*b*tan(c/2 + (d*x)/2)^7 + (a*b*tan(c/2 + (d*x)/2))/2))/(512*d) + (tan(c/2 + (d*x)/2)^3*(a^2/192 + (3*b^2)/128))/d - (tan(c/2 + (d*x)/2)^7*((3*a^2)/3584 - b^2/896))/d + (a*b*tan(c/2 + (d*x)/2)^2)/(64*d) + (a*b*tan(c/2 + (d*x)/2)^4)/(128*d) - (a*b*tan(c/2 + (d*x)/2)^6)/(192*d) + (a*b*tan(c/2 + (d*x)/2)^8)/(1024*d) - (5*a*b*log(tan(c/2 + (d*x)/2)))/(64*d)","B"
1254,1,394,210,11.934457,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^11,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{10240\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^2}{256}+\frac{5\,b^2}{128}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2+4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{4}-\frac{b^2}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{2}+\frac{8\,b^2}{3}\right)+\frac{a^2}{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2+8\,b^2\right)-\frac{12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{7}+\frac{32\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-24\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9}\right)}{1024\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{512}+\frac{b^2}{256}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{1024}+\frac{b^2}{128}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^2}{2048}+\frac{b^2}{384}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^2}{4096}-\frac{b^2}{2048}\right)}{d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{1792\,d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2304\,d}-\frac{3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^10)/(10240*d) - (log(tan(c/2 + (d*x)/2))*((3*a^2)/256 + (5*b^2)/128))/d - (cot(c/2 + (d*x)/2)^10*(tan(c/2 + (d*x)/2)^6*(2*a^2 + 4*b^2) - tan(c/2 + (d*x)/2)^2*(a^2/4 - b^2/2) - tan(c/2 + (d*x)/2)^4*(a^2/2 + (8*b^2)/3) + a^2/10 + tan(c/2 + (d*x)/2)^8*(a^2 + 8*b^2) - (12*a*b*tan(c/2 + (d*x)/2)^3)/7 + (32*a*b*tan(c/2 + (d*x)/2)^7)/3 - 24*a*b*tan(c/2 + (d*x)/2)^9 + (4*a*b*tan(c/2 + (d*x)/2))/9))/(1024*d) + (tan(c/2 + (d*x)/2)^4*(a^2/512 + b^2/256))/d + (tan(c/2 + (d*x)/2)^2*(a^2/1024 + b^2/128))/d - (tan(c/2 + (d*x)/2)^6*(a^2/2048 + b^2/384))/d - (tan(c/2 + (d*x)/2)^8*(a^2/4096 - b^2/2048))/d + (a*b*tan(c/2 + (d*x)/2)^3)/(96*d) - (3*a*b*tan(c/2 + (d*x)/2)^7)/(1792*d) + (a*b*tan(c/2 + (d*x)/2)^9)/(2304*d) - (3*a*b*tan(c/2 + (d*x)/2))/(128*d)","B"
1255,1,448,198,16.331591,"\text{Not used}","int((cos(c + d*x)^6*(a + b*sin(c + d*x))^2)/sin(c + d*x)^12,x)","-\frac{\frac{5\,a^2\,\cos\left(c+d\,x\right)}{96}+\frac{5\,b^2\,\cos\left(c+d\,x\right)}{768}+\frac{5\,a^2\,\cos\left(3\,c+3\,d\,x\right)}{168}+\frac{23\,a^2\,\cos\left(5\,c+5\,d\,x\right)}{2688}+\frac{5\,a^2\,\cos\left(7\,c+7\,d\,x\right)}{8064}-\frac{a^2\,\cos\left(9\,c+9\,d\,x\right)}{8064}+\frac{a^2\,\cos\left(11\,c+11\,d\,x\right)}{88704}-\frac{b^2\,\cos\left(3\,c+3\,d\,x\right)}{5376}-\frac{41\,b^2\,\cos\left(5\,c+5\,d\,x\right)}{10752}-\frac{71\,b^2\,\cos\left(7\,c+7\,d\,x\right)}{32256}-\frac{11\,b^2\,\cos\left(9\,c+9\,d\,x\right)}{32256}+\frac{b^2\,\cos\left(11\,c+11\,d\,x\right)}{32256}+\frac{841\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{32768}+\frac{27\,a\,b\,\sin\left(4\,c+4\,d\,x\right)}{1280}+\frac{3323\,a\,b\,\sin\left(6\,c+6\,d\,x\right)}{327680}+\frac{a\,b\,\sin\left(8\,c+8\,d\,x\right)}{2048}-\frac{3\,a\,b\,\sin\left(10\,c+10\,d\,x\right)}{65536}+\frac{693\,a\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{65536}-\frac{495\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{65536}+\frac{495\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(5\,c+5\,d\,x\right)}{131072}-\frac{165\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(7\,c+7\,d\,x\right)}{131072}+\frac{33\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(9\,c+9\,d\,x\right)}{131072}-\frac{3\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(11\,c+11\,d\,x\right)}{131072}}{d\,{\sin\left(c+d\,x\right)}^{11}}","Not used",1,"-((5*a^2*cos(c + d*x))/96 + (5*b^2*cos(c + d*x))/768 + (5*a^2*cos(3*c + 3*d*x))/168 + (23*a^2*cos(5*c + 5*d*x))/2688 + (5*a^2*cos(7*c + 7*d*x))/8064 - (a^2*cos(9*c + 9*d*x))/8064 + (a^2*cos(11*c + 11*d*x))/88704 - (b^2*cos(3*c + 3*d*x))/5376 - (41*b^2*cos(5*c + 5*d*x))/10752 - (71*b^2*cos(7*c + 7*d*x))/32256 - (11*b^2*cos(9*c + 9*d*x))/32256 + (b^2*cos(11*c + 11*d*x))/32256 + (841*a*b*sin(2*c + 2*d*x))/32768 + (27*a*b*sin(4*c + 4*d*x))/1280 + (3323*a*b*sin(6*c + 6*d*x))/327680 + (a*b*sin(8*c + 8*d*x))/2048 - (3*a*b*sin(10*c + 10*d*x))/65536 + (693*a*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/65536 - (495*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/65536 + (495*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(5*c + 5*d*x))/131072 - (165*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(7*c + 7*d*x))/131072 + (33*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(9*c + 9*d*x))/131072 - (3*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(11*c + 11*d*x))/131072)/(d*sin(c + d*x)^11)","B"
1256,1,3724,525,18.113103,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^3)/(a + b*sin(c + d*x))^2,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(32\,a^7-44\,a^5\,b^2+4\,a^3\,b^4+7\,a\,b^6\right)}{2\,b^8}-\frac{2\,\left(-840\,a^7+1435\,a^5\,b^2-588\,a^3\,b^4+15\,a\,b^6\right)}{105\,b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(168\,a^7-255\,a^5\,b^2+72\,a^3\,b^4+4\,a\,b^6\right)}{3\,b^8}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-840\,a^7+1435\,a^5\,b^2-588\,a^3\,b^4+15\,a\,b^6\right)}{3\,b^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(2016\,a^7-3284\,a^5\,b^2+1212\,a^3\,b^4+25\,a\,b^6\right)}{6\,b^8}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2520\,a^7+4465\,a^5\,b^2-1992\,a^3\,b^4+80\,a\,b^6\right)}{15\,b^8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-16800\,a^7+29500\,a^5\,b^2-12756\,a^3\,b^4+605\,a\,b^6\right)}{30\,b^8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-23520\,a^7+41300\,a^5\,b^2-18396\,a^3\,b^4+1215\,a\,b^6\right)}{210\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10080\,a^6-17500\,a^4\,b^2+7413\,a^2\,b^4-240\,b^6\right)}{420\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(32\,a^6-52\,a^4\,b^2+19\,a^2\,b^4\right)}{4\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(3168\,a^6-5532\,a^4\,b^2+2345\,a^2\,b^4\right)}{12\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(7200\,a^6-12212\,a^4\,b^2+4979\,a^2\,b^4\right)}{12\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9120\,a^6-15460\,a^4\,b^2+6103\,a^2\,b^4\right)}{60\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(864\,a^6-1500\,a^4\,b^2+661\,a^2\,b^4-48\,b^6\right)}{12\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(6240\,a^6-10748\,a^4\,b^2+4429\,a^2\,b^4-240\,b^6\right)}{12\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(24480\,a^6-41220\,a^4\,b^2+16499\,a^2\,b^4-720\,b^6\right)}{60\,b^7}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+14\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+42\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+70\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+70\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+56\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+42\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+28\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+14\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,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{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{2048\,a^{16}\,b^8-7680\,a^{14}\,b^{10}+11040\,a^{12}\,b^{12}-7520\,a^{10}\,b^{14}+2400\,a^8\,b^{16}-300\,a^6\,b^{18}+\frac{25\,a^4\,b^{20}}{2}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,a^{17}\,b^8+43008\,a^{15}\,b^{10}-90240\,a^{13}\,b^{12}+96320\,a^{11}\,b^{14}-54720\,a^9\,b^{16}+15576\,a^7\,b^{18}-1801\,a^5\,b^{20}+50\,a^3\,b^{22}\right)}{2\,b^{24}}-\frac{a\,\left(\frac{-128\,a^8\,b^{18}+272\,a^6\,b^{20}-164\,a^4\,b^{22}+20\,a^2\,b^{24}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-1024\,a^9\,b^{18}+2432\,a^7\,b^{20}-1792\,a^5\,b^{22}+384\,a^3\,b^{24}\right)}{2\,b^{24}}-\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{28}-128\,a^3\,b^{26}\right)}{2\,b^{24}}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)}{8\,b^9}+\frac{a\,\left(\frac{2048\,a^{16}\,b^8-7680\,a^{14}\,b^{10}+11040\,a^{12}\,b^{12}-7520\,a^{10}\,b^{14}+2400\,a^8\,b^{16}-300\,a^6\,b^{18}+\frac{25\,a^4\,b^{20}}{2}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,a^{17}\,b^8+43008\,a^{15}\,b^{10}-90240\,a^{13}\,b^{12}+96320\,a^{11}\,b^{14}-54720\,a^9\,b^{16}+15576\,a^7\,b^{18}-1801\,a^5\,b^{20}+50\,a^3\,b^{22}\right)}{2\,b^{24}}+\frac{a\,\left(\frac{-128\,a^8\,b^{18}+272\,a^6\,b^{20}-164\,a^4\,b^{22}+20\,a^2\,b^{24}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-1024\,a^9\,b^{18}+2432\,a^7\,b^{20}-1792\,a^5\,b^{22}+384\,a^3\,b^{24}\right)}{2\,b^{24}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{28}-128\,a^3\,b^{26}\right)}{2\,b^{24}}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)}{8\,b^9}}{\frac{16384\,a^{22}-96256\,a^{20}\,b^2+239872\,a^{18}\,b^4-329120\,a^{16}\,b^6+269608\,a^{14}\,b^8-133328\,a^{12}\,b^{10}+38085\,a^{10}\,b^{12}-5530\,a^8\,b^{14}+285\,a^6\,b^{16}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(65536\,a^{23}-401408\,a^{21}\,b^2+1051648\,a^{19}\,b^4-1534336\,a^{17}\,b^6+1358720\,a^{15}\,b^8-745600\,a^{13}\,b^{10}+247840\,a^{11}\,b^{12}-46550\,a^9\,b^{14}+4300\,a^7\,b^{16}-150\,a^5\,b^{18}\right)}{b^{24}}+\frac{a\,\left(\frac{2048\,a^{16}\,b^8-7680\,a^{14}\,b^{10}+11040\,a^{12}\,b^{12}-7520\,a^{10}\,b^{14}+2400\,a^8\,b^{16}-300\,a^6\,b^{18}+\frac{25\,a^4\,b^{20}}{2}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,a^{17}\,b^8+43008\,a^{15}\,b^{10}-90240\,a^{13}\,b^{12}+96320\,a^{11}\,b^{14}-54720\,a^9\,b^{16}+15576\,a^7\,b^{18}-1801\,a^5\,b^{20}+50\,a^3\,b^{22}\right)}{2\,b^{24}}-\frac{a\,\left(\frac{-128\,a^8\,b^{18}+272\,a^6\,b^{20}-164\,a^4\,b^{22}+20\,a^2\,b^{24}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-1024\,a^9\,b^{18}+2432\,a^7\,b^{20}-1792\,a^5\,b^{22}+384\,a^3\,b^{24}\right)}{2\,b^{24}}-\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{28}-128\,a^3\,b^{26}\right)}{2\,b^{24}}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}-\frac{a\,\left(\frac{2048\,a^{16}\,b^8-7680\,a^{14}\,b^{10}+11040\,a^{12}\,b^{12}-7520\,a^{10}\,b^{14}+2400\,a^8\,b^{16}-300\,a^6\,b^{18}+\frac{25\,a^4\,b^{20}}{2}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,a^{17}\,b^8+43008\,a^{15}\,b^{10}-90240\,a^{13}\,b^{12}+96320\,a^{11}\,b^{14}-54720\,a^9\,b^{16}+15576\,a^7\,b^{18}-1801\,a^5\,b^{20}+50\,a^3\,b^{22}\right)}{2\,b^{24}}+\frac{a\,\left(\frac{-128\,a^8\,b^{18}+272\,a^6\,b^{20}-164\,a^4\,b^{22}+20\,a^2\,b^{24}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-1024\,a^9\,b^{18}+2432\,a^7\,b^{20}-1792\,a^5\,b^{22}+384\,a^3\,b^{24}\right)}{2\,b^{24}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{28}-128\,a^3\,b^{26}\right)}{2\,b^{24}}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{8\,b^9}}\right)\,\left(64\,a^6-120\,a^4\,b^2+60\,a^2\,b^4-5\,b^6\right)}{4\,b^9\,d}-\frac{2\,a^2\,\mathrm{atanh}\left(\frac{75\,a^6\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{75\,a^6\,b^3-422\,a^8\,b+\frac{811\,a^{10}}{b}-\frac{656\,a^{12}}{b^3}+\frac{192\,a^{14}}{b^5}+1622\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+150\,a^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-844\,a^7\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1312\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{384\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}}-\frac{272\,a^8\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{811\,a^{10}\,b+75\,a^6\,b^5-422\,a^8\,b^3-\frac{656\,a^{12}}{b}+\frac{192\,a^{14}}{b^3}-1312\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+150\,a^5\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-844\,a^7\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1622\,a^9\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{384\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}+\frac{192\,a^{10}\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{75\,a^6\,b^7-656\,a^{12}\,b-422\,a^8\,b^5+811\,a^{10}\,b^3+\frac{192\,a^{14}}{b}+384\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+150\,a^5\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-844\,a^7\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1622\,a^9\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1312\,a^{11}\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{150\,a^5\,\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}}{75\,a^6\,b^2-422\,a^8+\frac{811\,a^{10}}{b^2}-\frac{656\,a^{12}}{b^4}+\frac{192\,a^{14}}{b^6}-844\,a^7\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+150\,a^5\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1622\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{1312\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+\frac{384\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}}-\frac{619\,a^7\,\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}}{811\,a^{10}+75\,a^6\,b^4-422\,a^8\,b^2-\frac{656\,a^{12}}{b^2}+\frac{192\,a^{14}}{b^4}+1622\,a^9\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+150\,a^5\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-844\,a^7\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1312\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{384\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}}+\frac{656\,a^9\,\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}}{75\,a^6\,b^6-656\,a^{12}-422\,a^8\,b^4+811\,a^{10}\,b^2+\frac{192\,a^{14}}{b^2}-1312\,a^{11}\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+150\,a^5\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-844\,a^7\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1622\,a^9\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{384\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}-\frac{192\,a^{11}\,\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}}{192\,a^{14}+384\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}\,b-656\,a^{12}\,b^2-1312\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^3+811\,a^{10}\,b^4+1622\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^5-422\,a^8\,b^6-844\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^7+75\,a^6\,b^8+150\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^9}\right)\,\left(8\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{b^9\,d}","Not used",1,"((tan(c/2 + (d*x)/2)^14*(7*a*b^6 + 32*a^7 + 4*a^3*b^4 - 44*a^5*b^2))/(2*b^8) - (2*(15*a*b^6 - 840*a^7 - 588*a^3*b^4 + 1435*a^5*b^2))/(105*b^8) + (2*tan(c/2 + (d*x)/2)^12*(4*a*b^6 + 168*a^7 + 72*a^3*b^4 - 255*a^5*b^2))/(3*b^8) - (2*tan(c/2 + (d*x)/2)^8*(15*a*b^6 - 840*a^7 - 588*a^3*b^4 + 1435*a^5*b^2))/(3*b^8) + (tan(c/2 + (d*x)/2)^10*(25*a*b^6 + 2016*a^7 + 1212*a^3*b^4 - 3284*a^5*b^2))/(6*b^8) - (2*tan(c/2 + (d*x)/2)^4*(80*a*b^6 - 2520*a^7 - 1992*a^3*b^4 + 4465*a^5*b^2))/(15*b^8) - (tan(c/2 + (d*x)/2)^6*(605*a*b^6 - 16800*a^7 - 12756*a^3*b^4 + 29500*a^5*b^2))/(30*b^8) - (tan(c/2 + (d*x)/2)^2*(1215*a*b^6 - 23520*a^7 - 18396*a^3*b^4 + 41300*a^5*b^2))/(210*b^8) + (tan(c/2 + (d*x)/2)*(10080*a^6 - 240*b^6 + 7413*a^2*b^4 - 17500*a^4*b^2))/(420*b^7) + (tan(c/2 + (d*x)/2)^15*(32*a^6 + 19*a^2*b^4 - 52*a^4*b^2))/(4*b^7) + (tan(c/2 + (d*x)/2)^11*(3168*a^6 + 2345*a^2*b^4 - 5532*a^4*b^2))/(12*b^7) + (tan(c/2 + (d*x)/2)^7*(7200*a^6 + 4979*a^2*b^4 - 12212*a^4*b^2))/(12*b^7) + (tan(c/2 + (d*x)/2)^3*(9120*a^6 + 6103*a^2*b^4 - 15460*a^4*b^2))/(60*b^7) + (tan(c/2 + (d*x)/2)^13*(864*a^6 - 48*b^6 + 661*a^2*b^4 - 1500*a^4*b^2))/(12*b^7) + (tan(c/2 + (d*x)/2)^9*(6240*a^6 - 240*b^6 + 4429*a^2*b^4 - 10748*a^4*b^2))/(12*b^7) + (tan(c/2 + (d*x)/2)^5*(24480*a^6 - 720*b^6 + 16499*a^2*b^4 - 41220*a^4*b^2))/(60*b^7))/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 8*a*tan(c/2 + (d*x)/2)^2 + 28*a*tan(c/2 + (d*x)/2)^4 + 56*a*tan(c/2 + (d*x)/2)^6 + 70*a*tan(c/2 + (d*x)/2)^8 + 56*a*tan(c/2 + (d*x)/2)^10 + 28*a*tan(c/2 + (d*x)/2)^12 + 8*a*tan(c/2 + (d*x)/2)^14 + a*tan(c/2 + (d*x)/2)^16 + 14*b*tan(c/2 + (d*x)/2)^3 + 42*b*tan(c/2 + (d*x)/2)^5 + 70*b*tan(c/2 + (d*x)/2)^7 + 70*b*tan(c/2 + (d*x)/2)^9 + 42*b*tan(c/2 + (d*x)/2)^11 + 14*b*tan(c/2 + (d*x)/2)^13 + 2*b*tan(c/2 + (d*x)/2)^15)) + (a*atan(((a*(((25*a^4*b^20)/2 - 300*a^6*b^18 + 2400*a^8*b^16 - 7520*a^10*b^14 + 11040*a^12*b^12 - 7680*a^14*b^10 + 2048*a^16*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a^3*b^22 - 1801*a^5*b^20 + 15576*a^7*b^18 - 54720*a^9*b^16 + 96320*a^11*b^14 - 90240*a^13*b^12 + 43008*a^15*b^10 - 8192*a^17*b^8))/(2*b^24) - (a*((20*a^2*b^24 - 164*a^4*b^22 + 272*a^6*b^20 - 128*a^8*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(384*a^3*b^24 - 1792*a^5*b^22 + 2432*a^7*b^20 - 1024*a^9*b^18))/(2*b^24) - (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^28 - 128*a^3*b^26))/(2*b^24))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2))/(8*b^9) + (a*(((25*a^4*b^20)/2 - 300*a^6*b^18 + 2400*a^8*b^16 - 7520*a^10*b^14 + 11040*a^12*b^12 - 7680*a^14*b^10 + 2048*a^16*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a^3*b^22 - 1801*a^5*b^20 + 15576*a^7*b^18 - 54720*a^9*b^16 + 96320*a^11*b^14 - 90240*a^13*b^12 + 43008*a^15*b^10 - 8192*a^17*b^8))/(2*b^24) + (a*((20*a^2*b^24 - 164*a^4*b^22 + 272*a^6*b^20 - 128*a^8*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(384*a^3*b^24 - 1792*a^5*b^22 + 2432*a^7*b^20 - 1024*a^9*b^18))/(2*b^24) + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^28 - 128*a^3*b^26))/(2*b^24))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2))/(8*b^9))/((16384*a^22 + 285*a^6*b^16 - 5530*a^8*b^14 + 38085*a^10*b^12 - 133328*a^12*b^10 + 269608*a^14*b^8 - 329120*a^16*b^6 + 239872*a^18*b^4 - 96256*a^20*b^2)/b^23 + (tan(c/2 + (d*x)/2)*(65536*a^23 - 150*a^5*b^18 + 4300*a^7*b^16 - 46550*a^9*b^14 + 247840*a^11*b^12 - 745600*a^13*b^10 + 1358720*a^15*b^8 - 1534336*a^17*b^6 + 1051648*a^19*b^4 - 401408*a^21*b^2))/b^24 + (a*(((25*a^4*b^20)/2 - 300*a^6*b^18 + 2400*a^8*b^16 - 7520*a^10*b^14 + 11040*a^12*b^12 - 7680*a^14*b^10 + 2048*a^16*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a^3*b^22 - 1801*a^5*b^20 + 15576*a^7*b^18 - 54720*a^9*b^16 + 96320*a^11*b^14 - 90240*a^13*b^12 + 43008*a^15*b^10 - 8192*a^17*b^8))/(2*b^24) - (a*((20*a^2*b^24 - 164*a^4*b^22 + 272*a^6*b^20 - 128*a^8*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(384*a^3*b^24 - 1792*a^5*b^22 + 2432*a^7*b^20 - 1024*a^9*b^18))/(2*b^24) - (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^28 - 128*a^3*b^26))/(2*b^24))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9) - (a*(((25*a^4*b^20)/2 - 300*a^6*b^18 + 2400*a^8*b^16 - 7520*a^10*b^14 + 11040*a^12*b^12 - 7680*a^14*b^10 + 2048*a^16*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a^3*b^22 - 1801*a^5*b^20 + 15576*a^7*b^18 - 54720*a^9*b^16 + 96320*a^11*b^14 - 90240*a^13*b^12 + 43008*a^15*b^10 - 8192*a^17*b^8))/(2*b^24) + (a*((20*a^2*b^24 - 164*a^4*b^22 + 272*a^6*b^20 - 128*a^8*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(384*a^3*b^24 - 1792*a^5*b^22 + 2432*a^7*b^20 - 1024*a^9*b^18))/(2*b^24) + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^28 - 128*a^3*b^26))/(2*b^24))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2)*1i)/(8*b^9)))*(64*a^6 - 5*b^6 + 60*a^2*b^4 - 120*a^4*b^2))/(4*b^9*d) - (2*a^2*atanh((75*a^6*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(75*a^6*b^3 - 422*a^8*b + (811*a^10)/b - (656*a^12)/b^3 + (192*a^14)/b^5 + 1622*a^9*tan(c/2 + (d*x)/2) + 150*a^5*b^4*tan(c/2 + (d*x)/2) - 844*a^7*b^2*tan(c/2 + (d*x)/2) - (1312*a^11*tan(c/2 + (d*x)/2))/b^2 + (384*a^13*tan(c/2 + (d*x)/2))/b^4) - (272*a^8*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(811*a^10*b + 75*a^6*b^5 - 422*a^8*b^3 - (656*a^12)/b + (192*a^14)/b^3 - 1312*a^11*tan(c/2 + (d*x)/2) + 150*a^5*b^6*tan(c/2 + (d*x)/2) - 844*a^7*b^4*tan(c/2 + (d*x)/2) + 1622*a^9*b^2*tan(c/2 + (d*x)/2) + (384*a^13*tan(c/2 + (d*x)/2))/b^2) + (192*a^10*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(75*a^6*b^7 - 656*a^12*b - 422*a^8*b^5 + 811*a^10*b^3 + (192*a^14)/b + 384*a^13*tan(c/2 + (d*x)/2) + 150*a^5*b^8*tan(c/2 + (d*x)/2) - 844*a^7*b^6*tan(c/2 + (d*x)/2) + 1622*a^9*b^4*tan(c/2 + (d*x)/2) - 1312*a^11*b^2*tan(c/2 + (d*x)/2)) + (150*a^5*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(75*a^6*b^2 - 422*a^8 + (811*a^10)/b^2 - (656*a^12)/b^4 + (192*a^14)/b^6 - 844*a^7*b*tan(c/2 + (d*x)/2) + 150*a^5*b^3*tan(c/2 + (d*x)/2) + (1622*a^9*tan(c/2 + (d*x)/2))/b - (1312*a^11*tan(c/2 + (d*x)/2))/b^3 + (384*a^13*tan(c/2 + (d*x)/2))/b^5) - (619*a^7*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(811*a^10 + 75*a^6*b^4 - 422*a^8*b^2 - (656*a^12)/b^2 + (192*a^14)/b^4 + 1622*a^9*b*tan(c/2 + (d*x)/2) + 150*a^5*b^5*tan(c/2 + (d*x)/2) - 844*a^7*b^3*tan(c/2 + (d*x)/2) - (1312*a^11*tan(c/2 + (d*x)/2))/b + (384*a^13*tan(c/2 + (d*x)/2))/b^3) + (656*a^9*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(75*a^6*b^6 - 656*a^12 - 422*a^8*b^4 + 811*a^10*b^2 + (192*a^14)/b^2 - 1312*a^11*b*tan(c/2 + (d*x)/2) + 150*a^5*b^7*tan(c/2 + (d*x)/2) - 844*a^7*b^5*tan(c/2 + (d*x)/2) + 1622*a^9*b^3*tan(c/2 + (d*x)/2) + (384*a^13*tan(c/2 + (d*x)/2))/b) - (192*a^11*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(192*a^14 + 75*a^6*b^8 - 422*a^8*b^6 + 811*a^10*b^4 - 656*a^12*b^2 + 384*a^13*b*tan(c/2 + (d*x)/2) + 150*a^5*b^9*tan(c/2 + (d*x)/2) - 844*a^7*b^7*tan(c/2 + (d*x)/2) + 1622*a^9*b^5*tan(c/2 + (d*x)/2) - 1312*a^11*b^3*tan(c/2 + (d*x)/2)))*(8*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^9*d)","B"
1257,1,4067,471,16.382099,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^2)/(a + b*sin(c + d*x))^2,x)","-\frac{\frac{2\,\left(105\,a^6-170\,a^4\,b^2+61\,a^2\,b^4\right)}{15\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(56\,a^5-86\,a^3\,b^2+27\,a\,b^4\right)}{8\,b^6}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(105\,a^5-170\,a^3\,b^2+61\,a\,b^4\right)}{3\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(336\,a^5-558\,a^3\,b^2+223\,a\,b^4\right)}{6\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3360\,a^5-5370\,a^3\,b^2+1813\,a\,b^4\right)}{30\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(4200\,a^5-6954\,a^3\,b^2+2533\,a\,b^4\right)}{24\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(5880\,a^5-9366\,a^3\,b^2+3323\,a\,b^4\right)}{24\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(56\,a^6-72\,a^4\,b^2+2\,a^2\,b^4+11\,b^6\right)}{4\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(1008\,a^6-1464\,a^4\,b^2+378\,a^2\,b^4-5\,b^6\right)}{12\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(1260\,a^6-1984\,a^4\,b^2+674\,a^2\,b^4+45\,b^6\right)}{6\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(1680\,a^6-2776\,a^4\,b^2+1034\,a^2\,b^4-45\,b^6\right)}{6\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5040\,a^6-8440\,a^4\,b^2+3386\,a^2\,b^4-165\,b^6\right)}{60\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12600\,a^6-21240\,a^4\,b^2+8358\,a^2\,b^4+25\,b^6\right)}{60\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2520\,a^5-4150\,a^3\,b^2+1547\,a\,b^4\right)}{120\,b^6}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+12\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+21\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+35\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+40\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+35\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+21\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+12\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+7\,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{\mathrm{atan}\left(\frac{\frac{\left(\frac{1568\,a^{14}\,b^7-5600\,a^{12}\,b^9+7520\,a^{10}\,b^{11}-4640\,a^8\,b^{13}+\frac{2525\,a^6\,b^{15}}{2}-\frac{225\,a^4\,b^{17}}{2}+\frac{25\,a^2\,b^{19}}{8}}{b^{20}}-\frac{\left(\frac{-112\,a^7\,b^{16}+228\,a^5\,b^{18}-126\,a^3\,b^{20}+10\,a\,b^{22}}{b^{20}}-\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3584\,a^8\,b^{16}+8192\,a^6\,b^{18}-5632\,a^4\,b^{20}+1024\,a^2\,b^{22}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-25088\,a^{15}\,b^7+127232\,a^{13}\,b^9-254720\,a^{11}\,b^{11}+254720\,a^9\,b^{13}-131700\,a^7\,b^{15}+32364\,a^5\,b^{17}-2849\,a^3\,b^{19}+50\,a\,b^{21}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^8}+\frac{\left(\frac{1568\,a^{14}\,b^7-5600\,a^{12}\,b^9+7520\,a^{10}\,b^{11}-4640\,a^8\,b^{13}+\frac{2525\,a^6\,b^{15}}{2}-\frac{225\,a^4\,b^{17}}{2}+\frac{25\,a^2\,b^{19}}{8}}{b^{20}}+\frac{\left(\frac{-112\,a^7\,b^{16}+228\,a^5\,b^{18}-126\,a^3\,b^{20}+10\,a\,b^{22}}{b^{20}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3584\,a^8\,b^{16}+8192\,a^6\,b^{18}-5632\,a^4\,b^{20}+1024\,a^2\,b^{22}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-25088\,a^{15}\,b^7+127232\,a^{13}\,b^9-254720\,a^{11}\,b^{11}+254720\,a^9\,b^{13}-131700\,a^7\,b^{15}+32364\,a^5\,b^{17}-2849\,a^3\,b^{19}+50\,a\,b^{21}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^8}}{\frac{10976\,a^{19}-61544\,a^{17}\,b^2+144788\,a^{15}\,b^4-184965\,a^{13}\,b^6+138577\,a^{11}\,b^8-\frac{244853\,a^9\,b^{10}}{4}+15115\,a^7\,b^{12}-\frac{7205\,a^5\,b^{14}}{4}+\frac{135\,a^3\,b^{16}}{2}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(175616\,a^{20}-1028608\,a^{18}\,b^2+2551808\,a^{16}\,b^4-3480576\,a^{14}\,b^6+2831960\,a^{12}\,b^8-1393080\,a^{10}\,b^{10}+399830\,a^8\,b^{12}-61000\,a^6\,b^{14}+4150\,a^4\,b^{16}-100\,a^2\,b^{18}\right)}{4\,b^{21}}+\frac{\left(\frac{1568\,a^{14}\,b^7-5600\,a^{12}\,b^9+7520\,a^{10}\,b^{11}-4640\,a^8\,b^{13}+\frac{2525\,a^6\,b^{15}}{2}-\frac{225\,a^4\,b^{17}}{2}+\frac{25\,a^2\,b^{19}}{8}}{b^{20}}-\frac{\left(\frac{-112\,a^7\,b^{16}+228\,a^5\,b^{18}-126\,a^3\,b^{20}+10\,a\,b^{22}}{b^{20}}-\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3584\,a^8\,b^{16}+8192\,a^6\,b^{18}-5632\,a^4\,b^{20}+1024\,a^2\,b^{22}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-25088\,a^{15}\,b^7+127232\,a^{13}\,b^9-254720\,a^{11}\,b^{11}+254720\,a^9\,b^{13}-131700\,a^7\,b^{15}+32364\,a^5\,b^{17}-2849\,a^3\,b^{19}+50\,a\,b^{21}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}-\frac{\left(\frac{1568\,a^{14}\,b^7-5600\,a^{12}\,b^9+7520\,a^{10}\,b^{11}-4640\,a^8\,b^{13}+\frac{2525\,a^6\,b^{15}}{2}-\frac{225\,a^4\,b^{17}}{2}+\frac{25\,a^2\,b^{19}}{8}}{b^{20}}+\frac{\left(\frac{-112\,a^7\,b^{16}+228\,a^5\,b^{18}-126\,a^3\,b^{20}+10\,a\,b^{22}}{b^{20}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3584\,a^8\,b^{16}+8192\,a^6\,b^{18}-5632\,a^4\,b^{20}+1024\,a^2\,b^{22}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-25088\,a^{15}\,b^7+127232\,a^{13}\,b^9-254720\,a^{11}\,b^{11}+254720\,a^9\,b^{13}-131700\,a^7\,b^{15}+32364\,a^5\,b^{17}-2849\,a^3\,b^{19}+50\,a\,b^{21}\right)}{8\,b^{21}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^8}}\right)\,\left(a^6\,112{}\mathrm{i}-a^4\,b^2\,200{}\mathrm{i}+a^2\,b^4\,90{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^8\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{1568\,a^{14}\,b^7-5600\,a^{12}\,b^9+7520\,a^{10}\,b^{11}-4640\,a^8\,b^{13}+\frac{2525\,a^6\,b^{15}}{2}-\frac{225\,a^4\,b^{17}}{2}+\frac{25\,a^2\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-25088\,a^{15}\,b^7+127232\,a^{13}\,b^9-254720\,a^{11}\,b^{11}+254720\,a^9\,b^{13}-131700\,a^7\,b^{15}+32364\,a^5\,b^{17}-2849\,a^3\,b^{19}+50\,a\,b^{21}\right)}{8\,b^{21}}+\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{-112\,a^7\,b^{16}+228\,a^5\,b^{18}-126\,a^3\,b^{20}+10\,a\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3584\,a^8\,b^{16}+8192\,a^6\,b^{18}-5632\,a^4\,b^{20}+1024\,a^2\,b^{22}\right)}{8\,b^{21}}+\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)}{b^8}\right)}{b^8}\right)\,1{}\mathrm{i}}{b^8}+\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{1568\,a^{14}\,b^7-5600\,a^{12}\,b^9+7520\,a^{10}\,b^{11}-4640\,a^8\,b^{13}+\frac{2525\,a^6\,b^{15}}{2}-\frac{225\,a^4\,b^{17}}{2}+\frac{25\,a^2\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-25088\,a^{15}\,b^7+127232\,a^{13}\,b^9-254720\,a^{11}\,b^{11}+254720\,a^9\,b^{13}-131700\,a^7\,b^{15}+32364\,a^5\,b^{17}-2849\,a^3\,b^{19}+50\,a\,b^{21}\right)}{8\,b^{21}}-\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{-112\,a^7\,b^{16}+228\,a^5\,b^{18}-126\,a^3\,b^{20}+10\,a\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3584\,a^8\,b^{16}+8192\,a^6\,b^{18}-5632\,a^4\,b^{20}+1024\,a^2\,b^{22}\right)}{8\,b^{21}}-\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)}{b^8}\right)}{b^8}\right)\,1{}\mathrm{i}}{b^8}}{\frac{10976\,a^{19}-61544\,a^{17}\,b^2+144788\,a^{15}\,b^4-184965\,a^{13}\,b^6+138577\,a^{11}\,b^8-\frac{244853\,a^9\,b^{10}}{4}+15115\,a^7\,b^{12}-\frac{7205\,a^5\,b^{14}}{4}+\frac{135\,a^3\,b^{16}}{2}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(175616\,a^{20}-1028608\,a^{18}\,b^2+2551808\,a^{16}\,b^4-3480576\,a^{14}\,b^6+2831960\,a^{12}\,b^8-1393080\,a^{10}\,b^{10}+399830\,a^8\,b^{12}-61000\,a^6\,b^{14}+4150\,a^4\,b^{16}-100\,a^2\,b^{18}\right)}{4\,b^{21}}-\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{1568\,a^{14}\,b^7-5600\,a^{12}\,b^9+7520\,a^{10}\,b^{11}-4640\,a^8\,b^{13}+\frac{2525\,a^6\,b^{15}}{2}-\frac{225\,a^4\,b^{17}}{2}+\frac{25\,a^2\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-25088\,a^{15}\,b^7+127232\,a^{13}\,b^9-254720\,a^{11}\,b^{11}+254720\,a^9\,b^{13}-131700\,a^7\,b^{15}+32364\,a^5\,b^{17}-2849\,a^3\,b^{19}+50\,a\,b^{21}\right)}{8\,b^{21}}+\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{-112\,a^7\,b^{16}+228\,a^5\,b^{18}-126\,a^3\,b^{20}+10\,a\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3584\,a^8\,b^{16}+8192\,a^6\,b^{18}-5632\,a^4\,b^{20}+1024\,a^2\,b^{22}\right)}{8\,b^{21}}+\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)}{b^8}\right)}{b^8}\right)}{b^8}+\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{1568\,a^{14}\,b^7-5600\,a^{12}\,b^9+7520\,a^{10}\,b^{11}-4640\,a^8\,b^{13}+\frac{2525\,a^6\,b^{15}}{2}-\frac{225\,a^4\,b^{17}}{2}+\frac{25\,a^2\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-25088\,a^{15}\,b^7+127232\,a^{13}\,b^9-254720\,a^{11}\,b^{11}+254720\,a^9\,b^{13}-131700\,a^7\,b^{15}+32364\,a^5\,b^{17}-2849\,a^3\,b^{19}+50\,a\,b^{21}\right)}{8\,b^{21}}-\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{-112\,a^7\,b^{16}+228\,a^5\,b^{18}-126\,a^3\,b^{20}+10\,a\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3584\,a^8\,b^{16}+8192\,a^6\,b^{18}-5632\,a^4\,b^{20}+1024\,a^2\,b^{22}\right)}{8\,b^{21}}-\frac{a\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)}{b^8}\right)}{b^8}\right)}{b^8}}\right)\,\left(7\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{b^8\,d}","Not used",1,"- ((2*(105*a^6 + 61*a^2*b^4 - 170*a^4*b^2))/(15*b^7) + (tan(c/2 + (d*x)/2)^13*(27*a*b^4 + 56*a^5 - 86*a^3*b^2))/(8*b^6) + (8*tan(c/2 + (d*x)/2)^7*(61*a*b^4 + 105*a^5 - 170*a^3*b^2))/(3*b^6) + (tan(c/2 + (d*x)/2)^11*(223*a*b^4 + 336*a^5 - 558*a^3*b^2))/(6*b^6) + (tan(c/2 + (d*x)/2)^3*(1813*a*b^4 + 3360*a^5 - 5370*a^3*b^2))/(30*b^6) + (tan(c/2 + (d*x)/2)^9*(2533*a*b^4 + 4200*a^5 - 6954*a^3*b^2))/(24*b^6) + (tan(c/2 + (d*x)/2)^5*(3323*a*b^4 + 5880*a^5 - 9366*a^3*b^2))/(24*b^6) + (tan(c/2 + (d*x)/2)^12*(56*a^6 + 11*b^6 + 2*a^2*b^4 - 72*a^4*b^2))/(4*b^7) + (tan(c/2 + (d*x)/2)^10*(1008*a^6 - 5*b^6 + 378*a^2*b^4 - 1464*a^4*b^2))/(12*b^7) + (tan(c/2 + (d*x)/2)^8*(1260*a^6 + 45*b^6 + 674*a^2*b^4 - 1984*a^4*b^2))/(6*b^7) + (tan(c/2 + (d*x)/2)^6*(1680*a^6 - 45*b^6 + 1034*a^2*b^4 - 2776*a^4*b^2))/(6*b^7) + (tan(c/2 + (d*x)/2)^2*(5040*a^6 - 165*b^6 + 3386*a^2*b^4 - 8440*a^4*b^2))/(60*b^7) + (tan(c/2 + (d*x)/2)^4*(12600*a^6 + 25*b^6 + 8358*a^2*b^4 - 21240*a^4*b^2))/(60*b^7) + (tan(c/2 + (d*x)/2)*(1547*a*b^4 + 2520*a^5 - 4150*a^3*b^2))/(120*b^6))/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 7*a*tan(c/2 + (d*x)/2)^2 + 21*a*tan(c/2 + (d*x)/2)^4 + 35*a*tan(c/2 + (d*x)/2)^6 + 35*a*tan(c/2 + (d*x)/2)^8 + 21*a*tan(c/2 + (d*x)/2)^10 + 7*a*tan(c/2 + (d*x)/2)^12 + a*tan(c/2 + (d*x)/2)^14 + 12*b*tan(c/2 + (d*x)/2)^3 + 30*b*tan(c/2 + (d*x)/2)^5 + 40*b*tan(c/2 + (d*x)/2)^7 + 30*b*tan(c/2 + (d*x)/2)^9 + 12*b*tan(c/2 + (d*x)/2)^11 + 2*b*tan(c/2 + (d*x)/2)^13)) - (atan((((((25*a^2*b^19)/8 - (225*a^4*b^17)/2 + (2525*a^6*b^15)/2 - 4640*a^8*b^13 + 7520*a^10*b^11 - 5600*a^12*b^9 + 1568*a^14*b^7)/b^20 - (((10*a*b^22 - 126*a^3*b^20 + 228*a^5*b^18 - 112*a^7*b^16)/b^20 - ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) + (tan(c/2 + (d*x)/2)*(1024*a^2*b^22 - 5632*a^4*b^20 + 8192*a^6*b^18 - 3584*a^8*b^16))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) + (tan(c/2 + (d*x)/2)*(50*a*b^21 - 2849*a^3*b^19 + 32364*a^5*b^17 - 131700*a^7*b^15 + 254720*a^9*b^13 - 254720*a^11*b^11 + 127232*a^13*b^9 - 25088*a^15*b^7))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i)*1i)/(16*b^8) + ((((25*a^2*b^19)/8 - (225*a^4*b^17)/2 + (2525*a^6*b^15)/2 - 4640*a^8*b^13 + 7520*a^10*b^11 - 5600*a^12*b^9 + 1568*a^14*b^7)/b^20 + (((10*a*b^22 - 126*a^3*b^20 + 228*a^5*b^18 - 112*a^7*b^16)/b^20 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) + (tan(c/2 + (d*x)/2)*(1024*a^2*b^22 - 5632*a^4*b^20 + 8192*a^6*b^18 - 3584*a^8*b^16))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) + (tan(c/2 + (d*x)/2)*(50*a*b^21 - 2849*a^3*b^19 + 32364*a^5*b^17 - 131700*a^7*b^15 + 254720*a^9*b^13 - 254720*a^11*b^11 + 127232*a^13*b^9 - 25088*a^15*b^7))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i)*1i)/(16*b^8))/((10976*a^19 + (135*a^3*b^16)/2 - (7205*a^5*b^14)/4 + 15115*a^7*b^12 - (244853*a^9*b^10)/4 + 138577*a^11*b^8 - 184965*a^13*b^6 + 144788*a^15*b^4 - 61544*a^17*b^2)/b^20 + (tan(c/2 + (d*x)/2)*(175616*a^20 - 100*a^2*b^18 + 4150*a^4*b^16 - 61000*a^6*b^14 + 399830*a^8*b^12 - 1393080*a^10*b^10 + 2831960*a^12*b^8 - 3480576*a^14*b^6 + 2551808*a^16*b^4 - 1028608*a^18*b^2))/(4*b^21) + ((((25*a^2*b^19)/8 - (225*a^4*b^17)/2 + (2525*a^6*b^15)/2 - 4640*a^8*b^13 + 7520*a^10*b^11 - 5600*a^12*b^9 + 1568*a^14*b^7)/b^20 - (((10*a*b^22 - 126*a^3*b^20 + 228*a^5*b^18 - 112*a^7*b^16)/b^20 - ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) + (tan(c/2 + (d*x)/2)*(1024*a^2*b^22 - 5632*a^4*b^20 + 8192*a^6*b^18 - 3584*a^8*b^16))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) + (tan(c/2 + (d*x)/2)*(50*a*b^21 - 2849*a^3*b^19 + 32364*a^5*b^17 - 131700*a^7*b^15 + 254720*a^9*b^13 - 254720*a^11*b^11 + 127232*a^13*b^9 - 25088*a^15*b^7))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) - ((((25*a^2*b^19)/8 - (225*a^4*b^17)/2 + (2525*a^6*b^15)/2 - 4640*a^8*b^13 + 7520*a^10*b^11 - 5600*a^12*b^9 + 1568*a^14*b^7)/b^20 + (((10*a*b^22 - 126*a^3*b^20 + 228*a^5*b^18 - 112*a^7*b^16)/b^20 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) + (tan(c/2 + (d*x)/2)*(1024*a^2*b^22 - 5632*a^4*b^20 + 8192*a^6*b^18 - 3584*a^8*b^16))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8) + (tan(c/2 + (d*x)/2)*(50*a*b^21 - 2849*a^3*b^19 + 32364*a^5*b^17 - 131700*a^7*b^15 + 254720*a^9*b^13 - 254720*a^11*b^11 + 127232*a^13*b^9 - 25088*a^15*b^7))/(8*b^21))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i))/(16*b^8)))*(a^6*112i - b^6*5i + a^2*b^4*90i - a^4*b^2*200i)*1i)/(8*b^8*d) - (a*atan(((a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(((25*a^2*b^19)/8 - (225*a^4*b^17)/2 + (2525*a^6*b^15)/2 - 4640*a^8*b^13 + 7520*a^10*b^11 - 5600*a^12*b^9 + 1568*a^14*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a*b^21 - 2849*a^3*b^19 + 32364*a^5*b^17 - 131700*a^7*b^15 + 254720*a^9*b^13 - 254720*a^11*b^11 + 127232*a^13*b^9 - 25088*a^15*b^7))/(8*b^21) + (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((10*a*b^22 - 126*a^3*b^20 + 228*a^5*b^18 - 112*a^7*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(1024*a^2*b^22 - 5632*a^4*b^20 + 8192*a^6*b^18 - 3584*a^8*b^16))/(8*b^21) + (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21)))/b^8))/b^8)*1i)/b^8 + (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(((25*a^2*b^19)/8 - (225*a^4*b^17)/2 + (2525*a^6*b^15)/2 - 4640*a^8*b^13 + 7520*a^10*b^11 - 5600*a^12*b^9 + 1568*a^14*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a*b^21 - 2849*a^3*b^19 + 32364*a^5*b^17 - 131700*a^7*b^15 + 254720*a^9*b^13 - 254720*a^11*b^11 + 127232*a^13*b^9 - 25088*a^15*b^7))/(8*b^21) - (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((10*a*b^22 - 126*a^3*b^20 + 228*a^5*b^18 - 112*a^7*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(1024*a^2*b^22 - 5632*a^4*b^20 + 8192*a^6*b^18 - 3584*a^8*b^16))/(8*b^21) - (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21)))/b^8))/b^8)*1i)/b^8)/((10976*a^19 + (135*a^3*b^16)/2 - (7205*a^5*b^14)/4 + 15115*a^7*b^12 - (244853*a^9*b^10)/4 + 138577*a^11*b^8 - 184965*a^13*b^6 + 144788*a^15*b^4 - 61544*a^17*b^2)/b^20 + (tan(c/2 + (d*x)/2)*(175616*a^20 - 100*a^2*b^18 + 4150*a^4*b^16 - 61000*a^6*b^14 + 399830*a^8*b^12 - 1393080*a^10*b^10 + 2831960*a^12*b^8 - 3480576*a^14*b^6 + 2551808*a^16*b^4 - 1028608*a^18*b^2))/(4*b^21) - (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(((25*a^2*b^19)/8 - (225*a^4*b^17)/2 + (2525*a^6*b^15)/2 - 4640*a^8*b^13 + 7520*a^10*b^11 - 5600*a^12*b^9 + 1568*a^14*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a*b^21 - 2849*a^3*b^19 + 32364*a^5*b^17 - 131700*a^7*b^15 + 254720*a^9*b^13 - 254720*a^11*b^11 + 127232*a^13*b^9 - 25088*a^15*b^7))/(8*b^21) + (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((10*a*b^22 - 126*a^3*b^20 + 228*a^5*b^18 - 112*a^7*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(1024*a^2*b^22 - 5632*a^4*b^20 + 8192*a^6*b^18 - 3584*a^8*b^16))/(8*b^21) + (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21)))/b^8))/b^8))/b^8 + (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(((25*a^2*b^19)/8 - (225*a^4*b^17)/2 + (2525*a^6*b^15)/2 - 4640*a^8*b^13 + 7520*a^10*b^11 - 5600*a^12*b^9 + 1568*a^14*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a*b^21 - 2849*a^3*b^19 + 32364*a^5*b^17 - 131700*a^7*b^15 + 254720*a^9*b^13 - 254720*a^11*b^11 + 127232*a^13*b^9 - 25088*a^15*b^7))/(8*b^21) - (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((10*a*b^22 - 126*a^3*b^20 + 228*a^5*b^18 - 112*a^7*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(1024*a^2*b^22 - 5632*a^4*b^20 + 8192*a^6*b^18 - 3584*a^8*b^16))/(8*b^21) - (a*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21)))/b^8))/b^8))/b^8))*(7*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(b^8*d)","B"
1258,1,3135,231,14.530049,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x))/(a + b*sin(c + d*x))^2,x)","\frac{\frac{2\,\left(90\,a^5-135\,a^3\,b^2+38\,a\,b^4\right)}{15\,b^6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(-12\,a^5+14\,a^3\,b^2+a\,b^4\right)}{b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(30\,a^5-41\,a^3\,b^2+9\,a\,b^4\right)}{b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(60\,a^5-94\,a^3\,b^2+29\,a\,b^4\right)}{b^6}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(90\,a^5-135\,a^3\,b^2+38\,a\,b^4\right)}{3\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(300\,a^5-470\,a^3\,b^2+157\,a\,b^4\right)}{5\,b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(540\,a^4-825\,a^2\,b^2+244\,b^4\right)}{30\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(12\,a^4-17\,a^2\,b^2+4\,b^4\right)}{2\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(84\,a^4-131\,a^2\,b^2+44\,b^4\right)}{2\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(108\,a^4-165\,a^2\,b^2+44\,b^4\right)}{b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(396\,a^4-585\,a^2\,b^2+172\,b^4\right)}{3\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(468\,a^4-687\,a^2\,b^2+172\,b^4\right)}{6\,b^5}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+10\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+20\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+10\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,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{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{2\,\left(576\,a^{12}\,b^6-1920\,a^{10}\,b^8+2320\,a^8\,b^{10}-1200\,a^6\,b^{12}+225\,a^4\,b^{14}\right)}{b^{17}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1152\,a^{13}\,b^6-5568\,a^{11}\,b^8+10400\,a^9\,b^{10}-9360\,a^7\,b^{12}+4065\,a^5\,b^{14}-706\,a^3\,b^{16}+16\,a\,b^{18}\right)}{b^{18}}+\frac{a\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-192\,a^7\,b^{14}+416\,a^5\,b^{16}-256\,a^3\,b^{18}+32\,a\,b^{20}\right)}{b^{18}}-\frac{2\,\left(48\,a^6\,b^{14}-92\,a^4\,b^{16}+44\,a^2\,b^{18}\right)}{b^{17}}+\frac{a\,\left(32\,a^2\,b^3+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a\,b^{22}-32\,a^3\,b^{20}\right)}{b^{18}}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{4\,b^7}\right)\,1{}\mathrm{i}}{4\,b^7}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)}{4\,b^7}+\frac{a\,\left(\frac{2\,\left(576\,a^{12}\,b^6-1920\,a^{10}\,b^8+2320\,a^8\,b^{10}-1200\,a^6\,b^{12}+225\,a^4\,b^{14}\right)}{b^{17}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1152\,a^{13}\,b^6-5568\,a^{11}\,b^8+10400\,a^9\,b^{10}-9360\,a^7\,b^{12}+4065\,a^5\,b^{14}-706\,a^3\,b^{16}+16\,a\,b^{18}\right)}{b^{18}}+\frac{a\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,\left(\frac{2\,\left(48\,a^6\,b^{14}-92\,a^4\,b^{16}+44\,a^2\,b^{18}\right)}{b^{17}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-192\,a^7\,b^{14}+416\,a^5\,b^{16}-256\,a^3\,b^{18}+32\,a\,b^{20}\right)}{b^{18}}+\frac{a\,\left(32\,a^2\,b^3+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a\,b^{22}-32\,a^3\,b^{20}\right)}{b^{18}}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{4\,b^7}\right)\,1{}\mathrm{i}}{4\,b^7}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)}{4\,b^7}}{\frac{4\,\left(1728\,a^{16}-9072\,a^{14}\,b^2+19584\,a^{12}\,b^4-22310\,a^{10}\,b^6+14291\,a^8\,b^8-5056\,a^6\,b^{10}+895\,a^4\,b^{12}-60\,a^2\,b^{14}\right)}{b^{17}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6912\,a^{17}-38016\,a^{15}\,b^2+86976\,a^{13}\,b^4-106592\,a^{11}\,b^6+74860\,a^9\,b^8-29690\,a^7\,b^{10}+6000\,a^5\,b^{12}-450\,a^3\,b^{14}\right)}{b^{18}}-\frac{a\,\left(\frac{2\,\left(576\,a^{12}\,b^6-1920\,a^{10}\,b^8+2320\,a^8\,b^{10}-1200\,a^6\,b^{12}+225\,a^4\,b^{14}\right)}{b^{17}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1152\,a^{13}\,b^6-5568\,a^{11}\,b^8+10400\,a^9\,b^{10}-9360\,a^7\,b^{12}+4065\,a^5\,b^{14}-706\,a^3\,b^{16}+16\,a\,b^{18}\right)}{b^{18}}+\frac{a\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-192\,a^7\,b^{14}+416\,a^5\,b^{16}-256\,a^3\,b^{18}+32\,a\,b^{20}\right)}{b^{18}}-\frac{2\,\left(48\,a^6\,b^{14}-92\,a^4\,b^{16}+44\,a^2\,b^{18}\right)}{b^{17}}+\frac{a\,\left(32\,a^2\,b^3+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a\,b^{22}-32\,a^3\,b^{20}\right)}{b^{18}}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{4\,b^7}\right)\,1{}\mathrm{i}}{4\,b^7}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{4\,b^7}+\frac{a\,\left(\frac{2\,\left(576\,a^{12}\,b^6-1920\,a^{10}\,b^8+2320\,a^8\,b^{10}-1200\,a^6\,b^{12}+225\,a^4\,b^{14}\right)}{b^{17}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1152\,a^{13}\,b^6-5568\,a^{11}\,b^8+10400\,a^9\,b^{10}-9360\,a^7\,b^{12}+4065\,a^5\,b^{14}-706\,a^3\,b^{16}+16\,a\,b^{18}\right)}{b^{18}}+\frac{a\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,\left(\frac{2\,\left(48\,a^6\,b^{14}-92\,a^4\,b^{16}+44\,a^2\,b^{18}\right)}{b^{17}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-192\,a^7\,b^{14}+416\,a^5\,b^{16}-256\,a^3\,b^{18}+32\,a\,b^{20}\right)}{b^{18}}+\frac{a\,\left(32\,a^2\,b^3+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a\,b^{22}-32\,a^3\,b^{20}\right)}{b^{18}}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{4\,b^7}\right)\,1{}\mathrm{i}}{4\,b^7}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{4\,b^7}}\right)\,\left(24\,a^4-40\,a^2\,b^2+15\,b^4\right)}{2\,b^7\,d}-\frac{2\,\mathrm{atanh}\left(\frac{64\,a^2\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{64\,a^2\,b^3-572\,a^4\,b+\frac{1312\,a^6}{b}-\frac{1164\,a^8}{b^3}+\frac{360\,a^{10}}{b^5}+2624\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+128\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1144\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2328\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{720\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}}-\frac{444\,a^4\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{1312\,a^6\,b+64\,a^2\,b^5-572\,a^4\,b^3-\frac{1164\,a^8}{b}+\frac{360\,a^{10}}{b^3}-2328\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+128\,a\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1144\,a^3\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2624\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{720\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}+\frac{360\,a^6\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{64\,a^2\,b^7-1164\,a^8\,b-572\,a^4\,b^5+1312\,a^6\,b^3+\frac{360\,a^{10}}{b}+720\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+128\,a\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1144\,a^3\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2624\,a^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2328\,a^7\,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{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{64\,a^2\,b^2-572\,a^4+\frac{1312\,a^6}{b^2}-\frac{1164\,a^8}{b^4}+\frac{360\,a^{10}}{b^6}+128\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1144\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2624\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{2328\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+\frac{720\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}}-\frac{952\,a^3\,\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}}{1312\,a^6+64\,a^2\,b^4-572\,a^4\,b^2-\frac{1164\,a^8}{b^2}+\frac{360\,a^{10}}{b^4}+128\,a\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2624\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1144\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2328\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{720\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}}+\frac{1164\,a^5\,\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}}{64\,a^2\,b^6-1164\,a^8-572\,a^4\,b^4+1312\,a^6\,b^2+\frac{360\,a^{10}}{b^2}+128\,a\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2328\,a^7\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1144\,a^3\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2624\,a^5\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{720\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}-\frac{360\,a^7\,\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}}{360\,a^{10}+720\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b-1164\,a^8\,b^2-2328\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^3+1312\,a^6\,b^4+2624\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^5-572\,a^4\,b^6-1144\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^7+64\,a^2\,b^8+128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^9}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{b^7\,d}","Not used",1,"((2*(38*a*b^4 + 90*a^5 - 135*a^3*b^2))/(15*b^6) - (tan(c/2 + (d*x)/2)^10*(a*b^4 - 12*a^5 + 14*a^3*b^2))/b^6 + (2*tan(c/2 + (d*x)/2)^8*(9*a*b^4 + 30*a^5 - 41*a^3*b^2))/b^6 + (2*tan(c/2 + (d*x)/2)^4*(29*a*b^4 + 60*a^5 - 94*a^3*b^2))/b^6 + (4*tan(c/2 + (d*x)/2)^6*(38*a*b^4 + 90*a^5 - 135*a^3*b^2))/(3*b^6) + (tan(c/2 + (d*x)/2)^2*(157*a*b^4 + 300*a^5 - 470*a^3*b^2))/(5*b^6) + (tan(c/2 + (d*x)/2)*(540*a^4 + 244*b^4 - 825*a^2*b^2))/(30*b^5) + (tan(c/2 + (d*x)/2)^11*(12*a^4 + 4*b^4 - 17*a^2*b^2))/(2*b^5) + (tan(c/2 + (d*x)/2)^9*(84*a^4 + 44*b^4 - 131*a^2*b^2))/(2*b^5) + (tan(c/2 + (d*x)/2)^7*(108*a^4 + 44*b^4 - 165*a^2*b^2))/b^5 + (tan(c/2 + (d*x)/2)^5*(396*a^4 + 172*b^4 - 585*a^2*b^2))/(3*b^5) + (tan(c/2 + (d*x)/2)^3*(468*a^4 + 172*b^4 - 687*a^2*b^2))/(6*b^5))/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 6*a*tan(c/2 + (d*x)/2)^2 + 15*a*tan(c/2 + (d*x)/2)^4 + 20*a*tan(c/2 + (d*x)/2)^6 + 15*a*tan(c/2 + (d*x)/2)^8 + 6*a*tan(c/2 + (d*x)/2)^10 + a*tan(c/2 + (d*x)/2)^12 + 10*b*tan(c/2 + (d*x)/2)^3 + 20*b*tan(c/2 + (d*x)/2)^5 + 20*b*tan(c/2 + (d*x)/2)^7 + 10*b*tan(c/2 + (d*x)/2)^9 + 2*b*tan(c/2 + (d*x)/2)^11)) + (a*atan(((a*((2*(225*a^4*b^14 - 1200*a^6*b^12 + 2320*a^8*b^10 - 1920*a^10*b^8 + 576*a^12*b^6))/b^17 - (2*tan(c/2 + (d*x)/2)*(16*a*b^18 - 706*a^3*b^16 + 4065*a^5*b^14 - 9360*a^7*b^12 + 10400*a^9*b^10 - 5568*a^11*b^8 + 1152*a^13*b^6))/b^18 + (a*(24*a^4 + 15*b^4 - 40*a^2*b^2)*((2*tan(c/2 + (d*x)/2)*(32*a*b^20 - 256*a^3*b^18 + 416*a^5*b^16 - 192*a^7*b^14))/b^18 - (2*(44*a^2*b^18 - 92*a^4*b^16 + 48*a^6*b^14))/b^17 + (a*(32*a^2*b^3 + (2*tan(c/2 + (d*x)/2)*(48*a*b^22 - 32*a^3*b^20))/b^18)*(24*a^4 + 15*b^4 - 40*a^2*b^2)*1i)/(4*b^7))*1i)/(4*b^7))*(24*a^4 + 15*b^4 - 40*a^2*b^2))/(4*b^7) + (a*((2*(225*a^4*b^14 - 1200*a^6*b^12 + 2320*a^8*b^10 - 1920*a^10*b^8 + 576*a^12*b^6))/b^17 - (2*tan(c/2 + (d*x)/2)*(16*a*b^18 - 706*a^3*b^16 + 4065*a^5*b^14 - 9360*a^7*b^12 + 10400*a^9*b^10 - 5568*a^11*b^8 + 1152*a^13*b^6))/b^18 + (a*(24*a^4 + 15*b^4 - 40*a^2*b^2)*((2*(44*a^2*b^18 - 92*a^4*b^16 + 48*a^6*b^14))/b^17 - (2*tan(c/2 + (d*x)/2)*(32*a*b^20 - 256*a^3*b^18 + 416*a^5*b^16 - 192*a^7*b^14))/b^18 + (a*(32*a^2*b^3 + (2*tan(c/2 + (d*x)/2)*(48*a*b^22 - 32*a^3*b^20))/b^18)*(24*a^4 + 15*b^4 - 40*a^2*b^2)*1i)/(4*b^7))*1i)/(4*b^7))*(24*a^4 + 15*b^4 - 40*a^2*b^2))/(4*b^7))/((4*(1728*a^16 - 60*a^2*b^14 + 895*a^4*b^12 - 5056*a^6*b^10 + 14291*a^8*b^8 - 22310*a^10*b^6 + 19584*a^12*b^4 - 9072*a^14*b^2))/b^17 + (4*tan(c/2 + (d*x)/2)*(6912*a^17 - 450*a^3*b^14 + 6000*a^5*b^12 - 29690*a^7*b^10 + 74860*a^9*b^8 - 106592*a^11*b^6 + 86976*a^13*b^4 - 38016*a^15*b^2))/b^18 - (a*((2*(225*a^4*b^14 - 1200*a^6*b^12 + 2320*a^8*b^10 - 1920*a^10*b^8 + 576*a^12*b^6))/b^17 - (2*tan(c/2 + (d*x)/2)*(16*a*b^18 - 706*a^3*b^16 + 4065*a^5*b^14 - 9360*a^7*b^12 + 10400*a^9*b^10 - 5568*a^11*b^8 + 1152*a^13*b^6))/b^18 + (a*(24*a^4 + 15*b^4 - 40*a^2*b^2)*((2*tan(c/2 + (d*x)/2)*(32*a*b^20 - 256*a^3*b^18 + 416*a^5*b^16 - 192*a^7*b^14))/b^18 - (2*(44*a^2*b^18 - 92*a^4*b^16 + 48*a^6*b^14))/b^17 + (a*(32*a^2*b^3 + (2*tan(c/2 + (d*x)/2)*(48*a*b^22 - 32*a^3*b^20))/b^18)*(24*a^4 + 15*b^4 - 40*a^2*b^2)*1i)/(4*b^7))*1i)/(4*b^7))*(24*a^4 + 15*b^4 - 40*a^2*b^2)*1i)/(4*b^7) + (a*((2*(225*a^4*b^14 - 1200*a^6*b^12 + 2320*a^8*b^10 - 1920*a^10*b^8 + 576*a^12*b^6))/b^17 - (2*tan(c/2 + (d*x)/2)*(16*a*b^18 - 706*a^3*b^16 + 4065*a^5*b^14 - 9360*a^7*b^12 + 10400*a^9*b^10 - 5568*a^11*b^8 + 1152*a^13*b^6))/b^18 + (a*(24*a^4 + 15*b^4 - 40*a^2*b^2)*((2*(44*a^2*b^18 - 92*a^4*b^16 + 48*a^6*b^14))/b^17 - (2*tan(c/2 + (d*x)/2)*(32*a*b^20 - 256*a^3*b^18 + 416*a^5*b^16 - 192*a^7*b^14))/b^18 + (a*(32*a^2*b^3 + (2*tan(c/2 + (d*x)/2)*(48*a*b^22 - 32*a^3*b^20))/b^18)*(24*a^4 + 15*b^4 - 40*a^2*b^2)*1i)/(4*b^7))*1i)/(4*b^7))*(24*a^4 + 15*b^4 - 40*a^2*b^2)*1i)/(4*b^7)))*(24*a^4 + 15*b^4 - 40*a^2*b^2))/(2*b^7*d) - (2*atanh((64*a^2*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(64*a^2*b^3 - 572*a^4*b + (1312*a^6)/b - (1164*a^8)/b^3 + (360*a^10)/b^5 + 2624*a^5*tan(c/2 + (d*x)/2) + 128*a*b^4*tan(c/2 + (d*x)/2) - 1144*a^3*b^2*tan(c/2 + (d*x)/2) - (2328*a^7*tan(c/2 + (d*x)/2))/b^2 + (720*a^9*tan(c/2 + (d*x)/2))/b^4) - (444*a^4*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(1312*a^6*b + 64*a^2*b^5 - 572*a^4*b^3 - (1164*a^8)/b + (360*a^10)/b^3 - 2328*a^7*tan(c/2 + (d*x)/2) + 128*a*b^6*tan(c/2 + (d*x)/2) - 1144*a^3*b^4*tan(c/2 + (d*x)/2) + 2624*a^5*b^2*tan(c/2 + (d*x)/2) + (720*a^9*tan(c/2 + (d*x)/2))/b^2) + (360*a^6*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(64*a^2*b^7 - 1164*a^8*b - 572*a^4*b^5 + 1312*a^6*b^3 + (360*a^10)/b + 720*a^9*tan(c/2 + (d*x)/2) + 128*a*b^8*tan(c/2 + (d*x)/2) - 1144*a^3*b^6*tan(c/2 + (d*x)/2) + 2624*a^5*b^4*tan(c/2 + (d*x)/2) - 2328*a^7*b^2*tan(c/2 + (d*x)/2)) + (128*a*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(64*a^2*b^2 - 572*a^4 + (1312*a^6)/b^2 - (1164*a^8)/b^4 + (360*a^10)/b^6 + 128*a*b^3*tan(c/2 + (d*x)/2) - 1144*a^3*b*tan(c/2 + (d*x)/2) + (2624*a^5*tan(c/2 + (d*x)/2))/b - (2328*a^7*tan(c/2 + (d*x)/2))/b^3 + (720*a^9*tan(c/2 + (d*x)/2))/b^5) - (952*a^3*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(1312*a^6 + 64*a^2*b^4 - 572*a^4*b^2 - (1164*a^8)/b^2 + (360*a^10)/b^4 + 128*a*b^5*tan(c/2 + (d*x)/2) + 2624*a^5*b*tan(c/2 + (d*x)/2) - 1144*a^3*b^3*tan(c/2 + (d*x)/2) - (2328*a^7*tan(c/2 + (d*x)/2))/b + (720*a^9*tan(c/2 + (d*x)/2))/b^3) + (1164*a^5*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(64*a^2*b^6 - 1164*a^8 - 572*a^4*b^4 + 1312*a^6*b^2 + (360*a^10)/b^2 + 128*a*b^7*tan(c/2 + (d*x)/2) - 2328*a^7*b*tan(c/2 + (d*x)/2) - 1144*a^3*b^5*tan(c/2 + (d*x)/2) + 2624*a^5*b^3*tan(c/2 + (d*x)/2) + (720*a^9*tan(c/2 + (d*x)/2))/b) - (360*a^7*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(360*a^10 + 64*a^2*b^8 - 572*a^4*b^6 + 1312*a^6*b^4 - 1164*a^8*b^2 + 128*a*b^9*tan(c/2 + (d*x)/2) + 720*a^9*b*tan(c/2 + (d*x)/2) - 1144*a^3*b^7*tan(c/2 + (d*x)/2) + 2624*a^5*b^5*tan(c/2 + (d*x)/2) - 2328*a^7*b^3*tan(c/2 + (d*x)/2)))*(6*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^7*d)","B"
1259,1,5197,266,13.601375,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)*(a + b*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{\frac{2\,\left(12\,a^4-13\,a^2\,b^2+3\,b^4\right)}{3\,a\,b^4}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,a^4-20\,a^2\,b^2+3\,b^4\right)}{3\,a^2\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^4-2\,a^2\,b^2+b^4\right)}{a^2\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^4-3\,a^2\,b^2+b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(10\,a^4-12\,a^2\,b^2+3\,b^4\right)}{a^2\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a^4-13\,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(14\,a^4-14\,a^2\,b^2+3\,b^4\right)}{a^2\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(36\,a^4-43\,a^2\,b^2+9\,b^4\right)}{3\,a\,b^4}}{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+4\,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\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,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{2\,a\,\mathrm{atan}\left(\frac{\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}\,b^4+1600\,a^{14}\,b^6-3792\,a^{12}\,b^8+4028\,a^{10}\,b^{10}-1414\,a^8\,b^{12}-560\,a^6\,b^{14}+390\,a^4\,b^{16}+4\,a^2\,b^{18}+b^{20}\right)}{a^3\,b^{16}}-\frac{32\,\left(-224\,a^{14}+960\,a^{12}\,b^2-1434\,a^{10}\,b^4+722\,a^8\,b^6+154\,a^6\,b^8-184\,a^4\,b^{10}+5\,a^2\,b^{12}\right)}{a^2\,b^{11}}+\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(-48\,a^{12}\,b^4+184\,a^{10}\,b^6-235\,a^8\,b^8+114\,a^6\,b^{10}-25\,a^4\,b^{12}+7\,a^2\,b^{14}+4\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{14}\,b^8-480\,a^{12}\,b^{10}+1434\,a^{10}\,b^{12}-1596\,a^8\,b^{14}+610\,a^6\,b^{16}+20\,a^4\,b^{18}-19\,a^2\,b^{20}\right)}{a^3\,b^{16}}+\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(14\,a^8\,b^{10}-25\,a^6\,b^{12}+4\,a^4\,b^{14}+8\,a^2\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^{14}+60\,a^8\,b^{16}-62\,a^6\,b^{18}+3\,a^4\,b^{20}+16\,a^2\,b^{22}\right)}{a^3\,b^{16}}+\frac{a\,\left(\frac{32\,\left(4\,a^4\,b^{16}-3\,a^6\,b^{14}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{18}-17\,a^6\,b^{20}+16\,a^4\,b^{22}\right)}{a^3\,b^{16}}\right)\,\left(4\,a^2-5\,b^2\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}\right)}{b^5}-\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(-224\,a^{14}+960\,a^{12}\,b^2-1434\,a^{10}\,b^4+722\,a^8\,b^6+154\,a^6\,b^8-184\,a^4\,b^{10}+5\,a^2\,b^{12}\right)}{a^2\,b^{11}}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}\,b^4+1600\,a^{14}\,b^6-3792\,a^{12}\,b^8+4028\,a^{10}\,b^{10}-1414\,a^8\,b^{12}-560\,a^6\,b^{14}+390\,a^4\,b^{16}+4\,a^2\,b^{18}+b^{20}\right)}{a^3\,b^{16}}+\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(-48\,a^{12}\,b^4+184\,a^{10}\,b^6-235\,a^8\,b^8+114\,a^6\,b^{10}-25\,a^4\,b^{12}+7\,a^2\,b^{14}+4\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{14}\,b^8-480\,a^{12}\,b^{10}+1434\,a^{10}\,b^{12}-1596\,a^8\,b^{14}+610\,a^6\,b^{16}+20\,a^4\,b^{18}-19\,a^2\,b^{20}\right)}{a^3\,b^{16}}-\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(14\,a^8\,b^{10}-25\,a^6\,b^{12}+4\,a^4\,b^{14}+8\,a^2\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^{14}+60\,a^8\,b^{16}-62\,a^6\,b^{18}+3\,a^4\,b^{20}+16\,a^2\,b^{22}\right)}{a^3\,b^{16}}-\frac{a\,\left(\frac{32\,\left(4\,a^4\,b^{16}-3\,a^6\,b^{14}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{18}-17\,a^6\,b^{20}+16\,a^4\,b^{22}\right)}{a^3\,b^{16}}\right)\,\left(4\,a^2-5\,b^2\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}\right)}{b^5}}{\frac{64\,\left(224\,a^{12}-960\,a^{10}\,b^2+1482\,a^8\,b^4-906\,a^6\,b^6+81\,a^4\,b^8+84\,a^2\,b^{10}-5\,b^{12}\right)}{a^2\,b^{11}}-\frac{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2048\,a^{18}-12288\,a^{16}\,b^2+29696\,a^{14}\,b^4-36160\,a^{12}\,b^6+21944\,a^{10}\,b^8-4540\,a^8\,b^{10}-1200\,a^6\,b^{12}+500\,a^4\,b^{14}\right)}{a^3\,b^{16}}+\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}\,b^4+1600\,a^{14}\,b^6-3792\,a^{12}\,b^8+4028\,a^{10}\,b^{10}-1414\,a^8\,b^{12}-560\,a^6\,b^{14}+390\,a^4\,b^{16}+4\,a^2\,b^{18}+b^{20}\right)}{a^3\,b^{16}}-\frac{32\,\left(-224\,a^{14}+960\,a^{12}\,b^2-1434\,a^{10}\,b^4+722\,a^8\,b^6+154\,a^6\,b^8-184\,a^4\,b^{10}+5\,a^2\,b^{12}\right)}{a^2\,b^{11}}+\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(-48\,a^{12}\,b^4+184\,a^{10}\,b^6-235\,a^8\,b^8+114\,a^6\,b^{10}-25\,a^4\,b^{12}+7\,a^2\,b^{14}+4\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{14}\,b^8-480\,a^{12}\,b^{10}+1434\,a^{10}\,b^{12}-1596\,a^8\,b^{14}+610\,a^6\,b^{16}+20\,a^4\,b^{18}-19\,a^2\,b^{20}\right)}{a^3\,b^{16}}+\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(14\,a^8\,b^{10}-25\,a^6\,b^{12}+4\,a^4\,b^{14}+8\,a^2\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^{14}+60\,a^8\,b^{16}-62\,a^6\,b^{18}+3\,a^4\,b^{20}+16\,a^2\,b^{22}\right)}{a^3\,b^{16}}+\frac{a\,\left(\frac{32\,\left(4\,a^4\,b^{16}-3\,a^6\,b^{14}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{18}-17\,a^6\,b^{20}+16\,a^4\,b^{22}\right)}{a^3\,b^{16}}\right)\,\left(4\,a^2-5\,b^2\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}+\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(-224\,a^{14}+960\,a^{12}\,b^2-1434\,a^{10}\,b^4+722\,a^8\,b^6+154\,a^6\,b^8-184\,a^4\,b^{10}+5\,a^2\,b^{12}\right)}{a^2\,b^{11}}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}\,b^4+1600\,a^{14}\,b^6-3792\,a^{12}\,b^8+4028\,a^{10}\,b^{10}-1414\,a^8\,b^{12}-560\,a^6\,b^{14}+390\,a^4\,b^{16}+4\,a^2\,b^{18}+b^{20}\right)}{a^3\,b^{16}}+\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(-48\,a^{12}\,b^4+184\,a^{10}\,b^6-235\,a^8\,b^8+114\,a^6\,b^{10}-25\,a^4\,b^{12}+7\,a^2\,b^{14}+4\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{14}\,b^8-480\,a^{12}\,b^{10}+1434\,a^{10}\,b^{12}-1596\,a^8\,b^{14}+610\,a^6\,b^{16}+20\,a^4\,b^{18}-19\,a^2\,b^{20}\right)}{a^3\,b^{16}}-\frac{a\,\left(4\,a^2-5\,b^2\right)\,\left(\frac{32\,\left(14\,a^8\,b^{10}-25\,a^6\,b^{12}+4\,a^4\,b^{14}+8\,a^2\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^{14}+60\,a^8\,b^{16}-62\,a^6\,b^{18}+3\,a^4\,b^{20}+16\,a^2\,b^{22}\right)}{a^3\,b^{16}}-\frac{a\,\left(\frac{32\,\left(4\,a^4\,b^{16}-3\,a^6\,b^{14}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{18}-17\,a^6\,b^{20}+16\,a^4\,b^{22}\right)}{a^3\,b^{16}}\right)\,\left(4\,a^2-5\,b^2\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}}\right)\,\left(4\,a^2-5\,b^2\right)}{b^5\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}\,b^4+1600\,a^{14}\,b^6-3792\,a^{12}\,b^8+4028\,a^{10}\,b^{10}-1414\,a^8\,b^{12}-560\,a^6\,b^{14}+390\,a^4\,b^{16}+4\,a^2\,b^{18}+b^{20}\right)}{a^3\,b^{16}}-\frac{32\,\left(-224\,a^{14}+960\,a^{12}\,b^2-1434\,a^{10}\,b^4+722\,a^8\,b^6+154\,a^6\,b^8-184\,a^4\,b^{10}+5\,a^2\,b^{12}\right)}{a^2\,b^{11}}+\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-48\,a^{12}\,b^4+184\,a^{10}\,b^6-235\,a^8\,b^8+114\,a^6\,b^{10}-25\,a^4\,b^{12}+7\,a^2\,b^{14}+4\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{14}\,b^8-480\,a^{12}\,b^{10}+1434\,a^{10}\,b^{12}-1596\,a^8\,b^{14}+610\,a^6\,b^{16}+20\,a^4\,b^{18}-19\,a^2\,b^{20}\right)}{a^3\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(14\,a^8\,b^{10}-25\,a^6\,b^{12}+4\,a^4\,b^{14}+8\,a^2\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^{14}+60\,a^8\,b^{16}-62\,a^6\,b^{18}+3\,a^4\,b^{20}+16\,a^2\,b^{22}\right)}{a^3\,b^{16}}+\frac{\left(\frac{32\,\left(4\,a^4\,b^{16}-3\,a^6\,b^{14}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{18}-17\,a^6\,b^{20}+16\,a^4\,b^{22}\right)}{a^3\,b^{16}}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)}{a^2\,b^5}\right)}{a^2\,b^5}\right)\,1{}\mathrm{i}}{a^2\,b^5}-\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-224\,a^{14}+960\,a^{12}\,b^2-1434\,a^{10}\,b^4+722\,a^8\,b^6+154\,a^6\,b^8-184\,a^4\,b^{10}+5\,a^2\,b^{12}\right)}{a^2\,b^{11}}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}\,b^4+1600\,a^{14}\,b^6-3792\,a^{12}\,b^8+4028\,a^{10}\,b^{10}-1414\,a^8\,b^{12}-560\,a^6\,b^{14}+390\,a^4\,b^{16}+4\,a^2\,b^{18}+b^{20}\right)}{a^3\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-48\,a^{12}\,b^4+184\,a^{10}\,b^6-235\,a^8\,b^8+114\,a^6\,b^{10}-25\,a^4\,b^{12}+7\,a^2\,b^{14}+4\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{14}\,b^8-480\,a^{12}\,b^{10}+1434\,a^{10}\,b^{12}-1596\,a^8\,b^{14}+610\,a^6\,b^{16}+20\,a^4\,b^{18}-19\,a^2\,b^{20}\right)}{a^3\,b^{16}}-\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(14\,a^8\,b^{10}-25\,a^6\,b^{12}+4\,a^4\,b^{14}+8\,a^2\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^{14}+60\,a^8\,b^{16}-62\,a^6\,b^{18}+3\,a^4\,b^{20}+16\,a^2\,b^{22}\right)}{a^3\,b^{16}}-\frac{\left(\frac{32\,\left(4\,a^4\,b^{16}-3\,a^6\,b^{14}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{18}-17\,a^6\,b^{20}+16\,a^4\,b^{22}\right)}{a^3\,b^{16}}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)}{a^2\,b^5}\right)}{a^2\,b^5}\right)\,1{}\mathrm{i}}{a^2\,b^5}}{\frac{64\,\left(224\,a^{12}-960\,a^{10}\,b^2+1482\,a^8\,b^4-906\,a^6\,b^6+81\,a^4\,b^8+84\,a^2\,b^{10}-5\,b^{12}\right)}{a^2\,b^{11}}-\frac{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2048\,a^{18}-12288\,a^{16}\,b^2+29696\,a^{14}\,b^4-36160\,a^{12}\,b^6+21944\,a^{10}\,b^8-4540\,a^8\,b^{10}-1200\,a^6\,b^{12}+500\,a^4\,b^{14}\right)}{a^3\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}\,b^4+1600\,a^{14}\,b^6-3792\,a^{12}\,b^8+4028\,a^{10}\,b^{10}-1414\,a^8\,b^{12}-560\,a^6\,b^{14}+390\,a^4\,b^{16}+4\,a^2\,b^{18}+b^{20}\right)}{a^3\,b^{16}}-\frac{32\,\left(-224\,a^{14}+960\,a^{12}\,b^2-1434\,a^{10}\,b^4+722\,a^8\,b^6+154\,a^6\,b^8-184\,a^4\,b^{10}+5\,a^2\,b^{12}\right)}{a^2\,b^{11}}+\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-48\,a^{12}\,b^4+184\,a^{10}\,b^6-235\,a^8\,b^8+114\,a^6\,b^{10}-25\,a^4\,b^{12}+7\,a^2\,b^{14}+4\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{14}\,b^8-480\,a^{12}\,b^{10}+1434\,a^{10}\,b^{12}-1596\,a^8\,b^{14}+610\,a^6\,b^{16}+20\,a^4\,b^{18}-19\,a^2\,b^{20}\right)}{a^3\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(14\,a^8\,b^{10}-25\,a^6\,b^{12}+4\,a^4\,b^{14}+8\,a^2\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^{14}+60\,a^8\,b^{16}-62\,a^6\,b^{18}+3\,a^4\,b^{20}+16\,a^2\,b^{22}\right)}{a^3\,b^{16}}+\frac{\left(\frac{32\,\left(4\,a^4\,b^{16}-3\,a^6\,b^{14}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{18}-17\,a^6\,b^{20}+16\,a^4\,b^{22}\right)}{a^3\,b^{16}}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)}{a^2\,b^5}\right)}{a^2\,b^5}\right)}{a^2\,b^5}+\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-224\,a^{14}+960\,a^{12}\,b^2-1434\,a^{10}\,b^4+722\,a^8\,b^6+154\,a^6\,b^8-184\,a^4\,b^{10}+5\,a^2\,b^{12}\right)}{a^2\,b^{11}}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}\,b^4+1600\,a^{14}\,b^6-3792\,a^{12}\,b^8+4028\,a^{10}\,b^{10}-1414\,a^8\,b^{12}-560\,a^6\,b^{14}+390\,a^4\,b^{16}+4\,a^2\,b^{18}+b^{20}\right)}{a^3\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-48\,a^{12}\,b^4+184\,a^{10}\,b^6-235\,a^8\,b^8+114\,a^6\,b^{10}-25\,a^4\,b^{12}+7\,a^2\,b^{14}+4\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{14}\,b^8-480\,a^{12}\,b^{10}+1434\,a^{10}\,b^{12}-1596\,a^8\,b^{14}+610\,a^6\,b^{16}+20\,a^4\,b^{18}-19\,a^2\,b^{20}\right)}{a^3\,b^{16}}-\frac{\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(14\,a^8\,b^{10}-25\,a^6\,b^{12}+4\,a^4\,b^{14}+8\,a^2\,b^{16}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^{14}+60\,a^8\,b^{16}-62\,a^6\,b^{18}+3\,a^4\,b^{20}+16\,a^2\,b^{22}\right)}{a^3\,b^{16}}-\frac{\left(\frac{32\,\left(4\,a^4\,b^{16}-3\,a^6\,b^{14}\right)}{a^2\,b^{11}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8\,b^{18}-17\,a^6\,b^{20}+16\,a^4\,b^{22}\right)}{a^3\,b^{16}}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)}{a^2\,b^5}\right)}{a^2\,b^5}\right)}{a^2\,b^5}}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^2\,b^5\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) + ((2*(12*a^4 + 3*b^4 - 13*a^2*b^2))/(3*a*b^4) + (2*tan(c/2 + (d*x)/2)*(18*a^4 + 3*b^4 - 20*a^2*b^2))/(3*a^2*b^3) + (2*tan(c/2 + (d*x)/2)^7*(2*a^4 + b^4 - 2*a^2*b^2))/(a^2*b^3) + (2*tan(c/2 + (d*x)/2)^6*(4*a^4 + b^4 - 3*a^2*b^2))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^5*(10*a^4 + 3*b^4 - 12*a^2*b^2))/(a^2*b^3) + (2*tan(c/2 + (d*x)/2)^4*(12*a^4 + 3*b^4 - 13*a^2*b^2))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^3*(14*a^4 + 3*b^4 - 14*a^2*b^2))/(a^2*b^3) + (2*tan(c/2 + (d*x)/2)^2*(36*a^4 + 9*b^4 - 43*a^2*b^2))/(3*a*b^4))/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 + 4*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)) + (2*a*atan(((a*(4*a^2 - 5*b^2)*((a*(4*a^2 - 5*b^2)*((32*(4*b^16 + 7*a^2*b^14 - 25*a^4*b^12 + 114*a^6*b^10 - 235*a^8*b^8 + 184*a^10*b^6 - 48*a^12*b^4))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(20*a^4*b^18 - 19*a^2*b^20 + 610*a^6*b^16 - 1596*a^8*b^14 + 1434*a^10*b^12 - 480*a^12*b^10 + 32*a^14*b^8))/(a^3*b^16) + (a*(4*a^2 - 5*b^2)*((32*(8*a^2*b^16 + 4*a^4*b^14 - 25*a^6*b^12 + 14*a^8*b^10))/(a^2*b^11) + (a*((32*(4*a^4*b^16 - 3*a^6*b^14))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^22 - 17*a^6*b^20 + 2*a^8*b^18))/(a^3*b^16))*(4*a^2 - 5*b^2)*1i)/b^5 + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^22 + 3*a^4*b^20 - 62*a^6*b^18 + 60*a^8*b^16 - 16*a^10*b^14))/(a^3*b^16))*1i)/b^5)*1i)/b^5 - (32*(5*a^2*b^12 - 224*a^14 - 184*a^4*b^10 + 154*a^6*b^8 + 722*a^8*b^6 - 1434*a^10*b^4 + 960*a^12*b^2))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(b^20 + 4*a^2*b^18 + 390*a^4*b^16 - 560*a^6*b^14 - 1414*a^8*b^12 + 4028*a^10*b^10 - 3792*a^12*b^8 + 1600*a^14*b^6 - 256*a^16*b^4))/(a^3*b^16)))/b^5 - (a*(4*a^2 - 5*b^2)*((32*(5*a^2*b^12 - 224*a^14 - 184*a^4*b^10 + 154*a^6*b^8 + 722*a^8*b^6 - 1434*a^10*b^4 + 960*a^12*b^2))/(a^2*b^11) + (a*(4*a^2 - 5*b^2)*((32*(4*b^16 + 7*a^2*b^14 - 25*a^4*b^12 + 114*a^6*b^10 - 235*a^8*b^8 + 184*a^10*b^6 - 48*a^12*b^4))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(20*a^4*b^18 - 19*a^2*b^20 + 610*a^6*b^16 - 1596*a^8*b^14 + 1434*a^10*b^12 - 480*a^12*b^10 + 32*a^14*b^8))/(a^3*b^16) - (a*(4*a^2 - 5*b^2)*((32*(8*a^2*b^16 + 4*a^4*b^14 - 25*a^6*b^12 + 14*a^8*b^10))/(a^2*b^11) - (a*((32*(4*a^4*b^16 - 3*a^6*b^14))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^22 - 17*a^6*b^20 + 2*a^8*b^18))/(a^3*b^16))*(4*a^2 - 5*b^2)*1i)/b^5 + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^22 + 3*a^4*b^20 - 62*a^6*b^18 + 60*a^8*b^16 - 16*a^10*b^14))/(a^3*b^16))*1i)/b^5)*1i)/b^5 - (32*tan(c/2 + (d*x)/2)*(b^20 + 4*a^2*b^18 + 390*a^4*b^16 - 560*a^6*b^14 - 1414*a^8*b^12 + 4028*a^10*b^10 - 3792*a^12*b^8 + 1600*a^14*b^6 - 256*a^16*b^4))/(a^3*b^16)))/b^5)/((64*(224*a^12 - 5*b^12 + 84*a^2*b^10 + 81*a^4*b^8 - 906*a^6*b^6 + 1482*a^8*b^4 - 960*a^10*b^2))/(a^2*b^11) - (64*tan(c/2 + (d*x)/2)*(2048*a^18 + 500*a^4*b^14 - 1200*a^6*b^12 - 4540*a^8*b^10 + 21944*a^10*b^8 - 36160*a^12*b^6 + 29696*a^14*b^4 - 12288*a^16*b^2))/(a^3*b^16) + (a*(4*a^2 - 5*b^2)*((a*(4*a^2 - 5*b^2)*((32*(4*b^16 + 7*a^2*b^14 - 25*a^4*b^12 + 114*a^6*b^10 - 235*a^8*b^8 + 184*a^10*b^6 - 48*a^12*b^4))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(20*a^4*b^18 - 19*a^2*b^20 + 610*a^6*b^16 - 1596*a^8*b^14 + 1434*a^10*b^12 - 480*a^12*b^10 + 32*a^14*b^8))/(a^3*b^16) + (a*(4*a^2 - 5*b^2)*((32*(8*a^2*b^16 + 4*a^4*b^14 - 25*a^6*b^12 + 14*a^8*b^10))/(a^2*b^11) + (a*((32*(4*a^4*b^16 - 3*a^6*b^14))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^22 - 17*a^6*b^20 + 2*a^8*b^18))/(a^3*b^16))*(4*a^2 - 5*b^2)*1i)/b^5 + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^22 + 3*a^4*b^20 - 62*a^6*b^18 + 60*a^8*b^16 - 16*a^10*b^14))/(a^3*b^16))*1i)/b^5)*1i)/b^5 - (32*(5*a^2*b^12 - 224*a^14 - 184*a^4*b^10 + 154*a^6*b^8 + 722*a^8*b^6 - 1434*a^10*b^4 + 960*a^12*b^2))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(b^20 + 4*a^2*b^18 + 390*a^4*b^16 - 560*a^6*b^14 - 1414*a^8*b^12 + 4028*a^10*b^10 - 3792*a^12*b^8 + 1600*a^14*b^6 - 256*a^16*b^4))/(a^3*b^16))*1i)/b^5 + (a*(4*a^2 - 5*b^2)*((32*(5*a^2*b^12 - 224*a^14 - 184*a^4*b^10 + 154*a^6*b^8 + 722*a^8*b^6 - 1434*a^10*b^4 + 960*a^12*b^2))/(a^2*b^11) + (a*(4*a^2 - 5*b^2)*((32*(4*b^16 + 7*a^2*b^14 - 25*a^4*b^12 + 114*a^6*b^10 - 235*a^8*b^8 + 184*a^10*b^6 - 48*a^12*b^4))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(20*a^4*b^18 - 19*a^2*b^20 + 610*a^6*b^16 - 1596*a^8*b^14 + 1434*a^10*b^12 - 480*a^12*b^10 + 32*a^14*b^8))/(a^3*b^16) - (a*(4*a^2 - 5*b^2)*((32*(8*a^2*b^16 + 4*a^4*b^14 - 25*a^6*b^12 + 14*a^8*b^10))/(a^2*b^11) - (a*((32*(4*a^4*b^16 - 3*a^6*b^14))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^22 - 17*a^6*b^20 + 2*a^8*b^18))/(a^3*b^16))*(4*a^2 - 5*b^2)*1i)/b^5 + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^22 + 3*a^4*b^20 - 62*a^6*b^18 + 60*a^8*b^16 - 16*a^10*b^14))/(a^3*b^16))*1i)/b^5)*1i)/b^5 - (32*tan(c/2 + (d*x)/2)*(b^20 + 4*a^2*b^18 + 390*a^4*b^16 - 560*a^6*b^14 - 1414*a^8*b^12 + 4028*a^10*b^10 - 3792*a^12*b^8 + 1600*a^14*b^6 - 256*a^16*b^4))/(a^3*b^16))*1i)/b^5))*(4*a^2 - 5*b^2))/(b^5*d) + (atan((((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(b^20 + 4*a^2*b^18 + 390*a^4*b^16 - 560*a^6*b^14 - 1414*a^8*b^12 + 4028*a^10*b^10 - 3792*a^12*b^8 + 1600*a^14*b^6 - 256*a^16*b^4))/(a^3*b^16) - (32*(5*a^2*b^12 - 224*a^14 - 184*a^4*b^10 + 154*a^6*b^8 + 722*a^8*b^6 - 1434*a^10*b^4 + 960*a^12*b^2))/(a^2*b^11) + ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*b^16 + 7*a^2*b^14 - 25*a^4*b^12 + 114*a^6*b^10 - 235*a^8*b^8 + 184*a^10*b^6 - 48*a^12*b^4))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(20*a^4*b^18 - 19*a^2*b^20 + 610*a^6*b^16 - 1596*a^8*b^14 + 1434*a^10*b^12 - 480*a^12*b^10 + 32*a^14*b^8))/(a^3*b^16) + ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(8*a^2*b^16 + 4*a^4*b^14 - 25*a^6*b^12 + 14*a^8*b^10))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^22 + 3*a^4*b^20 - 62*a^6*b^18 + 60*a^8*b^16 - 16*a^10*b^14))/(a^3*b^16) + (((32*(4*a^4*b^16 - 3*a^6*b^14))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^22 - 17*a^6*b^20 + 2*a^8*b^18))/(a^3*b^16))*(4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5)))/(a^2*b^5)))/(a^2*b^5))*1i)/(a^2*b^5) - ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(5*a^2*b^12 - 224*a^14 - 184*a^4*b^10 + 154*a^6*b^8 + 722*a^8*b^6 - 1434*a^10*b^4 + 960*a^12*b^2))/(a^2*b^11) - (32*tan(c/2 + (d*x)/2)*(b^20 + 4*a^2*b^18 + 390*a^4*b^16 - 560*a^6*b^14 - 1414*a^8*b^12 + 4028*a^10*b^10 - 3792*a^12*b^8 + 1600*a^14*b^6 - 256*a^16*b^4))/(a^3*b^16) + ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*b^16 + 7*a^2*b^14 - 25*a^4*b^12 + 114*a^6*b^10 - 235*a^8*b^8 + 184*a^10*b^6 - 48*a^12*b^4))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(20*a^4*b^18 - 19*a^2*b^20 + 610*a^6*b^16 - 1596*a^8*b^14 + 1434*a^10*b^12 - 480*a^12*b^10 + 32*a^14*b^8))/(a^3*b^16) - ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(8*a^2*b^16 + 4*a^4*b^14 - 25*a^6*b^12 + 14*a^8*b^10))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^22 + 3*a^4*b^20 - 62*a^6*b^18 + 60*a^8*b^16 - 16*a^10*b^14))/(a^3*b^16) - (((32*(4*a^4*b^16 - 3*a^6*b^14))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^22 - 17*a^6*b^20 + 2*a^8*b^18))/(a^3*b^16))*(4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5)))/(a^2*b^5)))/(a^2*b^5))*1i)/(a^2*b^5))/((64*(224*a^12 - 5*b^12 + 84*a^2*b^10 + 81*a^4*b^8 - 906*a^6*b^6 + 1482*a^8*b^4 - 960*a^10*b^2))/(a^2*b^11) - (64*tan(c/2 + (d*x)/2)*(2048*a^18 + 500*a^4*b^14 - 1200*a^6*b^12 - 4540*a^8*b^10 + 21944*a^10*b^8 - 36160*a^12*b^6 + 29696*a^14*b^4 - 12288*a^16*b^2))/(a^3*b^16) + ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(b^20 + 4*a^2*b^18 + 390*a^4*b^16 - 560*a^6*b^14 - 1414*a^8*b^12 + 4028*a^10*b^10 - 3792*a^12*b^8 + 1600*a^14*b^6 - 256*a^16*b^4))/(a^3*b^16) - (32*(5*a^2*b^12 - 224*a^14 - 184*a^4*b^10 + 154*a^6*b^8 + 722*a^8*b^6 - 1434*a^10*b^4 + 960*a^12*b^2))/(a^2*b^11) + ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*b^16 + 7*a^2*b^14 - 25*a^4*b^12 + 114*a^6*b^10 - 235*a^8*b^8 + 184*a^10*b^6 - 48*a^12*b^4))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(20*a^4*b^18 - 19*a^2*b^20 + 610*a^6*b^16 - 1596*a^8*b^14 + 1434*a^10*b^12 - 480*a^12*b^10 + 32*a^14*b^8))/(a^3*b^16) + ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(8*a^2*b^16 + 4*a^4*b^14 - 25*a^6*b^12 + 14*a^8*b^10))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^22 + 3*a^4*b^20 - 62*a^6*b^18 + 60*a^8*b^16 - 16*a^10*b^14))/(a^3*b^16) + (((32*(4*a^4*b^16 - 3*a^6*b^14))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^22 - 17*a^6*b^20 + 2*a^8*b^18))/(a^3*b^16))*(4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5)))/(a^2*b^5)))/(a^2*b^5)))/(a^2*b^5) + ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(5*a^2*b^12 - 224*a^14 - 184*a^4*b^10 + 154*a^6*b^8 + 722*a^8*b^6 - 1434*a^10*b^4 + 960*a^12*b^2))/(a^2*b^11) - (32*tan(c/2 + (d*x)/2)*(b^20 + 4*a^2*b^18 + 390*a^4*b^16 - 560*a^6*b^14 - 1414*a^8*b^12 + 4028*a^10*b^10 - 3792*a^12*b^8 + 1600*a^14*b^6 - 256*a^16*b^4))/(a^3*b^16) + ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*b^16 + 7*a^2*b^14 - 25*a^4*b^12 + 114*a^6*b^10 - 235*a^8*b^8 + 184*a^10*b^6 - 48*a^12*b^4))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(20*a^4*b^18 - 19*a^2*b^20 + 610*a^6*b^16 - 1596*a^8*b^14 + 1434*a^10*b^12 - 480*a^12*b^10 + 32*a^14*b^8))/(a^3*b^16) - ((4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(8*a^2*b^16 + 4*a^4*b^14 - 25*a^6*b^12 + 14*a^8*b^10))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^2*b^22 + 3*a^4*b^20 - 62*a^6*b^18 + 60*a^8*b^16 - 16*a^10*b^14))/(a^3*b^16) - (((32*(4*a^4*b^16 - 3*a^6*b^14))/(a^2*b^11) + (32*tan(c/2 + (d*x)/2)*(16*a^4*b^22 - 17*a^6*b^20 + 2*a^8*b^18))/(a^3*b^16))*(4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5)))/(a^2*b^5)))/(a^2*b^5)))/(a^2*b^5)))*(4*a^2 + b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^2*b^5*d)","B"
1260,1,5214,254,13.483472,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{a+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^4-4\,a^2\,b^2+3\,b^4\right)}{b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^4-2\,a^2\,b^2+3\,b^4\right)}{b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^4-5\,a^2\,b^2+3\,b^4\right)}{b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(6\,a^4-7\,a^2\,b^2+4\,b^4\right)}{a\,b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(18\,a^4-5\,a^2\,b^2+4\,b^4\right)}{a\,b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(24\,a^4-13\,a^2\,b^2+8\,b^4\right)}{a\,b^2}}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,b\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,b\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{8\,\left(378\,a^{15}-1215\,a^{13}\,b^2+1008\,a^{11}\,b^4+541\,a^9\,b^6-1158\,a^7\,b^8+488\,a^5\,b^{10}-40\,a^3\,b^{12}\right)}{a^6\,b^8}-\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{12}\,b^{11}-160\,a^{10}\,b^{13}+96\,a^8\,b^{15}+136\,a^6\,b^{17}-128\,a^4\,b^{19}\right)}{a^6\,b^{12}}+\frac{\left(\frac{8\,\left(16\,a^8\,b^{13}-12\,a^{10}\,b^{11}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{14}-68\,a^9\,b^{16}+64\,a^7\,b^{18}\right)}{a^6\,b^{12}}\right)\,\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)}{2\,b^4}-\frac{8\,\left(42\,a^{11}\,b^8-50\,a^9\,b^{10}-48\,a^7\,b^{12}+64\,a^5\,b^{14}\right)}{a^6\,b^8}\right)}{2\,b^4}-\frac{8\,\left(108\,a^{14}\,b^3-324\,a^{12}\,b^5+315\,a^{10}\,b^7-184\,a^8\,b^9+100\,a^6\,b^{11}+48\,a^4\,b^{13}-64\,a^2\,b^{15}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{15}\,b^6-1020\,a^{13}\,b^8+2369\,a^{11}\,b^{10}-1696\,a^9\,b^{12}+20\,a^7\,b^{14}+240\,a^5\,b^{16}+16\,a^3\,b^{18}\right)}{a^6\,b^{12}}\right)}{2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-432\,a^{16}\,b^3+2160\,a^{14}\,b^5-3564\,a^{12}\,b^7+1216\,a^{10}\,b^9+2502\,a^8\,b^{11}-2560\,a^6\,b^{13}+680\,a^4\,b^{15}-32\,a^2\,b^{17}+32\,b^{19}\right)}{a^6\,b^{12}}\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{8\,\left(378\,a^{15}-1215\,a^{13}\,b^2+1008\,a^{11}\,b^4+541\,a^9\,b^6-1158\,a^7\,b^8+488\,a^5\,b^{10}-40\,a^3\,b^{12}\right)}{a^6\,b^8}+\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{8\,\left(42\,a^{11}\,b^8-50\,a^9\,b^{10}-48\,a^7\,b^{12}+64\,a^5\,b^{14}\right)}{a^6\,b^8}+\frac{\left(\frac{8\,\left(16\,a^8\,b^{13}-12\,a^{10}\,b^{11}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{14}-68\,a^9\,b^{16}+64\,a^7\,b^{18}\right)}{a^6\,b^{12}}\right)\,\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)}{2\,b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{12}\,b^{11}-160\,a^{10}\,b^{13}+96\,a^8\,b^{15}+136\,a^6\,b^{17}-128\,a^4\,b^{19}\right)}{a^6\,b^{12}}\right)}{2\,b^4}-\frac{8\,\left(108\,a^{14}\,b^3-324\,a^{12}\,b^5+315\,a^{10}\,b^7-184\,a^8\,b^9+100\,a^6\,b^{11}+48\,a^4\,b^{13}-64\,a^2\,b^{15}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{15}\,b^6-1020\,a^{13}\,b^8+2369\,a^{11}\,b^{10}-1696\,a^9\,b^{12}+20\,a^7\,b^{14}+240\,a^5\,b^{16}+16\,a^3\,b^{18}\right)}{a^6\,b^{12}}\right)}{2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-432\,a^{16}\,b^3+2160\,a^{14}\,b^5-3564\,a^{12}\,b^7+1216\,a^{10}\,b^9+2502\,a^8\,b^{11}-2560\,a^6\,b^{13}+680\,a^4\,b^{15}-32\,a^2\,b^{17}+32\,b^{19}\right)}{a^6\,b^{12}}\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{8\,\left(378\,a^{15}-1215\,a^{13}\,b^2+1008\,a^{11}\,b^4+541\,a^9\,b^6-1158\,a^7\,b^8+488\,a^5\,b^{10}-40\,a^3\,b^{12}\right)}{a^6\,b^8}-\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{12}\,b^{11}-160\,a^{10}\,b^{13}+96\,a^8\,b^{15}+136\,a^6\,b^{17}-128\,a^4\,b^{19}\right)}{a^6\,b^{12}}+\frac{\left(\frac{8\,\left(16\,a^8\,b^{13}-12\,a^{10}\,b^{11}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{14}-68\,a^9\,b^{16}+64\,a^7\,b^{18}\right)}{a^6\,b^{12}}\right)\,\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)}{2\,b^4}-\frac{8\,\left(42\,a^{11}\,b^8-50\,a^9\,b^{10}-48\,a^7\,b^{12}+64\,a^5\,b^{14}\right)}{a^6\,b^8}\right)}{2\,b^4}-\frac{8\,\left(108\,a^{14}\,b^3-324\,a^{12}\,b^5+315\,a^{10}\,b^7-184\,a^8\,b^9+100\,a^6\,b^{11}+48\,a^4\,b^{13}-64\,a^2\,b^{15}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{15}\,b^6-1020\,a^{13}\,b^8+2369\,a^{11}\,b^{10}-1696\,a^9\,b^{12}+20\,a^7\,b^{14}+240\,a^5\,b^{16}+16\,a^3\,b^{18}\right)}{a^6\,b^{12}}\right)}{2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-432\,a^{16}\,b^3+2160\,a^{14}\,b^5-3564\,a^{12}\,b^7+1216\,a^{10}\,b^9+2502\,a^8\,b^{11}-2560\,a^6\,b^{13}+680\,a^4\,b^{15}-32\,a^2\,b^{17}+32\,b^{19}\right)}{a^6\,b^{12}}\right)}{2\,b^4}-\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{8\,\left(378\,a^{15}-1215\,a^{13}\,b^2+1008\,a^{11}\,b^4+541\,a^9\,b^6-1158\,a^7\,b^8+488\,a^5\,b^{10}-40\,a^3\,b^{12}\right)}{a^6\,b^8}+\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{8\,\left(42\,a^{11}\,b^8-50\,a^9\,b^{10}-48\,a^7\,b^{12}+64\,a^5\,b^{14}\right)}{a^6\,b^8}+\frac{\left(\frac{8\,\left(16\,a^8\,b^{13}-12\,a^{10}\,b^{11}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{14}-68\,a^9\,b^{16}+64\,a^7\,b^{18}\right)}{a^6\,b^{12}}\right)\,\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)}{2\,b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{12}\,b^{11}-160\,a^{10}\,b^{13}+96\,a^8\,b^{15}+136\,a^6\,b^{17}-128\,a^4\,b^{19}\right)}{a^6\,b^{12}}\right)}{2\,b^4}-\frac{8\,\left(108\,a^{14}\,b^3-324\,a^{12}\,b^5+315\,a^{10}\,b^7-184\,a^8\,b^9+100\,a^6\,b^{11}+48\,a^4\,b^{13}-64\,a^2\,b^{15}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{15}\,b^6-1020\,a^{13}\,b^8+2369\,a^{11}\,b^{10}-1696\,a^9\,b^{12}+20\,a^7\,b^{14}+240\,a^5\,b^{16}+16\,a^3\,b^{18}\right)}{a^6\,b^{12}}\right)}{2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-432\,a^{16}\,b^3+2160\,a^{14}\,b^5-3564\,a^{12}\,b^7+1216\,a^{10}\,b^9+2502\,a^8\,b^{11}-2560\,a^6\,b^{13}+680\,a^4\,b^{15}-32\,a^2\,b^{17}+32\,b^{19}\right)}{a^6\,b^{12}}\right)}{2\,b^4}+\frac{16\,\left(-756\,a^{12}\,b+2430\,a^{10}\,b^3-2448\,a^8\,b^5+214\,a^6\,b^7+1056\,a^4\,b^9-576\,a^2\,b^{11}+80\,b^{13}\right)}{a^6\,b^8}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2592\,a^{17}+11232\,a^{15}\,b^2-17064\,a^{13}\,b^4+8160\,a^{11}\,b^6+4504\,a^9\,b^8-5840\,a^7\,b^{10}+1600\,a^5\,b^{12}\right)}{a^6\,b^{12}}}\right)\,\left(a^2\,6{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4\,d}-\frac{2\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(378\,a^{15}-1215\,a^{13}\,b^2+1008\,a^{11}\,b^4+541\,a^9\,b^6-1158\,a^7\,b^8+488\,a^5\,b^{10}-40\,a^3\,b^{12}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-432\,a^{16}\,b^3+2160\,a^{14}\,b^5-3564\,a^{12}\,b^7+1216\,a^{10}\,b^9+2502\,a^8\,b^{11}-2560\,a^6\,b^{13}+680\,a^4\,b^{15}-32\,a^2\,b^{17}+32\,b^{19}\right)}{a^6\,b^{12}}+\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{15}\,b^6-1020\,a^{13}\,b^8+2369\,a^{11}\,b^{10}-1696\,a^9\,b^{12}+20\,a^7\,b^{14}+240\,a^5\,b^{16}+16\,a^3\,b^{18}\right)}{a^6\,b^{12}}-\frac{8\,\left(108\,a^{14}\,b^3-324\,a^{12}\,b^5+315\,a^{10}\,b^7-184\,a^8\,b^9+100\,a^6\,b^{11}+48\,a^4\,b^{13}-64\,a^2\,b^{15}\right)}{a^6\,b^8}+\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(42\,a^{11}\,b^8-50\,a^9\,b^{10}-48\,a^7\,b^{12}+64\,a^5\,b^{14}\right)}{a^6\,b^8}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{12}\,b^{11}-160\,a^{10}\,b^{13}+96\,a^8\,b^{15}+136\,a^6\,b^{17}-128\,a^4\,b^{19}\right)}{a^6\,b^{12}}+\frac{\left(\frac{8\,\left(16\,a^8\,b^{13}-12\,a^{10}\,b^{11}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{14}-68\,a^9\,b^{16}+64\,a^7\,b^{18}\right)}{a^6\,b^{12}}\right)\,\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^3\,b^4}\right)}{a^3\,b^4}\right)}{a^3\,b^4}\right)\,1{}\mathrm{i}}{a^3\,b^4}+\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(378\,a^{15}-1215\,a^{13}\,b^2+1008\,a^{11}\,b^4+541\,a^9\,b^6-1158\,a^7\,b^8+488\,a^5\,b^{10}-40\,a^3\,b^{12}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-432\,a^{16}\,b^3+2160\,a^{14}\,b^5-3564\,a^{12}\,b^7+1216\,a^{10}\,b^9+2502\,a^8\,b^{11}-2560\,a^6\,b^{13}+680\,a^4\,b^{15}-32\,a^2\,b^{17}+32\,b^{19}\right)}{a^6\,b^{12}}-\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{15}\,b^6-1020\,a^{13}\,b^8+2369\,a^{11}\,b^{10}-1696\,a^9\,b^{12}+20\,a^7\,b^{14}+240\,a^5\,b^{16}+16\,a^3\,b^{18}\right)}{a^6\,b^{12}}-\frac{8\,\left(108\,a^{14}\,b^3-324\,a^{12}\,b^5+315\,a^{10}\,b^7-184\,a^8\,b^9+100\,a^6\,b^{11}+48\,a^4\,b^{13}-64\,a^2\,b^{15}\right)}{a^6\,b^8}+\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{12}\,b^{11}-160\,a^{10}\,b^{13}+96\,a^8\,b^{15}+136\,a^6\,b^{17}-128\,a^4\,b^{19}\right)}{a^6\,b^{12}}-\frac{8\,\left(42\,a^{11}\,b^8-50\,a^9\,b^{10}-48\,a^7\,b^{12}+64\,a^5\,b^{14}\right)}{a^6\,b^8}+\frac{\left(\frac{8\,\left(16\,a^8\,b^{13}-12\,a^{10}\,b^{11}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{14}-68\,a^9\,b^{16}+64\,a^7\,b^{18}\right)}{a^6\,b^{12}}\right)\,\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^3\,b^4}\right)}{a^3\,b^4}\right)}{a^3\,b^4}\right)\,1{}\mathrm{i}}{a^3\,b^4}}{\frac{16\,\left(-756\,a^{12}\,b+2430\,a^{10}\,b^3-2448\,a^8\,b^5+214\,a^6\,b^7+1056\,a^4\,b^9-576\,a^2\,b^{11}+80\,b^{13}\right)}{a^6\,b^8}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2592\,a^{17}+11232\,a^{15}\,b^2-17064\,a^{13}\,b^4+8160\,a^{11}\,b^6+4504\,a^9\,b^8-5840\,a^7\,b^{10}+1600\,a^5\,b^{12}\right)}{a^6\,b^{12}}-\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(378\,a^{15}-1215\,a^{13}\,b^2+1008\,a^{11}\,b^4+541\,a^9\,b^6-1158\,a^7\,b^8+488\,a^5\,b^{10}-40\,a^3\,b^{12}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-432\,a^{16}\,b^3+2160\,a^{14}\,b^5-3564\,a^{12}\,b^7+1216\,a^{10}\,b^9+2502\,a^8\,b^{11}-2560\,a^6\,b^{13}+680\,a^4\,b^{15}-32\,a^2\,b^{17}+32\,b^{19}\right)}{a^6\,b^{12}}+\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{15}\,b^6-1020\,a^{13}\,b^8+2369\,a^{11}\,b^{10}-1696\,a^9\,b^{12}+20\,a^7\,b^{14}+240\,a^5\,b^{16}+16\,a^3\,b^{18}\right)}{a^6\,b^{12}}-\frac{8\,\left(108\,a^{14}\,b^3-324\,a^{12}\,b^5+315\,a^{10}\,b^7-184\,a^8\,b^9+100\,a^6\,b^{11}+48\,a^4\,b^{13}-64\,a^2\,b^{15}\right)}{a^6\,b^8}+\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(42\,a^{11}\,b^8-50\,a^9\,b^{10}-48\,a^7\,b^{12}+64\,a^5\,b^{14}\right)}{a^6\,b^8}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{12}\,b^{11}-160\,a^{10}\,b^{13}+96\,a^8\,b^{15}+136\,a^6\,b^{17}-128\,a^4\,b^{19}\right)}{a^6\,b^{12}}+\frac{\left(\frac{8\,\left(16\,a^8\,b^{13}-12\,a^{10}\,b^{11}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{14}-68\,a^9\,b^{16}+64\,a^7\,b^{18}\right)}{a^6\,b^{12}}\right)\,\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^3\,b^4}\right)}{a^3\,b^4}\right)}{a^3\,b^4}\right)}{a^3\,b^4}+\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(378\,a^{15}-1215\,a^{13}\,b^2+1008\,a^{11}\,b^4+541\,a^9\,b^6-1158\,a^7\,b^8+488\,a^5\,b^{10}-40\,a^3\,b^{12}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-432\,a^{16}\,b^3+2160\,a^{14}\,b^5-3564\,a^{12}\,b^7+1216\,a^{10}\,b^9+2502\,a^8\,b^{11}-2560\,a^6\,b^{13}+680\,a^4\,b^{15}-32\,a^2\,b^{17}+32\,b^{19}\right)}{a^6\,b^{12}}-\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{15}\,b^6-1020\,a^{13}\,b^8+2369\,a^{11}\,b^{10}-1696\,a^9\,b^{12}+20\,a^7\,b^{14}+240\,a^5\,b^{16}+16\,a^3\,b^{18}\right)}{a^6\,b^{12}}-\frac{8\,\left(108\,a^{14}\,b^3-324\,a^{12}\,b^5+315\,a^{10}\,b^7-184\,a^8\,b^9+100\,a^6\,b^{11}+48\,a^4\,b^{13}-64\,a^2\,b^{15}\right)}{a^6\,b^8}+\frac{\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{12}\,b^{11}-160\,a^{10}\,b^{13}+96\,a^8\,b^{15}+136\,a^6\,b^{17}-128\,a^4\,b^{19}\right)}{a^6\,b^{12}}-\frac{8\,\left(42\,a^{11}\,b^8-50\,a^9\,b^{10}-48\,a^7\,b^{12}+64\,a^5\,b^{14}\right)}{a^6\,b^8}+\frac{\left(\frac{8\,\left(16\,a^8\,b^{13}-12\,a^{10}\,b^{11}\right)}{a^6\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{14}-68\,a^9\,b^{16}+64\,a^7\,b^{18}\right)}{a^6\,b^{12}}\right)\,\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^3\,b^4}\right)}{a^3\,b^4}\right)}{a^3\,b^4}\right)}{a^3\,b^4}}\right)\,\left(3\,a^2+2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^3\,b^4\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^2*d) - (a + (2*tan(c/2 + (d*x)/2)*(6*a^4 + 3*b^4 - 4*a^2*b^2))/b^3 + (2*tan(c/2 + (d*x)/2)^5*(6*a^4 + 3*b^4 - 2*a^2*b^2))/b^3 + (4*tan(c/2 + (d*x)/2)^3*(6*a^4 + 3*b^4 - 5*a^2*b^2))/b^3 + (tan(c/2 + (d*x)/2)^6*(6*a^4 + 4*b^4 - 7*a^2*b^2))/(a*b^2) + (tan(c/2 + (d*x)/2)^2*(18*a^4 + 4*b^4 - 5*a^2*b^2))/(a*b^2) + (tan(c/2 + (d*x)/2)^4*(24*a^4 + 8*b^4 - 13*a^2*b^2))/(a*b^2))/(d*(6*a^3*tan(c/2 + (d*x)/2)^3 + 6*a^3*tan(c/2 + (d*x)/2)^5 + 2*a^3*tan(c/2 + (d*x)/2)^7 + 2*a^3*tan(c/2 + (d*x)/2) + 4*a^2*b*tan(c/2 + (d*x)/2)^2 + 8*a^2*b*tan(c/2 + (d*x)/2)^4 + 4*a^2*b*tan(c/2 + (d*x)/2)^6)) + (atan((((a^2*6i - b^2*5i)*((8*(378*a^15 - 40*a^3*b^12 + 488*a^5*b^10 - 1158*a^7*b^8 + 541*a^9*b^6 + 1008*a^11*b^4 - 1215*a^13*b^2))/(a^6*b^8) - ((a^2*6i - b^2*5i)*(((a^2*6i - b^2*5i)*((((8*(16*a^8*b^13 - 12*a^10*b^11))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^18 - 68*a^9*b^16 + 8*a^11*b^14))/(a^6*b^12))*(a^2*6i - b^2*5i))/(2*b^4) - (8*(64*a^5*b^14 - 48*a^7*b^12 - 50*a^9*b^10 + 42*a^11*b^8))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(136*a^6*b^17 - 128*a^4*b^19 + 96*a^8*b^15 - 160*a^10*b^13 + 48*a^12*b^11))/(a^6*b^12)))/(2*b^4) - (8*(48*a^4*b^13 - 64*a^2*b^15 + 100*a^6*b^11 - 184*a^8*b^9 + 315*a^10*b^7 - 324*a^12*b^5 + 108*a^14*b^3))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(16*a^3*b^18 + 240*a^5*b^16 + 20*a^7*b^14 - 1696*a^9*b^12 + 2369*a^11*b^10 - 1020*a^13*b^8 + 72*a^15*b^6))/(a^6*b^12)))/(2*b^4) + (8*tan(c/2 + (d*x)/2)*(32*b^19 - 32*a^2*b^17 + 680*a^4*b^15 - 2560*a^6*b^13 + 2502*a^8*b^11 + 1216*a^10*b^9 - 3564*a^12*b^7 + 2160*a^14*b^5 - 432*a^16*b^3))/(a^6*b^12))*1i)/(2*b^4) + ((a^2*6i - b^2*5i)*((8*(378*a^15 - 40*a^3*b^12 + 488*a^5*b^10 - 1158*a^7*b^8 + 541*a^9*b^6 + 1008*a^11*b^4 - 1215*a^13*b^2))/(a^6*b^8) + ((a^2*6i - b^2*5i)*(((a^2*6i - b^2*5i)*((8*(64*a^5*b^14 - 48*a^7*b^12 - 50*a^9*b^10 + 42*a^11*b^8))/(a^6*b^8) + (((8*(16*a^8*b^13 - 12*a^10*b^11))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^18 - 68*a^9*b^16 + 8*a^11*b^14))/(a^6*b^12))*(a^2*6i - b^2*5i))/(2*b^4) - (8*tan(c/2 + (d*x)/2)*(136*a^6*b^17 - 128*a^4*b^19 + 96*a^8*b^15 - 160*a^10*b^13 + 48*a^12*b^11))/(a^6*b^12)))/(2*b^4) - (8*(48*a^4*b^13 - 64*a^2*b^15 + 100*a^6*b^11 - 184*a^8*b^9 + 315*a^10*b^7 - 324*a^12*b^5 + 108*a^14*b^3))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(16*a^3*b^18 + 240*a^5*b^16 + 20*a^7*b^14 - 1696*a^9*b^12 + 2369*a^11*b^10 - 1020*a^13*b^8 + 72*a^15*b^6))/(a^6*b^12)))/(2*b^4) + (8*tan(c/2 + (d*x)/2)*(32*b^19 - 32*a^2*b^17 + 680*a^4*b^15 - 2560*a^6*b^13 + 2502*a^8*b^11 + 1216*a^10*b^9 - 3564*a^12*b^7 + 2160*a^14*b^5 - 432*a^16*b^3))/(a^6*b^12))*1i)/(2*b^4))/(((a^2*6i - b^2*5i)*((8*(378*a^15 - 40*a^3*b^12 + 488*a^5*b^10 - 1158*a^7*b^8 + 541*a^9*b^6 + 1008*a^11*b^4 - 1215*a^13*b^2))/(a^6*b^8) - ((a^2*6i - b^2*5i)*(((a^2*6i - b^2*5i)*((((8*(16*a^8*b^13 - 12*a^10*b^11))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^18 - 68*a^9*b^16 + 8*a^11*b^14))/(a^6*b^12))*(a^2*6i - b^2*5i))/(2*b^4) - (8*(64*a^5*b^14 - 48*a^7*b^12 - 50*a^9*b^10 + 42*a^11*b^8))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(136*a^6*b^17 - 128*a^4*b^19 + 96*a^8*b^15 - 160*a^10*b^13 + 48*a^12*b^11))/(a^6*b^12)))/(2*b^4) - (8*(48*a^4*b^13 - 64*a^2*b^15 + 100*a^6*b^11 - 184*a^8*b^9 + 315*a^10*b^7 - 324*a^12*b^5 + 108*a^14*b^3))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(16*a^3*b^18 + 240*a^5*b^16 + 20*a^7*b^14 - 1696*a^9*b^12 + 2369*a^11*b^10 - 1020*a^13*b^8 + 72*a^15*b^6))/(a^6*b^12)))/(2*b^4) + (8*tan(c/2 + (d*x)/2)*(32*b^19 - 32*a^2*b^17 + 680*a^4*b^15 - 2560*a^6*b^13 + 2502*a^8*b^11 + 1216*a^10*b^9 - 3564*a^12*b^7 + 2160*a^14*b^5 - 432*a^16*b^3))/(a^6*b^12)))/(2*b^4) - ((a^2*6i - b^2*5i)*((8*(378*a^15 - 40*a^3*b^12 + 488*a^5*b^10 - 1158*a^7*b^8 + 541*a^9*b^6 + 1008*a^11*b^4 - 1215*a^13*b^2))/(a^6*b^8) + ((a^2*6i - b^2*5i)*(((a^2*6i - b^2*5i)*((8*(64*a^5*b^14 - 48*a^7*b^12 - 50*a^9*b^10 + 42*a^11*b^8))/(a^6*b^8) + (((8*(16*a^8*b^13 - 12*a^10*b^11))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^18 - 68*a^9*b^16 + 8*a^11*b^14))/(a^6*b^12))*(a^2*6i - b^2*5i))/(2*b^4) - (8*tan(c/2 + (d*x)/2)*(136*a^6*b^17 - 128*a^4*b^19 + 96*a^8*b^15 - 160*a^10*b^13 + 48*a^12*b^11))/(a^6*b^12)))/(2*b^4) - (8*(48*a^4*b^13 - 64*a^2*b^15 + 100*a^6*b^11 - 184*a^8*b^9 + 315*a^10*b^7 - 324*a^12*b^5 + 108*a^14*b^3))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(16*a^3*b^18 + 240*a^5*b^16 + 20*a^7*b^14 - 1696*a^9*b^12 + 2369*a^11*b^10 - 1020*a^13*b^8 + 72*a^15*b^6))/(a^6*b^12)))/(2*b^4) + (8*tan(c/2 + (d*x)/2)*(32*b^19 - 32*a^2*b^17 + 680*a^4*b^15 - 2560*a^6*b^13 + 2502*a^8*b^11 + 1216*a^10*b^9 - 3564*a^12*b^7 + 2160*a^14*b^5 - 432*a^16*b^3))/(a^6*b^12)))/(2*b^4) + (16*(80*b^13 - 756*a^12*b - 576*a^2*b^11 + 1056*a^4*b^9 + 214*a^6*b^7 - 2448*a^8*b^5 + 2430*a^10*b^3))/(a^6*b^8) - (16*tan(c/2 + (d*x)/2)*(1600*a^5*b^12 - 2592*a^17 - 5840*a^7*b^10 + 4504*a^9*b^8 + 8160*a^11*b^6 - 17064*a^13*b^4 + 11232*a^15*b^2))/(a^6*b^12)))*(a^2*6i - b^2*5i)*1i)/(b^4*d) - (2*b*log(tan(c/2 + (d*x)/2)))/(a^3*d) + (atan((((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(378*a^15 - 40*a^3*b^12 + 488*a^5*b^10 - 1158*a^7*b^8 + 541*a^9*b^6 + 1008*a^11*b^4 - 1215*a^13*b^2))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(32*b^19 - 32*a^2*b^17 + 680*a^4*b^15 - 2560*a^6*b^13 + 2502*a^8*b^11 + 1216*a^10*b^9 - 3564*a^12*b^7 + 2160*a^14*b^5 - 432*a^16*b^3))/(a^6*b^12) + ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(16*a^3*b^18 + 240*a^5*b^16 + 20*a^7*b^14 - 1696*a^9*b^12 + 2369*a^11*b^10 - 1020*a^13*b^8 + 72*a^15*b^6))/(a^6*b^12) - (8*(48*a^4*b^13 - 64*a^2*b^15 + 100*a^6*b^11 - 184*a^8*b^9 + 315*a^10*b^7 - 324*a^12*b^5 + 108*a^14*b^3))/(a^6*b^8) + ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(64*a^5*b^14 - 48*a^7*b^12 - 50*a^9*b^10 + 42*a^11*b^8))/(a^6*b^8) - (8*tan(c/2 + (d*x)/2)*(136*a^6*b^17 - 128*a^4*b^19 + 96*a^8*b^15 - 160*a^10*b^13 + 48*a^12*b^11))/(a^6*b^12) + (((8*(16*a^8*b^13 - 12*a^10*b^11))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^18 - 68*a^9*b^16 + 8*a^11*b^14))/(a^6*b^12))*(3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^3*b^4)))/(a^3*b^4)))/(a^3*b^4))*1i)/(a^3*b^4) + ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(378*a^15 - 40*a^3*b^12 + 488*a^5*b^10 - 1158*a^7*b^8 + 541*a^9*b^6 + 1008*a^11*b^4 - 1215*a^13*b^2))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(32*b^19 - 32*a^2*b^17 + 680*a^4*b^15 - 2560*a^6*b^13 + 2502*a^8*b^11 + 1216*a^10*b^9 - 3564*a^12*b^7 + 2160*a^14*b^5 - 432*a^16*b^3))/(a^6*b^12) - ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(16*a^3*b^18 + 240*a^5*b^16 + 20*a^7*b^14 - 1696*a^9*b^12 + 2369*a^11*b^10 - 1020*a^13*b^8 + 72*a^15*b^6))/(a^6*b^12) - (8*(48*a^4*b^13 - 64*a^2*b^15 + 100*a^6*b^11 - 184*a^8*b^9 + 315*a^10*b^7 - 324*a^12*b^5 + 108*a^14*b^3))/(a^6*b^8) + ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(136*a^6*b^17 - 128*a^4*b^19 + 96*a^8*b^15 - 160*a^10*b^13 + 48*a^12*b^11))/(a^6*b^12) - (8*(64*a^5*b^14 - 48*a^7*b^12 - 50*a^9*b^10 + 42*a^11*b^8))/(a^6*b^8) + (((8*(16*a^8*b^13 - 12*a^10*b^11))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^18 - 68*a^9*b^16 + 8*a^11*b^14))/(a^6*b^12))*(3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^3*b^4)))/(a^3*b^4)))/(a^3*b^4))*1i)/(a^3*b^4))/((16*(80*b^13 - 756*a^12*b - 576*a^2*b^11 + 1056*a^4*b^9 + 214*a^6*b^7 - 2448*a^8*b^5 + 2430*a^10*b^3))/(a^6*b^8) - (16*tan(c/2 + (d*x)/2)*(1600*a^5*b^12 - 2592*a^17 - 5840*a^7*b^10 + 4504*a^9*b^8 + 8160*a^11*b^6 - 17064*a^13*b^4 + 11232*a^15*b^2))/(a^6*b^12) - ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(378*a^15 - 40*a^3*b^12 + 488*a^5*b^10 - 1158*a^7*b^8 + 541*a^9*b^6 + 1008*a^11*b^4 - 1215*a^13*b^2))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(32*b^19 - 32*a^2*b^17 + 680*a^4*b^15 - 2560*a^6*b^13 + 2502*a^8*b^11 + 1216*a^10*b^9 - 3564*a^12*b^7 + 2160*a^14*b^5 - 432*a^16*b^3))/(a^6*b^12) + ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(16*a^3*b^18 + 240*a^5*b^16 + 20*a^7*b^14 - 1696*a^9*b^12 + 2369*a^11*b^10 - 1020*a^13*b^8 + 72*a^15*b^6))/(a^6*b^12) - (8*(48*a^4*b^13 - 64*a^2*b^15 + 100*a^6*b^11 - 184*a^8*b^9 + 315*a^10*b^7 - 324*a^12*b^5 + 108*a^14*b^3))/(a^6*b^8) + ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(64*a^5*b^14 - 48*a^7*b^12 - 50*a^9*b^10 + 42*a^11*b^8))/(a^6*b^8) - (8*tan(c/2 + (d*x)/2)*(136*a^6*b^17 - 128*a^4*b^19 + 96*a^8*b^15 - 160*a^10*b^13 + 48*a^12*b^11))/(a^6*b^12) + (((8*(16*a^8*b^13 - 12*a^10*b^11))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^18 - 68*a^9*b^16 + 8*a^11*b^14))/(a^6*b^12))*(3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^3*b^4)))/(a^3*b^4)))/(a^3*b^4)))/(a^3*b^4) + ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(378*a^15 - 40*a^3*b^12 + 488*a^5*b^10 - 1158*a^7*b^8 + 541*a^9*b^6 + 1008*a^11*b^4 - 1215*a^13*b^2))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(32*b^19 - 32*a^2*b^17 + 680*a^4*b^15 - 2560*a^6*b^13 + 2502*a^8*b^11 + 1216*a^10*b^9 - 3564*a^12*b^7 + 2160*a^14*b^5 - 432*a^16*b^3))/(a^6*b^12) - ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(16*a^3*b^18 + 240*a^5*b^16 + 20*a^7*b^14 - 1696*a^9*b^12 + 2369*a^11*b^10 - 1020*a^13*b^8 + 72*a^15*b^6))/(a^6*b^12) - (8*(48*a^4*b^13 - 64*a^2*b^15 + 100*a^6*b^11 - 184*a^8*b^9 + 315*a^10*b^7 - 324*a^12*b^5 + 108*a^14*b^3))/(a^6*b^8) + ((3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(136*a^6*b^17 - 128*a^4*b^19 + 96*a^8*b^15 - 160*a^10*b^13 + 48*a^12*b^11))/(a^6*b^12) - (8*(64*a^5*b^14 - 48*a^7*b^12 - 50*a^9*b^10 + 42*a^11*b^8))/(a^6*b^8) + (((8*(16*a^8*b^13 - 12*a^10*b^11))/(a^6*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^18 - 68*a^9*b^16 + 8*a^11*b^14))/(a^6*b^12))*(3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^3*b^4)))/(a^3*b^4)))/(a^3*b^4)))/(a^3*b^4)))*(3*a^2 + 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^3*b^4*d)","B"
1261,1,4294,251,12.902351,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^3*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(16\,a^4-17\,a^2\,b^2+16\,b^4\right)}{b^2}-\frac{a^2}{2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(32\,a^4-33\,a^2\,b^2+32\,b^4\right)}{2\,b^2}+3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^4-3\,a^2\,b^2+2\,b^4\right)}{a\,b}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(24\,a^4-9\,a^2\,b^2+8\,b^4\right)}{a\,b}}{d\,\left(4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,b\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,b\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,a^2-6\,b^2\right)}{2\,a^4\,d}+\frac{4\,a\,\mathrm{atan}\left(\frac{2560\,a}{\frac{4800\,a^2}{b}-2560\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12160\,b+\frac{4480\,b^3}{a^2}+\frac{11520\,b^5}{a^4}-\frac{12096\,b^7}{a^6}+\frac{3456\,b^9}{a^8}+\frac{6144\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{5120\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{2304\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}+\frac{3840\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}}-\frac{12160\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{4480\,b^2}{a^2}+\frac{4800\,a^2}{b^2}+\frac{11520\,b^4}{a^4}-\frac{12096\,b^6}{a^6}+\frac{3456\,b^8}{a^8}-\frac{2560\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{6144\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{2304\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}-\frac{5120\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+\frac{3840\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}-12160}-\frac{6144}{6144\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{12160\,a}{b}+\frac{4480\,b}{a}+\frac{11520\,b^3}{a^3}+\frac{4800\,a^3}{b^3}-\frac{12096\,b^5}{a^5}+\frac{3456\,b^7}{a^7}-\frac{2304\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}-\frac{2560\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{5120\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{3840\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}+\frac{5120\,a^3}{4800\,a^2\,b-12160\,b^3+\frac{4480\,b^5}{a^2}+\frac{11520\,b^7}{a^4}-\frac{12096\,b^9}{a^6}+\frac{3456\,b^{11}}{a^8}-5120\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2560\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{6144\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{3840\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{2304\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}+\frac{2304\,b^2}{4480\,a\,b+\frac{11520\,b^3}{a}-\frac{12160\,a^3}{b}-\frac{12096\,b^5}{a^3}+\frac{4800\,a^5}{b^3}+\frac{3456\,b^7}{a^5}+6144\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2304\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2560\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{5120\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{3840\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}-\frac{3840\,a^5}{4800\,a^2\,b^3-12160\,b^5+\frac{4480\,b^7}{a^2}+\frac{11520\,b^9}{a^4}-\frac{12096\,b^{11}}{a^6}+\frac{3456\,b^{13}}{a^8}+3840\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2560\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5120\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{6144\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{2304\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}+\frac{4800\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4800\,a^2-12160\,b^2+\frac{4480\,b^4}{a^2}+\frac{11520\,b^6}{a^4}-\frac{12096\,b^8}{a^6}+\frac{3456\,b^{10}}{a^8}+\frac{6144\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{5120\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{2304\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}+\frac{3840\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}-2560\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{11520\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4480\,a^2\,b+11520\,b^3-\frac{12160\,a^4}{b}-\frac{12096\,b^5}{a^2}+\frac{4800\,a^6}{b^3}+\frac{3456\,b^7}{a^4}+6144\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2304\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2560\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{5120\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{3840\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}-\frac{12096\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4480\,a^4\,b-12096\,b^5+11520\,a^2\,b^3-\frac{12160\,a^6}{b}+\frac{3456\,b^7}{a^2}+\frac{4800\,a^8}{b^3}+6144\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2304\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2560\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{5120\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{3840\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}+\frac{3456\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4480\,a^6\,b+3456\,b^7-12096\,a^2\,b^5+11520\,a^4\,b^3-\frac{12160\,a^8}{b}+\frac{4800\,a^{10}}{b^3}+6144\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2304\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2560\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{5120\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{3840\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}+\frac{4480\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4480\,b+6144\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{12160\,a^2}{b}+\frac{11520\,b^3}{a^2}+\frac{4800\,a^4}{b^3}-\frac{12096\,b^5}{a^4}+\frac{3456\,b^7}{a^6}-\frac{2304\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{2560\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{5120\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{3840\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}\right)}{b^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(56\,a^{14}-224\,a^{10}\,b^4+232\,a^8\,b^6-96\,a^6\,b^8+36\,a^4\,b^{10}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{16}\,b^2+120\,a^{14}\,b^4+292\,a^{12}\,b^6-653\,a^{10}\,b^8+194\,a^8\,b^{10}+70\,a^6\,b^{12}+180\,a^4\,b^{14}-189\,a^2\,b^{16}+54\,b^{18}\right)}{a^9\,b^8}+\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(-24\,a^{14}\,b^2+32\,a^{12}\,b^4-35\,a^{10}\,b^6+42\,a^8\,b^8+95\,a^6\,b^{10}-174\,a^4\,b^{12}+72\,a^2\,b^{14}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^4-200\,a^{14}\,b^6+202\,a^{12}\,b^8+132\,a^{10}\,b^{10}-220\,a^8\,b^{12}+60\,a^6\,b^{14}+18\,a^4\,b^{16}\right)}{a^9\,b^8}+\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(14\,a^{12}\,b^6+15\,a^{10}\,b^8-76\,a^8\,b^{10}+48\,a^6\,b^{12}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{14}\,b^8+30\,a^{12}\,b^{10}+73\,a^{10}\,b^{12}-182\,a^8\,b^{14}+96\,a^6\,b^{16}\right)}{a^9\,b^8}+\frac{\left(\frac{16\,\left(8\,a^{10}\,b^{10}-6\,a^{12}\,b^8\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}\,b^{10}-34\,a^{12}\,b^{12}+32\,a^{10}\,b^{14}\right)}{a^9\,b^8}\right)\,\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^4\,b^3}\right)}{a^4\,b^3}\right)}{a^4\,b^3}\right)\,1{}\mathrm{i}}{a^4\,b^3}+\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(56\,a^{14}-224\,a^{10}\,b^4+232\,a^8\,b^6-96\,a^6\,b^8+36\,a^4\,b^{10}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{16}\,b^2+120\,a^{14}\,b^4+292\,a^{12}\,b^6-653\,a^{10}\,b^8+194\,a^8\,b^{10}+70\,a^6\,b^{12}+180\,a^4\,b^{14}-189\,a^2\,b^{16}+54\,b^{18}\right)}{a^9\,b^8}-\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(-24\,a^{14}\,b^2+32\,a^{12}\,b^4-35\,a^{10}\,b^6+42\,a^8\,b^8+95\,a^6\,b^{10}-174\,a^4\,b^{12}+72\,a^2\,b^{14}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^4-200\,a^{14}\,b^6+202\,a^{12}\,b^8+132\,a^{10}\,b^{10}-220\,a^8\,b^{12}+60\,a^6\,b^{14}+18\,a^4\,b^{16}\right)}{a^9\,b^8}-\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(14\,a^{12}\,b^6+15\,a^{10}\,b^8-76\,a^8\,b^{10}+48\,a^6\,b^{12}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{14}\,b^8+30\,a^{12}\,b^{10}+73\,a^{10}\,b^{12}-182\,a^8\,b^{14}+96\,a^6\,b^{16}\right)}{a^9\,b^8}-\frac{\left(\frac{16\,\left(8\,a^{10}\,b^{10}-6\,a^{12}\,b^8\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}\,b^{10}-34\,a^{12}\,b^{12}+32\,a^{10}\,b^{14}\right)}{a^9\,b^8}\right)\,\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^4\,b^3}\right)}{a^4\,b^3}\right)}{a^4\,b^3}\right)\,1{}\mathrm{i}}{a^4\,b^3}}{\frac{32\,\left(140\,a^{12}-318\,a^{10}\,b^2+556\,a^6\,b^6-648\,a^4\,b^8+378\,a^2\,b^{10}-108\,b^{12}\right)}{a^8\,b^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-256\,a^{16}+416\,a^{14}\,b^2+368\,a^{12}\,b^4-960\,a^{10}\,b^6+432\,a^8\,b^8\right)}{a^9\,b^8}-\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(56\,a^{14}-224\,a^{10}\,b^4+232\,a^8\,b^6-96\,a^6\,b^8+36\,a^4\,b^{10}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{16}\,b^2+120\,a^{14}\,b^4+292\,a^{12}\,b^6-653\,a^{10}\,b^8+194\,a^8\,b^{10}+70\,a^6\,b^{12}+180\,a^4\,b^{14}-189\,a^2\,b^{16}+54\,b^{18}\right)}{a^9\,b^8}+\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(-24\,a^{14}\,b^2+32\,a^{12}\,b^4-35\,a^{10}\,b^6+42\,a^8\,b^8+95\,a^6\,b^{10}-174\,a^4\,b^{12}+72\,a^2\,b^{14}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^4-200\,a^{14}\,b^6+202\,a^{12}\,b^8+132\,a^{10}\,b^{10}-220\,a^8\,b^{12}+60\,a^6\,b^{14}+18\,a^4\,b^{16}\right)}{a^9\,b^8}+\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(14\,a^{12}\,b^6+15\,a^{10}\,b^8-76\,a^8\,b^{10}+48\,a^6\,b^{12}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{14}\,b^8+30\,a^{12}\,b^{10}+73\,a^{10}\,b^{12}-182\,a^8\,b^{14}+96\,a^6\,b^{16}\right)}{a^9\,b^8}+\frac{\left(\frac{16\,\left(8\,a^{10}\,b^{10}-6\,a^{12}\,b^8\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}\,b^{10}-34\,a^{12}\,b^{12}+32\,a^{10}\,b^{14}\right)}{a^9\,b^8}\right)\,\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^4\,b^3}\right)}{a^4\,b^3}\right)}{a^4\,b^3}\right)}{a^4\,b^3}+\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(56\,a^{14}-224\,a^{10}\,b^4+232\,a^8\,b^6-96\,a^6\,b^8+36\,a^4\,b^{10}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{16}\,b^2+120\,a^{14}\,b^4+292\,a^{12}\,b^6-653\,a^{10}\,b^8+194\,a^8\,b^{10}+70\,a^6\,b^{12}+180\,a^4\,b^{14}-189\,a^2\,b^{16}+54\,b^{18}\right)}{a^9\,b^8}-\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(-24\,a^{14}\,b^2+32\,a^{12}\,b^4-35\,a^{10}\,b^6+42\,a^8\,b^8+95\,a^6\,b^{10}-174\,a^4\,b^{12}+72\,a^2\,b^{14}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^4-200\,a^{14}\,b^6+202\,a^{12}\,b^8+132\,a^{10}\,b^{10}-220\,a^8\,b^{12}+60\,a^6\,b^{14}+18\,a^4\,b^{16}\right)}{a^9\,b^8}-\frac{\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{16\,\left(14\,a^{12}\,b^6+15\,a^{10}\,b^8-76\,a^8\,b^{10}+48\,a^6\,b^{12}\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{14}\,b^8+30\,a^{12}\,b^{10}+73\,a^{10}\,b^{12}-182\,a^8\,b^{14}+96\,a^6\,b^{16}\right)}{a^9\,b^8}-\frac{\left(\frac{16\,\left(8\,a^{10}\,b^{10}-6\,a^{12}\,b^8\right)}{a^8\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}\,b^{10}-34\,a^{12}\,b^{12}+32\,a^{10}\,b^{14}\right)}{a^9\,b^8}\right)\,\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^4\,b^3}\right)}{a^4\,b^3}\right)}{a^4\,b^3}\right)}{a^4\,b^3}}\right)\,\left(2\,a^2+3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^4\,b^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) + ((tan(c/2 + (d*x)/2)^2*(16*a^4 + 16*b^4 - 17*a^2*b^2))/b^2 - a^2/2 + (tan(c/2 + (d*x)/2)^4*(32*a^4 + 32*b^4 - 33*a^2*b^2))/(2*b^2) + 3*a*b*tan(c/2 + (d*x)/2) + (4*tan(c/2 + (d*x)/2)^5*(2*a^4 + 2*b^4 - 3*a^2*b^2))/(a*b) + (tan(c/2 + (d*x)/2)^3*(24*a^4 + 8*b^4 - 9*a^2*b^2))/(a*b))/(d*(4*a^4*tan(c/2 + (d*x)/2)^2 + 8*a^4*tan(c/2 + (d*x)/2)^4 + 4*a^4*tan(c/2 + (d*x)/2)^6 + 8*a^3*b*tan(c/2 + (d*x)/2)^3 + 8*a^3*b*tan(c/2 + (d*x)/2)^5)) - (b*tan(c/2 + (d*x)/2))/(a^3*d) - (log(tan(c/2 + (d*x)/2))*(5*a^2 - 6*b^2))/(2*a^4*d) + (4*a*atan((2560*a)/((4800*a^2)/b - 2560*a*tan(c/2 + (d*x)/2) - 12160*b + (4480*b^3)/a^2 + (11520*b^5)/a^4 - (12096*b^7)/a^6 + (3456*b^9)/a^8 + (6144*b^2*tan(c/2 + (d*x)/2))/a - (5120*a^3*tan(c/2 + (d*x)/2))/b^2 - (2304*b^4*tan(c/2 + (d*x)/2))/a^3 + (3840*a^5*tan(c/2 + (d*x)/2))/b^4) - (12160*tan(c/2 + (d*x)/2))/((4480*b^2)/a^2 + (4800*a^2)/b^2 + (11520*b^4)/a^4 - (12096*b^6)/a^6 + (3456*b^8)/a^8 - (2560*a*tan(c/2 + (d*x)/2))/b + (6144*b*tan(c/2 + (d*x)/2))/a - (2304*b^3*tan(c/2 + (d*x)/2))/a^3 - (5120*a^3*tan(c/2 + (d*x)/2))/b^3 + (3840*a^5*tan(c/2 + (d*x)/2))/b^5 - 12160) - 6144/(6144*tan(c/2 + (d*x)/2) - (12160*a)/b + (4480*b)/a + (11520*b^3)/a^3 + (4800*a^3)/b^3 - (12096*b^5)/a^5 + (3456*b^7)/a^7 - (2304*b^2*tan(c/2 + (d*x)/2))/a^2 - (2560*a^2*tan(c/2 + (d*x)/2))/b^2 - (5120*a^4*tan(c/2 + (d*x)/2))/b^4 + (3840*a^6*tan(c/2 + (d*x)/2))/b^6) + (5120*a^3)/(4800*a^2*b - 12160*b^3 + (4480*b^5)/a^2 + (11520*b^7)/a^4 - (12096*b^9)/a^6 + (3456*b^11)/a^8 - 5120*a^3*tan(c/2 + (d*x)/2) - 2560*a*b^2*tan(c/2 + (d*x)/2) + (6144*b^4*tan(c/2 + (d*x)/2))/a + (3840*a^5*tan(c/2 + (d*x)/2))/b^2 - (2304*b^6*tan(c/2 + (d*x)/2))/a^3) + (2304*b^2)/(4480*a*b + (11520*b^3)/a - (12160*a^3)/b - (12096*b^5)/a^3 + (4800*a^5)/b^3 + (3456*b^7)/a^5 + 6144*a^2*tan(c/2 + (d*x)/2) - 2304*b^2*tan(c/2 + (d*x)/2) - (2560*a^4*tan(c/2 + (d*x)/2))/b^2 - (5120*a^6*tan(c/2 + (d*x)/2))/b^4 + (3840*a^8*tan(c/2 + (d*x)/2))/b^6) - (3840*a^5)/(4800*a^2*b^3 - 12160*b^5 + (4480*b^7)/a^2 + (11520*b^9)/a^4 - (12096*b^11)/a^6 + (3456*b^13)/a^8 + 3840*a^5*tan(c/2 + (d*x)/2) - 2560*a*b^4*tan(c/2 + (d*x)/2) - 5120*a^3*b^2*tan(c/2 + (d*x)/2) + (6144*b^6*tan(c/2 + (d*x)/2))/a - (2304*b^8*tan(c/2 + (d*x)/2))/a^3) + (4800*a^2*tan(c/2 + (d*x)/2))/(4800*a^2 - 12160*b^2 + (4480*b^4)/a^2 + (11520*b^6)/a^4 - (12096*b^8)/a^6 + (3456*b^10)/a^8 + (6144*b^3*tan(c/2 + (d*x)/2))/a - (5120*a^3*tan(c/2 + (d*x)/2))/b - (2304*b^5*tan(c/2 + (d*x)/2))/a^3 + (3840*a^5*tan(c/2 + (d*x)/2))/b^3 - 2560*a*b*tan(c/2 + (d*x)/2)) + (11520*b^3*tan(c/2 + (d*x)/2))/(4480*a^2*b + 11520*b^3 - (12160*a^4)/b - (12096*b^5)/a^2 + (4800*a^6)/b^3 + (3456*b^7)/a^4 + 6144*a^3*tan(c/2 + (d*x)/2) - 2304*a*b^2*tan(c/2 + (d*x)/2) - (2560*a^5*tan(c/2 + (d*x)/2))/b^2 - (5120*a^7*tan(c/2 + (d*x)/2))/b^4 + (3840*a^9*tan(c/2 + (d*x)/2))/b^6) - (12096*b^5*tan(c/2 + (d*x)/2))/(4480*a^4*b - 12096*b^5 + 11520*a^2*b^3 - (12160*a^6)/b + (3456*b^7)/a^2 + (4800*a^8)/b^3 + 6144*a^5*tan(c/2 + (d*x)/2) - 2304*a^3*b^2*tan(c/2 + (d*x)/2) - (2560*a^7*tan(c/2 + (d*x)/2))/b^2 - (5120*a^9*tan(c/2 + (d*x)/2))/b^4 + (3840*a^11*tan(c/2 + (d*x)/2))/b^6) + (3456*b^7*tan(c/2 + (d*x)/2))/(4480*a^6*b + 3456*b^7 - 12096*a^2*b^5 + 11520*a^4*b^3 - (12160*a^8)/b + (4800*a^10)/b^3 + 6144*a^7*tan(c/2 + (d*x)/2) - 2304*a^5*b^2*tan(c/2 + (d*x)/2) - (2560*a^9*tan(c/2 + (d*x)/2))/b^2 - (5120*a^11*tan(c/2 + (d*x)/2))/b^4 + (3840*a^13*tan(c/2 + (d*x)/2))/b^6) + (4480*b*tan(c/2 + (d*x)/2))/(4480*b + 6144*a*tan(c/2 + (d*x)/2) - (12160*a^2)/b + (11520*b^3)/a^2 + (4800*a^4)/b^3 - (12096*b^5)/a^4 + (3456*b^7)/a^6 - (2304*b^2*tan(c/2 + (d*x)/2))/a - (2560*a^3*tan(c/2 + (d*x)/2))/b^2 - (5120*a^5*tan(c/2 + (d*x)/2))/b^4 + (3840*a^7*tan(c/2 + (d*x)/2))/b^6)))/(b^3*d) - (atan((((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(56*a^14 + 36*a^4*b^10 - 96*a^6*b^8 + 232*a^8*b^6 - 224*a^10*b^4))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(54*b^18 - 189*a^2*b^16 + 180*a^4*b^14 + 70*a^6*b^12 + 194*a^8*b^10 - 653*a^10*b^8 + 292*a^12*b^6 + 120*a^14*b^4 - 64*a^16*b^2))/(a^9*b^8) + ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(72*a^2*b^14 - 174*a^4*b^12 + 95*a^6*b^10 + 42*a^8*b^8 - 35*a^10*b^6 + 32*a^12*b^4 - 24*a^14*b^2))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(18*a^4*b^16 + 60*a^6*b^14 - 220*a^8*b^12 + 132*a^10*b^10 + 202*a^12*b^8 - 200*a^14*b^6 + 16*a^16*b^4))/(a^9*b^8) + ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(48*a^6*b^12 - 76*a^8*b^10 + 15*a^10*b^8 + 14*a^12*b^6))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(96*a^6*b^16 - 182*a^8*b^14 + 73*a^10*b^12 + 30*a^12*b^10 - 16*a^14*b^8))/(a^9*b^8) + (((16*(8*a^10*b^10 - 6*a^12*b^8))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(32*a^10*b^14 - 34*a^12*b^12 + 4*a^14*b^10))/(a^9*b^8))*(2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^4*b^3)))/(a^4*b^3)))/(a^4*b^3))*1i)/(a^4*b^3) + ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(56*a^14 + 36*a^4*b^10 - 96*a^6*b^8 + 232*a^8*b^6 - 224*a^10*b^4))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(54*b^18 - 189*a^2*b^16 + 180*a^4*b^14 + 70*a^6*b^12 + 194*a^8*b^10 - 653*a^10*b^8 + 292*a^12*b^6 + 120*a^14*b^4 - 64*a^16*b^2))/(a^9*b^8) - ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(72*a^2*b^14 - 174*a^4*b^12 + 95*a^6*b^10 + 42*a^8*b^8 - 35*a^10*b^6 + 32*a^12*b^4 - 24*a^14*b^2))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(18*a^4*b^16 + 60*a^6*b^14 - 220*a^8*b^12 + 132*a^10*b^10 + 202*a^12*b^8 - 200*a^14*b^6 + 16*a^16*b^4))/(a^9*b^8) - ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(48*a^6*b^12 - 76*a^8*b^10 + 15*a^10*b^8 + 14*a^12*b^6))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(96*a^6*b^16 - 182*a^8*b^14 + 73*a^10*b^12 + 30*a^12*b^10 - 16*a^14*b^8))/(a^9*b^8) - (((16*(8*a^10*b^10 - 6*a^12*b^8))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(32*a^10*b^14 - 34*a^12*b^12 + 4*a^14*b^10))/(a^9*b^8))*(2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^4*b^3)))/(a^4*b^3)))/(a^4*b^3))*1i)/(a^4*b^3))/((32*(140*a^12 - 108*b^12 + 378*a^2*b^10 - 648*a^4*b^8 + 556*a^6*b^6 - 318*a^10*b^2))/(a^8*b^5) - (32*tan(c/2 + (d*x)/2)*(432*a^8*b^8 - 256*a^16 - 960*a^10*b^6 + 368*a^12*b^4 + 416*a^14*b^2))/(a^9*b^8) - ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(56*a^14 + 36*a^4*b^10 - 96*a^6*b^8 + 232*a^8*b^6 - 224*a^10*b^4))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(54*b^18 - 189*a^2*b^16 + 180*a^4*b^14 + 70*a^6*b^12 + 194*a^8*b^10 - 653*a^10*b^8 + 292*a^12*b^6 + 120*a^14*b^4 - 64*a^16*b^2))/(a^9*b^8) + ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(72*a^2*b^14 - 174*a^4*b^12 + 95*a^6*b^10 + 42*a^8*b^8 - 35*a^10*b^6 + 32*a^12*b^4 - 24*a^14*b^2))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(18*a^4*b^16 + 60*a^6*b^14 - 220*a^8*b^12 + 132*a^10*b^10 + 202*a^12*b^8 - 200*a^14*b^6 + 16*a^16*b^4))/(a^9*b^8) + ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(48*a^6*b^12 - 76*a^8*b^10 + 15*a^10*b^8 + 14*a^12*b^6))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(96*a^6*b^16 - 182*a^8*b^14 + 73*a^10*b^12 + 30*a^12*b^10 - 16*a^14*b^8))/(a^9*b^8) + (((16*(8*a^10*b^10 - 6*a^12*b^8))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(32*a^10*b^14 - 34*a^12*b^12 + 4*a^14*b^10))/(a^9*b^8))*(2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^4*b^3)))/(a^4*b^3)))/(a^4*b^3)))/(a^4*b^3) + ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(56*a^14 + 36*a^4*b^10 - 96*a^6*b^8 + 232*a^8*b^6 - 224*a^10*b^4))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(54*b^18 - 189*a^2*b^16 + 180*a^4*b^14 + 70*a^6*b^12 + 194*a^8*b^10 - 653*a^10*b^8 + 292*a^12*b^6 + 120*a^14*b^4 - 64*a^16*b^2))/(a^9*b^8) - ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(72*a^2*b^14 - 174*a^4*b^12 + 95*a^6*b^10 + 42*a^8*b^8 - 35*a^10*b^6 + 32*a^12*b^4 - 24*a^14*b^2))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(18*a^4*b^16 + 60*a^6*b^14 - 220*a^8*b^12 + 132*a^10*b^10 + 202*a^12*b^8 - 200*a^14*b^6 + 16*a^16*b^4))/(a^9*b^8) - ((2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((16*(48*a^6*b^12 - 76*a^8*b^10 + 15*a^10*b^8 + 14*a^12*b^6))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(96*a^6*b^16 - 182*a^8*b^14 + 73*a^10*b^12 + 30*a^12*b^10 - 16*a^14*b^8))/(a^9*b^8) - (((16*(8*a^10*b^10 - 6*a^12*b^8))/(a^8*b^5) + (16*tan(c/2 + (d*x)/2)*(32*a^10*b^14 - 34*a^12*b^12 + 4*a^14*b^10))/(a^9*b^8))*(2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^4*b^3)))/(a^4*b^3)))/(a^4*b^3)))/(a^4*b^3)))*(2*a^2 + 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^4*b^3*d)","B"
1262,1,4740,287,12.780776,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^4*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{24\,a^2+32\,b^2}{64\,a^4}+\frac{3}{4\,a^2}-\frac{2\,b^2}{a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a\,b^2-\frac{26\,a^3}{3}\right)+\frac{a^3}{3}-\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(7\,a^4-20\,a^2\,b^2+16\,b^4\right)}{a}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^4-13\,a^2\,b^2+10\,b^4\right)}{b}}{d\,\left(8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,b\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b+10\,a^{14}\,b^3-72\,a^{12}\,b^5+78\,a^{10}\,b^7-124\,a^8\,b^9+405\,a^6\,b^{11}-540\,a^4\,b^{13}+304\,a^2\,b^{15}-64\,b^{17}\right)}{a^{12}\,b^4}-\frac{32\,\left(6\,a^{15}+20\,a^{13}\,b^2-84\,a^{11}\,b^4+97\,a^9\,b^6-56\,a^7\,b^8+16\,a^5\,b^{10}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^2-20\,a^{15}\,b^4-6\,a^{13}\,b^6+44\,a^{11}\,b^8+5\,a^9\,b^{10}-40\,a^7\,b^{12}+16\,a^5\,b^{14}\right)}{a^{12}\,b^4}-\frac{32\,\left(3\,a^{16}\,b-4\,a^{14}\,b^3+5\,a^{12}\,b^5+71\,a^{10}\,b^7-220\,a^8\,b^9+208\,a^6\,b^{11}-64\,a^4\,b^{13}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b^5+10\,a^{14}\,b^7-97\,a^{12}\,b^9+148\,a^{10}\,b^{11}-64\,a^8\,b^{13}\right)}{a^{12}\,b^4}-\frac{32\,\left(a^{15}\,b^4+30\,a^{13}\,b^6-64\,a^{11}\,b^8+32\,a^9\,b^{10}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\left(4\,a^{14}\,b^7-3\,a^{16}\,b^5\right)}{a^{12}\,b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^6-17\,a^{15}\,b^8+16\,a^{13}\,b^{10}\right)}{a^{12}\,b^4}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}}{b^2}-\frac{\frac{32\,\left(6\,a^{15}+20\,a^{13}\,b^2-84\,a^{11}\,b^4+97\,a^9\,b^6-56\,a^7\,b^8+16\,a^5\,b^{10}\right)}{a^{12}\,b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b+10\,a^{14}\,b^3-72\,a^{12}\,b^5+78\,a^{10}\,b^7-124\,a^8\,b^9+405\,a^6\,b^{11}-540\,a^4\,b^{13}+304\,a^2\,b^{15}-64\,b^{17}\right)}{a^{12}\,b^4}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^2-20\,a^{15}\,b^4-6\,a^{13}\,b^6+44\,a^{11}\,b^8+5\,a^9\,b^{10}-40\,a^7\,b^{12}+16\,a^5\,b^{14}\right)}{a^{12}\,b^4}-\frac{32\,\left(3\,a^{16}\,b-4\,a^{14}\,b^3+5\,a^{12}\,b^5+71\,a^{10}\,b^7-220\,a^8\,b^9+208\,a^6\,b^{11}-64\,a^4\,b^{13}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\left(a^{15}\,b^4+30\,a^{13}\,b^6-64\,a^{11}\,b^8+32\,a^9\,b^{10}\right)}{a^{12}\,b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b^5+10\,a^{14}\,b^7-97\,a^{12}\,b^9+148\,a^{10}\,b^{11}-64\,a^8\,b^{13}\right)}{a^{12}\,b^4}+\frac{\left(\frac{32\,\left(4\,a^{14}\,b^7-3\,a^{16}\,b^5\right)}{a^{12}\,b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^6-17\,a^{15}\,b^8+16\,a^{13}\,b^{10}\right)}{a^{12}\,b^4}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}}{b^2}}{-\frac{64\,\left(30\,a^{12}\,b+a^{10}\,b^3-280\,a^8\,b^5+613\,a^6\,b^7-604\,a^4\,b^9+304\,a^2\,b^{11}-64\,b^{13}\right)}{a^{12}\,b^2}-\frac{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}+12\,a^{13}\,b^2-64\,a^{11}\,b^4+60\,a^9\,b^6-16\,a^7\,b^8\right)}{a^{12}\,b^4}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b+10\,a^{14}\,b^3-72\,a^{12}\,b^5+78\,a^{10}\,b^7-124\,a^8\,b^9+405\,a^6\,b^{11}-540\,a^4\,b^{13}+304\,a^2\,b^{15}-64\,b^{17}\right)}{a^{12}\,b^4}-\frac{32\,\left(6\,a^{15}+20\,a^{13}\,b^2-84\,a^{11}\,b^4+97\,a^9\,b^6-56\,a^7\,b^8+16\,a^5\,b^{10}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^2-20\,a^{15}\,b^4-6\,a^{13}\,b^6+44\,a^{11}\,b^8+5\,a^9\,b^{10}-40\,a^7\,b^{12}+16\,a^5\,b^{14}\right)}{a^{12}\,b^4}-\frac{32\,\left(3\,a^{16}\,b-4\,a^{14}\,b^3+5\,a^{12}\,b^5+71\,a^{10}\,b^7-220\,a^8\,b^9+208\,a^6\,b^{11}-64\,a^4\,b^{13}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b^5+10\,a^{14}\,b^7-97\,a^{12}\,b^9+148\,a^{10}\,b^{11}-64\,a^8\,b^{13}\right)}{a^{12}\,b^4}-\frac{32\,\left(a^{15}\,b^4+30\,a^{13}\,b^6-64\,a^{11}\,b^8+32\,a^9\,b^{10}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\left(4\,a^{14}\,b^7-3\,a^{16}\,b^5\right)}{a^{12}\,b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^6-17\,a^{15}\,b^8+16\,a^{13}\,b^{10}\right)}{a^{12}\,b^4}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}+\frac{\left(\frac{32\,\left(6\,a^{15}+20\,a^{13}\,b^2-84\,a^{11}\,b^4+97\,a^9\,b^6-56\,a^7\,b^8+16\,a^5\,b^{10}\right)}{a^{12}\,b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b+10\,a^{14}\,b^3-72\,a^{12}\,b^5+78\,a^{10}\,b^7-124\,a^8\,b^9+405\,a^6\,b^{11}-540\,a^4\,b^{13}+304\,a^2\,b^{15}-64\,b^{17}\right)}{a^{12}\,b^4}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^2-20\,a^{15}\,b^4-6\,a^{13}\,b^6+44\,a^{11}\,b^8+5\,a^9\,b^{10}-40\,a^7\,b^{12}+16\,a^5\,b^{14}\right)}{a^{12}\,b^4}-\frac{32\,\left(3\,a^{16}\,b-4\,a^{14}\,b^3+5\,a^{12}\,b^5+71\,a^{10}\,b^7-220\,a^8\,b^9+208\,a^6\,b^{11}-64\,a^4\,b^{13}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\left(a^{15}\,b^4+30\,a^{13}\,b^6-64\,a^{11}\,b^8+32\,a^9\,b^{10}\right)}{a^{12}\,b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b^5+10\,a^{14}\,b^7-97\,a^{12}\,b^9+148\,a^{10}\,b^{11}-64\,a^8\,b^{13}\right)}{a^{12}\,b^4}+\frac{\left(\frac{32\,\left(4\,a^{14}\,b^7-3\,a^{16}\,b^5\right)}{a^{12}\,b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^6-17\,a^{15}\,b^8+16\,a^{13}\,b^{10}\right)}{a^{12}\,b^4}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}}\right)}{b^2\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^3\,d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,a^2-4\,b^2\right)}{a^5\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b+10\,a^{14}\,b^3-72\,a^{12}\,b^5+78\,a^{10}\,b^7-124\,a^8\,b^9+405\,a^6\,b^{11}-540\,a^4\,b^{13}+304\,a^2\,b^{15}-64\,b^{17}\right)}{a^{12}\,b^4}-\frac{32\,\left(6\,a^{15}+20\,a^{13}\,b^2-84\,a^{11}\,b^4+97\,a^9\,b^6-56\,a^7\,b^8+16\,a^5\,b^{10}\right)}{a^{12}\,b^2}+\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^2-20\,a^{15}\,b^4-6\,a^{13}\,b^6+44\,a^{11}\,b^8+5\,a^9\,b^{10}-40\,a^7\,b^{12}+16\,a^5\,b^{14}\right)}{a^{12}\,b^4}-\frac{32\,\left(3\,a^{16}\,b-4\,a^{14}\,b^3+5\,a^{12}\,b^5+71\,a^{10}\,b^7-220\,a^8\,b^9+208\,a^6\,b^{11}-64\,a^4\,b^{13}\right)}{a^{12}\,b^2}+\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b^5+10\,a^{14}\,b^7-97\,a^{12}\,b^9+148\,a^{10}\,b^{11}-64\,a^8\,b^{13}\right)}{a^{12}\,b^4}-\frac{32\,\left(a^{15}\,b^4+30\,a^{13}\,b^6-64\,a^{11}\,b^8+32\,a^9\,b^{10}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\left(4\,a^{14}\,b^7-3\,a^{16}\,b^5\right)}{a^{12}\,b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^6-17\,a^{15}\,b^8+16\,a^{13}\,b^{10}\right)}{a^{12}\,b^4}\right)\,\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5\,b^2}\right)}{a^5\,b^2}\right)}{a^5\,b^2}\right)\,1{}\mathrm{i}}{a^5\,b^2}-\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(6\,a^{15}+20\,a^{13}\,b^2-84\,a^{11}\,b^4+97\,a^9\,b^6-56\,a^7\,b^8+16\,a^5\,b^{10}\right)}{a^{12}\,b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b+10\,a^{14}\,b^3-72\,a^{12}\,b^5+78\,a^{10}\,b^7-124\,a^8\,b^9+405\,a^6\,b^{11}-540\,a^4\,b^{13}+304\,a^2\,b^{15}-64\,b^{17}\right)}{a^{12}\,b^4}+\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^2-20\,a^{15}\,b^4-6\,a^{13}\,b^6+44\,a^{11}\,b^8+5\,a^9\,b^{10}-40\,a^7\,b^{12}+16\,a^5\,b^{14}\right)}{a^{12}\,b^4}-\frac{32\,\left(3\,a^{16}\,b-4\,a^{14}\,b^3+5\,a^{12}\,b^5+71\,a^{10}\,b^7-220\,a^8\,b^9+208\,a^6\,b^{11}-64\,a^4\,b^{13}\right)}{a^{12}\,b^2}+\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{15}\,b^4+30\,a^{13}\,b^6-64\,a^{11}\,b^8+32\,a^9\,b^{10}\right)}{a^{12}\,b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b^5+10\,a^{14}\,b^7-97\,a^{12}\,b^9+148\,a^{10}\,b^{11}-64\,a^8\,b^{13}\right)}{a^{12}\,b^4}+\frac{\left(\frac{32\,\left(4\,a^{14}\,b^7-3\,a^{16}\,b^5\right)}{a^{12}\,b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^6-17\,a^{15}\,b^8+16\,a^{13}\,b^{10}\right)}{a^{12}\,b^4}\right)\,\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5\,b^2}\right)}{a^5\,b^2}\right)}{a^5\,b^2}\right)\,1{}\mathrm{i}}{a^5\,b^2}}{\frac{64\,\left(30\,a^{12}\,b+a^{10}\,b^3-280\,a^8\,b^5+613\,a^6\,b^7-604\,a^4\,b^9+304\,a^2\,b^{11}-64\,b^{13}\right)}{a^{12}\,b^2}+\frac{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}+12\,a^{13}\,b^2-64\,a^{11}\,b^4+60\,a^9\,b^6-16\,a^7\,b^8\right)}{a^{12}\,b^4}-\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b+10\,a^{14}\,b^3-72\,a^{12}\,b^5+78\,a^{10}\,b^7-124\,a^8\,b^9+405\,a^6\,b^{11}-540\,a^4\,b^{13}+304\,a^2\,b^{15}-64\,b^{17}\right)}{a^{12}\,b^4}-\frac{32\,\left(6\,a^{15}+20\,a^{13}\,b^2-84\,a^{11}\,b^4+97\,a^9\,b^6-56\,a^7\,b^8+16\,a^5\,b^{10}\right)}{a^{12}\,b^2}+\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^2-20\,a^{15}\,b^4-6\,a^{13}\,b^6+44\,a^{11}\,b^8+5\,a^9\,b^{10}-40\,a^7\,b^{12}+16\,a^5\,b^{14}\right)}{a^{12}\,b^4}-\frac{32\,\left(3\,a^{16}\,b-4\,a^{14}\,b^3+5\,a^{12}\,b^5+71\,a^{10}\,b^7-220\,a^8\,b^9+208\,a^6\,b^{11}-64\,a^4\,b^{13}\right)}{a^{12}\,b^2}+\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b^5+10\,a^{14}\,b^7-97\,a^{12}\,b^9+148\,a^{10}\,b^{11}-64\,a^8\,b^{13}\right)}{a^{12}\,b^4}-\frac{32\,\left(a^{15}\,b^4+30\,a^{13}\,b^6-64\,a^{11}\,b^8+32\,a^9\,b^{10}\right)}{a^{12}\,b^2}+\frac{\left(\frac{32\,\left(4\,a^{14}\,b^7-3\,a^{16}\,b^5\right)}{a^{12}\,b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^6-17\,a^{15}\,b^8+16\,a^{13}\,b^{10}\right)}{a^{12}\,b^4}\right)\,\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5\,b^2}\right)}{a^5\,b^2}\right)}{a^5\,b^2}\right)}{a^5\,b^2}-\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(6\,a^{15}+20\,a^{13}\,b^2-84\,a^{11}\,b^4+97\,a^9\,b^6-56\,a^7\,b^8+16\,a^5\,b^{10}\right)}{a^{12}\,b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b+10\,a^{14}\,b^3-72\,a^{12}\,b^5+78\,a^{10}\,b^7-124\,a^8\,b^9+405\,a^6\,b^{11}-540\,a^4\,b^{13}+304\,a^2\,b^{15}-64\,b^{17}\right)}{a^{12}\,b^4}+\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^2-20\,a^{15}\,b^4-6\,a^{13}\,b^6+44\,a^{11}\,b^8+5\,a^9\,b^{10}-40\,a^7\,b^{12}+16\,a^5\,b^{14}\right)}{a^{12}\,b^4}-\frac{32\,\left(3\,a^{16}\,b-4\,a^{14}\,b^3+5\,a^{12}\,b^5+71\,a^{10}\,b^7-220\,a^8\,b^9+208\,a^6\,b^{11}-64\,a^4\,b^{13}\right)}{a^{12}\,b^2}+\frac{\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{15}\,b^4+30\,a^{13}\,b^6-64\,a^{11}\,b^8+32\,a^9\,b^{10}\right)}{a^{12}\,b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{16}\,b^5+10\,a^{14}\,b^7-97\,a^{12}\,b^9+148\,a^{10}\,b^{11}-64\,a^8\,b^{13}\right)}{a^{12}\,b^4}+\frac{\left(\frac{32\,\left(4\,a^{14}\,b^7-3\,a^{16}\,b^5\right)}{a^{12}\,b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{17}\,b^6-17\,a^{15}\,b^8+16\,a^{13}\,b^{10}\right)}{a^{12}\,b^4}\right)\,\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5\,b^2}\right)}{a^5\,b^2}\right)}{a^5\,b^2}\right)}{a^5\,b^2}}\right)\,\left(a^2+4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^5\,b^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^2*d) - (tan(c/2 + (d*x)/2)*((24*a^2 + 32*b^2)/(64*a^4) + 3/(4*a^2) - (2*b^2)/a^4))/d - (tan(c/2 + (d*x)/2)^2*(8*a*b^2 - (26*a^3)/3) + a^3/3 - (4*a^2*b*tan(c/2 + (d*x)/2))/3 + (tan(c/2 + (d*x)/2)^4*(7*a^4 + 16*b^4 - 20*a^2*b^2))/a + (4*tan(c/2 + (d*x)/2)^3*(4*a^4 + 10*b^4 - 13*a^2*b^2))/b)/(d*(8*a^5*tan(c/2 + (d*x)/2)^3 + 8*a^5*tan(c/2 + (d*x)/2)^5 + 16*a^4*b*tan(c/2 + (d*x)/2)^4)) + (2*atan((((((((((32*(4*a^14*b^7 - 3*a^16*b^5))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^13*b^10 - 17*a^15*b^8 + 2*a^17*b^6))/(a^12*b^4))*1i)/b^2 - (32*(32*a^9*b^10 - 64*a^11*b^8 + 30*a^13*b^6 + a^15*b^4))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(148*a^10*b^11 - 64*a^8*b^13 - 97*a^12*b^9 + 10*a^14*b^7 + 4*a^16*b^5))/(a^12*b^4))*1i)/b^2 - (32*(3*a^16*b - 64*a^4*b^13 + 208*a^6*b^11 - 220*a^8*b^9 + 71*a^10*b^7 + 5*a^12*b^5 - 4*a^14*b^3))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^5*b^14 - 40*a^7*b^12 + 5*a^9*b^10 + 44*a^11*b^8 - 6*a^13*b^6 - 20*a^15*b^4 + 2*a^17*b^2))/(a^12*b^4))*1i)/b^2 - (32*(6*a^15 + 16*a^5*b^10 - 56*a^7*b^8 + 97*a^9*b^6 - 84*a^11*b^4 + 20*a^13*b^2))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(4*a^16*b - 64*b^17 + 304*a^2*b^15 - 540*a^4*b^13 + 405*a^6*b^11 - 124*a^8*b^9 + 78*a^10*b^7 - 72*a^12*b^5 + 10*a^14*b^3))/(a^12*b^4))/b^2 - ((((((((32*(4*a^14*b^7 - 3*a^16*b^5))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^13*b^10 - 17*a^15*b^8 + 2*a^17*b^6))/(a^12*b^4))*1i)/b^2 + (32*(32*a^9*b^10 - 64*a^11*b^8 + 30*a^13*b^6 + a^15*b^4))/(a^12*b^2) - (32*tan(c/2 + (d*x)/2)*(148*a^10*b^11 - 64*a^8*b^13 - 97*a^12*b^9 + 10*a^14*b^7 + 4*a^16*b^5))/(a^12*b^4))*1i)/b^2 - (32*(3*a^16*b - 64*a^4*b^13 + 208*a^6*b^11 - 220*a^8*b^9 + 71*a^10*b^7 + 5*a^12*b^5 - 4*a^14*b^3))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^5*b^14 - 40*a^7*b^12 + 5*a^9*b^10 + 44*a^11*b^8 - 6*a^13*b^6 - 20*a^15*b^4 + 2*a^17*b^2))/(a^12*b^4))*1i)/b^2 + (32*(6*a^15 + 16*a^5*b^10 - 56*a^7*b^8 + 97*a^9*b^6 - 84*a^11*b^4 + 20*a^13*b^2))/(a^12*b^2) - (32*tan(c/2 + (d*x)/2)*(4*a^16*b - 64*b^17 + 304*a^2*b^15 - 540*a^4*b^13 + 405*a^6*b^11 - 124*a^8*b^9 + 78*a^10*b^7 - 72*a^12*b^5 + 10*a^14*b^3))/(a^12*b^4))/b^2)/((((((((((32*(4*a^14*b^7 - 3*a^16*b^5))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^13*b^10 - 17*a^15*b^8 + 2*a^17*b^6))/(a^12*b^4))*1i)/b^2 - (32*(32*a^9*b^10 - 64*a^11*b^8 + 30*a^13*b^6 + a^15*b^4))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(148*a^10*b^11 - 64*a^8*b^13 - 97*a^12*b^9 + 10*a^14*b^7 + 4*a^16*b^5))/(a^12*b^4))*1i)/b^2 - (32*(3*a^16*b - 64*a^4*b^13 + 208*a^6*b^11 - 220*a^8*b^9 + 71*a^10*b^7 + 5*a^12*b^5 - 4*a^14*b^3))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^5*b^14 - 40*a^7*b^12 + 5*a^9*b^10 + 44*a^11*b^8 - 6*a^13*b^6 - 20*a^15*b^4 + 2*a^17*b^2))/(a^12*b^4))*1i)/b^2 - (32*(6*a^15 + 16*a^5*b^10 - 56*a^7*b^8 + 97*a^9*b^6 - 84*a^11*b^4 + 20*a^13*b^2))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(4*a^16*b - 64*b^17 + 304*a^2*b^15 - 540*a^4*b^13 + 405*a^6*b^11 - 124*a^8*b^9 + 78*a^10*b^7 - 72*a^12*b^5 + 10*a^14*b^3))/(a^12*b^4))*1i)/b^2 + (((((((((32*(4*a^14*b^7 - 3*a^16*b^5))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^13*b^10 - 17*a^15*b^8 + 2*a^17*b^6))/(a^12*b^4))*1i)/b^2 + (32*(32*a^9*b^10 - 64*a^11*b^8 + 30*a^13*b^6 + a^15*b^4))/(a^12*b^2) - (32*tan(c/2 + (d*x)/2)*(148*a^10*b^11 - 64*a^8*b^13 - 97*a^12*b^9 + 10*a^14*b^7 + 4*a^16*b^5))/(a^12*b^4))*1i)/b^2 - (32*(3*a^16*b - 64*a^4*b^13 + 208*a^6*b^11 - 220*a^8*b^9 + 71*a^10*b^7 + 5*a^12*b^5 - 4*a^14*b^3))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^5*b^14 - 40*a^7*b^12 + 5*a^9*b^10 + 44*a^11*b^8 - 6*a^13*b^6 - 20*a^15*b^4 + 2*a^17*b^2))/(a^12*b^4))*1i)/b^2 + (32*(6*a^15 + 16*a^5*b^10 - 56*a^7*b^8 + 97*a^9*b^6 - 84*a^11*b^4 + 20*a^13*b^2))/(a^12*b^2) - (32*tan(c/2 + (d*x)/2)*(4*a^16*b - 64*b^17 + 304*a^2*b^15 - 540*a^4*b^13 + 405*a^6*b^11 - 124*a^8*b^9 + 78*a^10*b^7 - 72*a^12*b^5 + 10*a^14*b^3))/(a^12*b^4))*1i)/b^2 - (64*(30*a^12*b - 64*b^13 + 304*a^2*b^11 - 604*a^4*b^9 + 613*a^6*b^7 - 280*a^8*b^5 + a^10*b^3))/(a^12*b^2) - (64*tan(c/2 + (d*x)/2)*(8*a^15 - 16*a^7*b^8 + 60*a^9*b^6 - 64*a^11*b^4 + 12*a^13*b^2))/(a^12*b^4))))/(b^2*d) - (b*tan(c/2 + (d*x)/2)^2)/(4*a^3*d) + (b*log(tan(c/2 + (d*x)/2))*(5*a^2 - 4*b^2))/(a^5*d) - (atan((((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(4*a^16*b - 64*b^17 + 304*a^2*b^15 - 540*a^4*b^13 + 405*a^6*b^11 - 124*a^8*b^9 + 78*a^10*b^7 - 72*a^12*b^5 + 10*a^14*b^3))/(a^12*b^4) - (32*(6*a^15 + 16*a^5*b^10 - 56*a^7*b^8 + 97*a^9*b^6 - 84*a^11*b^4 + 20*a^13*b^2))/(a^12*b^2) + ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(16*a^5*b^14 - 40*a^7*b^12 + 5*a^9*b^10 + 44*a^11*b^8 - 6*a^13*b^6 - 20*a^15*b^4 + 2*a^17*b^2))/(a^12*b^4) - (32*(3*a^16*b - 64*a^4*b^13 + 208*a^6*b^11 - 220*a^8*b^9 + 71*a^10*b^7 + 5*a^12*b^5 - 4*a^14*b^3))/(a^12*b^2) + ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(148*a^10*b^11 - 64*a^8*b^13 - 97*a^12*b^9 + 10*a^14*b^7 + 4*a^16*b^5))/(a^12*b^4) - (32*(32*a^9*b^10 - 64*a^11*b^8 + 30*a^13*b^6 + a^15*b^4))/(a^12*b^2) + (((32*(4*a^14*b^7 - 3*a^16*b^5))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^13*b^10 - 17*a^15*b^8 + 2*a^17*b^6))/(a^12*b^4))*(a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^5*b^2)))/(a^5*b^2)))/(a^5*b^2))*1i)/(a^5*b^2) - ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(6*a^15 + 16*a^5*b^10 - 56*a^7*b^8 + 97*a^9*b^6 - 84*a^11*b^4 + 20*a^13*b^2))/(a^12*b^2) - (32*tan(c/2 + (d*x)/2)*(4*a^16*b - 64*b^17 + 304*a^2*b^15 - 540*a^4*b^13 + 405*a^6*b^11 - 124*a^8*b^9 + 78*a^10*b^7 - 72*a^12*b^5 + 10*a^14*b^3))/(a^12*b^4) + ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(16*a^5*b^14 - 40*a^7*b^12 + 5*a^9*b^10 + 44*a^11*b^8 - 6*a^13*b^6 - 20*a^15*b^4 + 2*a^17*b^2))/(a^12*b^4) - (32*(3*a^16*b - 64*a^4*b^13 + 208*a^6*b^11 - 220*a^8*b^9 + 71*a^10*b^7 + 5*a^12*b^5 - 4*a^14*b^3))/(a^12*b^2) + ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(32*a^9*b^10 - 64*a^11*b^8 + 30*a^13*b^6 + a^15*b^4))/(a^12*b^2) - (32*tan(c/2 + (d*x)/2)*(148*a^10*b^11 - 64*a^8*b^13 - 97*a^12*b^9 + 10*a^14*b^7 + 4*a^16*b^5))/(a^12*b^4) + (((32*(4*a^14*b^7 - 3*a^16*b^5))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^13*b^10 - 17*a^15*b^8 + 2*a^17*b^6))/(a^12*b^4))*(a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^5*b^2)))/(a^5*b^2)))/(a^5*b^2))*1i)/(a^5*b^2))/((64*(30*a^12*b - 64*b^13 + 304*a^2*b^11 - 604*a^4*b^9 + 613*a^6*b^7 - 280*a^8*b^5 + a^10*b^3))/(a^12*b^2) + (64*tan(c/2 + (d*x)/2)*(8*a^15 - 16*a^7*b^8 + 60*a^9*b^6 - 64*a^11*b^4 + 12*a^13*b^2))/(a^12*b^4) - ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(4*a^16*b - 64*b^17 + 304*a^2*b^15 - 540*a^4*b^13 + 405*a^6*b^11 - 124*a^8*b^9 + 78*a^10*b^7 - 72*a^12*b^5 + 10*a^14*b^3))/(a^12*b^4) - (32*(6*a^15 + 16*a^5*b^10 - 56*a^7*b^8 + 97*a^9*b^6 - 84*a^11*b^4 + 20*a^13*b^2))/(a^12*b^2) + ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(16*a^5*b^14 - 40*a^7*b^12 + 5*a^9*b^10 + 44*a^11*b^8 - 6*a^13*b^6 - 20*a^15*b^4 + 2*a^17*b^2))/(a^12*b^4) - (32*(3*a^16*b - 64*a^4*b^13 + 208*a^6*b^11 - 220*a^8*b^9 + 71*a^10*b^7 + 5*a^12*b^5 - 4*a^14*b^3))/(a^12*b^2) + ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(148*a^10*b^11 - 64*a^8*b^13 - 97*a^12*b^9 + 10*a^14*b^7 + 4*a^16*b^5))/(a^12*b^4) - (32*(32*a^9*b^10 - 64*a^11*b^8 + 30*a^13*b^6 + a^15*b^4))/(a^12*b^2) + (((32*(4*a^14*b^7 - 3*a^16*b^5))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^13*b^10 - 17*a^15*b^8 + 2*a^17*b^6))/(a^12*b^4))*(a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^5*b^2)))/(a^5*b^2)))/(a^5*b^2)))/(a^5*b^2) - ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(6*a^15 + 16*a^5*b^10 - 56*a^7*b^8 + 97*a^9*b^6 - 84*a^11*b^4 + 20*a^13*b^2))/(a^12*b^2) - (32*tan(c/2 + (d*x)/2)*(4*a^16*b - 64*b^17 + 304*a^2*b^15 - 540*a^4*b^13 + 405*a^6*b^11 - 124*a^8*b^9 + 78*a^10*b^7 - 72*a^12*b^5 + 10*a^14*b^3))/(a^12*b^4) + ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(16*a^5*b^14 - 40*a^7*b^12 + 5*a^9*b^10 + 44*a^11*b^8 - 6*a^13*b^6 - 20*a^15*b^4 + 2*a^17*b^2))/(a^12*b^4) - (32*(3*a^16*b - 64*a^4*b^13 + 208*a^6*b^11 - 220*a^8*b^9 + 71*a^10*b^7 + 5*a^12*b^5 - 4*a^14*b^3))/(a^12*b^2) + ((a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(32*a^9*b^10 - 64*a^11*b^8 + 30*a^13*b^6 + a^15*b^4))/(a^12*b^2) - (32*tan(c/2 + (d*x)/2)*(148*a^10*b^11 - 64*a^8*b^13 - 97*a^12*b^9 + 10*a^14*b^7 + 4*a^16*b^5))/(a^12*b^4) + (((32*(4*a^14*b^7 - 3*a^16*b^5))/(a^12*b^2) + (32*tan(c/2 + (d*x)/2)*(16*a^13*b^10 - 17*a^15*b^8 + 2*a^17*b^6))/(a^12*b^4))*(a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^5*b^2)))/(a^5*b^2)))/(a^5*b^2)))/(a^5*b^2)))*(a^2 + 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^5*b^2*d)","B"
1263,1,1117,303,12.031897,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^5*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(36\,a^4-142\,a^2\,b^2+96\,b^4\right)-\frac{a^4}{4}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{15\,a^4}{4}-\frac{10\,a^2\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(20\,a\,b^3-\frac{80\,a^3\,b}{3}\right)-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^4\,b+8\,a^2\,b^3-8\,b^5\right)}{a}+\frac{5\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6}}{d\,\left(16\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+32\,b\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{32\,a^2+64\,b^2}{512\,a^4}+\frac{3}{16\,a^2}-\frac{b^2}{2\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b\,\left(32\,a^2+64\,b^2\right)}{64\,a^5}-\frac{b}{4\,a^3}+\frac{4\,b\,\left(\frac{32\,a^2+64\,b^2}{256\,a^4}+\frac{3}{8\,a^2}-\frac{b^2}{a^4}\right)}{a}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,a^3\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(15\,a^4-60\,a^2\,b^2+40\,b^4\right)}{8\,a^6\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{10}-170\,a^8\,b^2+320\,a^6\,b^4-160\,a^4\,b^6\right)}{4\,a^9}-\frac{55\,a^{10}\,b-140\,a^8\,b^3+80\,a^6\,b^5}{4\,a^{10}}+\frac{5\,b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^6}\right)\,5{}\mathrm{i}}{a^6}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{55\,a^{10}\,b-140\,a^8\,b^3+80\,a^6\,b^5}{4\,a^{10}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{10}-170\,a^8\,b^2+320\,a^6\,b^4-160\,a^4\,b^6\right)}{4\,a^9}+\frac{5\,b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^6}\right)\,5{}\mathrm{i}}{a^6}}{\frac{75\,a^8\,b-450\,a^6\,b^3+875\,a^4\,b^5-700\,a^2\,b^7+200\,b^9}{2\,a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-250\,a^6\,b^2+700\,a^4\,b^4-650\,a^2\,b^6+200\,b^8\right)}{2\,a^9}+\frac{5\,b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{10}-170\,a^8\,b^2+320\,a^6\,b^4-160\,a^4\,b^6\right)}{4\,a^9}-\frac{55\,a^{10}\,b-140\,a^8\,b^3+80\,a^6\,b^5}{4\,a^{10}}+\frac{5\,b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^6}\right)}{a^6}+\frac{5\,b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{55\,a^{10}\,b-140\,a^8\,b^3+80\,a^6\,b^5}{4\,a^{10}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{10}-170\,a^8\,b^2+320\,a^6\,b^4-160\,a^4\,b^6\right)}{4\,a^9}+\frac{5\,b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^6}\right)}{a^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,10{}\mathrm{i}}{a^6\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a^2*d) + (tan(c/2 + (d*x)/2)^4*(36*a^4 + 96*b^4 - 142*a^2*b^2) - a^4/4 + tan(c/2 + (d*x)/2)^2*((15*a^4)/4 - (10*a^2*b^2)/3) + tan(c/2 + (d*x)/2)^3*(20*a*b^3 - (80*a^3*b)/3) - (4*tan(c/2 + (d*x)/2)^5*(a^4*b - 8*b^5 + 8*a^2*b^3))/a + (5*a^3*b*tan(c/2 + (d*x)/2))/6)/(d*(16*a^6*tan(c/2 + (d*x)/2)^4 + 16*a^6*tan(c/2 + (d*x)/2)^6 + 32*a^5*b*tan(c/2 + (d*x)/2)^5)) - (tan(c/2 + (d*x)/2)^2*((32*a^2 + 64*b^2)/(512*a^4) + 3/(16*a^2) - b^2/(2*a^4)))/d + (tan(c/2 + (d*x)/2)*((b*(32*a^2 + 64*b^2))/(64*a^5) - b/(4*a^3) + (4*b*((32*a^2 + 64*b^2)/(256*a^4) + 3/(8*a^2) - b^2/a^4))/a))/d - (b*tan(c/2 + (d*x)/2)^3)/(12*a^3*d) + (log(tan(c/2 + (d*x)/2))*(15*a^4 + 40*b^4 - 60*a^2*b^2))/(8*a^6*d) - (b*atan(((b*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(c/2 + (d*x)/2)*(15*a^10 - 160*a^4*b^6 + 320*a^6*b^4 - 170*a^8*b^2))/(4*a^9) - (55*a^10*b + 80*a^6*b^5 - 140*a^8*b^3)/(4*a^10) + (5*b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^3*(a - b)^3)^(1/2))/a^6)*5i)/a^6 - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((55*a^10*b + 80*a^6*b^5 - 140*a^8*b^3)/(4*a^10) - (tan(c/2 + (d*x)/2)*(15*a^10 - 160*a^4*b^6 + 320*a^6*b^4 - 170*a^8*b^2))/(4*a^9) + (5*b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^3*(a - b)^3)^(1/2))/a^6)*5i)/a^6)/((75*a^8*b + 200*b^9 - 700*a^2*b^7 + 875*a^4*b^5 - 450*a^6*b^3)/(2*a^10) + (tan(c/2 + (d*x)/2)*(200*b^8 - 650*a^2*b^6 + 700*a^4*b^4 - 250*a^6*b^2))/(2*a^9) + (5*b*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(c/2 + (d*x)/2)*(15*a^10 - 160*a^4*b^6 + 320*a^6*b^4 - 170*a^8*b^2))/(4*a^9) - (55*a^10*b + 80*a^6*b^5 - 140*a^8*b^3)/(4*a^10) + (5*b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^3*(a - b)^3)^(1/2))/a^6))/a^6 + (5*b*(-(a + b)^3*(a - b)^3)^(1/2)*((55*a^10*b + 80*a^6*b^5 - 140*a^8*b^3)/(4*a^10) - (tan(c/2 + (d*x)/2)*(15*a^10 - 160*a^4*b^6 + 320*a^6*b^4 - 170*a^8*b^2))/(4*a^9) + (5*b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^3*(a - b)^3)^(1/2))/a^6))/a^6))*(-(a + b)^3*(a - b)^3)^(1/2)*10i)/(a^6*d)","B"
1264,1,1424,424,12.161183,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^6*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1}{4\,a^2}+\frac{b^2}{2\,a^4}-\frac{4\,b\,\left(\frac{b\,\left(64\,a^2+128\,b^2\right)}{256\,a^5}-\frac{b}{8\,a^3}+\frac{4\,b\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{5}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{a}\right)}{a}+\frac{\left(64\,a^2+128\,b^2\right)\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{5}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{32\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{64\,a^2+128\,b^2}{3072\,a^4}+\frac{5}{96\,a^2}-\frac{b^2}{6\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{31\,a^4\,b}{3}-8\,a^2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{59\,a^5}{3}-72\,a^3\,b^2+48\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(124\,a^4\,b-360\,a^2\,b^3+224\,b^5\right)+\frac{a^5}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{32\,a^5}{15}-2\,a^3\,b^2\right)-\frac{3\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(11\,a^6-22\,a^4\,b^2-24\,a^2\,b^4+32\,b^6\right)}{a}}{d\,\left(32\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+64\,b\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b\,\left(64\,a^2+128\,b^2\right)}{512\,a^5}-\frac{b}{16\,a^3}+\frac{2\,b\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{5}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{a}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(15\,a^4\,b-40\,a^2\,b^3+24\,b^5\right)}{4\,a^7\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,a^{13}-47\,a^{11}\,b^2+92\,a^9\,b^4-48\,a^7\,b^6}{2\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,a^{11}\,b-134\,a^9\,b^3+208\,a^7\,b^5-96\,a^5\,b^7\right)}{2\,a^{11}}+\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{14}-16\,a^{12}\,b^2\right)}{2\,a^{11}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^7}\right)\,1{}\mathrm{i}}{a^7}+\frac{\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,a^{13}-47\,a^{11}\,b^2+92\,a^9\,b^4-48\,a^7\,b^6}{2\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,a^{11}\,b-134\,a^9\,b^3+208\,a^7\,b^5-96\,a^5\,b^7\right)}{2\,a^{11}}-\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{14}-16\,a^{12}\,b^2\right)}{2\,a^{11}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^7}\right)\,1{}\mathrm{i}}{a^7}}{\frac{15\,a^{10}\,b-160\,a^8\,b^3+539\,a^6\,b^5-802\,a^4\,b^7+552\,a^2\,b^9-144\,b^{11}}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-98\,a^8\,b^2+400\,a^6\,b^4-682\,a^4\,b^6+516\,a^2\,b^8-144\,b^{10}\right)}{a^{11}}-\frac{\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,a^{13}-47\,a^{11}\,b^2+92\,a^9\,b^4-48\,a^7\,b^6}{2\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,a^{11}\,b-134\,a^9\,b^3+208\,a^7\,b^5-96\,a^5\,b^7\right)}{2\,a^{11}}+\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{14}-16\,a^{12}\,b^2\right)}{2\,a^{11}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^7}\right)}{a^7}+\frac{\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,a^{13}-47\,a^{11}\,b^2+92\,a^9\,b^4-48\,a^7\,b^6}{2\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,a^{11}\,b-134\,a^9\,b^3+208\,a^7\,b^5-96\,a^5\,b^7\right)}{2\,a^{11}}-\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{14}-16\,a^{12}\,b^2\right)}{2\,a^{11}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^7}\right)}{a^7}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^7\,d}","Not used",1,"tan(c/2 + (d*x)/2)^5/(160*a^2*d) + (tan(c/2 + (d*x)/2)*(1/(4*a^2) + b^2/(2*a^4) - (4*b*((b*(64*a^2 + 128*b^2))/(256*a^5) - b/(8*a^3) + (4*b*((64*a^2 + 128*b^2)/(1024*a^4) + 5/(32*a^2) - b^2/(2*a^4)))/a))/a + ((64*a^2 + 128*b^2)*((64*a^2 + 128*b^2)/(1024*a^4) + 5/(32*a^2) - b^2/(2*a^4)))/(32*a^2)))/d - (tan(c/2 + (d*x)/2)^3*((64*a^2 + 128*b^2)/(3072*a^4) + 5/(96*a^2) - b^2/(6*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((31*a^4*b)/3 - 8*a^2*b^3) + tan(c/2 + (d*x)/2)^4*(48*a*b^4 + (59*a^5)/3 - 72*a^3*b^2) + tan(c/2 + (d*x)/2)^5*(124*a^4*b + 224*b^5 - 360*a^2*b^3) + a^5/5 - tan(c/2 + (d*x)/2)^2*((32*a^5)/15 - 2*a^3*b^2) - (3*a^4*b*tan(c/2 + (d*x)/2))/5 + (2*tan(c/2 + (d*x)/2)^6*(11*a^6 + 32*b^6 - 24*a^2*b^4 - 22*a^4*b^2))/a)/(d*(32*a^7*tan(c/2 + (d*x)/2)^5 + 32*a^7*tan(c/2 + (d*x)/2)^7 + 64*a^6*b*tan(c/2 + (d*x)/2)^6)) + (tan(c/2 + (d*x)/2)^2*((b*(64*a^2 + 128*b^2))/(512*a^5) - b/(16*a^3) + (2*b*((64*a^2 + 128*b^2)/(1024*a^4) + 5/(32*a^2) - b^2/(2*a^4)))/a))/d - (log(tan(c/2 + (d*x)/2))*(15*a^4*b + 24*b^5 - 40*a^2*b^3))/(4*a^7*d) - (b*tan(c/2 + (d*x)/2)^4)/(32*a^3*d) - (atan((((a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((4*a^13 - 48*a^7*b^6 + 92*a^9*b^4 - 47*a^11*b^2)/(2*a^12) + (tan(c/2 + (d*x)/2)*(23*a^11*b - 96*a^5*b^7 + 208*a^7*b^5 - 134*a^9*b^3))/(2*a^11) + ((2*a^2*b - (tan(c/2 + (d*x)/2)*(12*a^14 - 16*a^12*b^2))/(2*a^11))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^7)*1i)/a^7 + ((a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((4*a^13 - 48*a^7*b^6 + 92*a^9*b^4 - 47*a^11*b^2)/(2*a^12) + (tan(c/2 + (d*x)/2)*(23*a^11*b - 96*a^5*b^7 + 208*a^7*b^5 - 134*a^9*b^3))/(2*a^11) - ((2*a^2*b - (tan(c/2 + (d*x)/2)*(12*a^14 - 16*a^12*b^2))/(2*a^11))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^7)*1i)/a^7)/((15*a^10*b - 144*b^11 + 552*a^2*b^9 - 802*a^4*b^7 + 539*a^6*b^5 - 160*a^8*b^3)/a^12 + (tan(c/2 + (d*x)/2)*(8*a^10 - 144*b^10 + 516*a^2*b^8 - 682*a^4*b^6 + 400*a^6*b^4 - 98*a^8*b^2))/a^11 - ((a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((4*a^13 - 48*a^7*b^6 + 92*a^9*b^4 - 47*a^11*b^2)/(2*a^12) + (tan(c/2 + (d*x)/2)*(23*a^11*b - 96*a^5*b^7 + 208*a^7*b^5 - 134*a^9*b^3))/(2*a^11) + ((2*a^2*b - (tan(c/2 + (d*x)/2)*(12*a^14 - 16*a^12*b^2))/(2*a^11))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^7))/a^7 + ((a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((4*a^13 - 48*a^7*b^6 + 92*a^9*b^4 - 47*a^11*b^2)/(2*a^12) + (tan(c/2 + (d*x)/2)*(23*a^11*b - 96*a^5*b^7 + 208*a^7*b^5 - 134*a^9*b^3))/(2*a^11) - ((2*a^2*b - (tan(c/2 + (d*x)/2)*(12*a^14 - 16*a^12*b^2))/(2*a^11))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^7))/a^7))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^7*d)","B"
1265,1,1810,480,12.579170,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^7*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{128\,a^2+256\,b^2}{16384\,a^4}+\frac{1}{64\,a^2}-\frac{b^2}{16\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3}{128\,a^2}+\frac{b^2}{8\,a^4}-\frac{2\,b\,\left(\frac{b\,\left(128\,a^2+256\,b^2\right)}{1024\,a^5}-\frac{b}{16\,a^3}+\frac{4\,b\,\left(\frac{128\,a^2+256\,b^2}{4096\,a^4}+\frac{1}{16\,a^2}-\frac{b^2}{4\,a^4}\right)}{a}\right)}{a}+\frac{\left(128\,a^2+256\,b^2\right)\,\left(\frac{128\,a^2+256\,b^2}{4096\,a^4}+\frac{1}{16\,a^2}-\frac{b^2}{4\,a^4}\right)}{128\,a^2}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{16\,a^3}-\frac{\left(128\,a^2+256\,b^2\right)\,\left(\frac{b\,\left(128\,a^2+256\,b^2\right)}{1024\,a^5}-\frac{b}{16\,a^3}+\frac{4\,b\,\left(\frac{128\,a^2+256\,b^2}{4096\,a^4}+\frac{1}{16\,a^2}-\frac{b^2}{4\,a^4}\right)}{a}\right)}{64\,a^2}+\frac{4\,b\,\left(\frac{128\,a^2+256\,b^2}{4096\,a^4}+\frac{1}{16\,a^2}-\frac{b^2}{4\,a^4}\right)}{a}-\frac{4\,b\,\left(\frac{3}{64\,a^2}+\frac{b^2}{4\,a^4}-\frac{4\,b\,\left(\frac{b\,\left(128\,a^2+256\,b^2\right)}{1024\,a^5}-\frac{b}{16\,a^3}+\frac{4\,b\,\left(\frac{128\,a^2+256\,b^2}{4096\,a^4}+\frac{1}{16\,a^2}-\frac{b^2}{4\,a^4}\right)}{a}\right)}{a}+\frac{\left(128\,a^2+256\,b^2\right)\,\left(\frac{128\,a^2+256\,b^2}{4096\,a^4}+\frac{1}{16\,a^2}-\frac{b^2}{4\,a^4}\right)}{64\,a^2}\right)}{a}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{b\,\left(128\,a^2+256\,b^2\right)}{3072\,a^5}-\frac{b}{48\,a^3}+\frac{4\,b\,\left(\frac{128\,a^2+256\,b^2}{4096\,a^4}+\frac{1}{16\,a^2}-\frac{b^2}{4\,a^4}\right)}{3\,a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{83\,a^5\,b}{15}-\frac{14\,a^3\,b^3}{3}\right)+\frac{a^6}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^6-\frac{79\,a^4\,b^2}{3}+\frac{56\,a^2\,b^4}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{191\,a^5\,b}{3}-\frac{544\,a^3\,b^3}{3}+112\,a\,b^5\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{4\,a^6}{3}-\frac{7\,a^4\,b^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{15\,a^6}{2}-352\,a^4\,b^2+872\,a^2\,b^4-512\,b^6\right)-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(11\,a^6\,b-20\,a^4\,b^3-8\,a^2\,b^5+16\,b^7\right)}{a}-\frac{7\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}}{d\,\left(64\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+64\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+128\,b\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{80\,a^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,a^6-90\,a^4\,b^2+200\,a^2\,b^4-112\,b^6\right)}{16\,a^8\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{14}-164\,a^{12}\,b^2+732\,a^{10}\,b^4-1024\,a^8\,b^6+448\,a^6\,b^8\right)}{8\,a^{13}}-\frac{37\,a^{14}\,b-266\,a^{12}\,b^3+456\,a^{10}\,b^5-224\,a^8\,b^7}{8\,a^{14}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{16}-64\,a^{14}\,b^2\right)}{8\,a^{13}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}\right)\,1{}\mathrm{i}}{a^8}-\frac{b\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{37\,a^{14}\,b-266\,a^{12}\,b^3+456\,a^{10}\,b^5-224\,a^8\,b^7}{8\,a^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{14}-164\,a^{12}\,b^2+732\,a^{10}\,b^4-1024\,a^8\,b^6+448\,a^6\,b^8\right)}{8\,a^{13}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{16}-64\,a^{14}\,b^2\right)}{8\,a^{13}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}\right)\,1{}\mathrm{i}}{a^8}}{\frac{10\,a^{12}\,b-235\,a^{10}\,b^3+1470\,a^8\,b^5-3899\,a^6\,b^7+5062\,a^4\,b^9-3192\,a^2\,b^{11}+784\,b^{13}}{4\,a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-108\,a^{10}\,b^2+938\,a^8\,b^4-2980\,a^6\,b^6+4362\,a^4\,b^8-2996\,a^2\,b^{10}+784\,b^{12}\right)}{4\,a^{13}}+\frac{b\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{14}-164\,a^{12}\,b^2+732\,a^{10}\,b^4-1024\,a^8\,b^6+448\,a^6\,b^8\right)}{8\,a^{13}}-\frac{37\,a^{14}\,b-266\,a^{12}\,b^3+456\,a^{10}\,b^5-224\,a^8\,b^7}{8\,a^{14}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{16}-64\,a^{14}\,b^2\right)}{8\,a^{13}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}\right)}{a^8}+\frac{b\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{37\,a^{14}\,b-266\,a^{12}\,b^3+456\,a^{10}\,b^5-224\,a^8\,b^7}{8\,a^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{14}-164\,a^{12}\,b^2+732\,a^{10}\,b^4-1024\,a^8\,b^6+448\,a^6\,b^8\right)}{8\,a^{13}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{16}-64\,a^{14}\,b^2\right)}{8\,a^{13}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}\right)}{a^8}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^8\,d}","Not used",1,"tan(c/2 + (d*x)/2)^6/(384*a^2*d) - (tan(c/2 + (d*x)/2)^4*((128*a^2 + 256*b^2)/(16384*a^4) + 1/(64*a^2) - b^2/(16*a^4)))/d + (tan(c/2 + (d*x)/2)^2*(3/(128*a^2) + b^2/(8*a^4) - (2*b*((b*(128*a^2 + 256*b^2))/(1024*a^5) - b/(16*a^3) + (4*b*((128*a^2 + 256*b^2)/(4096*a^4) + 1/(16*a^2) - b^2/(4*a^4)))/a))/a + ((128*a^2 + 256*b^2)*((128*a^2 + 256*b^2)/(4096*a^4) + 1/(16*a^2) - b^2/(4*a^4)))/(128*a^2)))/d + (tan(c/2 + (d*x)/2)*(b/(16*a^3) - ((128*a^2 + 256*b^2)*((b*(128*a^2 + 256*b^2))/(1024*a^5) - b/(16*a^3) + (4*b*((128*a^2 + 256*b^2)/(4096*a^4) + 1/(16*a^2) - b^2/(4*a^4)))/a))/(64*a^2) + (4*b*((128*a^2 + 256*b^2)/(4096*a^4) + 1/(16*a^2) - b^2/(4*a^4)))/a - (4*b*(3/(64*a^2) + b^2/(4*a^4) - (4*b*((b*(128*a^2 + 256*b^2))/(1024*a^5) - b/(16*a^3) + (4*b*((128*a^2 + 256*b^2)/(4096*a^4) + 1/(16*a^2) - b^2/(4*a^4)))/a))/a + ((128*a^2 + 256*b^2)*((128*a^2 + 256*b^2)/(4096*a^4) + 1/(16*a^2) - b^2/(4*a^4)))/(64*a^2)))/a))/d + (tan(c/2 + (d*x)/2)^3*((b*(128*a^2 + 256*b^2))/(3072*a^5) - b/(48*a^3) + (4*b*((128*a^2 + 256*b^2)/(4096*a^4) + 1/(16*a^2) - b^2/(4*a^4)))/(3*a)))/d - (tan(c/2 + (d*x)/2)^3*((83*a^5*b)/15 - (14*a^3*b^3)/3) + a^6/6 + tan(c/2 + (d*x)/2)^4*(6*a^6 + (56*a^2*b^4)/3 - (79*a^4*b^2)/3) - tan(c/2 + (d*x)/2)^5*(112*a*b^5 + (191*a^5*b)/3 - (544*a^3*b^3)/3) - tan(c/2 + (d*x)/2)^2*((4*a^6)/3 - (7*a^4*b^2)/5) + tan(c/2 + (d*x)/2)^6*((15*a^6)/2 - 512*b^6 + 872*a^2*b^4 - 352*a^4*b^2) - (8*tan(c/2 + (d*x)/2)^7*(11*a^6*b + 16*b^7 - 8*a^2*b^5 - 20*a^4*b^3))/a - (7*a^5*b*tan(c/2 + (d*x)/2))/15)/(d*(64*a^8*tan(c/2 + (d*x)/2)^6 + 64*a^8*tan(c/2 + (d*x)/2)^8 + 128*a^7*b*tan(c/2 + (d*x)/2)^7)) - (b*tan(c/2 + (d*x)/2)^5)/(80*a^3*d) - (log(tan(c/2 + (d*x)/2))*(5*a^6 - 112*b^6 + 200*a^2*b^4 - 90*a^4*b^2))/(16*a^8*d) + (b*atan(((b*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(c/2 + (d*x)/2)*(5*a^14 + 448*a^6*b^8 - 1024*a^8*b^6 + 732*a^10*b^4 - 164*a^12*b^2))/(8*a^13) - (37*a^14*b - 224*a^8*b^7 + 456*a^10*b^5 - 266*a^12*b^3)/(8*a^14) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^16 - 64*a^14*b^2))/(8*a^13))*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^8)*1i)/a^8 - (b*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((37*a^14*b - 224*a^8*b^7 + 456*a^10*b^5 - 266*a^12*b^3)/(8*a^14) - (tan(c/2 + (d*x)/2)*(5*a^14 + 448*a^6*b^8 - 1024*a^8*b^6 + 732*a^10*b^4 - 164*a^12*b^2))/(8*a^13) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^16 - 64*a^14*b^2))/(8*a^13))*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^8)*1i)/a^8)/((10*a^12*b + 784*b^13 - 3192*a^2*b^11 + 5062*a^4*b^9 - 3899*a^6*b^7 + 1470*a^8*b^5 - 235*a^10*b^3)/(4*a^14) + (tan(c/2 + (d*x)/2)*(784*b^12 - 2996*a^2*b^10 + 4362*a^4*b^8 - 2980*a^6*b^6 + 938*a^8*b^4 - 108*a^10*b^2))/(4*a^13) + (b*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(c/2 + (d*x)/2)*(5*a^14 + 448*a^6*b^8 - 1024*a^8*b^6 + 732*a^10*b^4 - 164*a^12*b^2))/(8*a^13) - (37*a^14*b - 224*a^8*b^7 + 456*a^10*b^5 - 266*a^12*b^3)/(8*a^14) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^16 - 64*a^14*b^2))/(8*a^13))*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^8))/a^8 + (b*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((37*a^14*b - 224*a^8*b^7 + 456*a^10*b^5 - 266*a^12*b^3)/(8*a^14) - (tan(c/2 + (d*x)/2)*(5*a^14 + 448*a^6*b^8 - 1024*a^8*b^6 + 732*a^10*b^4 - 164*a^12*b^2))/(8*a^13) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^16 - 64*a^14*b^2))/(8*a^13))*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^8))/a^8))*(2*a^2 - 7*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^8*d)","B"
1266,1,4362,536,48.182195,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^3)/(a + b*sin(c + d*x))^3,x)","-\frac{\frac{840\,a^7-985\,a^5\,b^2+213\,a^3\,b^4}{15\,b^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(112\,a^7+18\,a^5\,b^2-138\,a^3\,b^4+31\,a\,b^6\right)}{2\,b^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(1176\,a^7+189\,a^5\,b^2-1533\,a^3\,b^4+410\,a\,b^6\right)}{3\,b^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(7056\,a^7+686\,a^5\,b^2-8766\,a^3\,b^4+2281\,a\,b^6\right)}{6\,b^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(11760\,a^7-9310\,a^5\,b^2-2402\,a^3\,b^4+1239\,a\,b^6\right)}{30\,b^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(17640\,a^7-8365\,a^5\,b^2-10011\,a^3\,b^4+3062\,a\,b^6\right)}{15\,b^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(58800\,a^7-12950\,a^5\,b^2-50514\,a^3\,b^4+14155\,a\,b^6\right)}{30\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23520\,a^6-27860\,a^4\,b^2+6171\,a^2\,b^4\right)}{120\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(224\,a^6-244\,a^4\,b^2+43\,a^2\,b^4\right)}{8\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(8736\,a^6-9516\,a^4\,b^2+1453\,a^2\,b^4+132\,b^6\right)}{24\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(38304\,a^6-43068\,a^4\,b^2+8033\,a^2\,b^4-20\,b^6\right)}{24\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(84000\,a^6-97324\,a^4\,b^2+20341\,a^2\,b^4+360\,b^6\right)}{24\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(104160\,a^6-123316\,a^4\,b^2+27371\,a^2\,b^4-360\,b^6\right)}{24\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(144480\,a^6-173060\,a^4\,b^2+40447\,a^2\,b^4-660\,b^6\right)}{120\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(372960\,a^6-446580\,a^4\,b^2+102971\,a^2\,b^4+100\,b^6\right)}{120\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(7\,a^2+8\,b^2\right)\,\left(840\,a^5-985\,a^3\,b^2+213\,a\,b^4\right)}{3\,b^8}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(8\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(28\,a^2+24\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(28\,a^2+24\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(56\,a^2+60\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(56\,a^2+60\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(70\,a^2+80\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+a^2+28\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+84\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+140\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+140\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+84\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+28\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{25088\,a^{14}\,b^8-67200\,a^{12}\,b^{10}+65160\,a^{10}\,b^{12}-27560\,a^8\,b^{14}+4800\,a^6\,b^{16}-225\,a^4\,b^{18}+\frac{25\,a^2\,b^{20}}{8}}{b^{23}}-\frac{\left(\frac{-448\,a^7\,b^{18}+712\,a^5\,b^{20}-274\,a^3\,b^{22}+10\,a\,b^{24}}{b^{23}}-\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{28}-512\,a^3\,b^{26}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14336\,a^8\,b^{18}+26368\,a^6\,b^{20}-13568\,a^4\,b^{22}+1536\,a^2\,b^{24}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-401408\,a^{15}\,b^8+1677312\,a^{13}\,b^{10}-2655360\,a^{11}\,b^{12}+2004800\,a^9\,b^{14}-738240\,a^7\,b^{16}+119304\,a^5\,b^{18}-5929\,a^3\,b^{20}+50\,a\,b^{22}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^9}+\frac{\left(\frac{25088\,a^{14}\,b^8-67200\,a^{12}\,b^{10}+65160\,a^{10}\,b^{12}-27560\,a^8\,b^{14}+4800\,a^6\,b^{16}-225\,a^4\,b^{18}+\frac{25\,a^2\,b^{20}}{8}}{b^{23}}+\frac{\left(\frac{-448\,a^7\,b^{18}+712\,a^5\,b^{20}-274\,a^3\,b^{22}+10\,a\,b^{24}}{b^{23}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{28}-512\,a^3\,b^{26}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14336\,a^8\,b^{18}+26368\,a^6\,b^{20}-13568\,a^4\,b^{22}+1536\,a^2\,b^{24}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-401408\,a^{15}\,b^8+1677312\,a^{13}\,b^{10}-2655360\,a^{11}\,b^{12}+2004800\,a^9\,b^{14}-738240\,a^7\,b^{16}+119304\,a^5\,b^{18}-5929\,a^3\,b^{20}+50\,a\,b^{22}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^9}}{\frac{702464\,a^{19}-2998016\,a^{17}\,b^2+5244512\,a^{15}\,b^4-4837780\,a^{13}\,b^6+2522213\,a^{11}\,b^8-740668\,a^9\,b^{10}+\frac{922065\,a^7\,b^{12}}{8}-\frac{65155\,a^5\,b^{14}}{8}+\frac{645\,a^3\,b^{16}}{4}}{b^{23}}+\frac{\left(\frac{25088\,a^{14}\,b^8-67200\,a^{12}\,b^{10}+65160\,a^{10}\,b^{12}-27560\,a^8\,b^{14}+4800\,a^6\,b^{16}-225\,a^4\,b^{18}+\frac{25\,a^2\,b^{20}}{8}}{b^{23}}-\frac{\left(\frac{-448\,a^7\,b^{18}+712\,a^5\,b^{20}-274\,a^3\,b^{22}+10\,a\,b^{24}}{b^{23}}-\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{28}-512\,a^3\,b^{26}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14336\,a^8\,b^{18}+26368\,a^6\,b^{20}-13568\,a^4\,b^{22}+1536\,a^2\,b^{24}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-401408\,a^{15}\,b^8+1677312\,a^{13}\,b^{10}-2655360\,a^{11}\,b^{12}+2004800\,a^9\,b^{14}-738240\,a^7\,b^{16}+119304\,a^5\,b^{18}-5929\,a^3\,b^{20}+50\,a\,b^{22}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}-\frac{\left(\frac{25088\,a^{14}\,b^8-67200\,a^{12}\,b^{10}+65160\,a^{10}\,b^{12}-27560\,a^8\,b^{14}+4800\,a^6\,b^{16}-225\,a^4\,b^{18}+\frac{25\,a^2\,b^{20}}{8}}{b^{23}}+\frac{\left(\frac{-448\,a^7\,b^{18}+712\,a^5\,b^{20}-274\,a^3\,b^{22}+10\,a\,b^{24}}{b^{23}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{28}-512\,a^3\,b^{26}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14336\,a^8\,b^{18}+26368\,a^6\,b^{20}-13568\,a^4\,b^{22}+1536\,a^2\,b^{24}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-401408\,a^{15}\,b^8+1677312\,a^{13}\,b^{10}-2655360\,a^{11}\,b^{12}+2004800\,a^9\,b^{14}-738240\,a^7\,b^{16}+119304\,a^5\,b^{18}-5929\,a^3\,b^{20}+50\,a\,b^{22}\right)}{8\,b^{24}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11239424\,a^{20}-50778112\,a^{18}\,b^2+95201792\,a^{16}\,b^4-95735744\,a^{14}\,b^6+55713280\,a^{12}\,b^8-18869120\,a^{10}\,b^{10}+3544880\,a^8\,b^{12}-328375\,a^6\,b^{14}+12125\,a^4\,b^{16}-150\,a^2\,b^{18}\right)}{4\,b^{24}}}\right)\,\left(a^6\,448{}\mathrm{i}-a^4\,b^2\,600{}\mathrm{i}+a^2\,b^4\,180{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^9\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)\,\left(\frac{25088\,a^{14}\,b^8-67200\,a^{12}\,b^{10}+65160\,a^{10}\,b^{12}-27560\,a^8\,b^{14}+4800\,a^6\,b^{16}-225\,a^4\,b^{18}+\frac{25\,a^2\,b^{20}}{8}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-401408\,a^{15}\,b^8+1677312\,a^{13}\,b^{10}-2655360\,a^{11}\,b^{12}+2004800\,a^9\,b^{14}-738240\,a^7\,b^{16}+119304\,a^5\,b^{18}-5929\,a^3\,b^{20}+50\,a\,b^{22}\right)}{8\,b^{24}}-\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-448\,a^7\,b^{18}+712\,a^5\,b^{20}-274\,a^3\,b^{22}+10\,a\,b^{24}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14336\,a^8\,b^{18}+26368\,a^6\,b^{20}-13568\,a^4\,b^{22}+1536\,a^2\,b^{24}\right)}{8\,b^{24}}-\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{28}-512\,a^3\,b^{26}\right)}{8\,b^{24}}\right)\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)}{2\,b^9}\right)\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)}{2\,b^9}\right)\,1{}\mathrm{i}}{2\,b^9}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)\,\left(\frac{25088\,a^{14}\,b^8-67200\,a^{12}\,b^{10}+65160\,a^{10}\,b^{12}-27560\,a^8\,b^{14}+4800\,a^6\,b^{16}-225\,a^4\,b^{18}+\frac{25\,a^2\,b^{20}}{8}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-401408\,a^{15}\,b^8+1677312\,a^{13}\,b^{10}-2655360\,a^{11}\,b^{12}+2004800\,a^9\,b^{14}-738240\,a^7\,b^{16}+119304\,a^5\,b^{18}-5929\,a^3\,b^{20}+50\,a\,b^{22}\right)}{8\,b^{24}}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-448\,a^7\,b^{18}+712\,a^5\,b^{20}-274\,a^3\,b^{22}+10\,a\,b^{24}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14336\,a^8\,b^{18}+26368\,a^6\,b^{20}-13568\,a^4\,b^{22}+1536\,a^2\,b^{24}\right)}{8\,b^{24}}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{28}-512\,a^3\,b^{26}\right)}{8\,b^{24}}\right)\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)}{2\,b^9}\right)\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)}{2\,b^9}\right)\,1{}\mathrm{i}}{2\,b^9}}{\frac{702464\,a^{19}-2998016\,a^{17}\,b^2+5244512\,a^{15}\,b^4-4837780\,a^{13}\,b^6+2522213\,a^{11}\,b^8-740668\,a^9\,b^{10}+\frac{922065\,a^7\,b^{12}}{8}-\frac{65155\,a^5\,b^{14}}{8}+\frac{645\,a^3\,b^{16}}{4}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11239424\,a^{20}-50778112\,a^{18}\,b^2+95201792\,a^{16}\,b^4-95735744\,a^{14}\,b^6+55713280\,a^{12}\,b^8-18869120\,a^{10}\,b^{10}+3544880\,a^8\,b^{12}-328375\,a^6\,b^{14}+12125\,a^4\,b^{16}-150\,a^2\,b^{18}\right)}{4\,b^{24}}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)\,\left(\frac{25088\,a^{14}\,b^8-67200\,a^{12}\,b^{10}+65160\,a^{10}\,b^{12}-27560\,a^8\,b^{14}+4800\,a^6\,b^{16}-225\,a^4\,b^{18}+\frac{25\,a^2\,b^{20}}{8}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-401408\,a^{15}\,b^8+1677312\,a^{13}\,b^{10}-2655360\,a^{11}\,b^{12}+2004800\,a^9\,b^{14}-738240\,a^7\,b^{16}+119304\,a^5\,b^{18}-5929\,a^3\,b^{20}+50\,a\,b^{22}\right)}{8\,b^{24}}-\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-448\,a^7\,b^{18}+712\,a^5\,b^{20}-274\,a^3\,b^{22}+10\,a\,b^{24}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14336\,a^8\,b^{18}+26368\,a^6\,b^{20}-13568\,a^4\,b^{22}+1536\,a^2\,b^{24}\right)}{8\,b^{24}}-\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{28}-512\,a^3\,b^{26}\right)}{8\,b^{24}}\right)\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)}{2\,b^9}\right)\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)}{2\,b^9}\right)}{2\,b^9}-\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)\,\left(\frac{25088\,a^{14}\,b^8-67200\,a^{12}\,b^{10}+65160\,a^{10}\,b^{12}-27560\,a^8\,b^{14}+4800\,a^6\,b^{16}-225\,a^4\,b^{18}+\frac{25\,a^2\,b^{20}}{8}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-401408\,a^{15}\,b^8+1677312\,a^{13}\,b^{10}-2655360\,a^{11}\,b^{12}+2004800\,a^9\,b^{14}-738240\,a^7\,b^{16}+119304\,a^5\,b^{18}-5929\,a^3\,b^{20}+50\,a\,b^{22}\right)}{8\,b^{24}}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-448\,a^7\,b^{18}+712\,a^5\,b^{20}-274\,a^3\,b^{22}+10\,a\,b^{24}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14336\,a^8\,b^{18}+26368\,a^6\,b^{20}-13568\,a^4\,b^{22}+1536\,a^2\,b^{24}\right)}{8\,b^{24}}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{28}-512\,a^3\,b^{26}\right)}{8\,b^{24}}\right)\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)}{2\,b^9}\right)\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)}{2\,b^9}\right)}{2\,b^9}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(56\,a^4-47\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{b^9\,d}","Not used",1,"- ((840*a^7 + 213*a^3*b^4 - 985*a^5*b^2)/(15*b^8) + (tan(c/2 + (d*x)/2)^14*(31*a*b^6 + 112*a^7 - 138*a^3*b^4 + 18*a^5*b^2))/(2*b^8) + (tan(c/2 + (d*x)/2)^12*(410*a*b^6 + 1176*a^7 - 1533*a^3*b^4 + 189*a^5*b^2))/(3*b^8) + (tan(c/2 + (d*x)/2)^10*(2281*a*b^6 + 7056*a^7 - 8766*a^3*b^4 + 686*a^5*b^2))/(6*b^8) + (tan(c/2 + (d*x)/2)^2*(1239*a*b^6 + 11760*a^7 - 2402*a^3*b^4 - 9310*a^5*b^2))/(30*b^8) + (tan(c/2 + (d*x)/2)^4*(3062*a*b^6 + 17640*a^7 - 10011*a^3*b^4 - 8365*a^5*b^2))/(15*b^8) + (tan(c/2 + (d*x)/2)^6*(14155*a*b^6 + 58800*a^7 - 50514*a^3*b^4 - 12950*a^5*b^2))/(30*b^8) + (tan(c/2 + (d*x)/2)*(23520*a^6 + 6171*a^2*b^4 - 27860*a^4*b^2))/(120*b^7) + (tan(c/2 + (d*x)/2)^15*(224*a^6 + 43*a^2*b^4 - 244*a^4*b^2))/(8*b^7) + (tan(c/2 + (d*x)/2)^13*(8736*a^6 + 132*b^6 + 1453*a^2*b^4 - 9516*a^4*b^2))/(24*b^7) + (tan(c/2 + (d*x)/2)^11*(38304*a^6 - 20*b^6 + 8033*a^2*b^4 - 43068*a^4*b^2))/(24*b^7) + (tan(c/2 + (d*x)/2)^9*(84000*a^6 + 360*b^6 + 20341*a^2*b^4 - 97324*a^4*b^2))/(24*b^7) + (tan(c/2 + (d*x)/2)^7*(104160*a^6 - 360*b^6 + 27371*a^2*b^4 - 123316*a^4*b^2))/(24*b^7) + (tan(c/2 + (d*x)/2)^3*(144480*a^6 - 660*b^6 + 40447*a^2*b^4 - 173060*a^4*b^2))/(120*b^7) + (tan(c/2 + (d*x)/2)^5*(372960*a^6 + 100*b^6 + 102971*a^2*b^4 - 446580*a^4*b^2))/(120*b^7) + (tan(c/2 + (d*x)/2)^8*(7*a^2 + 8*b^2)*(213*a*b^4 + 840*a^5 - 985*a^3*b^2))/(3*b^8))/(d*(tan(c/2 + (d*x)/2)^2*(8*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^14*(8*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(28*a^2 + 24*b^2) + tan(c/2 + (d*x)/2)^12*(28*a^2 + 24*b^2) + tan(c/2 + (d*x)/2)^6*(56*a^2 + 60*b^2) + tan(c/2 + (d*x)/2)^10*(56*a^2 + 60*b^2) + tan(c/2 + (d*x)/2)^8*(70*a^2 + 80*b^2) + a^2*tan(c/2 + (d*x)/2)^16 + a^2 + 28*a*b*tan(c/2 + (d*x)/2)^3 + 84*a*b*tan(c/2 + (d*x)/2)^5 + 140*a*b*tan(c/2 + (d*x)/2)^7 + 140*a*b*tan(c/2 + (d*x)/2)^9 + 84*a*b*tan(c/2 + (d*x)/2)^11 + 28*a*b*tan(c/2 + (d*x)/2)^13 + 4*a*b*tan(c/2 + (d*x)/2)^15 + 4*a*b*tan(c/2 + (d*x)/2))) - (atan((((((25*a^2*b^20)/8 - 225*a^4*b^18 + 4800*a^6*b^16 - 27560*a^8*b^14 + 65160*a^10*b^12 - 67200*a^12*b^10 + 25088*a^14*b^8)/b^23 - (((10*a*b^24 - 274*a^3*b^22 + 712*a^5*b^20 - 448*a^7*b^18)/b^23 - ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^28 - 512*a^3*b^26))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(1536*a^2*b^24 - 13568*a^4*b^22 + 26368*a^6*b^20 - 14336*a^8*b^18))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(50*a*b^22 - 5929*a^3*b^20 + 119304*a^5*b^18 - 738240*a^7*b^16 + 2004800*a^9*b^14 - 2655360*a^11*b^12 + 1677312*a^13*b^10 - 401408*a^15*b^8))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i)*1i)/(16*b^9) + ((((25*a^2*b^20)/8 - 225*a^4*b^18 + 4800*a^6*b^16 - 27560*a^8*b^14 + 65160*a^10*b^12 - 67200*a^12*b^10 + 25088*a^14*b^8)/b^23 + (((10*a*b^24 - 274*a^3*b^22 + 712*a^5*b^20 - 448*a^7*b^18)/b^23 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^28 - 512*a^3*b^26))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(1536*a^2*b^24 - 13568*a^4*b^22 + 26368*a^6*b^20 - 14336*a^8*b^18))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(50*a*b^22 - 5929*a^3*b^20 + 119304*a^5*b^18 - 738240*a^7*b^16 + 2004800*a^9*b^14 - 2655360*a^11*b^12 + 1677312*a^13*b^10 - 401408*a^15*b^8))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i)*1i)/(16*b^9))/((702464*a^19 + (645*a^3*b^16)/4 - (65155*a^5*b^14)/8 + (922065*a^7*b^12)/8 - 740668*a^9*b^10 + 2522213*a^11*b^8 - 4837780*a^13*b^6 + 5244512*a^15*b^4 - 2998016*a^17*b^2)/b^23 + ((((25*a^2*b^20)/8 - 225*a^4*b^18 + 4800*a^6*b^16 - 27560*a^8*b^14 + 65160*a^10*b^12 - 67200*a^12*b^10 + 25088*a^14*b^8)/b^23 - (((10*a*b^24 - 274*a^3*b^22 + 712*a^5*b^20 - 448*a^7*b^18)/b^23 - ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^28 - 512*a^3*b^26))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(1536*a^2*b^24 - 13568*a^4*b^22 + 26368*a^6*b^20 - 14336*a^8*b^18))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(50*a*b^22 - 5929*a^3*b^20 + 119304*a^5*b^18 - 738240*a^7*b^16 + 2004800*a^9*b^14 - 2655360*a^11*b^12 + 1677312*a^13*b^10 - 401408*a^15*b^8))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) - ((((25*a^2*b^20)/8 - 225*a^4*b^18 + 4800*a^6*b^16 - 27560*a^8*b^14 + 65160*a^10*b^12 - 67200*a^12*b^10 + 25088*a^14*b^8)/b^23 + (((10*a*b^24 - 274*a^3*b^22 + 712*a^5*b^20 - 448*a^7*b^18)/b^23 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^28 - 512*a^3*b^26))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(1536*a^2*b^24 - 13568*a^4*b^22 + 26368*a^6*b^20 - 14336*a^8*b^18))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(50*a*b^22 - 5929*a^3*b^20 + 119304*a^5*b^18 - 738240*a^7*b^16 + 2004800*a^9*b^14 - 2655360*a^11*b^12 + 1677312*a^13*b^10 - 401408*a^15*b^8))/(8*b^24))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i))/(16*b^9) + (tan(c/2 + (d*x)/2)*(11239424*a^20 - 150*a^2*b^18 + 12125*a^4*b^16 - 328375*a^6*b^14 + 3544880*a^8*b^12 - 18869120*a^10*b^10 + 55713280*a^12*b^8 - 95735744*a^14*b^6 + 95201792*a^16*b^4 - 50778112*a^18*b^2))/(4*b^24)))*(a^6*448i - b^6*5i + a^2*b^4*180i - a^4*b^2*600i)*1i)/(8*b^9*d) - (a*atan(((a*(-(a + b)*(a - b))^(1/2)*(56*a^4 + 6*b^4 - 47*a^2*b^2)*(((25*a^2*b^20)/8 - 225*a^4*b^18 + 4800*a^6*b^16 - 27560*a^8*b^14 + 65160*a^10*b^12 - 67200*a^12*b^10 + 25088*a^14*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a*b^22 - 5929*a^3*b^20 + 119304*a^5*b^18 - 738240*a^7*b^16 + 2004800*a^9*b^14 - 2655360*a^11*b^12 + 1677312*a^13*b^10 - 401408*a^15*b^8))/(8*b^24) - (a*(-(a + b)*(a - b))^(1/2)*((10*a*b^24 - 274*a^3*b^22 + 712*a^5*b^20 - 448*a^7*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(1536*a^2*b^24 - 13568*a^4*b^22 + 26368*a^6*b^20 - 14336*a^8*b^18))/(8*b^24) - (a*(-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^28 - 512*a^3*b^26))/(8*b^24))*(56*a^4 + 6*b^4 - 47*a^2*b^2))/(2*b^9))*(56*a^4 + 6*b^4 - 47*a^2*b^2))/(2*b^9))*1i)/(2*b^9) + (a*(-(a + b)*(a - b))^(1/2)*(56*a^4 + 6*b^4 - 47*a^2*b^2)*(((25*a^2*b^20)/8 - 225*a^4*b^18 + 4800*a^6*b^16 - 27560*a^8*b^14 + 65160*a^10*b^12 - 67200*a^12*b^10 + 25088*a^14*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a*b^22 - 5929*a^3*b^20 + 119304*a^5*b^18 - 738240*a^7*b^16 + 2004800*a^9*b^14 - 2655360*a^11*b^12 + 1677312*a^13*b^10 - 401408*a^15*b^8))/(8*b^24) + (a*(-(a + b)*(a - b))^(1/2)*((10*a*b^24 - 274*a^3*b^22 + 712*a^5*b^20 - 448*a^7*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(1536*a^2*b^24 - 13568*a^4*b^22 + 26368*a^6*b^20 - 14336*a^8*b^18))/(8*b^24) + (a*(-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^28 - 512*a^3*b^26))/(8*b^24))*(56*a^4 + 6*b^4 - 47*a^2*b^2))/(2*b^9))*(56*a^4 + 6*b^4 - 47*a^2*b^2))/(2*b^9))*1i)/(2*b^9))/((702464*a^19 + (645*a^3*b^16)/4 - (65155*a^5*b^14)/8 + (922065*a^7*b^12)/8 - 740668*a^9*b^10 + 2522213*a^11*b^8 - 4837780*a^13*b^6 + 5244512*a^15*b^4 - 2998016*a^17*b^2)/b^23 + (tan(c/2 + (d*x)/2)*(11239424*a^20 - 150*a^2*b^18 + 12125*a^4*b^16 - 328375*a^6*b^14 + 3544880*a^8*b^12 - 18869120*a^10*b^10 + 55713280*a^12*b^8 - 95735744*a^14*b^6 + 95201792*a^16*b^4 - 50778112*a^18*b^2))/(4*b^24) + (a*(-(a + b)*(a - b))^(1/2)*(56*a^4 + 6*b^4 - 47*a^2*b^2)*(((25*a^2*b^20)/8 - 225*a^4*b^18 + 4800*a^6*b^16 - 27560*a^8*b^14 + 65160*a^10*b^12 - 67200*a^12*b^10 + 25088*a^14*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a*b^22 - 5929*a^3*b^20 + 119304*a^5*b^18 - 738240*a^7*b^16 + 2004800*a^9*b^14 - 2655360*a^11*b^12 + 1677312*a^13*b^10 - 401408*a^15*b^8))/(8*b^24) - (a*(-(a + b)*(a - b))^(1/2)*((10*a*b^24 - 274*a^3*b^22 + 712*a^5*b^20 - 448*a^7*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(1536*a^2*b^24 - 13568*a^4*b^22 + 26368*a^6*b^20 - 14336*a^8*b^18))/(8*b^24) - (a*(-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^28 - 512*a^3*b^26))/(8*b^24))*(56*a^4 + 6*b^4 - 47*a^2*b^2))/(2*b^9))*(56*a^4 + 6*b^4 - 47*a^2*b^2))/(2*b^9)))/(2*b^9) - (a*(-(a + b)*(a - b))^(1/2)*(56*a^4 + 6*b^4 - 47*a^2*b^2)*(((25*a^2*b^20)/8 - 225*a^4*b^18 + 4800*a^6*b^16 - 27560*a^8*b^14 + 65160*a^10*b^12 - 67200*a^12*b^10 + 25088*a^14*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a*b^22 - 5929*a^3*b^20 + 119304*a^5*b^18 - 738240*a^7*b^16 + 2004800*a^9*b^14 - 2655360*a^11*b^12 + 1677312*a^13*b^10 - 401408*a^15*b^8))/(8*b^24) + (a*(-(a + b)*(a - b))^(1/2)*((10*a*b^24 - 274*a^3*b^22 + 712*a^5*b^20 - 448*a^7*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(1536*a^2*b^24 - 13568*a^4*b^22 + 26368*a^6*b^20 - 14336*a^8*b^18))/(8*b^24) + (a*(-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^28 - 512*a^3*b^26))/(8*b^24))*(56*a^4 + 6*b^4 - 47*a^2*b^2))/(2*b^9))*(56*a^4 + 6*b^4 - 47*a^2*b^2))/(2*b^9)))/(2*b^9)))*(-(a + b)*(a - b))^(1/2)*(56*a^4 + 6*b^4 - 47*a^2*b^2)*1i)/(b^9*d)","B"
1267,1,3700,485,23.853468,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^2)/(a + b*sin(c + d*x))^3,x)","\frac{\frac{630\,a^6-645\,a^4\,b^2+91\,a^2\,b^4}{15\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(84\,a^5-79\,a^3\,b^2+8\,a\,b^4\right)}{4\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(252\,a^5-237\,a^3\,b^2+17\,a\,b^4\right)}{b^6}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(630\,a^5-645\,a^3\,b^2+91\,a\,b^4\right)}{3\,b^6}+\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(700\,a^5-733\,a^3\,b^2+112\,a\,b^4\right)}{4\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(3780\,a^5-3723\,a^3\,b^2+448\,a\,b^4\right)}{4\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3780\,a^5-3975\,a^3\,b^2+643\,a\,b^4\right)}{5\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(42\,a^6+13\,a^4\,b^2-48\,a^2\,b^4+6\,b^6\right)}{b^7}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(84\,a^6+26\,a^4\,b^2-103\,a^2\,b^4+18\,b^6\right)}{b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(1260\,a^6+54\,a^4\,b^2-1187\,a^2\,b^4+202\,b^6\right)}{3\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(1890\,a^6+417\,a^4\,b^2-2149\,a^2\,b^4+324\,b^6\right)}{3\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3780\,a^6-2190\,a^4\,b^2-1223\,a^2\,b^4+274\,b^6\right)}{15\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(9450\,a^6-2115\,a^4\,b^2-6354\,a^2\,b^4+1010\,b^6\right)}{15\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8820\,a^5-9135\,a^3\,b^2+1336\,a\,b^4\right)}{60\,b^6}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(7\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(21\,a^2+20\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(21\,a^2+20\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(35\,a^2+40\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(35\,a^2+40\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+a^2+24\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+60\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+80\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+60\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{14112\,a^{12}\,b^7-33600\,a^{10}\,b^9+27560\,a^8\,b^{11}-9000\,a^6\,b^{13}+\frac{2025\,a^4\,b^{15}}{2}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56448\,a^{13}\,b^7-219072\,a^{11}\,b^9+311840\,a^9\,b^{11}-201360\,a^7\,b^{13}+57945\,a^5\,b^{15}-6034\,a^3\,b^{17}+64\,a\,b^{19}\right)}{2\,b^{21}}+\frac{a\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,\left(\frac{336\,a^6\,b^{16}-484\,a^4\,b^{18}+148\,a^2\,b^{20}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2688\,a^7\,b^{16}+4544\,a^5\,b^{18}-1984\,a^3\,b^{20}+128\,a\,b^{22}\right)}{2\,b^{21}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{25}-128\,a^3\,b^{23}\right)}{2\,b^{21}}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,1{}\mathrm{i}}{8\,b^8}\right)\,1{}\mathrm{i}}{8\,b^8}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)}{8\,b^8}+\frac{a\,\left(\frac{14112\,a^{12}\,b^7-33600\,a^{10}\,b^9+27560\,a^8\,b^{11}-9000\,a^6\,b^{13}+\frac{2025\,a^4\,b^{15}}{2}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56448\,a^{13}\,b^7-219072\,a^{11}\,b^9+311840\,a^9\,b^{11}-201360\,a^7\,b^{13}+57945\,a^5\,b^{15}-6034\,a^3\,b^{17}+64\,a\,b^{19}\right)}{2\,b^{21}}+\frac{a\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2688\,a^7\,b^{16}+4544\,a^5\,b^{18}-1984\,a^3\,b^{20}+128\,a\,b^{22}\right)}{2\,b^{21}}-\frac{336\,a^6\,b^{16}-484\,a^4\,b^{18}+148\,a^2\,b^{20}}{b^{20}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{25}-128\,a^3\,b^{23}\right)}{2\,b^{21}}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,1{}\mathrm{i}}{8\,b^8}\right)\,1{}\mathrm{i}}{8\,b^8}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)}{8\,b^8}}{\frac{296352\,a^{16}-1132488\,a^{14}\,b^2+1725696\,a^{12}\,b^4-1331285\,a^{10}\,b^6+\frac{1089913\,a^8\,b^8}{2}-\frac{227213\,a^6\,b^{10}}{2}+10735\,a^4\,b^{12}-360\,a^2\,b^{14}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1185408\,a^{17}-4826304\,a^{15}\,b^2+7961184\,a^{13}\,b^4-6809168\,a^{11}\,b^6+3206170\,a^9\,b^8-812015\,a^7\,b^{10}+98775\,a^5\,b^{12}-4050\,a^3\,b^{14}\right)}{b^{21}}+\frac{a\,\left(\frac{14112\,a^{12}\,b^7-33600\,a^{10}\,b^9+27560\,a^8\,b^{11}-9000\,a^6\,b^{13}+\frac{2025\,a^4\,b^{15}}{2}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56448\,a^{13}\,b^7-219072\,a^{11}\,b^9+311840\,a^9\,b^{11}-201360\,a^7\,b^{13}+57945\,a^5\,b^{15}-6034\,a^3\,b^{17}+64\,a\,b^{19}\right)}{2\,b^{21}}+\frac{a\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,\left(\frac{336\,a^6\,b^{16}-484\,a^4\,b^{18}+148\,a^2\,b^{20}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2688\,a^7\,b^{16}+4544\,a^5\,b^{18}-1984\,a^3\,b^{20}+128\,a\,b^{22}\right)}{2\,b^{21}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{25}-128\,a^3\,b^{23}\right)}{2\,b^{21}}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,1{}\mathrm{i}}{8\,b^8}\right)\,1{}\mathrm{i}}{8\,b^8}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,1{}\mathrm{i}}{8\,b^8}-\frac{a\,\left(\frac{14112\,a^{12}\,b^7-33600\,a^{10}\,b^9+27560\,a^8\,b^{11}-9000\,a^6\,b^{13}+\frac{2025\,a^4\,b^{15}}{2}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56448\,a^{13}\,b^7-219072\,a^{11}\,b^9+311840\,a^9\,b^{11}-201360\,a^7\,b^{13}+57945\,a^5\,b^{15}-6034\,a^3\,b^{17}+64\,a\,b^{19}\right)}{2\,b^{21}}+\frac{a\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2688\,a^7\,b^{16}+4544\,a^5\,b^{18}-1984\,a^3\,b^{20}+128\,a\,b^{22}\right)}{2\,b^{21}}-\frac{336\,a^6\,b^{16}-484\,a^4\,b^{18}+148\,a^2\,b^{20}}{b^{20}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{25}-128\,a^3\,b^{23}\right)}{2\,b^{21}}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,1{}\mathrm{i}}{8\,b^8}\right)\,1{}\mathrm{i}}{8\,b^8}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)\,1{}\mathrm{i}}{8\,b^8}}\right)\,\left(168\,a^4-200\,a^2\,b^2+45\,b^4\right)}{4\,b^8\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{14112\,a^{12}\,b^7-33600\,a^{10}\,b^9+27560\,a^8\,b^{11}-9000\,a^6\,b^{13}+\frac{2025\,a^4\,b^{15}}{2}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56448\,a^{13}\,b^7-219072\,a^{11}\,b^9+311840\,a^9\,b^{11}-201360\,a^7\,b^{13}+57945\,a^5\,b^{15}-6034\,a^3\,b^{17}+64\,a\,b^{19}\right)}{2\,b^{21}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{336\,a^6\,b^{16}-484\,a^4\,b^{18}+148\,a^2\,b^{20}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2688\,a^7\,b^{16}+4544\,a^5\,b^{18}-1984\,a^3\,b^{20}+128\,a\,b^{22}\right)}{2\,b^{21}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{25}-128\,a^3\,b^{23}\right)}{2\,b^{21}}\right)\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)}{b^8}\right)}{b^8}\right)\,1{}\mathrm{i}}{b^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{14112\,a^{12}\,b^7-33600\,a^{10}\,b^9+27560\,a^8\,b^{11}-9000\,a^6\,b^{13}+\frac{2025\,a^4\,b^{15}}{2}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56448\,a^{13}\,b^7-219072\,a^{11}\,b^9+311840\,a^9\,b^{11}-201360\,a^7\,b^{13}+57945\,a^5\,b^{15}-6034\,a^3\,b^{17}+64\,a\,b^{19}\right)}{2\,b^{21}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2688\,a^7\,b^{16}+4544\,a^5\,b^{18}-1984\,a^3\,b^{20}+128\,a\,b^{22}\right)}{2\,b^{21}}-\frac{336\,a^6\,b^{16}-484\,a^4\,b^{18}+148\,a^2\,b^{20}}{b^{20}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{25}-128\,a^3\,b^{23}\right)}{2\,b^{21}}\right)\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)}{b^8}\right)}{b^8}\right)\,1{}\mathrm{i}}{b^8}}{\frac{296352\,a^{16}-1132488\,a^{14}\,b^2+1725696\,a^{12}\,b^4-1331285\,a^{10}\,b^6+\frac{1089913\,a^8\,b^8}{2}-\frac{227213\,a^6\,b^{10}}{2}+10735\,a^4\,b^{12}-360\,a^2\,b^{14}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1185408\,a^{17}-4826304\,a^{15}\,b^2+7961184\,a^{13}\,b^4-6809168\,a^{11}\,b^6+3206170\,a^9\,b^8-812015\,a^7\,b^{10}+98775\,a^5\,b^{12}-4050\,a^3\,b^{14}\right)}{b^{21}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{14112\,a^{12}\,b^7-33600\,a^{10}\,b^9+27560\,a^8\,b^{11}-9000\,a^6\,b^{13}+\frac{2025\,a^4\,b^{15}}{2}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56448\,a^{13}\,b^7-219072\,a^{11}\,b^9+311840\,a^9\,b^{11}-201360\,a^7\,b^{13}+57945\,a^5\,b^{15}-6034\,a^3\,b^{17}+64\,a\,b^{19}\right)}{2\,b^{21}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{336\,a^6\,b^{16}-484\,a^4\,b^{18}+148\,a^2\,b^{20}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2688\,a^7\,b^{16}+4544\,a^5\,b^{18}-1984\,a^3\,b^{20}+128\,a\,b^{22}\right)}{2\,b^{21}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{25}-128\,a^3\,b^{23}\right)}{2\,b^{21}}\right)\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)}{b^8}\right)}{b^8}\right)}{b^8}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{14112\,a^{12}\,b^7-33600\,a^{10}\,b^9+27560\,a^8\,b^{11}-9000\,a^6\,b^{13}+\frac{2025\,a^4\,b^{15}}{2}}{b^{20}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56448\,a^{13}\,b^7-219072\,a^{11}\,b^9+311840\,a^9\,b^{11}-201360\,a^7\,b^{13}+57945\,a^5\,b^{15}-6034\,a^3\,b^{17}+64\,a\,b^{19}\right)}{2\,b^{21}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2688\,a^7\,b^{16}+4544\,a^5\,b^{18}-1984\,a^3\,b^{20}+128\,a\,b^{22}\right)}{2\,b^{21}}-\frac{336\,a^6\,b^{16}-484\,a^4\,b^{18}+148\,a^2\,b^{20}}{b^{20}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{25}-128\,a^3\,b^{23}\right)}{2\,b^{21}}\right)\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)}{b^8}\right)}{b^8}\right)}{b^8}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(21\,a^4-\frac{29\,a^2\,b^2}{2}+b^4\right)\,2{}\mathrm{i}}{b^8\,d}","Not used",1,"((630*a^6 + 91*a^2*b^4 - 645*a^4*b^2)/(15*b^7) + (tan(c/2 + (d*x)/2)^13*(8*a*b^4 + 84*a^5 - 79*a^3*b^2))/(4*b^6) + (tan(c/2 + (d*x)/2)^11*(17*a*b^4 + 252*a^5 - 237*a^3*b^2))/b^6 + (8*tan(c/2 + (d*x)/2)^7*(91*a*b^4 + 630*a^5 - 645*a^3*b^2))/(3*b^6) + (9*tan(c/2 + (d*x)/2)^5*(112*a*b^4 + 700*a^5 - 733*a^3*b^2))/(4*b^6) + (tan(c/2 + (d*x)/2)^9*(448*a*b^4 + 3780*a^5 - 3723*a^3*b^2))/(4*b^6) + (tan(c/2 + (d*x)/2)^3*(643*a*b^4 + 3780*a^5 - 3975*a^3*b^2))/(5*b^6) + (tan(c/2 + (d*x)/2)^12*(42*a^6 + 6*b^6 - 48*a^2*b^4 + 13*a^4*b^2))/b^7 + (3*tan(c/2 + (d*x)/2)^10*(84*a^6 + 18*b^6 - 103*a^2*b^4 + 26*a^4*b^2))/b^7 + (2*tan(c/2 + (d*x)/2)^6*(1260*a^6 + 202*b^6 - 1187*a^2*b^4 + 54*a^4*b^2))/(3*b^7) + (tan(c/2 + (d*x)/2)^8*(1890*a^6 + 324*b^6 - 2149*a^2*b^4 + 417*a^4*b^2))/(3*b^7) + (tan(c/2 + (d*x)/2)^2*(3780*a^6 + 274*b^6 - 1223*a^2*b^4 - 2190*a^4*b^2))/(15*b^7) + (tan(c/2 + (d*x)/2)^4*(9450*a^6 + 1010*b^6 - 6354*a^2*b^4 - 2115*a^4*b^2))/(15*b^7) + (tan(c/2 + (d*x)/2)*(1336*a*b^4 + 8820*a^5 - 9135*a^3*b^2))/(60*b^6))/(d*(tan(c/2 + (d*x)/2)^2*(7*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^12*(7*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(21*a^2 + 20*b^2) + tan(c/2 + (d*x)/2)^10*(21*a^2 + 20*b^2) + tan(c/2 + (d*x)/2)^6*(35*a^2 + 40*b^2) + tan(c/2 + (d*x)/2)^8*(35*a^2 + 40*b^2) + a^2*tan(c/2 + (d*x)/2)^14 + a^2 + 24*a*b*tan(c/2 + (d*x)/2)^3 + 60*a*b*tan(c/2 + (d*x)/2)^5 + 80*a*b*tan(c/2 + (d*x)/2)^7 + 60*a*b*tan(c/2 + (d*x)/2)^9 + 24*a*b*tan(c/2 + (d*x)/2)^11 + 4*a*b*tan(c/2 + (d*x)/2)^13 + 4*a*b*tan(c/2 + (d*x)/2))) + (a*atan(((a*(((2025*a^4*b^15)/2 - 9000*a^6*b^13 + 27560*a^8*b^11 - 33600*a^10*b^9 + 14112*a^12*b^7)/b^20 - (tan(c/2 + (d*x)/2)*(64*a*b^19 - 6034*a^3*b^17 + 57945*a^5*b^15 - 201360*a^7*b^13 + 311840*a^9*b^11 - 219072*a^11*b^9 + 56448*a^13*b^7))/(2*b^21) + (a*(168*a^4 + 45*b^4 - 200*a^2*b^2)*((148*a^2*b^20 - 484*a^4*b^18 + 336*a^6*b^16)/b^20 - (tan(c/2 + (d*x)/2)*(128*a*b^22 - 1984*a^3*b^20 + 4544*a^5*b^18 - 2688*a^7*b^16))/(2*b^21) + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^25 - 128*a^3*b^23))/(2*b^21))*(168*a^4 + 45*b^4 - 200*a^2*b^2)*1i)/(8*b^8))*1i)/(8*b^8))*(168*a^4 + 45*b^4 - 200*a^2*b^2))/(8*b^8) + (a*(((2025*a^4*b^15)/2 - 9000*a^6*b^13 + 27560*a^8*b^11 - 33600*a^10*b^9 + 14112*a^12*b^7)/b^20 - (tan(c/2 + (d*x)/2)*(64*a*b^19 - 6034*a^3*b^17 + 57945*a^5*b^15 - 201360*a^7*b^13 + 311840*a^9*b^11 - 219072*a^11*b^9 + 56448*a^13*b^7))/(2*b^21) + (a*(168*a^4 + 45*b^4 - 200*a^2*b^2)*((tan(c/2 + (d*x)/2)*(128*a*b^22 - 1984*a^3*b^20 + 4544*a^5*b^18 - 2688*a^7*b^16))/(2*b^21) - (148*a^2*b^20 - 484*a^4*b^18 + 336*a^6*b^16)/b^20 + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^25 - 128*a^3*b^23))/(2*b^21))*(168*a^4 + 45*b^4 - 200*a^2*b^2)*1i)/(8*b^8))*1i)/(8*b^8))*(168*a^4 + 45*b^4 - 200*a^2*b^2))/(8*b^8))/((296352*a^16 - 360*a^2*b^14 + 10735*a^4*b^12 - (227213*a^6*b^10)/2 + (1089913*a^8*b^8)/2 - 1331285*a^10*b^6 + 1725696*a^12*b^4 - 1132488*a^14*b^2)/b^20 + (tan(c/2 + (d*x)/2)*(1185408*a^17 - 4050*a^3*b^14 + 98775*a^5*b^12 - 812015*a^7*b^10 + 3206170*a^9*b^8 - 6809168*a^11*b^6 + 7961184*a^13*b^4 - 4826304*a^15*b^2))/b^21 + (a*(((2025*a^4*b^15)/2 - 9000*a^6*b^13 + 27560*a^8*b^11 - 33600*a^10*b^9 + 14112*a^12*b^7)/b^20 - (tan(c/2 + (d*x)/2)*(64*a*b^19 - 6034*a^3*b^17 + 57945*a^5*b^15 - 201360*a^7*b^13 + 311840*a^9*b^11 - 219072*a^11*b^9 + 56448*a^13*b^7))/(2*b^21) + (a*(168*a^4 + 45*b^4 - 200*a^2*b^2)*((148*a^2*b^20 - 484*a^4*b^18 + 336*a^6*b^16)/b^20 - (tan(c/2 + (d*x)/2)*(128*a*b^22 - 1984*a^3*b^20 + 4544*a^5*b^18 - 2688*a^7*b^16))/(2*b^21) + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^25 - 128*a^3*b^23))/(2*b^21))*(168*a^4 + 45*b^4 - 200*a^2*b^2)*1i)/(8*b^8))*1i)/(8*b^8))*(168*a^4 + 45*b^4 - 200*a^2*b^2)*1i)/(8*b^8) - (a*(((2025*a^4*b^15)/2 - 9000*a^6*b^13 + 27560*a^8*b^11 - 33600*a^10*b^9 + 14112*a^12*b^7)/b^20 - (tan(c/2 + (d*x)/2)*(64*a*b^19 - 6034*a^3*b^17 + 57945*a^5*b^15 - 201360*a^7*b^13 + 311840*a^9*b^11 - 219072*a^11*b^9 + 56448*a^13*b^7))/(2*b^21) + (a*(168*a^4 + 45*b^4 - 200*a^2*b^2)*((tan(c/2 + (d*x)/2)*(128*a*b^22 - 1984*a^3*b^20 + 4544*a^5*b^18 - 2688*a^7*b^16))/(2*b^21) - (148*a^2*b^20 - 484*a^4*b^18 + 336*a^6*b^16)/b^20 + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^25 - 128*a^3*b^23))/(2*b^21))*(168*a^4 + 45*b^4 - 200*a^2*b^2)*1i)/(8*b^8))*1i)/(8*b^8))*(168*a^4 + 45*b^4 - 200*a^2*b^2)*1i)/(8*b^8)))*(168*a^4 + 45*b^4 - 200*a^2*b^2))/(4*b^8*d) + (atan((((-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*(((2025*a^4*b^15)/2 - 9000*a^6*b^13 + 27560*a^8*b^11 - 33600*a^10*b^9 + 14112*a^12*b^7)/b^20 - (tan(c/2 + (d*x)/2)*(64*a*b^19 - 6034*a^3*b^17 + 57945*a^5*b^15 - 201360*a^7*b^13 + 311840*a^9*b^11 - 219072*a^11*b^9 + 56448*a^13*b^7))/(2*b^21) + ((-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*((148*a^2*b^20 - 484*a^4*b^18 + 336*a^6*b^16)/b^20 - (tan(c/2 + (d*x)/2)*(128*a*b^22 - 1984*a^3*b^20 + 4544*a^5*b^18 - 2688*a^7*b^16))/(2*b^21) + ((-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^25 - 128*a^3*b^23))/(2*b^21))*(21*a^4 + b^4 - (29*a^2*b^2)/2))/b^8))/b^8)*1i)/b^8 + ((-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*(((2025*a^4*b^15)/2 - 9000*a^6*b^13 + 27560*a^8*b^11 - 33600*a^10*b^9 + 14112*a^12*b^7)/b^20 - (tan(c/2 + (d*x)/2)*(64*a*b^19 - 6034*a^3*b^17 + 57945*a^5*b^15 - 201360*a^7*b^13 + 311840*a^9*b^11 - 219072*a^11*b^9 + 56448*a^13*b^7))/(2*b^21) + ((-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*((tan(c/2 + (d*x)/2)*(128*a*b^22 - 1984*a^3*b^20 + 4544*a^5*b^18 - 2688*a^7*b^16))/(2*b^21) - (148*a^2*b^20 - 484*a^4*b^18 + 336*a^6*b^16)/b^20 + ((-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^25 - 128*a^3*b^23))/(2*b^21))*(21*a^4 + b^4 - (29*a^2*b^2)/2))/b^8))/b^8)*1i)/b^8)/((296352*a^16 - 360*a^2*b^14 + 10735*a^4*b^12 - (227213*a^6*b^10)/2 + (1089913*a^8*b^8)/2 - 1331285*a^10*b^6 + 1725696*a^12*b^4 - 1132488*a^14*b^2)/b^20 + (tan(c/2 + (d*x)/2)*(1185408*a^17 - 4050*a^3*b^14 + 98775*a^5*b^12 - 812015*a^7*b^10 + 3206170*a^9*b^8 - 6809168*a^11*b^6 + 7961184*a^13*b^4 - 4826304*a^15*b^2))/b^21 + ((-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*(((2025*a^4*b^15)/2 - 9000*a^6*b^13 + 27560*a^8*b^11 - 33600*a^10*b^9 + 14112*a^12*b^7)/b^20 - (tan(c/2 + (d*x)/2)*(64*a*b^19 - 6034*a^3*b^17 + 57945*a^5*b^15 - 201360*a^7*b^13 + 311840*a^9*b^11 - 219072*a^11*b^9 + 56448*a^13*b^7))/(2*b^21) + ((-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*((148*a^2*b^20 - 484*a^4*b^18 + 336*a^6*b^16)/b^20 - (tan(c/2 + (d*x)/2)*(128*a*b^22 - 1984*a^3*b^20 + 4544*a^5*b^18 - 2688*a^7*b^16))/(2*b^21) + ((-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^25 - 128*a^3*b^23))/(2*b^21))*(21*a^4 + b^4 - (29*a^2*b^2)/2))/b^8))/b^8))/b^8 - ((-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*(((2025*a^4*b^15)/2 - 9000*a^6*b^13 + 27560*a^8*b^11 - 33600*a^10*b^9 + 14112*a^12*b^7)/b^20 - (tan(c/2 + (d*x)/2)*(64*a*b^19 - 6034*a^3*b^17 + 57945*a^5*b^15 - 201360*a^7*b^13 + 311840*a^9*b^11 - 219072*a^11*b^9 + 56448*a^13*b^7))/(2*b^21) + ((-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*((tan(c/2 + (d*x)/2)*(128*a*b^22 - 1984*a^3*b^20 + 4544*a^5*b^18 - 2688*a^7*b^16))/(2*b^21) - (148*a^2*b^20 - 484*a^4*b^18 + 336*a^6*b^16)/b^20 + ((-(a + b)*(a - b))^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^25 - 128*a^3*b^23))/(2*b^21))*(21*a^4 + b^4 - (29*a^2*b^2)/2))/b^8))/b^8))/b^8))*(-(a + b)*(a - b))^(1/2)*(21*a^4 + b^4 - (29*a^2*b^2)/2)*2i)/(b^8*d)","B"
1268,1,2529,237,16.794659,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x))/(a + b*sin(c + d*x))^3,x)","-\frac{\frac{30\,a^5-25\,a^3\,b^2+a\,b^4}{b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(420\,a^4-355\,a^2\,b^2+16\,b^4\right)}{4\,b^5}+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(4\,a^4-3\,a^2\,b^2\right)}{4\,b^5}+\frac{15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(68\,a^4-55\,a^2\,b^2+2\,b^4\right)}{2\,b^5}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-132\,a^4+99\,a^2\,b^2+4\,b^4\right)}{4\,b^5}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(276\,a^4-235\,a^2\,b^2+10\,b^4\right)}{2\,b^5}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(348\,a^4-301\,a^2\,b^2+20\,b^4\right)}{4\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(30\,a^6+15\,a^4\,b^2-30\,a^2\,b^4+2\,b^6\right)}{a\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(150\,a^6-45\,a^4\,b^2-64\,a^2\,b^4+2\,b^6\right)}{a\,b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(150\,a^6+15\,a^4\,b^2-110\,a^2\,b^4+4\,b^6\right)}{a\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(150\,a^6+75\,a^4\,b^2-165\,a^2\,b^4+8\,b^6\right)}{a\,b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5\,a^2+6\,b^2\right)\,\left(30\,a^4-25\,a^2\,b^2+b^4\right)}{a\,b^6}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(6\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(15\,a^2+16\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(15\,a^2+16\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(20\,a^2+24\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+a^2+20\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+40\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+40\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,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)}^{11}+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atanh}\left(\frac{3375\,a^3\,\sqrt{b^2-a^2}}{2\,\left(\frac{3375\,a^3\,b}{2}-\frac{10125\,a^5}{2\,b}+\frac{3375\,a^7}{b^3}-10125\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3375\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{6750\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}\right)}-\frac{3375\,a^5\,\sqrt{b^2-a^2}}{\frac{3375\,a^3\,b^3}{2}-\frac{10125\,a^5\,b}{2}+\frac{3375\,a^7}{b}+6750\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3375\,a^2\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-10125\,a^4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{3375\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\frac{3375\,a^3}{2}-\frac{10125\,a^5}{2\,b^2}+\frac{3375\,a^7}{b^4}+3375\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{10125\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{6750\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}}-\frac{16875\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{2\,\left(\frac{3375\,a^3\,b^2}{2}-\frac{10125\,a^5}{2}+\frac{3375\,a^7}{b^2}-10125\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3375\,a^2\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{6750\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}\right)}+\frac{3375\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{3375\,a^7+6750\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b-\frac{10125\,a^5\,b^2}{2}-10125\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^3+\frac{3375\,a^3\,b^4}{2}+3375\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^5}\right)\,\left(30\,a^3\,\sqrt{b^2-a^2}-15\,a\,b^2\,\sqrt{b^2-a^2}\right)}{b^7\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{7200\,a^{10}\,b^6-14400\,a^8\,b^8+9000\,a^6\,b^{10}-1800\,a^4\,b^{12}+\frac{225\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+100800\,a^9\,b^8-122400\,a^7\,b^{10}+61200\,a^5\,b^{12}-11025\,a^3\,b^{14}+450\,a\,b^{16}\right)}{2\,b^{18}}-\frac{15\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{240\,a^5\,b^{14}-300\,a^3\,b^{16}+60\,a\,b^{18}}{b^{17}}-\frac{15\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2880\,a^4\,b^{16}+960\,a^2\,b^{18}\right)}{2\,b^{18}}\right)}{8\,b^7}\right)\,15{}\mathrm{i}}{8\,b^7}+\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{7200\,a^{10}\,b^6-14400\,a^8\,b^8+9000\,a^6\,b^{10}-1800\,a^4\,b^{12}+\frac{225\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+100800\,a^9\,b^8-122400\,a^7\,b^{10}+61200\,a^5\,b^{12}-11025\,a^3\,b^{14}+450\,a\,b^{16}\right)}{2\,b^{18}}+\frac{15\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{240\,a^5\,b^{14}-300\,a^3\,b^{16}+60\,a\,b^{18}}{b^{17}}+\frac{15\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2880\,a^4\,b^{16}+960\,a^2\,b^{18}\right)}{2\,b^{18}}\right)}{8\,b^7}\right)\,15{}\mathrm{i}}{8\,b^7}}{\frac{108000\,a^{13}-351000\,a^{11}\,b^2+432000\,a^9\,b^4-246375\,a^7\,b^6+\frac{124875\,a^5\,b^8}{2}-\frac{10125\,a^3\,b^{10}}{2}}{b^{17}}-\frac{15\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{7200\,a^{10}\,b^6-14400\,a^8\,b^8+9000\,a^6\,b^{10}-1800\,a^4\,b^{12}+\frac{225\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+100800\,a^9\,b^8-122400\,a^7\,b^{10}+61200\,a^5\,b^{12}-11025\,a^3\,b^{14}+450\,a\,b^{16}\right)}{2\,b^{18}}-\frac{15\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{240\,a^5\,b^{14}-300\,a^3\,b^{16}+60\,a\,b^{18}}{b^{17}}-\frac{15\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2880\,a^4\,b^{16}+960\,a^2\,b^{18}\right)}{2\,b^{18}}\right)}{8\,b^7}\right)}{8\,b^7}+\frac{15\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{7200\,a^{10}\,b^6-14400\,a^8\,b^8+9000\,a^6\,b^{10}-1800\,a^4\,b^{12}+\frac{225\,a^2\,b^{14}}{2}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-28800\,a^{11}\,b^6+100800\,a^9\,b^8-122400\,a^7\,b^{10}+61200\,a^5\,b^{12}-11025\,a^3\,b^{14}+450\,a\,b^{16}\right)}{2\,b^{18}}+\frac{15\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(\frac{240\,a^5\,b^{14}-300\,a^3\,b^{16}+60\,a\,b^{18}}{b^{17}}+\frac{15\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{22}-128\,a^3\,b^{20}\right)}{2\,b^{18}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1920\,a^6\,b^{14}-2880\,a^4\,b^{16}+960\,a^2\,b^{18}\right)}{2\,b^{18}}\right)}{8\,b^7}\right)}{8\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(432000\,a^{14}-1512000\,a^{12}\,b^2+2052000\,a^{10}\,b^4-1350000\,a^8\,b^6+438750\,a^6\,b^8-64125\,a^4\,b^{10}+3375\,a^2\,b^{12}\right)}{b^{18}}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,8{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,15{}\mathrm{i}}{4\,b^7\,d}","Not used",1,"- ((a*b^4 + 30*a^5 - 25*a^3*b^2)/b^6 + (tan(c/2 + (d*x)/2)*(420*a^4 + 16*b^4 - 355*a^2*b^2))/(4*b^5) + (15*tan(c/2 + (d*x)/2)^11*(4*a^4 - 3*a^2*b^2))/(4*b^5) + (15*tan(c/2 + (d*x)/2)^7*(68*a^4 + 2*b^4 - 55*a^2*b^2))/(2*b^5) - (5*tan(c/2 + (d*x)/2)^9*(4*b^4 - 132*a^4 + 99*a^2*b^2))/(4*b^5) + (5*tan(c/2 + (d*x)/2)^5*(276*a^4 + 10*b^4 - 235*a^2*b^2))/(2*b^5) + (5*tan(c/2 + (d*x)/2)^3*(348*a^4 + 20*b^4 - 301*a^2*b^2))/(4*b^5) + (tan(c/2 + (d*x)/2)^10*(30*a^6 + 2*b^6 - 30*a^2*b^4 + 15*a^4*b^2))/(a*b^6) + (tan(c/2 + (d*x)/2)^2*(150*a^6 + 2*b^6 - 64*a^2*b^4 - 45*a^4*b^2))/(a*b^6) + (2*tan(c/2 + (d*x)/2)^4*(150*a^6 + 4*b^6 - 110*a^2*b^4 + 15*a^4*b^2))/(a*b^6) + (tan(c/2 + (d*x)/2)^8*(150*a^6 + 8*b^6 - 165*a^2*b^4 + 75*a^4*b^2))/(a*b^6) + (2*tan(c/2 + (d*x)/2)^6*(5*a^2 + 6*b^2)*(30*a^4 + b^4 - 25*a^2*b^2))/(a*b^6))/(d*(tan(c/2 + (d*x)/2)^2*(6*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^10*(6*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(15*a^2 + 16*b^2) + tan(c/2 + (d*x)/2)^8*(15*a^2 + 16*b^2) + tan(c/2 + (d*x)/2)^6*(20*a^2 + 24*b^2) + a^2*tan(c/2 + (d*x)/2)^12 + a^2 + 20*a*b*tan(c/2 + (d*x)/2)^3 + 40*a*b*tan(c/2 + (d*x)/2)^5 + 40*a*b*tan(c/2 + (d*x)/2)^7 + 20*a*b*tan(c/2 + (d*x)/2)^9 + 4*a*b*tan(c/2 + (d*x)/2)^11 + 4*a*b*tan(c/2 + (d*x)/2))) - (atanh((3375*a^3*(b^2 - a^2)^(1/2))/(2*((3375*a^3*b)/2 - (10125*a^5)/(2*b) + (3375*a^7)/b^3 - 10125*a^4*tan(c/2 + (d*x)/2) + 3375*a^2*b^2*tan(c/2 + (d*x)/2) + (6750*a^6*tan(c/2 + (d*x)/2))/b^2)) - (3375*a^5*(b^2 - a^2)^(1/2))/((3375*a^3*b^3)/2 - (10125*a^5*b)/2 + (3375*a^7)/b + 6750*a^6*tan(c/2 + (d*x)/2) + 3375*a^2*b^4*tan(c/2 + (d*x)/2) - 10125*a^4*b^2*tan(c/2 + (d*x)/2)) + (3375*a^2*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/((3375*a^3)/2 - (10125*a^5)/(2*b^2) + (3375*a^7)/b^4 + 3375*a^2*b*tan(c/2 + (d*x)/2) - (10125*a^4*tan(c/2 + (d*x)/2))/b + (6750*a^6*tan(c/2 + (d*x)/2))/b^3) - (16875*a^4*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(2*((3375*a^3*b^2)/2 - (10125*a^5)/2 + (3375*a^7)/b^2 - 10125*a^4*b*tan(c/2 + (d*x)/2) + 3375*a^2*b^3*tan(c/2 + (d*x)/2) + (6750*a^6*tan(c/2 + (d*x)/2))/b)) + (3375*a^6*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(3375*a^7 + (3375*a^3*b^4)/2 - (10125*a^5*b^2)/2 + 6750*a^6*b*tan(c/2 + (d*x)/2) + 3375*a^2*b^5*tan(c/2 + (d*x)/2) - 10125*a^4*b^3*tan(c/2 + (d*x)/2)))*(30*a^3*(b^2 - a^2)^(1/2) - 15*a*b^2*(b^2 - a^2)^(1/2)))/(b^7*d) - (atan((((a^4*8i + b^4*1i - a^2*b^2*8i)*(((225*a^2*b^14)/2 - 1800*a^4*b^12 + 9000*a^6*b^10 - 14400*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(450*a*b^16 - 11025*a^3*b^14 + 61200*a^5*b^12 - 122400*a^7*b^10 + 100800*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) - (15*(a^4*8i + b^4*1i - a^2*b^2*8i)*((60*a*b^18 - 300*a^3*b^16 + 240*a^5*b^14)/b^17 - (15*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(a^4*8i + b^4*1i - a^2*b^2*8i))/(8*b^7) + (tan(c/2 + (d*x)/2)*(960*a^2*b^18 - 2880*a^4*b^16 + 1920*a^6*b^14))/(2*b^18)))/(8*b^7))*15i)/(8*b^7) + ((a^4*8i + b^4*1i - a^2*b^2*8i)*(((225*a^2*b^14)/2 - 1800*a^4*b^12 + 9000*a^6*b^10 - 14400*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(450*a*b^16 - 11025*a^3*b^14 + 61200*a^5*b^12 - 122400*a^7*b^10 + 100800*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) + (15*(a^4*8i + b^4*1i - a^2*b^2*8i)*((60*a*b^18 - 300*a^3*b^16 + 240*a^5*b^14)/b^17 + (15*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(a^4*8i + b^4*1i - a^2*b^2*8i))/(8*b^7) + (tan(c/2 + (d*x)/2)*(960*a^2*b^18 - 2880*a^4*b^16 + 1920*a^6*b^14))/(2*b^18)))/(8*b^7))*15i)/(8*b^7))/((108000*a^13 - (10125*a^3*b^10)/2 + (124875*a^5*b^8)/2 - 246375*a^7*b^6 + 432000*a^9*b^4 - 351000*a^11*b^2)/b^17 - (15*(a^4*8i + b^4*1i - a^2*b^2*8i)*(((225*a^2*b^14)/2 - 1800*a^4*b^12 + 9000*a^6*b^10 - 14400*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(450*a*b^16 - 11025*a^3*b^14 + 61200*a^5*b^12 - 122400*a^7*b^10 + 100800*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) - (15*(a^4*8i + b^4*1i - a^2*b^2*8i)*((60*a*b^18 - 300*a^3*b^16 + 240*a^5*b^14)/b^17 - (15*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(a^4*8i + b^4*1i - a^2*b^2*8i))/(8*b^7) + (tan(c/2 + (d*x)/2)*(960*a^2*b^18 - 2880*a^4*b^16 + 1920*a^6*b^14))/(2*b^18)))/(8*b^7)))/(8*b^7) + (15*(a^4*8i + b^4*1i - a^2*b^2*8i)*(((225*a^2*b^14)/2 - 1800*a^4*b^12 + 9000*a^6*b^10 - 14400*a^8*b^8 + 7200*a^10*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(450*a*b^16 - 11025*a^3*b^14 + 61200*a^5*b^12 - 122400*a^7*b^10 + 100800*a^9*b^8 - 28800*a^11*b^6))/(2*b^18) + (15*(a^4*8i + b^4*1i - a^2*b^2*8i)*((60*a*b^18 - 300*a^3*b^16 + 240*a^5*b^14)/b^17 + (15*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^22 - 128*a^3*b^20))/(2*b^18))*(a^4*8i + b^4*1i - a^2*b^2*8i))/(8*b^7) + (tan(c/2 + (d*x)/2)*(960*a^2*b^18 - 2880*a^4*b^16 + 1920*a^6*b^14))/(2*b^18)))/(8*b^7)))/(8*b^7) + (tan(c/2 + (d*x)/2)*(432000*a^14 + 3375*a^2*b^12 - 64125*a^4*b^10 + 438750*a^6*b^8 - 1350000*a^8*b^6 + 2052000*a^10*b^4 - 1512000*a^12*b^2))/b^18))*(a^4*8i + b^4*1i - a^2*b^2*8i)*15i)/(4*b^7*d)","B"
1269,1,5354,399,14.550726,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)*(a + b*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{\frac{3\,\left(-4\,a^4+a^2\,b^2+b^4\right)}{a\,b^4}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-42\,a^4+11\,a^2\,b^2+8\,b^4\right)}{a^2\,b^3}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a^6+13\,a^4\,b^2-7\,a^2\,b^4-4\,b^6\right)}{a^3\,b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(12\,a^6+13\,a^4\,b^2-9\,a^2\,b^4-6\,b^6\right)}{a^3\,b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(36\,a^6+23\,a^4\,b^2-15\,a^2\,b^4-6\,b^6\right)}{a^3\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-6\,a^4+a^2\,b^2+4\,b^4\right)}{a^2\,b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-54\,a^4+9\,a^2\,b^2+16\,b^4\right)}{a^2\,b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-90\,a^4+27\,a^2\,b^2+20\,b^4\right)}{a^2\,b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2+8\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+a^2+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,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)}^7+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-6048\,a^{15}+10800\,a^{13}\,b^2-7038\,a^{11}\,b^4+3979\,a^9\,b^6-1947\,a^7\,b^8+332\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^{11}}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-864\,a^{14}\,b^4+1872\,a^{12}\,b^6-1110\,a^{10}\,b^8+32\,a^8\,b^{10}+160\,a^6\,b^{12}-24\,a^4\,b^{14}+32\,a^2\,b^{16}\right)}{a^6\,b^{11}}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-168\,a^{11}\,b^{10}+160\,a^9\,b^{12}-48\,a^7\,b^{14}+64\,a^5\,b^{16}\right)}{a^6\,b^{11}}-\frac{\left(\frac{4\,\left(32\,a^8\,b^{16}-24\,a^{10}\,b^{14}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{18}-68\,a^9\,b^{20}+64\,a^7\,b^{22}\right)}{a^6\,b^{16}}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(96\,a^{12}\,b^{14}-280\,a^{10}\,b^{16}+192\,a^8\,b^{18}-68\,a^6\,b^{20}+64\,a^4\,b^{22}\right)}{a^6\,b^{16}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{15}\,b^8-3840\,a^{13}\,b^{10}+6506\,a^{11}\,b^{12}-3454\,a^9\,b^{14}+725\,a^7\,b^{16}-180\,a^5\,b^{18}+4\,a^3\,b^{20}\right)}{a^6\,b^{16}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3456\,a^{16}\,b^4-12960\,a^{14}\,b^6+15912\,a^{12}\,b^8-9958\,a^{10}\,b^{10}+5544\,a^8\,b^{12}-2390\,a^6\,b^{14}+445\,a^4\,b^{16}-4\,a^2\,b^{18}+4\,b^{20}\right)}{a^6\,b^{16}}\right)\,1{}\mathrm{i}}{2\,b^5}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-6048\,a^{15}+10800\,a^{13}\,b^2-7038\,a^{11}\,b^4+3979\,a^9\,b^6-1947\,a^7\,b^8+332\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^{11}}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-168\,a^{11}\,b^{10}+160\,a^9\,b^{12}-48\,a^7\,b^{14}+64\,a^5\,b^{16}\right)}{a^6\,b^{11}}+\frac{\left(\frac{4\,\left(32\,a^8\,b^{16}-24\,a^{10}\,b^{14}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{18}-68\,a^9\,b^{20}+64\,a^7\,b^{22}\right)}{a^6\,b^{16}}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(96\,a^{12}\,b^{14}-280\,a^{10}\,b^{16}+192\,a^8\,b^{18}-68\,a^6\,b^{20}+64\,a^4\,b^{22}\right)}{a^6\,b^{16}}\right)}{2\,b^5}+\frac{4\,\left(-864\,a^{14}\,b^4+1872\,a^{12}\,b^6-1110\,a^{10}\,b^8+32\,a^8\,b^{10}+160\,a^6\,b^{12}-24\,a^4\,b^{14}+32\,a^2\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{15}\,b^8-3840\,a^{13}\,b^{10}+6506\,a^{11}\,b^{12}-3454\,a^9\,b^{14}+725\,a^7\,b^{16}-180\,a^5\,b^{18}+4\,a^3\,b^{20}\right)}{a^6\,b^{16}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3456\,a^{16}\,b^4-12960\,a^{14}\,b^6+15912\,a^{12}\,b^8-9958\,a^{10}\,b^{10}+5544\,a^8\,b^{12}-2390\,a^6\,b^{14}+445\,a^4\,b^{16}-4\,a^2\,b^{18}+4\,b^{20}\right)}{a^6\,b^{16}}\right)\,1{}\mathrm{i}}{2\,b^5}}{\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-6048\,a^{15}+10800\,a^{13}\,b^2-7038\,a^{11}\,b^4+3979\,a^9\,b^6-1947\,a^7\,b^8+332\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^{11}}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-864\,a^{14}\,b^4+1872\,a^{12}\,b^6-1110\,a^{10}\,b^8+32\,a^8\,b^{10}+160\,a^6\,b^{12}-24\,a^4\,b^{14}+32\,a^2\,b^{16}\right)}{a^6\,b^{11}}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-168\,a^{11}\,b^{10}+160\,a^9\,b^{12}-48\,a^7\,b^{14}+64\,a^5\,b^{16}\right)}{a^6\,b^{11}}-\frac{\left(\frac{4\,\left(32\,a^8\,b^{16}-24\,a^{10}\,b^{14}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{18}-68\,a^9\,b^{20}+64\,a^7\,b^{22}\right)}{a^6\,b^{16}}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(96\,a^{12}\,b^{14}-280\,a^{10}\,b^{16}+192\,a^8\,b^{18}-68\,a^6\,b^{20}+64\,a^4\,b^{22}\right)}{a^6\,b^{16}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{15}\,b^8-3840\,a^{13}\,b^{10}+6506\,a^{11}\,b^{12}-3454\,a^9\,b^{14}+725\,a^7\,b^{16}-180\,a^5\,b^{18}+4\,a^3\,b^{20}\right)}{a^6\,b^{16}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3456\,a^{16}\,b^4-12960\,a^{14}\,b^6+15912\,a^{12}\,b^8-9958\,a^{10}\,b^{10}+5544\,a^8\,b^{12}-2390\,a^6\,b^{14}+445\,a^4\,b^{16}-4\,a^2\,b^{18}+4\,b^{20}\right)}{a^6\,b^{16}}\right)}{2\,b^5}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-6048\,a^{15}+10800\,a^{13}\,b^2-7038\,a^{11}\,b^4+3979\,a^9\,b^6-1947\,a^7\,b^8+332\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^{11}}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,\left(\frac{4\,\left(-168\,a^{11}\,b^{10}+160\,a^9\,b^{12}-48\,a^7\,b^{14}+64\,a^5\,b^{16}\right)}{a^6\,b^{11}}+\frac{\left(\frac{4\,\left(32\,a^8\,b^{16}-24\,a^{10}\,b^{14}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{18}-68\,a^9\,b^{20}+64\,a^7\,b^{22}\right)}{a^6\,b^{16}}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(96\,a^{12}\,b^{14}-280\,a^{10}\,b^{16}+192\,a^8\,b^{18}-68\,a^6\,b^{20}+64\,a^4\,b^{22}\right)}{a^6\,b^{16}}\right)}{2\,b^5}+\frac{4\,\left(-864\,a^{14}\,b^4+1872\,a^{12}\,b^6-1110\,a^{10}\,b^8+32\,a^8\,b^{10}+160\,a^6\,b^{12}-24\,a^4\,b^{14}+32\,a^2\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{15}\,b^8-3840\,a^{13}\,b^{10}+6506\,a^{11}\,b^{12}-3454\,a^9\,b^{14}+725\,a^7\,b^{16}-180\,a^5\,b^{18}+4\,a^3\,b^{20}\right)}{a^6\,b^{16}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3456\,a^{16}\,b^4-12960\,a^{14}\,b^6+15912\,a^{12}\,b^8-9958\,a^{10}\,b^{10}+5544\,a^8\,b^{12}-2390\,a^6\,b^{14}+445\,a^4\,b^{16}-4\,a^2\,b^{18}+4\,b^{20}\right)}{a^6\,b^{16}}\right)}{2\,b^5}-\frac{8\,\left(-6048\,a^{12}+10800\,a^{10}\,b^2-6174\,a^8\,b^4+2107\,a^6\,b^6-837\,a^4\,b^8+132\,a^2\,b^{10}+20\,b^{12}\right)}{a^6\,b^{11}}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(41472\,a^{17}-110592\,a^{15}\,b^2+108864\,a^{13}\,b^4-55200\,a^{11}\,b^6+21386\,a^9\,b^8-7030\,a^7\,b^{10}+1100\,a^5\,b^{12}\right)}{a^6\,b^{16}}}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{4\,\left(-6048\,a^{15}+10800\,a^{13}\,b^2-7038\,a^{11}\,b^4+3979\,a^9\,b^6-1947\,a^7\,b^8+332\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3456\,a^{16}\,b^4-12960\,a^{14}\,b^6+15912\,a^{12}\,b^8-9958\,a^{10}\,b^{10}+5544\,a^8\,b^{12}-2390\,a^6\,b^{14}+445\,a^4\,b^{16}-4\,a^2\,b^{18}+4\,b^{20}\right)}{a^6\,b^{16}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{4\,\left(-864\,a^{14}\,b^4+1872\,a^{12}\,b^6-1110\,a^{10}\,b^8+32\,a^8\,b^{10}+160\,a^6\,b^{12}-24\,a^4\,b^{14}+32\,a^2\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{15}\,b^8-3840\,a^{13}\,b^{10}+6506\,a^{11}\,b^{12}-3454\,a^9\,b^{14}+725\,a^7\,b^{16}-180\,a^5\,b^{18}+4\,a^3\,b^{20}\right)}{a^6\,b^{16}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(-168\,a^{11}\,b^{10}+160\,a^9\,b^{12}-48\,a^7\,b^{14}+64\,a^5\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(96\,a^{12}\,b^{14}-280\,a^{10}\,b^{16}+192\,a^8\,b^{18}-68\,a^6\,b^{20}+64\,a^4\,b^{22}\right)}{a^6\,b^{16}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(32\,a^8\,b^{16}-24\,a^{10}\,b^{14}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{18}-68\,a^9\,b^{20}+64\,a^7\,b^{22}\right)}{a^6\,b^{16}}\right)\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5}\right)\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5}\right)}{a^3\,b^5}\right)\,1{}\mathrm{i}}{a^3\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{4\,\left(-6048\,a^{15}+10800\,a^{13}\,b^2-7038\,a^{11}\,b^4+3979\,a^9\,b^6-1947\,a^7\,b^8+332\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3456\,a^{16}\,b^4-12960\,a^{14}\,b^6+15912\,a^{12}\,b^8-9958\,a^{10}\,b^{10}+5544\,a^8\,b^{12}-2390\,a^6\,b^{14}+445\,a^4\,b^{16}-4\,a^2\,b^{18}+4\,b^{20}\right)}{a^6\,b^{16}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{4\,\left(-864\,a^{14}\,b^4+1872\,a^{12}\,b^6-1110\,a^{10}\,b^8+32\,a^8\,b^{10}+160\,a^6\,b^{12}-24\,a^4\,b^{14}+32\,a^2\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{15}\,b^8-3840\,a^{13}\,b^{10}+6506\,a^{11}\,b^{12}-3454\,a^9\,b^{14}+725\,a^7\,b^{16}-180\,a^5\,b^{18}+4\,a^3\,b^{20}\right)}{a^6\,b^{16}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(-168\,a^{11}\,b^{10}+160\,a^9\,b^{12}-48\,a^7\,b^{14}+64\,a^5\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(96\,a^{12}\,b^{14}-280\,a^{10}\,b^{16}+192\,a^8\,b^{18}-68\,a^6\,b^{20}+64\,a^4\,b^{22}\right)}{a^6\,b^{16}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(32\,a^8\,b^{16}-24\,a^{10}\,b^{14}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{18}-68\,a^9\,b^{20}+64\,a^7\,b^{22}\right)}{a^6\,b^{16}}\right)\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5}\right)\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5}\right)}{a^3\,b^5}\right)\,1{}\mathrm{i}}{a^3\,b^5}}{\frac{8\,\left(-6048\,a^{12}+10800\,a^{10}\,b^2-6174\,a^8\,b^4+2107\,a^6\,b^6-837\,a^4\,b^8+132\,a^2\,b^{10}+20\,b^{12}\right)}{a^6\,b^{11}}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(41472\,a^{17}-110592\,a^{15}\,b^2+108864\,a^{13}\,b^4-55200\,a^{11}\,b^6+21386\,a^9\,b^8-7030\,a^7\,b^{10}+1100\,a^5\,b^{12}\right)}{a^6\,b^{16}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{4\,\left(-6048\,a^{15}+10800\,a^{13}\,b^2-7038\,a^{11}\,b^4+3979\,a^9\,b^6-1947\,a^7\,b^8+332\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3456\,a^{16}\,b^4-12960\,a^{14}\,b^6+15912\,a^{12}\,b^8-9958\,a^{10}\,b^{10}+5544\,a^8\,b^{12}-2390\,a^6\,b^{14}+445\,a^4\,b^{16}-4\,a^2\,b^{18}+4\,b^{20}\right)}{a^6\,b^{16}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{4\,\left(-864\,a^{14}\,b^4+1872\,a^{12}\,b^6-1110\,a^{10}\,b^8+32\,a^8\,b^{10}+160\,a^6\,b^{12}-24\,a^4\,b^{14}+32\,a^2\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{15}\,b^8-3840\,a^{13}\,b^{10}+6506\,a^{11}\,b^{12}-3454\,a^9\,b^{14}+725\,a^7\,b^{16}-180\,a^5\,b^{18}+4\,a^3\,b^{20}\right)}{a^6\,b^{16}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(-168\,a^{11}\,b^{10}+160\,a^9\,b^{12}-48\,a^7\,b^{14}+64\,a^5\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(96\,a^{12}\,b^{14}-280\,a^{10}\,b^{16}+192\,a^8\,b^{18}-68\,a^6\,b^{20}+64\,a^4\,b^{22}\right)}{a^6\,b^{16}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(32\,a^8\,b^{16}-24\,a^{10}\,b^{14}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{18}-68\,a^9\,b^{20}+64\,a^7\,b^{22}\right)}{a^6\,b^{16}}\right)\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5}\right)\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5}\right)}{a^3\,b^5}\right)}{a^3\,b^5}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{4\,\left(-6048\,a^{15}+10800\,a^{13}\,b^2-7038\,a^{11}\,b^4+3979\,a^9\,b^6-1947\,a^7\,b^8+332\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3456\,a^{16}\,b^4-12960\,a^{14}\,b^6+15912\,a^{12}\,b^8-9958\,a^{10}\,b^{10}+5544\,a^8\,b^{12}-2390\,a^6\,b^{14}+445\,a^4\,b^{16}-4\,a^2\,b^{18}+4\,b^{20}\right)}{a^6\,b^{16}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,\left(\frac{4\,\left(-864\,a^{14}\,b^4+1872\,a^{12}\,b^6-1110\,a^{10}\,b^8+32\,a^8\,b^{10}+160\,a^6\,b^{12}-24\,a^4\,b^{14}+32\,a^2\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{15}\,b^8-3840\,a^{13}\,b^{10}+6506\,a^{11}\,b^{12}-3454\,a^9\,b^{14}+725\,a^7\,b^{16}-180\,a^5\,b^{18}+4\,a^3\,b^{20}\right)}{a^6\,b^{16}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(-168\,a^{11}\,b^{10}+160\,a^9\,b^{12}-48\,a^7\,b^{14}+64\,a^5\,b^{16}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(96\,a^{12}\,b^{14}-280\,a^{10}\,b^{16}+192\,a^8\,b^{18}-68\,a^6\,b^{20}+64\,a^4\,b^{22}\right)}{a^6\,b^{16}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(32\,a^8\,b^{16}-24\,a^{10}\,b^{14}\right)}{a^6\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b^{18}-68\,a^9\,b^{20}+64\,a^7\,b^{22}\right)}{a^6\,b^{16}}\right)\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5}\right)\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)}{a^3\,b^5}\right)}{a^3\,b^5}\right)}{a^3\,b^5}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4+\frac{a^2\,b^2}{2}+b^4\right)\,2{}\mathrm{i}}{a^3\,b^5\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) + ((3*(b^4 - 4*a^4 + a^2*b^2))/(a*b^4) + (tan(c/2 + (d*x)/2)*(8*b^4 - 42*a^4 + 11*a^2*b^2))/(a^2*b^3) - (3*tan(c/2 + (d*x)/2)^4*(12*a^6 - 4*b^6 - 7*a^2*b^4 + 13*a^4*b^2))/(a^3*b^4) - (tan(c/2 + (d*x)/2)^6*(12*a^6 - 6*b^6 - 9*a^2*b^4 + 13*a^4*b^2))/(a^3*b^4) - (tan(c/2 + (d*x)/2)^2*(36*a^6 - 6*b^6 - 15*a^2*b^4 + 23*a^4*b^2))/(a^3*b^4) + (tan(c/2 + (d*x)/2)^7*(4*b^4 - 6*a^4 + a^2*b^2))/(a^2*b^3) + (tan(c/2 + (d*x)/2)^5*(16*b^4 - 54*a^4 + 9*a^2*b^2))/(a^2*b^3) + (tan(c/2 + (d*x)/2)^3*(20*b^4 - 90*a^4 + 27*a^2*b^2))/(a^2*b^3))/(d*(tan(c/2 + (d*x)/2)^2*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^6*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(6*a^2 + 8*b^2) + a^2*tan(c/2 + (d*x)/2)^8 + a^2 + 12*a*b*tan(c/2 + (d*x)/2)^3 + 12*a*b*tan(c/2 + (d*x)/2)^5 + 4*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2))) - (atan((((a^2*12i - b^2*5i)*((4*(20*a^3*b^12 - 6048*a^15 + 332*a^5*b^10 - 1947*a^7*b^8 + 3979*a^9*b^6 - 7038*a^11*b^4 + 10800*a^13*b^2))/(a^6*b^11) - ((a^2*12i - b^2*5i)*((4*(32*a^2*b^16 - 24*a^4*b^14 + 160*a^6*b^12 + 32*a^8*b^10 - 1110*a^10*b^8 + 1872*a^12*b^6 - 864*a^14*b^4))/(a^6*b^11) - ((a^2*12i - b^2*5i)*((4*(64*a^5*b^16 - 48*a^7*b^14 + 160*a^9*b^12 - 168*a^11*b^10))/(a^6*b^11) - (((4*(32*a^8*b^16 - 24*a^10*b^14))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^22 - 68*a^9*b^20 + 8*a^11*b^18))/(a^6*b^16))*(a^2*12i - b^2*5i))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^22 - 68*a^6*b^20 + 192*a^8*b^18 - 280*a^10*b^16 + 96*a^12*b^14))/(a^6*b^16)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^20 - 180*a^5*b^18 + 725*a^7*b^16 - 3454*a^9*b^14 + 6506*a^11*b^12 - 3840*a^13*b^10 + 288*a^15*b^8))/(a^6*b^16)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(4*b^20 - 4*a^2*b^18 + 445*a^4*b^16 - 2390*a^6*b^14 + 5544*a^8*b^12 - 9958*a^10*b^10 + 15912*a^12*b^8 - 12960*a^14*b^6 + 3456*a^16*b^4))/(a^6*b^16))*1i)/(2*b^5) + ((a^2*12i - b^2*5i)*((4*(20*a^3*b^12 - 6048*a^15 + 332*a^5*b^10 - 1947*a^7*b^8 + 3979*a^9*b^6 - 7038*a^11*b^4 + 10800*a^13*b^2))/(a^6*b^11) + ((a^2*12i - b^2*5i)*(((a^2*12i - b^2*5i)*((4*(64*a^5*b^16 - 48*a^7*b^14 + 160*a^9*b^12 - 168*a^11*b^10))/(a^6*b^11) + (((4*(32*a^8*b^16 - 24*a^10*b^14))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^22 - 68*a^9*b^20 + 8*a^11*b^18))/(a^6*b^16))*(a^2*12i - b^2*5i))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^22 - 68*a^6*b^20 + 192*a^8*b^18 - 280*a^10*b^16 + 96*a^12*b^14))/(a^6*b^16)))/(2*b^5) + (4*(32*a^2*b^16 - 24*a^4*b^14 + 160*a^6*b^12 + 32*a^8*b^10 - 1110*a^10*b^8 + 1872*a^12*b^6 - 864*a^14*b^4))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^20 - 180*a^5*b^18 + 725*a^7*b^16 - 3454*a^9*b^14 + 6506*a^11*b^12 - 3840*a^13*b^10 + 288*a^15*b^8))/(a^6*b^16)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(4*b^20 - 4*a^2*b^18 + 445*a^4*b^16 - 2390*a^6*b^14 + 5544*a^8*b^12 - 9958*a^10*b^10 + 15912*a^12*b^8 - 12960*a^14*b^6 + 3456*a^16*b^4))/(a^6*b^16))*1i)/(2*b^5))/(((a^2*12i - b^2*5i)*((4*(20*a^3*b^12 - 6048*a^15 + 332*a^5*b^10 - 1947*a^7*b^8 + 3979*a^9*b^6 - 7038*a^11*b^4 + 10800*a^13*b^2))/(a^6*b^11) - ((a^2*12i - b^2*5i)*((4*(32*a^2*b^16 - 24*a^4*b^14 + 160*a^6*b^12 + 32*a^8*b^10 - 1110*a^10*b^8 + 1872*a^12*b^6 - 864*a^14*b^4))/(a^6*b^11) - ((a^2*12i - b^2*5i)*((4*(64*a^5*b^16 - 48*a^7*b^14 + 160*a^9*b^12 - 168*a^11*b^10))/(a^6*b^11) - (((4*(32*a^8*b^16 - 24*a^10*b^14))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^22 - 68*a^9*b^20 + 8*a^11*b^18))/(a^6*b^16))*(a^2*12i - b^2*5i))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^22 - 68*a^6*b^20 + 192*a^8*b^18 - 280*a^10*b^16 + 96*a^12*b^14))/(a^6*b^16)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^20 - 180*a^5*b^18 + 725*a^7*b^16 - 3454*a^9*b^14 + 6506*a^11*b^12 - 3840*a^13*b^10 + 288*a^15*b^8))/(a^6*b^16)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(4*b^20 - 4*a^2*b^18 + 445*a^4*b^16 - 2390*a^6*b^14 + 5544*a^8*b^12 - 9958*a^10*b^10 + 15912*a^12*b^8 - 12960*a^14*b^6 + 3456*a^16*b^4))/(a^6*b^16)))/(2*b^5) - ((a^2*12i - b^2*5i)*((4*(20*a^3*b^12 - 6048*a^15 + 332*a^5*b^10 - 1947*a^7*b^8 + 3979*a^9*b^6 - 7038*a^11*b^4 + 10800*a^13*b^2))/(a^6*b^11) + ((a^2*12i - b^2*5i)*(((a^2*12i - b^2*5i)*((4*(64*a^5*b^16 - 48*a^7*b^14 + 160*a^9*b^12 - 168*a^11*b^10))/(a^6*b^11) + (((4*(32*a^8*b^16 - 24*a^10*b^14))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^22 - 68*a^9*b^20 + 8*a^11*b^18))/(a^6*b^16))*(a^2*12i - b^2*5i))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^22 - 68*a^6*b^20 + 192*a^8*b^18 - 280*a^10*b^16 + 96*a^12*b^14))/(a^6*b^16)))/(2*b^5) + (4*(32*a^2*b^16 - 24*a^4*b^14 + 160*a^6*b^12 + 32*a^8*b^10 - 1110*a^10*b^8 + 1872*a^12*b^6 - 864*a^14*b^4))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^20 - 180*a^5*b^18 + 725*a^7*b^16 - 3454*a^9*b^14 + 6506*a^11*b^12 - 3840*a^13*b^10 + 288*a^15*b^8))/(a^6*b^16)))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(4*b^20 - 4*a^2*b^18 + 445*a^4*b^16 - 2390*a^6*b^14 + 5544*a^8*b^12 - 9958*a^10*b^10 + 15912*a^12*b^8 - 12960*a^14*b^6 + 3456*a^16*b^4))/(a^6*b^16)))/(2*b^5) - (8*(20*b^12 - 6048*a^12 + 132*a^2*b^10 - 837*a^4*b^8 + 2107*a^6*b^6 - 6174*a^8*b^4 + 10800*a^10*b^2))/(a^6*b^11) + (16*tan(c/2 + (d*x)/2)*(41472*a^17 + 1100*a^5*b^12 - 7030*a^7*b^10 + 21386*a^9*b^8 - 55200*a^11*b^6 + 108864*a^13*b^4 - 110592*a^15*b^2))/(a^6*b^16)))*(a^2*12i - b^2*5i)*1i)/(b^5*d) + (atan((((-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*((4*(20*a^3*b^12 - 6048*a^15 + 332*a^5*b^10 - 1947*a^7*b^8 + 3979*a^9*b^6 - 7038*a^11*b^4 + 10800*a^13*b^2))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*b^20 - 4*a^2*b^18 + 445*a^4*b^16 - 2390*a^6*b^14 + 5544*a^8*b^12 - 9958*a^10*b^10 + 15912*a^12*b^8 - 12960*a^14*b^6 + 3456*a^16*b^4))/(a^6*b^16) + ((-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*((4*(32*a^2*b^16 - 24*a^4*b^14 + 160*a^6*b^12 + 32*a^8*b^10 - 1110*a^10*b^8 + 1872*a^12*b^6 - 864*a^14*b^4))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^20 - 180*a^5*b^18 + 725*a^7*b^16 - 3454*a^9*b^14 + 6506*a^11*b^12 - 3840*a^13*b^10 + 288*a^15*b^8))/(a^6*b^16) + ((-(a + b)*(a - b))^(1/2)*((4*(64*a^5*b^16 - 48*a^7*b^14 + 160*a^9*b^12 - 168*a^11*b^10))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^22 - 68*a^6*b^20 + 192*a^8*b^18 - 280*a^10*b^16 + 96*a^12*b^14))/(a^6*b^16) + ((-(a + b)*(a - b))^(1/2)*((4*(32*a^8*b^16 - 24*a^10*b^14))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^22 - 68*a^9*b^20 + 8*a^11*b^18))/(a^6*b^16))*(6*a^4 + b^4 + (a^2*b^2)/2))/(a^3*b^5))*(6*a^4 + b^4 + (a^2*b^2)/2))/(a^3*b^5)))/(a^3*b^5))*1i)/(a^3*b^5) + ((-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*((4*(20*a^3*b^12 - 6048*a^15 + 332*a^5*b^10 - 1947*a^7*b^8 + 3979*a^9*b^6 - 7038*a^11*b^4 + 10800*a^13*b^2))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*b^20 - 4*a^2*b^18 + 445*a^4*b^16 - 2390*a^6*b^14 + 5544*a^8*b^12 - 9958*a^10*b^10 + 15912*a^12*b^8 - 12960*a^14*b^6 + 3456*a^16*b^4))/(a^6*b^16) - ((-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*((4*(32*a^2*b^16 - 24*a^4*b^14 + 160*a^6*b^12 + 32*a^8*b^10 - 1110*a^10*b^8 + 1872*a^12*b^6 - 864*a^14*b^4))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^20 - 180*a^5*b^18 + 725*a^7*b^16 - 3454*a^9*b^14 + 6506*a^11*b^12 - 3840*a^13*b^10 + 288*a^15*b^8))/(a^6*b^16) - ((-(a + b)*(a - b))^(1/2)*((4*(64*a^5*b^16 - 48*a^7*b^14 + 160*a^9*b^12 - 168*a^11*b^10))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^22 - 68*a^6*b^20 + 192*a^8*b^18 - 280*a^10*b^16 + 96*a^12*b^14))/(a^6*b^16) - ((-(a + b)*(a - b))^(1/2)*((4*(32*a^8*b^16 - 24*a^10*b^14))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^22 - 68*a^9*b^20 + 8*a^11*b^18))/(a^6*b^16))*(6*a^4 + b^4 + (a^2*b^2)/2))/(a^3*b^5))*(6*a^4 + b^4 + (a^2*b^2)/2))/(a^3*b^5)))/(a^3*b^5))*1i)/(a^3*b^5))/((8*(20*b^12 - 6048*a^12 + 132*a^2*b^10 - 837*a^4*b^8 + 2107*a^6*b^6 - 6174*a^8*b^4 + 10800*a^10*b^2))/(a^6*b^11) - (16*tan(c/2 + (d*x)/2)*(41472*a^17 + 1100*a^5*b^12 - 7030*a^7*b^10 + 21386*a^9*b^8 - 55200*a^11*b^6 + 108864*a^13*b^4 - 110592*a^15*b^2))/(a^6*b^16) + ((-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*((4*(20*a^3*b^12 - 6048*a^15 + 332*a^5*b^10 - 1947*a^7*b^8 + 3979*a^9*b^6 - 7038*a^11*b^4 + 10800*a^13*b^2))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*b^20 - 4*a^2*b^18 + 445*a^4*b^16 - 2390*a^6*b^14 + 5544*a^8*b^12 - 9958*a^10*b^10 + 15912*a^12*b^8 - 12960*a^14*b^6 + 3456*a^16*b^4))/(a^6*b^16) + ((-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*((4*(32*a^2*b^16 - 24*a^4*b^14 + 160*a^6*b^12 + 32*a^8*b^10 - 1110*a^10*b^8 + 1872*a^12*b^6 - 864*a^14*b^4))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^20 - 180*a^5*b^18 + 725*a^7*b^16 - 3454*a^9*b^14 + 6506*a^11*b^12 - 3840*a^13*b^10 + 288*a^15*b^8))/(a^6*b^16) + ((-(a + b)*(a - b))^(1/2)*((4*(64*a^5*b^16 - 48*a^7*b^14 + 160*a^9*b^12 - 168*a^11*b^10))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^22 - 68*a^6*b^20 + 192*a^8*b^18 - 280*a^10*b^16 + 96*a^12*b^14))/(a^6*b^16) + ((-(a + b)*(a - b))^(1/2)*((4*(32*a^8*b^16 - 24*a^10*b^14))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^22 - 68*a^9*b^20 + 8*a^11*b^18))/(a^6*b^16))*(6*a^4 + b^4 + (a^2*b^2)/2))/(a^3*b^5))*(6*a^4 + b^4 + (a^2*b^2)/2))/(a^3*b^5)))/(a^3*b^5)))/(a^3*b^5) - ((-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*((4*(20*a^3*b^12 - 6048*a^15 + 332*a^5*b^10 - 1947*a^7*b^8 + 3979*a^9*b^6 - 7038*a^11*b^4 + 10800*a^13*b^2))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*b^20 - 4*a^2*b^18 + 445*a^4*b^16 - 2390*a^6*b^14 + 5544*a^8*b^12 - 9958*a^10*b^10 + 15912*a^12*b^8 - 12960*a^14*b^6 + 3456*a^16*b^4))/(a^6*b^16) - ((-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*((4*(32*a^2*b^16 - 24*a^4*b^14 + 160*a^6*b^12 + 32*a^8*b^10 - 1110*a^10*b^8 + 1872*a^12*b^6 - 864*a^14*b^4))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(4*a^3*b^20 - 180*a^5*b^18 + 725*a^7*b^16 - 3454*a^9*b^14 + 6506*a^11*b^12 - 3840*a^13*b^10 + 288*a^15*b^8))/(a^6*b^16) - ((-(a + b)*(a - b))^(1/2)*((4*(64*a^5*b^16 - 48*a^7*b^14 + 160*a^9*b^12 - 168*a^11*b^10))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^22 - 68*a^6*b^20 + 192*a^8*b^18 - 280*a^10*b^16 + 96*a^12*b^14))/(a^6*b^16) - ((-(a + b)*(a - b))^(1/2)*((4*(32*a^8*b^16 - 24*a^10*b^14))/(a^6*b^11) + (8*tan(c/2 + (d*x)/2)*(64*a^7*b^22 - 68*a^9*b^20 + 8*a^11*b^18))/(a^6*b^16))*(6*a^4 + b^4 + (a^2*b^2)/2))/(a^3*b^5))*(6*a^4 + b^4 + (a^2*b^2)/2))/(a^3*b^5)))/(a^3*b^5)))/(a^3*b^5)))*(-(a + b)*(a - b))^(1/2)*(6*a^4 + b^4 + (a^2*b^2)/2)*2i)/(a^3*b^5*d)","B"
1270,1,4223,314,13.694692,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(6\,a^4+5\,a^2\,b^2-12\,b^4\right)}{b^2}-a^2-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-42\,a^4+a^2\,b^2+32\,b^4\right)}{b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(48\,a^4+5\,a^2\,b^2-44\,b^4\right)}{b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^5+a^3\,b^2-7\,a\,b^4\right)}{b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^6+9\,a^4\,b^2-6\,a^2\,b^4-5\,b^6\right)}{a\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^6+9\,a^4\,b^2-5\,a^2\,b^4-10\,b^6\right)}{a\,b^3}}{d\,\left(2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^5+8\,a^3\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^5+8\,a^3\,b^2\right)+2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+16\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}+\frac{6\,a\,\mathrm{atan}\left(\frac{6480\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{6480\,b^4}{a^4}-\frac{12960\,b^2}{a^2}-\frac{5184\,b^6}{a^6}+\frac{5184\,b^8}{a^8}+\frac{6480\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{5184\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{5184\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}-\frac{12960\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+\frac{6480\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}+6480}-\frac{12960\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{6480\,b^2}{a^2}+\frac{6480\,a^2}{b^2}-\frac{5184\,b^4}{a^4}+\frac{5184\,b^6}{a^6}-\frac{5184\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{5184\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{6480\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}-\frac{12960\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}+\frac{6480\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^7}-12960}-\frac{6480\,a}{6480\,b+6480\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{12960\,b^3}{a^2}+\frac{6480\,b^5}{a^4}-\frac{5184\,b^7}{a^6}+\frac{5184\,b^9}{a^8}-\frac{5184\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{12960\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{5184\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}+\frac{6480\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}}+\frac{5184}{\frac{6480\,a}{b}-5184\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{12960\,b}{a}+\frac{6480\,b^3}{a^3}-\frac{5184\,b^5}{a^5}+\frac{5184\,b^7}{a^7}+\frac{5184\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}+\frac{6480\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{12960\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{6480\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}-\frac{5184}{5184\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{12960\,a}{b}+\frac{6480\,b}{a}-\frac{5184\,b^3}{a^3}+\frac{6480\,a^3}{b^3}+\frac{5184\,b^5}{a^5}-\frac{5184\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{6480\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}-\frac{12960\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}+\frac{6480\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^8}}+\frac{6480\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{5184\,b^4}{a^4}-\frac{12960\,a^2}{b^2}-\frac{5184\,b^2}{a^2}+\frac{6480\,a^4}{b^4}+\frac{5184\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{5184\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+\frac{6480\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}-\frac{12960\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^7}+\frac{6480\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^9}+6480}+\frac{12960\,a^3}{6480\,b^3-\frac{12960\,b^5}{a^2}+\frac{6480\,b^7}{a^4}-\frac{5184\,b^9}{a^6}+\frac{5184\,b^{11}}{a^8}-12960\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6480\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{5184\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{6480\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{5184\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}-\frac{6480\,a^5}{6480\,b^5-\frac{12960\,b^7}{a^2}+\frac{6480\,b^9}{a^4}-\frac{5184\,b^{11}}{a^6}+\frac{5184\,b^{13}}{a^8}+6480\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6480\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12960\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{5184\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{5184\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}-\frac{5184\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{6480\,a^2}{b}-5184\,b+\frac{5184\,b^3}{a^2}-\frac{12960\,a^4}{b^3}+\frac{6480\,a^6}{b^5}+\frac{5184\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{5184\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{6480\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}-\frac{12960\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^8}+\frac{6480\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^{10}}}+\frac{5184\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5184\,b^3-5184\,a^2\,b+\frac{6480\,a^4}{b}-\frac{12960\,a^6}{b^3}+\frac{6480\,a^8}{b^5}+\frac{5184\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{5184\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{6480\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}-\frac{12960\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^8}+\frac{6480\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^{10}}}\right)}{b^4\,d}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(432\,a^{16}\,b^3-1080\,a^{14}\,b^5+864\,a^{12}\,b^7-1836\,a^{10}\,b^9+1863\,a^8\,b^{11}-270\,a^6\,b^{13}+135\,a^4\,b^{15}-108\,a^2\,b^{17}+108\,b^{19}\right)}{a^9\,b^{12}}-\frac{8\,\left(378\,a^{14}-135\,a^{12}\,b^2+378\,a^{10}\,b^4-729\,a^8\,b^6-108\,a^6\,b^8+108\,a^4\,b^{10}\right)}{a^8\,b^8}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-108\,a^{14}\,b^3+144\,a^{12}\,b^5-126\,a^8\,b^9+90\,a^6\,b^{11}-108\,a^4\,b^{13}+144\,a^2\,b^{15}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{16}\,b^6-900\,a^{14}\,b^8+909\,a^{12}\,b^{10}-306\,a^{10}\,b^{12}+405\,a^8\,b^{14}-180\,a^6\,b^{16}+36\,a^4\,b^{18}\right)}{a^9\,b^{12}}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-42\,a^{12}\,b^8+30\,a^{10}\,b^{10}-72\,a^8\,b^{12}+96\,a^6\,b^{14}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{14}\,b^{11}-120\,a^{12}\,b^{13}+96\,a^{10}\,b^{15}-204\,a^8\,b^{17}+192\,a^6\,b^{19}\right)}{a^9\,b^{12}}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(16\,a^{10}\,b^{13}-12\,a^{12}\,b^{11}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^{14}-68\,a^{12}\,b^{16}+64\,a^{10}\,b^{18}\right)}{a^9\,b^{12}}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,3{}\mathrm{i}}{2\,a^4\,b^4}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)\,\left(\frac{8\,\left(378\,a^{14}-135\,a^{12}\,b^2+378\,a^{10}\,b^4-729\,a^8\,b^6-108\,a^6\,b^8+108\,a^4\,b^{10}\right)}{a^8\,b^8}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(432\,a^{16}\,b^3-1080\,a^{14}\,b^5+864\,a^{12}\,b^7-1836\,a^{10}\,b^9+1863\,a^8\,b^{11}-270\,a^6\,b^{13}+135\,a^4\,b^{15}-108\,a^2\,b^{17}+108\,b^{19}\right)}{a^9\,b^{12}}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-108\,a^{14}\,b^3+144\,a^{12}\,b^5-126\,a^8\,b^9+90\,a^6\,b^{11}-108\,a^4\,b^{13}+144\,a^2\,b^{15}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{16}\,b^6-900\,a^{14}\,b^8+909\,a^{12}\,b^{10}-306\,a^{10}\,b^{12}+405\,a^8\,b^{14}-180\,a^6\,b^{16}+36\,a^4\,b^{18}\right)}{a^9\,b^{12}}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-42\,a^{12}\,b^8+30\,a^{10}\,b^{10}-72\,a^8\,b^{12}+96\,a^6\,b^{14}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{14}\,b^{11}-120\,a^{12}\,b^{13}+96\,a^{10}\,b^{15}-204\,a^8\,b^{17}+192\,a^6\,b^{19}\right)}{a^9\,b^{12}}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(16\,a^{10}\,b^{13}-12\,a^{12}\,b^{11}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^{14}-68\,a^{12}\,b^{16}+64\,a^{10}\,b^{18}\right)}{a^9\,b^{12}}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,3{}\mathrm{i}}{2\,a^4\,b^4}}{\frac{16\,\left(1134\,a^{10}\,b-405\,a^8\,b^3+162\,a^6\,b^5-891\,a^4\,b^7-324\,a^2\,b^9+324\,b^{11}\right)}{a^8\,b^8}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2592\,a^{16}-2592\,a^{14}\,b^2+1944\,a^{12}\,b^4-3240\,a^{10}\,b^6+1296\,a^8\,b^8\right)}{a^9\,b^{12}}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(432\,a^{16}\,b^3-1080\,a^{14}\,b^5+864\,a^{12}\,b^7-1836\,a^{10}\,b^9+1863\,a^8\,b^{11}-270\,a^6\,b^{13}+135\,a^4\,b^{15}-108\,a^2\,b^{17}+108\,b^{19}\right)}{a^9\,b^{12}}-\frac{8\,\left(378\,a^{14}-135\,a^{12}\,b^2+378\,a^{10}\,b^4-729\,a^8\,b^6-108\,a^6\,b^8+108\,a^4\,b^{10}\right)}{a^8\,b^8}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-108\,a^{14}\,b^3+144\,a^{12}\,b^5-126\,a^8\,b^9+90\,a^6\,b^{11}-108\,a^4\,b^{13}+144\,a^2\,b^{15}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{16}\,b^6-900\,a^{14}\,b^8+909\,a^{12}\,b^{10}-306\,a^{10}\,b^{12}+405\,a^8\,b^{14}-180\,a^6\,b^{16}+36\,a^4\,b^{18}\right)}{a^9\,b^{12}}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-42\,a^{12}\,b^8+30\,a^{10}\,b^{10}-72\,a^8\,b^{12}+96\,a^6\,b^{14}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{14}\,b^{11}-120\,a^{12}\,b^{13}+96\,a^{10}\,b^{15}-204\,a^8\,b^{17}+192\,a^6\,b^{19}\right)}{a^9\,b^{12}}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(16\,a^{10}\,b^{13}-12\,a^{12}\,b^{11}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^{14}-68\,a^{12}\,b^{16}+64\,a^{10}\,b^{18}\right)}{a^9\,b^{12}}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)}{2\,a^4\,b^4}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)\,\left(\frac{8\,\left(378\,a^{14}-135\,a^{12}\,b^2+378\,a^{10}\,b^4-729\,a^8\,b^6-108\,a^6\,b^8+108\,a^4\,b^{10}\right)}{a^8\,b^8}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(432\,a^{16}\,b^3-1080\,a^{14}\,b^5+864\,a^{12}\,b^7-1836\,a^{10}\,b^9+1863\,a^8\,b^{11}-270\,a^6\,b^{13}+135\,a^4\,b^{15}-108\,a^2\,b^{17}+108\,b^{19}\right)}{a^9\,b^{12}}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-108\,a^{14}\,b^3+144\,a^{12}\,b^5-126\,a^8\,b^9+90\,a^6\,b^{11}-108\,a^4\,b^{13}+144\,a^2\,b^{15}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{16}\,b^6-900\,a^{14}\,b^8+909\,a^{12}\,b^{10}-306\,a^{10}\,b^{12}+405\,a^8\,b^{14}-180\,a^6\,b^{16}+36\,a^4\,b^{18}\right)}{a^9\,b^{12}}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(-42\,a^{12}\,b^8+30\,a^{10}\,b^{10}-72\,a^8\,b^{12}+96\,a^6\,b^{14}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{14}\,b^{11}-120\,a^{12}\,b^{13}+96\,a^{10}\,b^{15}-204\,a^8\,b^{17}+192\,a^6\,b^{19}\right)}{a^9\,b^{12}}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(16\,a^{10}\,b^{13}-12\,a^{12}\,b^{11}\right)}{a^8\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^{14}-68\,a^{12}\,b^{16}+64\,a^{10}\,b^{18}\right)}{a^9\,b^{12}}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)}{2\,a^4\,b^4}\right)}{2\,a^4\,b^4}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4+a^2\,b^2+2\,b^4\right)\,3{}\mathrm{i}}{a^4\,b^4\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) + ((tan(c/2 + (d*x)/2)^6*(6*a^4 - 12*b^4 + 5*a^2*b^2))/b^2 - a^2 - (tan(c/2 + (d*x)/2)^2*(32*b^4 - 42*a^4 + a^2*b^2))/b^2 + (tan(c/2 + (d*x)/2)^4*(48*a^4 - 44*b^4 + 5*a^2*b^2))/b^2 + (2*tan(c/2 + (d*x)/2)*(6*a^5 - 7*a*b^4 + a^3*b^2))/b^3 + (4*tan(c/2 + (d*x)/2)^3*(6*a^6 - 5*b^6 - 6*a^2*b^4 + 9*a^4*b^2))/(a*b^3) + (2*tan(c/2 + (d*x)/2)^5*(6*a^6 - 10*b^6 - 5*a^2*b^4 + 9*a^4*b^2))/(a*b^3))/(d*(2*a^5*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^3*(6*a^5 + 8*a^3*b^2) + tan(c/2 + (d*x)/2)^5*(6*a^5 + 8*a^3*b^2) + 2*a^5*tan(c/2 + (d*x)/2) + 8*a^4*b*tan(c/2 + (d*x)/2)^2 + 16*a^4*b*tan(c/2 + (d*x)/2)^4 + 8*a^4*b*tan(c/2 + (d*x)/2)^6)) + (6*a*atan((6480*tan(c/2 + (d*x)/2))/((6480*b^4)/a^4 - (12960*b^2)/a^2 - (5184*b^6)/a^6 + (5184*b^8)/a^8 + (6480*a*tan(c/2 + (d*x)/2))/b - (5184*b*tan(c/2 + (d*x)/2))/a + (5184*b^3*tan(c/2 + (d*x)/2))/a^3 - (12960*a^3*tan(c/2 + (d*x)/2))/b^3 + (6480*a^5*tan(c/2 + (d*x)/2))/b^5 + 6480) - (12960*tan(c/2 + (d*x)/2))/((6480*b^2)/a^2 + (6480*a^2)/b^2 - (5184*b^4)/a^4 + (5184*b^6)/a^6 - (5184*a*tan(c/2 + (d*x)/2))/b + (5184*b*tan(c/2 + (d*x)/2))/a + (6480*a^3*tan(c/2 + (d*x)/2))/b^3 - (12960*a^5*tan(c/2 + (d*x)/2))/b^5 + (6480*a^7*tan(c/2 + (d*x)/2))/b^7 - 12960) - (6480*a)/(6480*b + 6480*a*tan(c/2 + (d*x)/2) - (12960*b^3)/a^2 + (6480*b^5)/a^4 - (5184*b^7)/a^6 + (5184*b^9)/a^8 - (5184*b^2*tan(c/2 + (d*x)/2))/a - (12960*a^3*tan(c/2 + (d*x)/2))/b^2 + (5184*b^4*tan(c/2 + (d*x)/2))/a^3 + (6480*a^5*tan(c/2 + (d*x)/2))/b^4) + 5184/((6480*a)/b - 5184*tan(c/2 + (d*x)/2) - (12960*b)/a + (6480*b^3)/a^3 - (5184*b^5)/a^5 + (5184*b^7)/a^7 + (5184*b^2*tan(c/2 + (d*x)/2))/a^2 + (6480*a^2*tan(c/2 + (d*x)/2))/b^2 - (12960*a^4*tan(c/2 + (d*x)/2))/b^4 + (6480*a^6*tan(c/2 + (d*x)/2))/b^6) - 5184/(5184*tan(c/2 + (d*x)/2) - (12960*a)/b + (6480*b)/a - (5184*b^3)/a^3 + (6480*a^3)/b^3 + (5184*b^5)/a^5 - (5184*a^2*tan(c/2 + (d*x)/2))/b^2 + (6480*a^4*tan(c/2 + (d*x)/2))/b^4 - (12960*a^6*tan(c/2 + (d*x)/2))/b^6 + (6480*a^8*tan(c/2 + (d*x)/2))/b^8) + (6480*tan(c/2 + (d*x)/2))/((5184*b^4)/a^4 - (12960*a^2)/b^2 - (5184*b^2)/a^2 + (6480*a^4)/b^4 + (5184*a*tan(c/2 + (d*x)/2))/b - (5184*a^3*tan(c/2 + (d*x)/2))/b^3 + (6480*a^5*tan(c/2 + (d*x)/2))/b^5 - (12960*a^7*tan(c/2 + (d*x)/2))/b^7 + (6480*a^9*tan(c/2 + (d*x)/2))/b^9 + 6480) + (12960*a^3)/(6480*b^3 - (12960*b^5)/a^2 + (6480*b^7)/a^4 - (5184*b^9)/a^6 + (5184*b^11)/a^8 - 12960*a^3*tan(c/2 + (d*x)/2) + 6480*a*b^2*tan(c/2 + (d*x)/2) - (5184*b^4*tan(c/2 + (d*x)/2))/a + (6480*a^5*tan(c/2 + (d*x)/2))/b^2 + (5184*b^6*tan(c/2 + (d*x)/2))/a^3) - (6480*a^5)/(6480*b^5 - (12960*b^7)/a^2 + (6480*b^9)/a^4 - (5184*b^11)/a^6 + (5184*b^13)/a^8 + 6480*a^5*tan(c/2 + (d*x)/2) + 6480*a*b^4*tan(c/2 + (d*x)/2) - 12960*a^3*b^2*tan(c/2 + (d*x)/2) - (5184*b^6*tan(c/2 + (d*x)/2))/a + (5184*b^8*tan(c/2 + (d*x)/2))/a^3) - (5184*b*tan(c/2 + (d*x)/2))/((6480*a^2)/b - 5184*b + (5184*b^3)/a^2 - (12960*a^4)/b^3 + (6480*a^6)/b^5 + (5184*a^3*tan(c/2 + (d*x)/2))/b^2 - (5184*a^5*tan(c/2 + (d*x)/2))/b^4 + (6480*a^7*tan(c/2 + (d*x)/2))/b^6 - (12960*a^9*tan(c/2 + (d*x)/2))/b^8 + (6480*a^11*tan(c/2 + (d*x)/2))/b^10) + (5184*b^3*tan(c/2 + (d*x)/2))/(5184*b^3 - 5184*a^2*b + (6480*a^4)/b - (12960*a^6)/b^3 + (6480*a^8)/b^5 + (5184*a^5*tan(c/2 + (d*x)/2))/b^2 - (5184*a^7*tan(c/2 + (d*x)/2))/b^4 + (6480*a^9*tan(c/2 + (d*x)/2))/b^6 - (12960*a^11*tan(c/2 + (d*x)/2))/b^8 + (6480*a^13*tan(c/2 + (d*x)/2))/b^10)))/(b^4*d) - (3*b*log(tan(c/2 + (d*x)/2)))/(a^4*d) + (atan((((-(a + b)*(a - b))^(1/2)*(2*a^4 + 2*b^4 + a^2*b^2)*((8*tan(c/2 + (d*x)/2)*(108*b^19 - 108*a^2*b^17 + 135*a^4*b^15 - 270*a^6*b^13 + 1863*a^8*b^11 - 1836*a^10*b^9 + 864*a^12*b^7 - 1080*a^14*b^5 + 432*a^16*b^3))/(a^9*b^12) - (8*(378*a^14 + 108*a^4*b^10 - 108*a^6*b^8 - 729*a^8*b^6 + 378*a^10*b^4 - 135*a^12*b^2))/(a^8*b^8) + (3*(-(a + b)*(a - b))^(1/2)*((8*(144*a^2*b^15 - 108*a^4*b^13 + 90*a^6*b^11 - 126*a^8*b^9 + 144*a^12*b^5 - 108*a^14*b^3))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(36*a^4*b^18 - 180*a^6*b^16 + 405*a^8*b^14 - 306*a^10*b^12 + 909*a^12*b^10 - 900*a^14*b^8 + 72*a^16*b^6))/(a^9*b^12) + (3*(-(a + b)*(a - b))^(1/2)*((8*(96*a^6*b^14 - 72*a^8*b^12 + 30*a^10*b^10 - 42*a^12*b^8))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(192*a^6*b^19 - 204*a^8*b^17 + 96*a^10*b^15 - 120*a^12*b^13 + 48*a^14*b^11))/(a^9*b^12) + (3*(-(a + b)*(a - b))^(1/2)*((8*(16*a^10*b^13 - 12*a^12*b^11))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^10*b^18 - 68*a^12*b^16 + 8*a^14*b^14))/(a^9*b^12))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*3i)/(2*a^4*b^4) - ((-(a + b)*(a - b))^(1/2)*(2*a^4 + 2*b^4 + a^2*b^2)*((8*(378*a^14 + 108*a^4*b^10 - 108*a^6*b^8 - 729*a^8*b^6 + 378*a^10*b^4 - 135*a^12*b^2))/(a^8*b^8) - (8*tan(c/2 + (d*x)/2)*(108*b^19 - 108*a^2*b^17 + 135*a^4*b^15 - 270*a^6*b^13 + 1863*a^8*b^11 - 1836*a^10*b^9 + 864*a^12*b^7 - 1080*a^14*b^5 + 432*a^16*b^3))/(a^9*b^12) + (3*(-(a + b)*(a - b))^(1/2)*((8*(144*a^2*b^15 - 108*a^4*b^13 + 90*a^6*b^11 - 126*a^8*b^9 + 144*a^12*b^5 - 108*a^14*b^3))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(36*a^4*b^18 - 180*a^6*b^16 + 405*a^8*b^14 - 306*a^10*b^12 + 909*a^12*b^10 - 900*a^14*b^8 + 72*a^16*b^6))/(a^9*b^12) - (3*(-(a + b)*(a - b))^(1/2)*((8*(96*a^6*b^14 - 72*a^8*b^12 + 30*a^10*b^10 - 42*a^12*b^8))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(192*a^6*b^19 - 204*a^8*b^17 + 96*a^10*b^15 - 120*a^12*b^13 + 48*a^14*b^11))/(a^9*b^12) - (3*(-(a + b)*(a - b))^(1/2)*((8*(16*a^10*b^13 - 12*a^12*b^11))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^10*b^18 - 68*a^12*b^16 + 8*a^14*b^14))/(a^9*b^12))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*3i)/(2*a^4*b^4))/((16*(1134*a^10*b + 324*b^11 - 324*a^2*b^9 - 891*a^4*b^7 + 162*a^6*b^5 - 405*a^8*b^3))/(a^8*b^8) + (16*tan(c/2 + (d*x)/2)*(2592*a^16 + 1296*a^8*b^8 - 3240*a^10*b^6 + 1944*a^12*b^4 - 2592*a^14*b^2))/(a^9*b^12) - (3*(-(a + b)*(a - b))^(1/2)*(2*a^4 + 2*b^4 + a^2*b^2)*((8*tan(c/2 + (d*x)/2)*(108*b^19 - 108*a^2*b^17 + 135*a^4*b^15 - 270*a^6*b^13 + 1863*a^8*b^11 - 1836*a^10*b^9 + 864*a^12*b^7 - 1080*a^14*b^5 + 432*a^16*b^3))/(a^9*b^12) - (8*(378*a^14 + 108*a^4*b^10 - 108*a^6*b^8 - 729*a^8*b^6 + 378*a^10*b^4 - 135*a^12*b^2))/(a^8*b^8) + (3*(-(a + b)*(a - b))^(1/2)*((8*(144*a^2*b^15 - 108*a^4*b^13 + 90*a^6*b^11 - 126*a^8*b^9 + 144*a^12*b^5 - 108*a^14*b^3))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(36*a^4*b^18 - 180*a^6*b^16 + 405*a^8*b^14 - 306*a^10*b^12 + 909*a^12*b^10 - 900*a^14*b^8 + 72*a^16*b^6))/(a^9*b^12) + (3*(-(a + b)*(a - b))^(1/2)*((8*(96*a^6*b^14 - 72*a^8*b^12 + 30*a^10*b^10 - 42*a^12*b^8))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(192*a^6*b^19 - 204*a^8*b^17 + 96*a^10*b^15 - 120*a^12*b^13 + 48*a^14*b^11))/(a^9*b^12) + (3*(-(a + b)*(a - b))^(1/2)*((8*(16*a^10*b^13 - 12*a^12*b^11))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^10*b^18 - 68*a^12*b^16 + 8*a^14*b^14))/(a^9*b^12))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4)))/(2*a^4*b^4) - (3*(-(a + b)*(a - b))^(1/2)*(2*a^4 + 2*b^4 + a^2*b^2)*((8*(378*a^14 + 108*a^4*b^10 - 108*a^6*b^8 - 729*a^8*b^6 + 378*a^10*b^4 - 135*a^12*b^2))/(a^8*b^8) - (8*tan(c/2 + (d*x)/2)*(108*b^19 - 108*a^2*b^17 + 135*a^4*b^15 - 270*a^6*b^13 + 1863*a^8*b^11 - 1836*a^10*b^9 + 864*a^12*b^7 - 1080*a^14*b^5 + 432*a^16*b^3))/(a^9*b^12) + (3*(-(a + b)*(a - b))^(1/2)*((8*(144*a^2*b^15 - 108*a^4*b^13 + 90*a^6*b^11 - 126*a^8*b^9 + 144*a^12*b^5 - 108*a^14*b^3))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(36*a^4*b^18 - 180*a^6*b^16 + 405*a^8*b^14 - 306*a^10*b^12 + 909*a^12*b^10 - 900*a^14*b^8 + 72*a^16*b^6))/(a^9*b^12) - (3*(-(a + b)*(a - b))^(1/2)*((8*(96*a^6*b^14 - 72*a^8*b^12 + 30*a^10*b^10 - 42*a^12*b^8))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(192*a^6*b^19 - 204*a^8*b^17 + 96*a^10*b^15 - 120*a^12*b^13 + 48*a^14*b^11))/(a^9*b^12) - (3*(-(a + b)*(a - b))^(1/2)*((8*(16*a^10*b^13 - 12*a^12*b^11))/(a^8*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^10*b^18 - 68*a^12*b^16 + 8*a^14*b^14))/(a^9*b^12))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4))*(2*a^4 + 2*b^4 + a^2*b^2))/(2*a^4*b^4)))/(2*a^4*b^4)))*(-(a + b)*(a - b))^(1/2)*(2*a^4 + 2*b^4 + a^2*b^2)*3i)/(a^4*b^4*d)","B"
1271,1,4381,395,13.018902,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^3*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{2\,\mathrm{atan}\left(\frac{1800\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{7120\,b^2}{a^2}-\frac{12520\,b^4}{a^4}+\frac{24480\,b^6}{a^6}-\frac{31104\,b^8}{a^8}+\frac{13824\,b^{10}}{a^{10}}-\frac{1120\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{2320\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{4224\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}+\frac{720\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+\frac{2304\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^5}-1800}-\frac{7120\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{24480\,b^4}{a^4}-\frac{1800\,a^2}{b^2}-\frac{12520\,b^2}{a^2}-\frac{31104\,b^6}{a^6}+\frac{13824\,b^8}{a^8}+\frac{2320\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{4224\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{2304\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}-\frac{1120\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+\frac{720\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^5}+7120}+\frac{720\,a}{720\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1800\,b^3}{a^2}+\frac{7120\,b^5}{a^4}-\frac{12520\,b^7}{a^6}+\frac{24480\,b^9}{a^8}-\frac{31104\,b^{11}}{a^{10}}+\frac{13824\,b^{13}}{a^{12}}-\frac{1120\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{2320\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}-\frac{4224\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^5}+\frac{2304\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^7}}-\frac{4224}{\frac{7120\,a}{b}-4224\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{12520\,b}{a}+\frac{24480\,b^3}{a^3}-\frac{1800\,a^3}{b^3}-\frac{31104\,b^5}{a^5}+\frac{13824\,b^7}{a^7}+\frac{2304\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}+\frac{2320\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{1120\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{720\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}+\frac{2320}{2320\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1800\,a}{b}+\frac{7120\,b}{a}-\frac{12520\,b^3}{a^3}+\frac{24480\,b^5}{a^5}-\frac{31104\,b^7}{a^7}+\frac{13824\,b^9}{a^9}-\frac{4224\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}-\frac{1120\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}+\frac{2304\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4}+\frac{720\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}}+\frac{2304\,b^2}{\frac{24480\,b^3}{a}-12520\,a\,b+\frac{7120\,a^3}{b}-\frac{31104\,b^5}{a^3}-\frac{1800\,a^5}{b^3}+\frac{13824\,b^7}{a^5}-4224\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2304\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2320\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{1120\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{720\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}-\frac{1120}{\frac{7120\,b^3}{a^3}-\frac{1800\,b}{a}-1120\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{12520\,b^5}{a^5}+\frac{24480\,b^7}{a^7}-\frac{31104\,b^9}{a^9}+\frac{13824\,b^{11}}{a^{11}}+\frac{2320\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}+\frac{720\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{4224\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4}+\frac{2304\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^6}}-\frac{24480\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{24480\,b^3-12520\,a^2\,b+\frac{7120\,a^4}{b}-\frac{31104\,b^5}{a^2}-\frac{1800\,a^6}{b^3}+\frac{13824\,b^7}{a^4}-4224\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2304\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2320\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{1120\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{720\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}+\frac{31104\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{24480\,a^2\,b^3-31104\,b^5-12520\,a^4\,b+\frac{7120\,a^6}{b}+\frac{13824\,b^7}{a^2}-\frac{1800\,a^8}{b^3}-4224\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2304\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2320\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{1120\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{720\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}-\frac{13824\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{13824\,b^7-12520\,a^6\,b-31104\,a^2\,b^5+24480\,a^4\,b^3+\frac{7120\,a^8}{b}-\frac{1800\,a^{10}}{b^3}-4224\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2304\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2320\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{1120\,a^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{720\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}+\frac{12520\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{7120\,a^2}{b}-4224\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12520\,b+\frac{24480\,b^3}{a^2}-\frac{1800\,a^4}{b^3}-\frac{31104\,b^5}{a^4}+\frac{13824\,b^7}{a^6}+\frac{2304\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{2320\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}-\frac{1120\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^4}+\frac{720\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^6}}\right)}{b^3\,d}-\frac{\frac{a^3}{2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^5+21\,a^3\,b^2-50\,a\,b^4\right)}{b^2}-4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^4+11\,a^2\,b^2-16\,b^4\right)}{b}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(14\,a^4+21\,a^2\,b^2-52\,b^4\right)}{b}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(16\,a^6+73\,a^4\,b^2-24\,a^2\,b^4-112\,b^6\right)}{2\,a\,b^2}}{d\,\left(4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^6+16\,a^4\,b^2\right)+16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,a^2-12\,b^2\right)}{2\,a^5\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-120\,a^{14}\,b^4+484\,a^{12}\,b^6-1361\,a^{10}\,b^8+1658\,a^8\,b^{10}-1565\,a^6\,b^{12}+3060\,a^4\,b^{14}-3888\,a^2\,b^{16}+1728\,b^{18}\right)}{a^{12}\,b^8}-\frac{4\,\left(28\,a^{15}-30\,a^{13}\,b^2+308\,a^{11}\,b^4-94\,a^9\,b^6-528\,a^7\,b^8+288\,a^5\,b^{10}\right)}{a^{12}\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,\left(\frac{4\,\left(-24\,a^{16}\,b^2+32\,a^{14}\,b^4+70\,a^{12}\,b^6-318\,a^{10}\,b^8+920\,a^8\,b^{10}-1824\,a^6\,b^{12}+1152\,a^4\,b^{14}\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^4-200\,a^{15}\,b^6+202\,a^{13}\,b^8-468\,a^{11}\,b^{10}+410\,a^9\,b^{12}-240\,a^7\,b^{14}+288\,a^5\,b^{16}\right)}{a^{12}\,b^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(-28\,a^{15}\,b^6+120\,a^{13}\,b^8-448\,a^{11}\,b^{10}+384\,a^9\,b^{12}\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^8-120\,a^{14}\,b^{10}+484\,a^{12}\,b^{12}-1136\,a^{10}\,b^{14}+768\,a^8\,b^{16}\right)}{a^{12}\,b^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(32\,a^{14}\,b^{10}-24\,a^{16}\,b^8\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^{10}-136\,a^{15}\,b^{12}+128\,a^{13}\,b^{14}\right)}{a^{12}\,b^8}\right)\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)}{a^5\,b^3}\right)\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)}{a^5\,b^3}\right)}{a^5\,b^3}\right)\,1{}\mathrm{i}}{a^5\,b^3}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,\left(\frac{4\,\left(28\,a^{15}-30\,a^{13}\,b^2+308\,a^{11}\,b^4-94\,a^9\,b^6-528\,a^7\,b^8+288\,a^5\,b^{10}\right)}{a^{12}\,b^5}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-120\,a^{14}\,b^4+484\,a^{12}\,b^6-1361\,a^{10}\,b^8+1658\,a^8\,b^{10}-1565\,a^6\,b^{12}+3060\,a^4\,b^{14}-3888\,a^2\,b^{16}+1728\,b^{18}\right)}{a^{12}\,b^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,\left(\frac{4\,\left(-24\,a^{16}\,b^2+32\,a^{14}\,b^4+70\,a^{12}\,b^6-318\,a^{10}\,b^8+920\,a^8\,b^{10}-1824\,a^6\,b^{12}+1152\,a^4\,b^{14}\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^4-200\,a^{15}\,b^6+202\,a^{13}\,b^8-468\,a^{11}\,b^{10}+410\,a^9\,b^{12}-240\,a^7\,b^{14}+288\,a^5\,b^{16}\right)}{a^{12}\,b^8}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(-28\,a^{15}\,b^6+120\,a^{13}\,b^8-448\,a^{11}\,b^{10}+384\,a^9\,b^{12}\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^8-120\,a^{14}\,b^{10}+484\,a^{12}\,b^{12}-1136\,a^{10}\,b^{14}+768\,a^8\,b^{16}\right)}{a^{12}\,b^8}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(32\,a^{14}\,b^{10}-24\,a^{16}\,b^8\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^{10}-136\,a^{15}\,b^{12}+128\,a^{13}\,b^{14}\right)}{a^{12}\,b^8}\right)\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)}{a^5\,b^3}\right)\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)}{a^5\,b^3}\right)}{a^5\,b^3}\right)\,1{}\mathrm{i}}{a^5\,b^3}}{\frac{8\,\left(-70\,a^{12}+93\,a^{10}\,b^2-30\,a^8\,b^4+259\,a^6\,b^6+1908\,a^4\,b^8-3888\,a^2\,b^{10}+1728\,b^{12}\right)}{a^{12}\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{15}+16\,a^{13}\,b^2+328\,a^{11}\,b^4-120\,a^9\,b^6-288\,a^7\,b^8\right)}{a^{12}\,b^8}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-120\,a^{14}\,b^4+484\,a^{12}\,b^6-1361\,a^{10}\,b^8+1658\,a^8\,b^{10}-1565\,a^6\,b^{12}+3060\,a^4\,b^{14}-3888\,a^2\,b^{16}+1728\,b^{18}\right)}{a^{12}\,b^8}-\frac{4\,\left(28\,a^{15}-30\,a^{13}\,b^2+308\,a^{11}\,b^4-94\,a^9\,b^6-528\,a^7\,b^8+288\,a^5\,b^{10}\right)}{a^{12}\,b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,\left(\frac{4\,\left(-24\,a^{16}\,b^2+32\,a^{14}\,b^4+70\,a^{12}\,b^6-318\,a^{10}\,b^8+920\,a^8\,b^{10}-1824\,a^6\,b^{12}+1152\,a^4\,b^{14}\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^4-200\,a^{15}\,b^6+202\,a^{13}\,b^8-468\,a^{11}\,b^{10}+410\,a^9\,b^{12}-240\,a^7\,b^{14}+288\,a^5\,b^{16}\right)}{a^{12}\,b^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(-28\,a^{15}\,b^6+120\,a^{13}\,b^8-448\,a^{11}\,b^{10}+384\,a^9\,b^{12}\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^8-120\,a^{14}\,b^{10}+484\,a^{12}\,b^{12}-1136\,a^{10}\,b^{14}+768\,a^8\,b^{16}\right)}{a^{12}\,b^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(32\,a^{14}\,b^{10}-24\,a^{16}\,b^8\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^{10}-136\,a^{15}\,b^{12}+128\,a^{13}\,b^{14}\right)}{a^{12}\,b^8}\right)\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)}{a^5\,b^3}\right)\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)}{a^5\,b^3}\right)}{a^5\,b^3}\right)}{a^5\,b^3}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,\left(\frac{4\,\left(28\,a^{15}-30\,a^{13}\,b^2+308\,a^{11}\,b^4-94\,a^9\,b^6-528\,a^7\,b^8+288\,a^5\,b^{10}\right)}{a^{12}\,b^5}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-120\,a^{14}\,b^4+484\,a^{12}\,b^6-1361\,a^{10}\,b^8+1658\,a^8\,b^{10}-1565\,a^6\,b^{12}+3060\,a^4\,b^{14}-3888\,a^2\,b^{16}+1728\,b^{18}\right)}{a^{12}\,b^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,\left(\frac{4\,\left(-24\,a^{16}\,b^2+32\,a^{14}\,b^4+70\,a^{12}\,b^6-318\,a^{10}\,b^8+920\,a^8\,b^{10}-1824\,a^6\,b^{12}+1152\,a^4\,b^{14}\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^4-200\,a^{15}\,b^6+202\,a^{13}\,b^8-468\,a^{11}\,b^{10}+410\,a^9\,b^{12}-240\,a^7\,b^{14}+288\,a^5\,b^{16}\right)}{a^{12}\,b^8}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(-28\,a^{15}\,b^6+120\,a^{13}\,b^8-448\,a^{11}\,b^{10}+384\,a^9\,b^{12}\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^8-120\,a^{14}\,b^{10}+484\,a^{12}\,b^{12}-1136\,a^{10}\,b^{14}+768\,a^8\,b^{16}\right)}{a^{12}\,b^8}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{4\,\left(32\,a^{14}\,b^{10}-24\,a^{16}\,b^8\right)}{a^{12}\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^{10}-136\,a^{15}\,b^{12}+128\,a^{13}\,b^{14}\right)}{a^{12}\,b^8}\right)\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)}{a^5\,b^3}\right)\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)}{a^5\,b^3}\right)}{a^5\,b^3}\right)}{a^5\,b^3}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4+\frac{a^2\,b^2}{2}+6\,b^4\right)\,2{}\mathrm{i}}{a^5\,b^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^3*d) + (2*atan((1800*tan(c/2 + (d*x)/2))/((7120*b^2)/a^2 - (12520*b^4)/a^4 + (24480*b^6)/a^6 - (31104*b^8)/a^8 + (13824*b^10)/a^10 - (1120*a*tan(c/2 + (d*x)/2))/b + (2320*b*tan(c/2 + (d*x)/2))/a - (4224*b^3*tan(c/2 + (d*x)/2))/a^3 + (720*a^3*tan(c/2 + (d*x)/2))/b^3 + (2304*b^5*tan(c/2 + (d*x)/2))/a^5 - 1800) - (7120*tan(c/2 + (d*x)/2))/((24480*b^4)/a^4 - (1800*a^2)/b^2 - (12520*b^2)/a^2 - (31104*b^6)/a^6 + (13824*b^8)/a^8 + (2320*a*tan(c/2 + (d*x)/2))/b - (4224*b*tan(c/2 + (d*x)/2))/a + (2304*b^3*tan(c/2 + (d*x)/2))/a^3 - (1120*a^3*tan(c/2 + (d*x)/2))/b^3 + (720*a^5*tan(c/2 + (d*x)/2))/b^5 + 7120) + (720*a)/(720*a*tan(c/2 + (d*x)/2) - (1800*b^3)/a^2 + (7120*b^5)/a^4 - (12520*b^7)/a^6 + (24480*b^9)/a^8 - (31104*b^11)/a^10 + (13824*b^13)/a^12 - (1120*b^2*tan(c/2 + (d*x)/2))/a + (2320*b^4*tan(c/2 + (d*x)/2))/a^3 - (4224*b^6*tan(c/2 + (d*x)/2))/a^5 + (2304*b^8*tan(c/2 + (d*x)/2))/a^7) - 4224/((7120*a)/b - 4224*tan(c/2 + (d*x)/2) - (12520*b)/a + (24480*b^3)/a^3 - (1800*a^3)/b^3 - (31104*b^5)/a^5 + (13824*b^7)/a^7 + (2304*b^2*tan(c/2 + (d*x)/2))/a^2 + (2320*a^2*tan(c/2 + (d*x)/2))/b^2 - (1120*a^4*tan(c/2 + (d*x)/2))/b^4 + (720*a^6*tan(c/2 + (d*x)/2))/b^6) + 2320/(2320*tan(c/2 + (d*x)/2) - (1800*a)/b + (7120*b)/a - (12520*b^3)/a^3 + (24480*b^5)/a^5 - (31104*b^7)/a^7 + (13824*b^9)/a^9 - (4224*b^2*tan(c/2 + (d*x)/2))/a^2 - (1120*a^2*tan(c/2 + (d*x)/2))/b^2 + (2304*b^4*tan(c/2 + (d*x)/2))/a^4 + (720*a^4*tan(c/2 + (d*x)/2))/b^4) + (2304*b^2)/((24480*b^3)/a - 12520*a*b + (7120*a^3)/b - (31104*b^5)/a^3 - (1800*a^5)/b^3 + (13824*b^7)/a^5 - 4224*a^2*tan(c/2 + (d*x)/2) + 2304*b^2*tan(c/2 + (d*x)/2) + (2320*a^4*tan(c/2 + (d*x)/2))/b^2 - (1120*a^6*tan(c/2 + (d*x)/2))/b^4 + (720*a^8*tan(c/2 + (d*x)/2))/b^6) - 1120/((7120*b^3)/a^3 - (1800*b)/a - 1120*tan(c/2 + (d*x)/2) - (12520*b^5)/a^5 + (24480*b^7)/a^7 - (31104*b^9)/a^9 + (13824*b^11)/a^11 + (2320*b^2*tan(c/2 + (d*x)/2))/a^2 + (720*a^2*tan(c/2 + (d*x)/2))/b^2 - (4224*b^4*tan(c/2 + (d*x)/2))/a^4 + (2304*b^6*tan(c/2 + (d*x)/2))/a^6) - (24480*b^3*tan(c/2 + (d*x)/2))/(24480*b^3 - 12520*a^2*b + (7120*a^4)/b - (31104*b^5)/a^2 - (1800*a^6)/b^3 + (13824*b^7)/a^4 - 4224*a^3*tan(c/2 + (d*x)/2) + 2304*a*b^2*tan(c/2 + (d*x)/2) + (2320*a^5*tan(c/2 + (d*x)/2))/b^2 - (1120*a^7*tan(c/2 + (d*x)/2))/b^4 + (720*a^9*tan(c/2 + (d*x)/2))/b^6) + (31104*b^5*tan(c/2 + (d*x)/2))/(24480*a^2*b^3 - 31104*b^5 - 12520*a^4*b + (7120*a^6)/b + (13824*b^7)/a^2 - (1800*a^8)/b^3 - 4224*a^5*tan(c/2 + (d*x)/2) + 2304*a^3*b^2*tan(c/2 + (d*x)/2) + (2320*a^7*tan(c/2 + (d*x)/2))/b^2 - (1120*a^9*tan(c/2 + (d*x)/2))/b^4 + (720*a^11*tan(c/2 + (d*x)/2))/b^6) - (13824*b^7*tan(c/2 + (d*x)/2))/(13824*b^7 - 12520*a^6*b - 31104*a^2*b^5 + 24480*a^4*b^3 + (7120*a^8)/b - (1800*a^10)/b^3 - 4224*a^7*tan(c/2 + (d*x)/2) + 2304*a^5*b^2*tan(c/2 + (d*x)/2) + (2320*a^9*tan(c/2 + (d*x)/2))/b^2 - (1120*a^11*tan(c/2 + (d*x)/2))/b^4 + (720*a^13*tan(c/2 + (d*x)/2))/b^6) + (12520*b*tan(c/2 + (d*x)/2))/((7120*a^2)/b - 4224*a*tan(c/2 + (d*x)/2) - 12520*b + (24480*b^3)/a^2 - (1800*a^4)/b^3 - (31104*b^5)/a^4 + (13824*b^7)/a^6 + (2304*b^2*tan(c/2 + (d*x)/2))/a + (2320*a^3*tan(c/2 + (d*x)/2))/b^2 - (1120*a^5*tan(c/2 + (d*x)/2))/b^4 + (720*a^7*tan(c/2 + (d*x)/2))/b^6)))/(b^3*d) - (a^3/2 + (tan(c/2 + (d*x)/2)^2*(8*a^5 - 50*a*b^4 + 21*a^3*b^2))/b^2 - 4*a^2*b*tan(c/2 + (d*x)/2) + (2*tan(c/2 + (d*x)/2)^5*(2*a^4 - 16*b^4 + 11*a^2*b^2))/b + (2*tan(c/2 + (d*x)/2)^3*(14*a^4 - 52*b^4 + 21*a^2*b^2))/b + (tan(c/2 + (d*x)/2)^4*(16*a^6 - 112*b^6 - 24*a^2*b^4 + 73*a^4*b^2))/(2*a*b^2))/(d*(4*a^6*tan(c/2 + (d*x)/2)^2 + 4*a^6*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^4*(8*a^6 + 16*a^4*b^2) + 16*a^5*b*tan(c/2 + (d*x)/2)^3 + 16*a^5*b*tan(c/2 + (d*x)/2)^5)) - (3*b*tan(c/2 + (d*x)/2))/(2*a^4*d) - (log(tan(c/2 + (d*x)/2))*(5*a^2 - 12*b^2))/(2*a^5*d) - (atan((((-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*((4*tan(c/2 + (d*x)/2)*(1728*b^18 - 3888*a^2*b^16 + 3060*a^4*b^14 - 1565*a^6*b^12 + 1658*a^8*b^10 - 1361*a^10*b^8 + 484*a^12*b^6 - 120*a^14*b^4 + 32*a^16*b^2))/(a^12*b^8) - (4*(28*a^15 + 288*a^5*b^10 - 528*a^7*b^8 - 94*a^9*b^6 + 308*a^11*b^4 - 30*a^13*b^2))/(a^12*b^5) + ((-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*((4*(1152*a^4*b^14 - 1824*a^6*b^12 + 920*a^8*b^10 - 318*a^10*b^8 + 70*a^12*b^6 + 32*a^14*b^4 - 24*a^16*b^2))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(288*a^5*b^16 - 240*a^7*b^14 + 410*a^9*b^12 - 468*a^11*b^10 + 202*a^13*b^8 - 200*a^15*b^6 + 16*a^17*b^4))/(a^12*b^8) + ((-(a + b)*(a - b))^(1/2)*((4*(384*a^9*b^12 - 448*a^11*b^10 + 120*a^13*b^8 - 28*a^15*b^6))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(768*a^8*b^16 - 1136*a^10*b^14 + 484*a^12*b^12 - 120*a^14*b^10 + 32*a^16*b^8))/(a^12*b^8) + ((-(a + b)*(a - b))^(1/2)*((4*(32*a^14*b^10 - 24*a^16*b^8))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^14 - 136*a^15*b^12 + 16*a^17*b^10))/(a^12*b^8))*(a^4 + 6*b^4 + (a^2*b^2)/2))/(a^5*b^3))*(a^4 + 6*b^4 + (a^2*b^2)/2))/(a^5*b^3)))/(a^5*b^3))*1i)/(a^5*b^3) - ((-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*((4*(28*a^15 + 288*a^5*b^10 - 528*a^7*b^8 - 94*a^9*b^6 + 308*a^11*b^4 - 30*a^13*b^2))/(a^12*b^5) - (4*tan(c/2 + (d*x)/2)*(1728*b^18 - 3888*a^2*b^16 + 3060*a^4*b^14 - 1565*a^6*b^12 + 1658*a^8*b^10 - 1361*a^10*b^8 + 484*a^12*b^6 - 120*a^14*b^4 + 32*a^16*b^2))/(a^12*b^8) + ((-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*((4*(1152*a^4*b^14 - 1824*a^6*b^12 + 920*a^8*b^10 - 318*a^10*b^8 + 70*a^12*b^6 + 32*a^14*b^4 - 24*a^16*b^2))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(288*a^5*b^16 - 240*a^7*b^14 + 410*a^9*b^12 - 468*a^11*b^10 + 202*a^13*b^8 - 200*a^15*b^6 + 16*a^17*b^4))/(a^12*b^8) - ((-(a + b)*(a - b))^(1/2)*((4*(384*a^9*b^12 - 448*a^11*b^10 + 120*a^13*b^8 - 28*a^15*b^6))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(768*a^8*b^16 - 1136*a^10*b^14 + 484*a^12*b^12 - 120*a^14*b^10 + 32*a^16*b^8))/(a^12*b^8) - ((-(a + b)*(a - b))^(1/2)*((4*(32*a^14*b^10 - 24*a^16*b^8))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^14 - 136*a^15*b^12 + 16*a^17*b^10))/(a^12*b^8))*(a^4 + 6*b^4 + (a^2*b^2)/2))/(a^5*b^3))*(a^4 + 6*b^4 + (a^2*b^2)/2))/(a^5*b^3)))/(a^5*b^3))*1i)/(a^5*b^3))/((8*(1728*b^12 - 70*a^12 - 3888*a^2*b^10 + 1908*a^4*b^8 + 259*a^6*b^6 - 30*a^8*b^4 + 93*a^10*b^2))/(a^12*b^5) + (8*tan(c/2 + (d*x)/2)*(64*a^15 - 288*a^7*b^8 - 120*a^9*b^6 + 328*a^11*b^4 + 16*a^13*b^2))/(a^12*b^8) - ((-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*((4*tan(c/2 + (d*x)/2)*(1728*b^18 - 3888*a^2*b^16 + 3060*a^4*b^14 - 1565*a^6*b^12 + 1658*a^8*b^10 - 1361*a^10*b^8 + 484*a^12*b^6 - 120*a^14*b^4 + 32*a^16*b^2))/(a^12*b^8) - (4*(28*a^15 + 288*a^5*b^10 - 528*a^7*b^8 - 94*a^9*b^6 + 308*a^11*b^4 - 30*a^13*b^2))/(a^12*b^5) + ((-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*((4*(1152*a^4*b^14 - 1824*a^6*b^12 + 920*a^8*b^10 - 318*a^10*b^8 + 70*a^12*b^6 + 32*a^14*b^4 - 24*a^16*b^2))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(288*a^5*b^16 - 240*a^7*b^14 + 410*a^9*b^12 - 468*a^11*b^10 + 202*a^13*b^8 - 200*a^15*b^6 + 16*a^17*b^4))/(a^12*b^8) + ((-(a + b)*(a - b))^(1/2)*((4*(384*a^9*b^12 - 448*a^11*b^10 + 120*a^13*b^8 - 28*a^15*b^6))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(768*a^8*b^16 - 1136*a^10*b^14 + 484*a^12*b^12 - 120*a^14*b^10 + 32*a^16*b^8))/(a^12*b^8) + ((-(a + b)*(a - b))^(1/2)*((4*(32*a^14*b^10 - 24*a^16*b^8))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^14 - 136*a^15*b^12 + 16*a^17*b^10))/(a^12*b^8))*(a^4 + 6*b^4 + (a^2*b^2)/2))/(a^5*b^3))*(a^4 + 6*b^4 + (a^2*b^2)/2))/(a^5*b^3)))/(a^5*b^3)))/(a^5*b^3) - ((-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*((4*(28*a^15 + 288*a^5*b^10 - 528*a^7*b^8 - 94*a^9*b^6 + 308*a^11*b^4 - 30*a^13*b^2))/(a^12*b^5) - (4*tan(c/2 + (d*x)/2)*(1728*b^18 - 3888*a^2*b^16 + 3060*a^4*b^14 - 1565*a^6*b^12 + 1658*a^8*b^10 - 1361*a^10*b^8 + 484*a^12*b^6 - 120*a^14*b^4 + 32*a^16*b^2))/(a^12*b^8) + ((-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*((4*(1152*a^4*b^14 - 1824*a^6*b^12 + 920*a^8*b^10 - 318*a^10*b^8 + 70*a^12*b^6 + 32*a^14*b^4 - 24*a^16*b^2))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(288*a^5*b^16 - 240*a^7*b^14 + 410*a^9*b^12 - 468*a^11*b^10 + 202*a^13*b^8 - 200*a^15*b^6 + 16*a^17*b^4))/(a^12*b^8) - ((-(a + b)*(a - b))^(1/2)*((4*(384*a^9*b^12 - 448*a^11*b^10 + 120*a^13*b^8 - 28*a^15*b^6))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(768*a^8*b^16 - 1136*a^10*b^14 + 484*a^12*b^12 - 120*a^14*b^10 + 32*a^16*b^8))/(a^12*b^8) - ((-(a + b)*(a - b))^(1/2)*((4*(32*a^14*b^10 - 24*a^16*b^8))/(a^12*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^14 - 136*a^15*b^12 + 16*a^17*b^10))/(a^12*b^8))*(a^4 + 6*b^4 + (a^2*b^2)/2))/(a^5*b^3))*(a^4 + 6*b^4 + (a^2*b^2)/2))/(a^5*b^3)))/(a^5*b^3)))/(a^5*b^3)))*(-(a + b)*(a - b))^(1/2)*(a^4 + 6*b^4 + (a^2*b^2)/2)*2i)/(a^5*b^3*d)","B"
1272,1,1082,329,12.413050,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^4*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{77\,a^4}{3}+200\,a^2\,b^2-304\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^4+64\,a^2\,b^2-80\,b^4\right)-\frac{a^4}{3}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{25\,a^4}{3}-\frac{40\,a^2\,b^2}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(156\,a\,b^3-\frac{338\,a^3\,b}{3}\right)-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-37\,a^4\,b+8\,a^2\,b^3+48\,b^5\right)}{a}+\frac{5\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{d\,\left(8\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(16\,a^7+32\,a^5\,b^2\right)+32\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+32\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{8\,a^5}+\frac{3}{4\,a^3}-\frac{9\,b^2}{2\,a^5}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(15\,a^2\,b-20\,b^3\right)}{2\,a^6\,d}-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{5\,a^{10}-40\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^8\,b-100\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}-\frac{5\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{2\,a^6}\right)\,5{}\mathrm{i}}{2\,a^6}+\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{5\,a^{10}-40\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^8\,b-100\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}+\frac{5\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{2\,a^6}\right)\,5{}\mathrm{i}}{2\,a^6}}{\frac{75\,a^6\,b-475\,a^4\,b^3+800\,a^2\,b^5-400\,b^7}{a^{10}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^6-175\,a^4\,b^2+350\,a^2\,b^4-200\,b^6\right)}{a^9}+\frac{5\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{5\,a^{10}-40\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^8\,b-100\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}-\frac{5\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{2\,a^6}\right)}{2\,a^6}-\frac{5\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{5\,a^{10}-40\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^8\,b-100\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}+\frac{5\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{2\,a^6}\right)}{2\,a^6}}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,5{}\mathrm{i}}{a^6\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^3*d) + (tan(c/2 + (d*x)/2)^4*((77*a^4)/3 - 304*b^4 + 200*a^2*b^2) + tan(c/2 + (d*x)/2)^6*(a^4 - 80*b^4 + 64*a^2*b^2) - a^4/3 + tan(c/2 + (d*x)/2)^2*((25*a^4)/3 - (40*a^2*b^2)/3) - tan(c/2 + (d*x)/2)^3*(156*a*b^3 - (338*a^3*b)/3) - (3*tan(c/2 + (d*x)/2)^5*(48*b^5 - 37*a^4*b + 8*a^2*b^3))/a + (5*a^3*b*tan(c/2 + (d*x)/2))/3)/(d*(8*a^7*tan(c/2 + (d*x)/2)^3 + 8*a^7*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^5*(16*a^7 + 32*a^5*b^2) + 32*a^6*b*tan(c/2 + (d*x)/2)^4 + 32*a^6*b*tan(c/2 + (d*x)/2)^6)) - (tan(c/2 + (d*x)/2)*((3*(a^2 + 4*b^2))/(8*a^5) + 3/(4*a^3) - (9*b^2)/(2*a^5)))/d + (log(tan(c/2 + (d*x)/2))*(15*a^2*b - 20*b^3))/(2*a^6*d) - (3*b*tan(c/2 + (d*x)/2)^2)/(8*a^4*d) + (atan((((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((5*a^10 + 40*a^6*b^4 - 40*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(25*a^8*b + 80*a^4*b^5 - 100*a^6*b^3))/a^9 - (5*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/(2*a^6))*5i)/(2*a^6) + ((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((5*a^10 + 40*a^6*b^4 - 40*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(25*a^8*b + 80*a^4*b^5 - 100*a^6*b^3))/a^9 + (5*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/(2*a^6))*5i)/(2*a^6))/((75*a^6*b - 400*b^7 + 800*a^2*b^5 - 475*a^4*b^3)/a^10 + (2*tan(c/2 + (d*x)/2)*(25*a^6 - 200*b^6 + 350*a^2*b^4 - 175*a^4*b^2))/a^9 + (5*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((5*a^10 + 40*a^6*b^4 - 40*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(25*a^8*b + 80*a^4*b^5 - 100*a^6*b^3))/a^9 - (5*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/(2*a^6)))/(2*a^6) - (5*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((5*a^10 + 40*a^6*b^4 - 40*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(25*a^8*b + 80*a^4*b^5 - 100*a^6*b^3))/a^9 + (5*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/(2*a^6)))/(2*a^6)))*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*5i)/(a^6*d)","B"
1273,1,1275,355,12.553759,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^5*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(35\,a^4\,b-40\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{159\,a^5}{4}-424\,a^3\,b^2+448\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,a^4\,b+160\,a^2\,b^3-192\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(10\,a^4\,b+696\,a^2\,b^3-832\,b^5\right)+\frac{a^5}{4}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{7\,a^5}{2}-5\,a^3\,b^2\right)-a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(9\,a^6-93\,a^4\,b^2+20\,a^2\,b^4+88\,b^6\right)}{a}}{d\,\left(16\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+16\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(32\,a^8+64\,a^6\,b^2\right)+64\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+64\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{5}{32\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{16\,a^5}+\frac{5}{16\,a^3}-\frac{9\,b^2}{4\,a^5}\right)}{a}-\frac{192\,a^2\,b+128\,b^3}{256\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{8\,a^6}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^4\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{15\,a^4}{8}-15\,a^2\,b^2+15\,b^4\right)}{a^7\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)\,\left(\frac{\frac{75\,a^{11}\,b}{4}-75\,a^9\,b^3+60\,a^7\,b^5}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{11}-270\,a^9\,b^2+720\,a^7\,b^4-480\,a^5\,b^6\right)}{4\,a^{11}}+\frac{15\,b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}-32\,a^{12}\,b^2\right)}{4\,a^{11}}\right)\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)}{2\,a^7}\right)\,15{}\mathrm{i}}{2\,a^7}-\frac{b\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{11}-270\,a^9\,b^2+720\,a^7\,b^4-480\,a^5\,b^6\right)}{4\,a^{11}}-\frac{\frac{75\,a^{11}\,b}{4}-75\,a^9\,b^3+60\,a^7\,b^5}{a^{12}}+\frac{15\,b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}-32\,a^{12}\,b^2\right)}{4\,a^{11}}\right)\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)}{2\,a^7}\right)\,15{}\mathrm{i}}{2\,a^7}}{\frac{\frac{225\,a^8\,b}{4}-\frac{2475\,a^6\,b^3}{4}+\frac{3825\,a^4\,b^5}{2}-2250\,a^2\,b^7+900\,b^9}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-675\,a^6\,b^2+2925\,a^4\,b^4-4050\,a^2\,b^6+1800\,b^8\right)}{2\,a^{11}}+\frac{15\,b\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)\,\left(\frac{\frac{75\,a^{11}\,b}{4}-75\,a^9\,b^3+60\,a^7\,b^5}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{11}-270\,a^9\,b^2+720\,a^7\,b^4-480\,a^5\,b^6\right)}{4\,a^{11}}+\frac{15\,b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}-32\,a^{12}\,b^2\right)}{4\,a^{11}}\right)\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)}{2\,a^7}\right)}{2\,a^7}+\frac{15\,b\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{11}-270\,a^9\,b^2+720\,a^7\,b^4-480\,a^5\,b^6\right)}{4\,a^{11}}-\frac{\frac{75\,a^{11}\,b}{4}-75\,a^9\,b^3+60\,a^7\,b^5}{a^{12}}+\frac{15\,b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}-32\,a^{12}\,b^2\right)}{4\,a^{11}}\right)\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)}{2\,a^7}\right)}{2\,a^7}}\right)\,\sqrt{b^2-a^2}\,\left(a^2-2\,b^2\right)\,15{}\mathrm{i}}{a^7\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a^3*d) - (tan(c/2 + (d*x)/2)^3*(35*a^4*b - 40*a^2*b^3) - tan(c/2 + (d*x)/2)^4*(448*a*b^4 + (159*a^5)/4 - 424*a^3*b^2) + tan(c/2 + (d*x)/2)^7*(6*a^4*b - 192*b^5 + 160*a^2*b^3) + tan(c/2 + (d*x)/2)^5*(10*a^4*b - 832*b^5 + 696*a^2*b^3) + a^5/4 - tan(c/2 + (d*x)/2)^2*((7*a^5)/2 - 5*a^3*b^2) - a^4*b*tan(c/2 + (d*x)/2) - (4*tan(c/2 + (d*x)/2)^6*(9*a^6 + 88*b^6 + 20*a^2*b^4 - 93*a^4*b^2))/a)/(d*(16*a^8*tan(c/2 + (d*x)/2)^4 + 16*a^8*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^6*(32*a^8 + 64*a^6*b^2) + 64*a^7*b*tan(c/2 + (d*x)/2)^5 + 64*a^7*b*tan(c/2 + (d*x)/2)^7)) - (tan(c/2 + (d*x)/2)^2*((3*(a^2 + 4*b^2))/(32*a^5) + 5/(32*a^3) - (9*b^2)/(8*a^5)))/d + (tan(c/2 + (d*x)/2)*((6*b*((3*(a^2 + 4*b^2))/(16*a^5) + 5/(16*a^3) - (9*b^2)/(4*a^5)))/a - (192*a^2*b + 128*b^3)/(256*a^6) + (9*b*(a^2 + 4*b^2))/(8*a^6)))/d - (b*tan(c/2 + (d*x)/2)^3)/(8*a^4*d) + (log(tan(c/2 + (d*x)/2))*((15*a^4)/8 + 15*b^4 - 15*a^2*b^2))/(a^7*d) + (b*atan(((b*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2)*(((75*a^11*b)/4 + 60*a^7*b^5 - 75*a^9*b^3)/a^12 - (tan(c/2 + (d*x)/2)*(15*a^11 - 480*a^5*b^6 + 720*a^7*b^4 - 270*a^9*b^2))/(4*a^11) + (15*b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^14 - 32*a^12*b^2))/(4*a^11))*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2))/(2*a^7))*15i)/(2*a^7) - (b*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2)*((tan(c/2 + (d*x)/2)*(15*a^11 - 480*a^5*b^6 + 720*a^7*b^4 - 270*a^9*b^2))/(4*a^11) - ((75*a^11*b)/4 + 60*a^7*b^5 - 75*a^9*b^3)/a^12 + (15*b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^14 - 32*a^12*b^2))/(4*a^11))*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2))/(2*a^7))*15i)/(2*a^7))/(((225*a^8*b)/4 + 900*b^9 - 2250*a^2*b^7 + (3825*a^4*b^5)/2 - (2475*a^6*b^3)/4)/a^12 + (tan(c/2 + (d*x)/2)*(1800*b^8 - 4050*a^2*b^6 + 2925*a^4*b^4 - 675*a^6*b^2))/(2*a^11) + (15*b*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2)*(((75*a^11*b)/4 + 60*a^7*b^5 - 75*a^9*b^3)/a^12 - (tan(c/2 + (d*x)/2)*(15*a^11 - 480*a^5*b^6 + 720*a^7*b^4 - 270*a^9*b^2))/(4*a^11) + (15*b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^14 - 32*a^12*b^2))/(4*a^11))*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2))/(2*a^7)))/(2*a^7) + (15*b*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2)*((tan(c/2 + (d*x)/2)*(15*a^11 - 480*a^5*b^6 + 720*a^7*b^4 - 270*a^9*b^2))/(4*a^11) - ((75*a^11*b)/4 + 60*a^7*b^5 - 75*a^9*b^3)/a^12 + (15*b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^14 - 32*a^12*b^2))/(4*a^11))*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2))/(2*a^7)))/(2*a^7)))*(b^2 - a^2)^(1/2)*(a^2 - 2*b^2)*15i)/(a^7*d)","B"
1274,1,1614,492,12.625688,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^6*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2+4\,b^2}{32\,a^5}+\frac{1}{24\,a^3}-\frac{3\,b^2}{8\,a^5}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1}{8\,a^3}-\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}-\frac{6\,b\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{1}{8\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{a}-\frac{384\,a^2\,b+256\,b^3}{1024\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{16\,a^6}\right)}{a}+\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{1}{8\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{a^2}+\frac{3\,b\,\left(384\,a^2\,b+256\,b^3\right)}{512\,a^7}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{187\,a^5\,b}{15}-14\,a^3\,b^3\right)+\frac{a^6}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{263\,a^6}{15}-\frac{358\,a^4\,b^2}{3}+112\,a^2\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{1519\,a^5\,b}{6}-1360\,a^3\,b^3+1216\,a\,b^5\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{29\,a^6}{15}-\frac{14\,a^4\,b^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(22\,a^6-56\,a^4\,b^2-368\,a^2\,b^4+448\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{125\,a^6}{3}+112\,a^4\,b^2-2112\,a^2\,b^4+2176\,b^6\right)+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(30\,a^6\,b-149\,a^4\,b^3+36\,a^2\,b^5+104\,b^7\right)}{a}-\frac{7\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{10}}{d\,\left(32\,a^9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+32\,a^9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(64\,a^9+128\,a^7\,b^2\right)+128\,a^8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+128\,a^8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{1}{8\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{a}-\frac{384\,a^2\,b+256\,b^3}{2048\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{32\,a^6}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(45\,a^4\,b-200\,a^2\,b^3+168\,b^5\right)}{8\,a^8\,d}-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,\left(\frac{2\,a^{14}-\frac{169\,a^{12}\,b^2}{4}+121\,a^{10}\,b^4-84\,a^8\,b^6}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(61\,a^{12}\,b-538\,a^{10}\,b^3+1136\,a^8\,b^5-672\,a^6\,b^7\right)}{4\,a^{13}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{16}-32\,a^{14}\,b^2\right)}{4\,a^{13}}\right)\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)}{a^8}\right)\,1{}\mathrm{i}}{a^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,\left(\frac{2\,a^{14}-\frac{169\,a^{12}\,b^2}{4}+121\,a^{10}\,b^4-84\,a^8\,b^6}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(61\,a^{12}\,b-538\,a^{10}\,b^3+1136\,a^8\,b^5-672\,a^6\,b^7\right)}{4\,a^{13}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{16}-32\,a^{14}\,b^2\right)}{4\,a^{13}}\right)\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)}{a^8}\right)\,1{}\mathrm{i}}{a^8}}{\frac{\frac{45\,a^{10}\,b}{2}-\frac{1795\,a^8\,b^3}{4}+\frac{9731\,a^6\,b^5}{4}-\frac{10649\,a^4\,b^7}{2}+5082\,a^2\,b^9-1764\,b^{11}}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}-406\,a^8\,b^2+3185\,a^6\,b^4-8549\,a^4\,b^6+9282\,a^2\,b^8-3528\,b^{10}\right)}{2\,a^{13}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,\left(\frac{2\,a^{14}-\frac{169\,a^{12}\,b^2}{4}+121\,a^{10}\,b^4-84\,a^8\,b^6}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(61\,a^{12}\,b-538\,a^{10}\,b^3+1136\,a^8\,b^5-672\,a^6\,b^7\right)}{4\,a^{13}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{16}-32\,a^{14}\,b^2\right)}{4\,a^{13}}\right)\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)}{a^8}\right)}{a^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,\left(\frac{2\,a^{14}-\frac{169\,a^{12}\,b^2}{4}+121\,a^{10}\,b^4-84\,a^8\,b^6}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(61\,a^{12}\,b-538\,a^{10}\,b^3+1136\,a^8\,b^5-672\,a^6\,b^7\right)}{4\,a^{13}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{16}-32\,a^{14}\,b^2\right)}{4\,a^{13}}\right)\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)}{a^8}\right)}{a^8}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,2{}\mathrm{i}}{a^8\,d}","Not used",1,"tan(c/2 + (d*x)/2)^5/(160*a^3*d) - (tan(c/2 + (d*x)/2)^3*((a^2 + 4*b^2)/(32*a^5) + 1/(24*a^3) - (3*b^2)/(8*a^5)))/d + (tan(c/2 + (d*x)/2)*(1/(8*a^3) - (3*(a^2 + 4*b^2))/(32*a^5) - (6*b*((6*b*((3*(a^2 + 4*b^2))/(32*a^5) + 1/(8*a^3) - (9*b^2)/(8*a^5)))/a - (384*a^2*b + 256*b^3)/(1024*a^6) + (9*b*(a^2 + 4*b^2))/(16*a^6)))/a + (3*(a^2 + 4*b^2)*((3*(a^2 + 4*b^2))/(32*a^5) + 1/(8*a^3) - (9*b^2)/(8*a^5)))/a^2 + (3*b*(384*a^2*b + 256*b^3))/(512*a^7)))/d - (tan(c/2 + (d*x)/2)^3*((187*a^5*b)/15 - 14*a^3*b^3) + a^6/5 + tan(c/2 + (d*x)/2)^4*((263*a^6)/15 + 112*a^2*b^4 - (358*a^4*b^2)/3) + tan(c/2 + (d*x)/2)^5*(1216*a*b^5 + (1519*a^5*b)/6 - 1360*a^3*b^3) - tan(c/2 + (d*x)/2)^2*((29*a^6)/15 - (14*a^4*b^2)/5) + tan(c/2 + (d*x)/2)^8*(22*a^6 + 448*b^6 - 368*a^2*b^4 - 56*a^4*b^2) + tan(c/2 + (d*x)/2)^6*((125*a^6)/3 + 2176*b^6 - 2112*a^2*b^4 + 112*a^4*b^2) + (8*tan(c/2 + (d*x)/2)^7*(30*a^6*b + 104*b^7 + 36*a^2*b^5 - 149*a^4*b^3))/a - (7*a^5*b*tan(c/2 + (d*x)/2))/10)/(d*(32*a^9*tan(c/2 + (d*x)/2)^5 + 32*a^9*tan(c/2 + (d*x)/2)^9 + tan(c/2 + (d*x)/2)^7*(64*a^9 + 128*a^7*b^2) + 128*a^8*b*tan(c/2 + (d*x)/2)^6 + 128*a^8*b*tan(c/2 + (d*x)/2)^8)) + (tan(c/2 + (d*x)/2)^2*((3*b*((3*(a^2 + 4*b^2))/(32*a^5) + 1/(8*a^3) - (9*b^2)/(8*a^5)))/a - (384*a^2*b + 256*b^3)/(2048*a^6) + (9*b*(a^2 + 4*b^2))/(32*a^6)))/d - (log(tan(c/2 + (d*x)/2))*(45*a^4*b + 168*b^5 - 200*a^2*b^3))/(8*a^8*d) - (3*b*tan(c/2 + (d*x)/2)^4)/(64*a^4*d) - (atan((((-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*((2*a^14 - 84*a^8*b^6 + 121*a^10*b^4 - (169*a^12*b^2)/4)/a^14 + (tan(c/2 + (d*x)/2)*(61*a^12*b - 672*a^6*b^7 + 1136*a^8*b^5 - 538*a^10*b^3))/(4*a^13) + ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^16 - 32*a^14*b^2))/(4*a^13))*(a^4 + 21*b^4 - (29*a^2*b^2)/2))/a^8)*1i)/a^8 + ((-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*((2*a^14 - 84*a^8*b^6 + 121*a^10*b^4 - (169*a^12*b^2)/4)/a^14 + (tan(c/2 + (d*x)/2)*(61*a^12*b - 672*a^6*b^7 + 1136*a^8*b^5 - 538*a^10*b^3))/(4*a^13) - ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^16 - 32*a^14*b^2))/(4*a^13))*(a^4 + 21*b^4 - (29*a^2*b^2)/2))/a^8)*1i)/a^8)/(((45*a^10*b)/2 - 1764*b^11 + 5082*a^2*b^9 - (10649*a^4*b^7)/2 + (9731*a^6*b^5)/4 - (1795*a^8*b^3)/4)/a^14 + (tan(c/2 + (d*x)/2)*(16*a^10 - 3528*b^10 + 9282*a^2*b^8 - 8549*a^4*b^6 + 3185*a^6*b^4 - 406*a^8*b^2))/(2*a^13) - ((-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*((2*a^14 - 84*a^8*b^6 + 121*a^10*b^4 - (169*a^12*b^2)/4)/a^14 + (tan(c/2 + (d*x)/2)*(61*a^12*b - 672*a^6*b^7 + 1136*a^8*b^5 - 538*a^10*b^3))/(4*a^13) + ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^16 - 32*a^14*b^2))/(4*a^13))*(a^4 + 21*b^4 - (29*a^2*b^2)/2))/a^8))/a^8 + ((-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*((2*a^14 - 84*a^8*b^6 + 121*a^10*b^4 - (169*a^12*b^2)/4)/a^14 + (tan(c/2 + (d*x)/2)*(61*a^12*b - 672*a^6*b^7 + 1136*a^8*b^5 - 538*a^10*b^3))/(4*a^13) - ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^16 - 32*a^14*b^2))/(4*a^13))*(a^4 + 21*b^4 - (29*a^2*b^2)/2))/a^8))/a^8))*(-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*2i)/(a^8*d)","B"
1275,1,2795,600,13.286281,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^8*(a + b*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7}{128\,a^3}+\frac{9\,b^2}{32\,a^5}-\frac{6\,b\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{3}{128\,a^3}+\frac{6\,b\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a}-\frac{1536\,a^2\,b+1024\,b^3}{16384\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{64\,a^6}\right)}{a}-\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a^2}-\frac{3\,b\,\left(1536\,a^2\,b+1024\,b^3\right)}{8192\,a^7}\right)}{a}-\frac{3\,b}{64\,a^4}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{64\,a^6}+\frac{\left(1536\,a^2\,b+1024\,b^3\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{128\,a^3}-\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a}-\frac{1536\,a^2\,b+1024\,b^3}{16384\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{64\,a^6}\right)}{a^2}\right)}{a}+\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a^2}-\frac{\left(1536\,a^2\,b+1024\,b^3\right)\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a}-\frac{1536\,a^2\,b+1024\,b^3}{16384\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{64\,a^6}\right)}{128\,a^3}+\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{3}{128\,a^3}+\frac{6\,b\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a}-\frac{1536\,a^2\,b+1024\,b^3}{16384\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{64\,a^6}\right)}{a}-\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a^2}-\frac{3\,b\,\left(1536\,a^2\,b+1024\,b^3\right)}{8192\,a^7}\right)}{a^2}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{640\,a^5}+\frac{1}{320\,a^3}-\frac{9\,b^2}{160\,a^5}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{3}{128\,a^3}+\frac{6\,b\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a}-\frac{1536\,a^2\,b+1024\,b^3}{16384\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{64\,a^6}\right)}{a}-\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a^2}-\frac{3\,b\,\left(1536\,a^2\,b+1024\,b^3\right)}{8192\,a^7}\right)}{a}-\frac{3\,b}{128\,a^4}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{128\,a^6}+\frac{\left(1536\,a^2\,b+1024\,b^3\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{256\,a^3}-\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a}-\frac{1536\,a^2\,b+1024\,b^3}{16384\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{64\,a^6}\right)}{2\,a^2}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{3\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{2\,a}-\frac{1536\,a^2\,b+1024\,b^3}{65536\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{256\,a^6}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2+4\,b^2}{128\,a^5}+\frac{1}{128\,a^3}+\frac{2\,b\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a}-\frac{1536\,a^2\,b+1024\,b^3}{16384\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{64\,a^6}\right)}{a}-\frac{\left(a^2+4\,b^2\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{128\,a^5}+\frac{1}{64\,a^3}-\frac{9\,b^2}{32\,a^5}\right)}{a^2}-\frac{b\,\left(1536\,a^2\,b+1024\,b^3\right)}{8192\,a^7}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{25\,a^7\,b}{7}-\frac{24\,a^5\,b^3}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(20\,a^7\,b-\frac{556\,a^5\,b^3}{5}+96\,a^3\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{1444\,a^6\,b^2}{5}-1024\,a^4\,b^4+768\,a^2\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-89\,a^7\,b+3352\,a^5\,b^3-10912\,a^3\,b^5+8000\,a\,b^7\right)+\frac{a^8}{7}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{8\,a^8}{7}-\frac{92\,a^6\,b^2}{5}+\frac{96\,a^4\,b^4}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(5\,a^8-528\,a^6\,b^2+1008\,a^4\,b^4+1664\,a^2\,b^6-2304\,b^8\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-7\,a^8+800\,a^6\,b^2+2096\,a^4\,b^4-15744\,a^2\,b^6+13568\,b^8\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{5\,a^8}{7}-\frac{48\,a^6\,b^2}{35}\right)-\frac{3\,a^7\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-65\,a^8\,b+3456\,a^6\,b^3-10128\,a^4\,b^5+2944\,a^2\,b^7+4352\,b^9\right)}{a}}{d\,\left(128\,a^{11}\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+128\,a^{11}\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(256\,a^{11}+512\,a^9\,b^2\right)+512\,a^{10}\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+512\,a^{10}\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\right)}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128\,a^4\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(15\,a^6\,b-300\,a^4\,b^3+840\,a^2\,b^5-576\,b^7\right)}{16\,a^{10}\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)\,\left(\frac{-222\,a^{16}\,b^2+1896\,a^{14}\,b^4-3936\,a^{12}\,b^6+2304\,a^{10}\,b^8}{16\,a^{18}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{16}\,b-522\,a^{14}\,b^3+2736\,a^{12}\,b^5-4512\,a^{10}\,b^7+2304\,a^8\,b^9\right)}{8\,a^{17}}-\frac{3\,b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{20}-64\,a^{18}\,b^2\right)}{8\,a^{17}}\right)\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)}{2\,a^{10}}\right)\,3{}\mathrm{i}}{2\,a^{10}}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)\,\left(\frac{-222\,a^{16}\,b^2+1896\,a^{14}\,b^4-3936\,a^{12}\,b^6+2304\,a^{10}\,b^8}{16\,a^{18}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{16}\,b-522\,a^{14}\,b^3+2736\,a^{12}\,b^5-4512\,a^{10}\,b^7+2304\,a^8\,b^9\right)}{8\,a^{17}}+\frac{3\,b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{20}-64\,a^{18}\,b^2\right)}{8\,a^{17}}\right)\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)}{2\,a^{10}}\right)\,3{}\mathrm{i}}{2\,a^{10}}}{\frac{180\,a^{12}\,b^3-4815\,a^{10}\,b^5+36495\,a^8\,b^7-118332\,a^6\,b^9+186696\,a^4\,b^{11}-141696\,a^2\,b^{13}+41472\,b^{15}}{8\,a^{18}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-972\,a^{10}\,b^4+10737\,a^8\,b^6-43065\,a^6\,b^8+78228\,a^4\,b^{10}-65664\,a^2\,b^{12}+20736\,b^{14}\right)}{4\,a^{17}}-\frac{3\,b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)\,\left(\frac{-222\,a^{16}\,b^2+1896\,a^{14}\,b^4-3936\,a^{12}\,b^6+2304\,a^{10}\,b^8}{16\,a^{18}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{16}\,b-522\,a^{14}\,b^3+2736\,a^{12}\,b^5-4512\,a^{10}\,b^7+2304\,a^8\,b^9\right)}{8\,a^{17}}-\frac{3\,b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{20}-64\,a^{18}\,b^2\right)}{8\,a^{17}}\right)\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)}{2\,a^{10}}\right)}{2\,a^{10}}+\frac{3\,b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)\,\left(\frac{-222\,a^{16}\,b^2+1896\,a^{14}\,b^4-3936\,a^{12}\,b^6+2304\,a^{10}\,b^8}{16\,a^{18}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^{16}\,b-522\,a^{14}\,b^3+2736\,a^{12}\,b^5-4512\,a^{10}\,b^7+2304\,a^8\,b^9\right)}{8\,a^{17}}+\frac{3\,b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{20}-64\,a^{18}\,b^2\right)}{8\,a^{17}}\right)\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)}{2\,a^{10}}\right)}{2\,a^{10}}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^4-23\,a^2\,b^2+24\,b^4\right)\,3{}\mathrm{i}}{a^{10}\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(7/(128*a^3) + (9*b^2)/(32*a^5) - (6*b*((6*b*((3*(a^2 + 4*b^2))/(128*a^5) + 3/(128*a^3) + (6*b*((6*b*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a - (1536*a^2*b + 1024*b^3)/(16384*a^6) + (9*b*(a^2 + 4*b^2))/(64*a^6)))/a - (3*(a^2 + 4*b^2)*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a^2 - (3*b*(1536*a^2*b + 1024*b^3))/(8192*a^7)))/a - (3*b)/(64*a^4) + (9*b*(a^2 + 4*b^2))/(64*a^6) + ((1536*a^2*b + 1024*b^3)*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/(128*a^3) - (3*(a^2 + 4*b^2)*((6*b*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a - (1536*a^2*b + 1024*b^3)/(16384*a^6) + (9*b*(a^2 + 4*b^2))/(64*a^6)))/a^2))/a + (3*(a^2 + 4*b^2)*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a^2 - ((1536*a^2*b + 1024*b^3)*((6*b*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a - (1536*a^2*b + 1024*b^3)/(16384*a^6) + (9*b*(a^2 + 4*b^2))/(64*a^6)))/(128*a^3) + (3*(a^2 + 4*b^2)*((3*(a^2 + 4*b^2))/(128*a^5) + 3/(128*a^3) + (6*b*((6*b*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a - (1536*a^2*b + 1024*b^3)/(16384*a^6) + (9*b*(a^2 + 4*b^2))/(64*a^6)))/a - (3*(a^2 + 4*b^2)*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a^2 - (3*b*(1536*a^2*b + 1024*b^3))/(8192*a^7)))/a^2))/d + tan(c/2 + (d*x)/2)^7/(896*a^3*d) - (tan(c/2 + (d*x)/2)^5*((3*(a^2 + 4*b^2))/(640*a^5) + 1/(320*a^3) - (9*b^2)/(160*a^5)))/d + (tan(c/2 + (d*x)/2)^2*((3*b*((3*(a^2 + 4*b^2))/(128*a^5) + 3/(128*a^3) + (6*b*((6*b*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a - (1536*a^2*b + 1024*b^3)/(16384*a^6) + (9*b*(a^2 + 4*b^2))/(64*a^6)))/a - (3*(a^2 + 4*b^2)*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a^2 - (3*b*(1536*a^2*b + 1024*b^3))/(8192*a^7)))/a - (3*b)/(128*a^4) + (9*b*(a^2 + 4*b^2))/(128*a^6) + ((1536*a^2*b + 1024*b^3)*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/(256*a^3) - (3*(a^2 + 4*b^2)*((6*b*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a - (1536*a^2*b + 1024*b^3)/(16384*a^6) + (9*b*(a^2 + 4*b^2))/(64*a^6)))/(2*a^2)))/d + (tan(c/2 + (d*x)/2)^4*((3*b*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/(2*a) - (1536*a^2*b + 1024*b^3)/(65536*a^6) + (9*b*(a^2 + 4*b^2))/(256*a^6)))/d - (tan(c/2 + (d*x)/2)^3*((a^2 + 4*b^2)/(128*a^5) + 1/(128*a^3) + (2*b*((6*b*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a - (1536*a^2*b + 1024*b^3)/(16384*a^6) + (9*b*(a^2 + 4*b^2))/(64*a^6)))/a - ((a^2 + 4*b^2)*((3*(a^2 + 4*b^2))/(128*a^5) + 1/(64*a^3) - (9*b^2)/(32*a^5)))/a^2 - (b*(1536*a^2*b + 1024*b^3))/(8192*a^7)))/d - (tan(c/2 + (d*x)/2)^3*((25*a^7*b)/7 - (24*a^5*b^3)/5) - tan(c/2 + (d*x)/2)^5*(20*a^7*b + 96*a^3*b^5 - (556*a^5*b^3)/5) + tan(c/2 + (d*x)/2)^6*(768*a^2*b^6 - 1024*a^4*b^4 + (1444*a^6*b^2)/5) + tan(c/2 + (d*x)/2)^7*(8000*a*b^7 - 89*a^7*b - 10912*a^3*b^5 + 3352*a^5*b^3) + a^8/7 + tan(c/2 + (d*x)/2)^4*((8*a^8)/7 + (96*a^4*b^4)/5 - (92*a^6*b^2)/5) - tan(c/2 + (d*x)/2)^10*(5*a^8 - 2304*b^8 + 1664*a^2*b^6 + 1008*a^4*b^4 - 528*a^6*b^2) + tan(c/2 + (d*x)/2)^8*(13568*b^8 - 7*a^8 - 15744*a^2*b^6 + 2096*a^4*b^4 + 800*a^6*b^2) - tan(c/2 + (d*x)/2)^2*((5*a^8)/7 - (48*a^6*b^2)/35) - (3*a^7*b*tan(c/2 + (d*x)/2))/7 + (tan(c/2 + (d*x)/2)^9*(4352*b^9 - 65*a^8*b + 2944*a^2*b^7 - 10128*a^4*b^5 + 3456*a^6*b^3))/a)/(d*(128*a^11*tan(c/2 + (d*x)/2)^7 + 128*a^11*tan(c/2 + (d*x)/2)^11 + tan(c/2 + (d*x)/2)^9*(256*a^11 + 512*a^9*b^2) + 512*a^10*b*tan(c/2 + (d*x)/2)^8 + 512*a^10*b*tan(c/2 + (d*x)/2)^10)) - (b*tan(c/2 + (d*x)/2)^6)/(128*a^4*d) + (log(tan(c/2 + (d*x)/2))*(15*a^6*b - 576*b^7 + 840*a^2*b^5 - 300*a^4*b^3))/(16*a^10*d) - (b^2*atan(((b^2*(-(a + b)*(a - b))^(1/2)*(4*a^4 + 24*b^4 - 23*a^2*b^2)*((2304*a^10*b^8 - 3936*a^12*b^6 + 1896*a^14*b^4 - 222*a^16*b^2)/(16*a^18) + (tan(c/2 + (d*x)/2)*(15*a^16*b + 2304*a^8*b^9 - 4512*a^10*b^7 + 2736*a^12*b^5 - 522*a^14*b^3))/(8*a^17) - (3*b^2*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^20 - 64*a^18*b^2))/(8*a^17))*(4*a^4 + 24*b^4 - 23*a^2*b^2))/(2*a^10))*3i)/(2*a^10) + (b^2*(-(a + b)*(a - b))^(1/2)*(4*a^4 + 24*b^4 - 23*a^2*b^2)*((2304*a^10*b^8 - 3936*a^12*b^6 + 1896*a^14*b^4 - 222*a^16*b^2)/(16*a^18) + (tan(c/2 + (d*x)/2)*(15*a^16*b + 2304*a^8*b^9 - 4512*a^10*b^7 + 2736*a^12*b^5 - 522*a^14*b^3))/(8*a^17) + (3*b^2*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^20 - 64*a^18*b^2))/(8*a^17))*(4*a^4 + 24*b^4 - 23*a^2*b^2))/(2*a^10))*3i)/(2*a^10))/((41472*b^15 - 141696*a^2*b^13 + 186696*a^4*b^11 - 118332*a^6*b^9 + 36495*a^8*b^7 - 4815*a^10*b^5 + 180*a^12*b^3)/(8*a^18) + (tan(c/2 + (d*x)/2)*(20736*b^14 - 65664*a^2*b^12 + 78228*a^4*b^10 - 43065*a^6*b^8 + 10737*a^8*b^6 - 972*a^10*b^4))/(4*a^17) - (3*b^2*(-(a + b)*(a - b))^(1/2)*(4*a^4 + 24*b^4 - 23*a^2*b^2)*((2304*a^10*b^8 - 3936*a^12*b^6 + 1896*a^14*b^4 - 222*a^16*b^2)/(16*a^18) + (tan(c/2 + (d*x)/2)*(15*a^16*b + 2304*a^8*b^9 - 4512*a^10*b^7 + 2736*a^12*b^5 - 522*a^14*b^3))/(8*a^17) - (3*b^2*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^20 - 64*a^18*b^2))/(8*a^17))*(4*a^4 + 24*b^4 - 23*a^2*b^2))/(2*a^10)))/(2*a^10) + (3*b^2*(-(a + b)*(a - b))^(1/2)*(4*a^4 + 24*b^4 - 23*a^2*b^2)*((2304*a^10*b^8 - 3936*a^12*b^6 + 1896*a^14*b^4 - 222*a^16*b^2)/(16*a^18) + (tan(c/2 + (d*x)/2)*(15*a^16*b + 2304*a^8*b^9 - 4512*a^10*b^7 + 2736*a^12*b^5 - 522*a^14*b^3))/(8*a^17) + (3*b^2*(-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^20 - 64*a^18*b^2))/(8*a^17))*(4*a^4 + 24*b^4 - 23*a^2*b^2))/(2*a^10)))/(2*a^10)))*(-(a + b)*(a - b))^(1/2)*(4*a^4 + 24*b^4 - 23*a^2*b^2)*3i)/(a^10*d)","B"
1276,0,-1,712,0.000000,"\text{Not used}","int(cos(e + f*x)^6/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(13/2)),x)","\int \frac{{\cos\left(e+f\,x\right)}^6}{\sqrt{d\,\sin\left(e+f\,x\right)}\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{13/2}} \,d x","Not used",1,"int(cos(e + f*x)^6/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(13/2)), x)","F"
1277,0,-1,159,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2/((g*cos(e + f*x))^(5/2)*(d*sin(e + f*x))^(1/2)),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2/((g*cos(e + f*x))^(5/2)*(d*sin(e + f*x))^(1/2)), x)","F"
1278,0,-1,193,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2/((g*cos(e + f*x))^(7/2)*(d*sin(e + f*x))^(1/2)),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{7/2}\,\sqrt{d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2/((g*cos(e + f*x))^(7/2)*(d*sin(e + f*x))^(1/2)), x)","F"
1279,1,64,76,0.067559,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^3)/(a + b*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^3}{3\,b}-\frac{a^3\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{b^4}-\frac{a\,{\sin\left(c+d\,x\right)}^2}{2\,b^2}+\frac{a^2\,\sin\left(c+d\,x\right)}{b^3}}{d}","Not used",1,"(sin(c + d*x)^3/(3*b) - (a^3*log(a + b*sin(c + d*x)))/b^4 - (a*sin(c + d*x)^2)/(2*b^2) + (a^2*sin(c + d*x))/b^3)/d","B"
1280,1,47,55,0.065468,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x)^2)/(a + b*sin(c + d*x)),x)","\frac{2\,a^2\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)+b^2\,{\sin\left(c+d\,x\right)}^2-2\,a\,b\,\sin\left(c+d\,x\right)}{2\,b^3\,d}","Not used",1,"(2*a^2*log(a + b*sin(c + d*x)) + b^2*sin(c + d*x)^2 - 2*a*b*sin(c + d*x))/(2*b^3*d)","B"
1281,1,31,34,0.055481,"\text{Not used}","int((cos(c + d*x)*sin(c + d*x))/(a + b*sin(c + d*x)),x)","-\frac{a\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)-b\,\sin\left(c+d\,x\right)}{b^2\,d}","Not used",1,"-(a*log(a + b*sin(c + d*x)) - b*sin(c + d*x))/(b^2*d)","B"
1282,1,48,34,11.825897,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\ln\left(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)}{a\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)) - log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(a*d)","B"
1283,1,89,50,11.812136,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{b\,\ln\left(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)}{a^2\,d}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{1}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}}{a\,d}","Not used",1,"(b*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(a^2*d) - (b*log(tan(c/2 + (d*x)/2)))/(a^2*d) - (tan(c/2 + (d*x)/2)/2 + 1/(2*tan(c/2 + (d*x)/2)))/(a*d)","B"
1284,1,132,72,11.785445,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{b^2\,\ln\left(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)}{a^3\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a}{2}-2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a^2\,d}+\frac{b^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(2*a^2*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) - (b^2*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(a^3*d) - (cot(c/2 + (d*x)/2)^2*(a/2 - 2*b*tan(c/2 + (d*x)/2)))/(4*a^2*d) + (b^2*log(tan(c/2 + (d*x)/2)))/(a^3*d)","B"
1285,1,376,235,13.389900,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^4)/(a + b*sin(c + d*x)),x)","\frac{a^4\,\cos\left(c+d\,x\right)}{b^5\,d}-\frac{\frac{\cos\left(c+d\,x\right)}{8}+\frac{\cos\left(3\,c+3\,d\,x\right)}{48}-\frac{\cos\left(5\,c+5\,d\,x\right)}{80}}{b\,d}-\frac{\frac{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)}{4}-\frac{a\,\sin\left(4\,c+4\,d\,x\right)}{32}}{b^2\,d}-\frac{\frac{a^2\,\cos\left(c+d\,x\right)}{4}+\frac{a^2\,\cos\left(3\,c+3\,d\,x\right)}{12}}{b^3\,d}-\frac{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)+\frac{a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}}{b^4\,d}+\frac{2\,a^5\,\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^6\,d}-\frac{2\,a^4\,\mathrm{atanh}\left(\frac{2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\sqrt{b^2-a^2}}{b^6\,d}","Not used",1,"(a^4*cos(c + d*x))/(b^5*d) - (cos(c + d*x)/8 + cos(3*c + 3*d*x)/48 - cos(5*c + 5*d*x)/80)/(b*d) - ((a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 - (a*sin(4*c + 4*d*x))/32)/(b^2*d) - ((a^2*cos(c + d*x))/4 + (a^2*cos(3*c + 3*d*x))/12)/(b^3*d) - (a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (a^3*sin(2*c + 2*d*x))/4)/(b^4*d) + (2*a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^6*d) - (2*a^4*atanh((2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + a*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^3*cos(c/2 + (d*x)/2) - 2*b^3*sin(c/2 + (d*x)/2) - a*b^2*cos(c/2 + (d*x)/2) + 2*a^2*b*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(b^6*d)","B"
1286,1,2616,191,13.348228,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^3)/(a + b*sin(c + d*x)),x)","\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4\,d\,\left(b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b\,{\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)}^4+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\right)}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4\,d\,\left(b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b\,{\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)}^4+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4\,d\,\left(b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b\,{\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)}^4+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\right)}+\frac{2\,a}{3\,d\,\left(b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2\right)}-\frac{2\,a^3}{d\,\left(b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^4\right)}+\frac{\mathrm{atan}\left(\frac{11\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{a\,b^2}{8}+\frac{11\,a^3}{8}+\frac{3\,a^5}{2\,b^2}-\frac{11\,a^7}{b^4}+\frac{8\,a^9}{b^6}\right)}+\frac{3\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{a\,b^4}{8}+\frac{3\,a^5}{2}+\frac{11\,a^3\,b^2}{8}-\frac{11\,a^7}{b^2}+\frac{8\,a^9}{b^4}\right)}-\frac{11\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{a\,b^6}{8}-11\,a^7+\frac{11\,a^3\,b^4}{8}+\frac{3\,a^5\,b^2}{2}+\frac{8\,a^9}{b^2}}+\frac{8\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^9-11\,a^7\,b^2+\frac{3\,a^5\,b^4}{2}+\frac{11\,a^3\,b^6}{8}+\frac{a\,b^8}{8}}+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{a\,b}{8}+\frac{11\,a^3}{8\,b}+\frac{3\,a^5}{2\,b^3}-\frac{11\,a^7}{b^5}+\frac{8\,a^9}{b^7}\right)}\right)}{4\,b\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d\,\left(b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b\,{\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)}^4+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\right)}+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3\,d\,\left(b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2\right)}+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d\,\left(b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2\right)}+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left(b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^3\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{11\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{a\,b^2}{8}+\frac{11\,a^3}{8}+\frac{3\,a^5}{2\,b^2}-\frac{11\,a^7}{b^4}+\frac{8\,a^9}{b^6}\right)}+\frac{3\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{a\,b^4}{8}+\frac{3\,a^5}{2}+\frac{11\,a^3\,b^2}{8}-\frac{11\,a^7}{b^2}+\frac{8\,a^9}{b^4}\right)}-\frac{11\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{a\,b^6}{8}-11\,a^7+\frac{11\,a^3\,b^4}{8}+\frac{3\,a^5\,b^2}{2}+\frac{8\,a^9}{b^2}}+\frac{8\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^9-11\,a^7\,b^2+\frac{3\,a^5\,b^4}{2}+\frac{11\,a^3\,b^6}{8}+\frac{a\,b^8}{8}}+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{a\,b}{8}+\frac{11\,a^3}{8\,b}+\frac{3\,a^5}{2\,b^3}-\frac{11\,a^7}{b^5}+\frac{8\,a^9}{b^7}\right)}\right)}{b^3\,d}-\frac{2\,a^4\,\mathrm{atan}\left(\frac{11\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{a\,b^2}{8}+\frac{11\,a^3}{8}+\frac{3\,a^5}{2\,b^2}-\frac{11\,a^7}{b^4}+\frac{8\,a^9}{b^6}\right)}+\frac{3\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{a\,b^4}{8}+\frac{3\,a^5}{2}+\frac{11\,a^3\,b^2}{8}-\frac{11\,a^7}{b^2}+\frac{8\,a^9}{b^4}\right)}-\frac{11\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{a\,b^6}{8}-11\,a^7+\frac{11\,a^3\,b^4}{8}+\frac{3\,a^5\,b^2}{2}+\frac{8\,a^9}{b^2}}+\frac{8\,a^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^9-11\,a^7\,b^2+\frac{3\,a^5\,b^4}{2}+\frac{11\,a^3\,b^6}{8}+\frac{a\,b^8}{8}}+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{a\,b}{8}+\frac{11\,a^3}{8\,b}+\frac{3\,a^5}{2\,b^3}-\frac{11\,a^7}{b^5}+\frac{8\,a^9}{b^7}\right)}\right)}{b^5\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^3\right)}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{d\,\left(b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^3\right)}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{d\,\left(b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^3\right)}-\frac{6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d\,\left(b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^4\right)}-\frac{6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d\,\left(b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^4\right)}-\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left(b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^4\right)}-\frac{2\,a^3\,\mathrm{atanh}\left(\frac{a^5\,\sqrt{b^2-a^2}}{a^5\,b+\frac{7\,a^7}{b}-\frac{8\,a^9}{b^3}+14\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,a^4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{16\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}+\frac{8\,a^7\,\sqrt{b^2-a^2}}{7\,a^7\,b+a^5\,b^3-\frac{8\,a^9}{b}-16\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,a^4\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+14\,a^6\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{a^5+\frac{7\,a^7}{b^2}-\frac{8\,a^9}{b^4}+2\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{14\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{16\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}}+\frac{15\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{7\,a^7+a^5\,b^2-\frac{8\,a^9}{b^2}+14\,a^6\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,a^4\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{16\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}-\frac{8\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{-8\,a^9-16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b+7\,a^7\,b^2+14\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^3+a^5\,b^4+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^5}\right)\,\sqrt{b^2-a^2}}{b^5\,d}","Not used",1,"(7*tan(c/2 + (d*x)/2)^3)/(4*d*(b + 4*b*tan(c/2 + (d*x)/2)^2 + 6*b*tan(c/2 + (d*x)/2)^4 + 4*b*tan(c/2 + (d*x)/2)^6 + b*tan(c/2 + (d*x)/2)^8)) - (7*tan(c/2 + (d*x)/2)^5)/(4*d*(b + 4*b*tan(c/2 + (d*x)/2)^2 + 6*b*tan(c/2 + (d*x)/2)^4 + 4*b*tan(c/2 + (d*x)/2)^6 + b*tan(c/2 + (d*x)/2)^8)) + tan(c/2 + (d*x)/2)^7/(4*d*(b + 4*b*tan(c/2 + (d*x)/2)^2 + 6*b*tan(c/2 + (d*x)/2)^4 + 4*b*tan(c/2 + (d*x)/2)^6 + b*tan(c/2 + (d*x)/2)^8)) + (2*a)/(3*d*(4*b^2*tan(c/2 + (d*x)/2)^2 + 6*b^2*tan(c/2 + (d*x)/2)^4 + 4*b^2*tan(c/2 + (d*x)/2)^6 + b^2*tan(c/2 + (d*x)/2)^8 + b^2)) - (2*a^3)/(d*(4*b^4*tan(c/2 + (d*x)/2)^2 + 6*b^4*tan(c/2 + (d*x)/2)^4 + 4*b^4*tan(c/2 + (d*x)/2)^6 + b^4*tan(c/2 + (d*x)/2)^8 + b^4)) + atan((11*a^3*tan(c/2 + (d*x)/2))/(8*((a*b^2)/8 + (11*a^3)/8 + (3*a^5)/(2*b^2) - (11*a^7)/b^4 + (8*a^9)/b^6)) + (3*a^5*tan(c/2 + (d*x)/2))/(2*((a*b^4)/8 + (3*a^5)/2 + (11*a^3*b^2)/8 - (11*a^7)/b^2 + (8*a^9)/b^4)) - (11*a^7*tan(c/2 + (d*x)/2))/((a*b^6)/8 - 11*a^7 + (11*a^3*b^4)/8 + (3*a^5*b^2)/2 + (8*a^9)/b^2) + (8*a^9*tan(c/2 + (d*x)/2))/((a*b^8)/8 + 8*a^9 + (11*a^3*b^6)/8 + (3*a^5*b^4)/2 - 11*a^7*b^2) + (a*b*tan(c/2 + (d*x)/2))/(8*((a*b)/8 + (11*a^3)/(8*b) + (3*a^5)/(2*b^3) - (11*a^7)/b^5 + (8*a^9)/b^7)))/(4*b*d) - tan(c/2 + (d*x)/2)/(4*d*(b + 4*b*tan(c/2 + (d*x)/2)^2 + 6*b*tan(c/2 + (d*x)/2)^4 + 4*b*tan(c/2 + (d*x)/2)^6 + b*tan(c/2 + (d*x)/2)^8)) + (2*a*tan(c/2 + (d*x)/2)^2)/(3*d*(4*b^2*tan(c/2 + (d*x)/2)^2 + 6*b^2*tan(c/2 + (d*x)/2)^4 + 4*b^2*tan(c/2 + (d*x)/2)^6 + b^2*tan(c/2 + (d*x)/2)^8 + b^2)) + (2*a*tan(c/2 + (d*x)/2)^4)/(d*(4*b^2*tan(c/2 + (d*x)/2)^2 + 6*b^2*tan(c/2 + (d*x)/2)^4 + 4*b^2*tan(c/2 + (d*x)/2)^6 + b^2*tan(c/2 + (d*x)/2)^8 + b^2)) + (2*a*tan(c/2 + (d*x)/2)^6)/(d*(4*b^2*tan(c/2 + (d*x)/2)^2 + 6*b^2*tan(c/2 + (d*x)/2)^4 + 4*b^2*tan(c/2 + (d*x)/2)^6 + b^2*tan(c/2 + (d*x)/2)^8 + b^2)) + (a^2*tan(c/2 + (d*x)/2))/(d*(4*b^3*tan(c/2 + (d*x)/2)^2 + 6*b^3*tan(c/2 + (d*x)/2)^4 + 4*b^3*tan(c/2 + (d*x)/2)^6 + b^3*tan(c/2 + (d*x)/2)^8 + b^3)) + (a^2*atan((11*a^3*tan(c/2 + (d*x)/2))/(8*((a*b^2)/8 + (11*a^3)/8 + (3*a^5)/(2*b^2) - (11*a^7)/b^4 + (8*a^9)/b^6)) + (3*a^5*tan(c/2 + (d*x)/2))/(2*((a*b^4)/8 + (3*a^5)/2 + (11*a^3*b^2)/8 - (11*a^7)/b^2 + (8*a^9)/b^4)) - (11*a^7*tan(c/2 + (d*x)/2))/((a*b^6)/8 - 11*a^7 + (11*a^3*b^4)/8 + (3*a^5*b^2)/2 + (8*a^9)/b^2) + (8*a^9*tan(c/2 + (d*x)/2))/((a*b^8)/8 + 8*a^9 + (11*a^3*b^6)/8 + (3*a^5*b^4)/2 - 11*a^7*b^2) + (a*b*tan(c/2 + (d*x)/2))/(8*((a*b)/8 + (11*a^3)/(8*b) + (3*a^5)/(2*b^3) - (11*a^7)/b^5 + (8*a^9)/b^7))))/(b^3*d) - (2*a^4*atan((11*a^3*tan(c/2 + (d*x)/2))/(8*((a*b^2)/8 + (11*a^3)/8 + (3*a^5)/(2*b^2) - (11*a^7)/b^4 + (8*a^9)/b^6)) + (3*a^5*tan(c/2 + (d*x)/2))/(2*((a*b^4)/8 + (3*a^5)/2 + (11*a^3*b^2)/8 - (11*a^7)/b^2 + (8*a^9)/b^4)) - (11*a^7*tan(c/2 + (d*x)/2))/((a*b^6)/8 - 11*a^7 + (11*a^3*b^4)/8 + (3*a^5*b^2)/2 + (8*a^9)/b^2) + (8*a^9*tan(c/2 + (d*x)/2))/((a*b^8)/8 + 8*a^9 + (11*a^3*b^6)/8 + (3*a^5*b^4)/2 - 11*a^7*b^2) + (a*b*tan(c/2 + (d*x)/2))/(8*((a*b)/8 + (11*a^3)/(8*b) + (3*a^5)/(2*b^3) - (11*a^7)/b^5 + (8*a^9)/b^7))))/(b^5*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(d*(4*b^3*tan(c/2 + (d*x)/2)^2 + 6*b^3*tan(c/2 + (d*x)/2)^4 + 4*b^3*tan(c/2 + (d*x)/2)^6 + b^3*tan(c/2 + (d*x)/2)^8 + b^3)) - (a^2*tan(c/2 + (d*x)/2)^5)/(d*(4*b^3*tan(c/2 + (d*x)/2)^2 + 6*b^3*tan(c/2 + (d*x)/2)^4 + 4*b^3*tan(c/2 + (d*x)/2)^6 + b^3*tan(c/2 + (d*x)/2)^8 + b^3)) - (a^2*tan(c/2 + (d*x)/2)^7)/(d*(4*b^3*tan(c/2 + (d*x)/2)^2 + 6*b^3*tan(c/2 + (d*x)/2)^4 + 4*b^3*tan(c/2 + (d*x)/2)^6 + b^3*tan(c/2 + (d*x)/2)^8 + b^3)) - (6*a^3*tan(c/2 + (d*x)/2)^2)/(d*(4*b^4*tan(c/2 + (d*x)/2)^2 + 6*b^4*tan(c/2 + (d*x)/2)^4 + 4*b^4*tan(c/2 + (d*x)/2)^6 + b^4*tan(c/2 + (d*x)/2)^8 + b^4)) - (6*a^3*tan(c/2 + (d*x)/2)^4)/(d*(4*b^4*tan(c/2 + (d*x)/2)^2 + 6*b^4*tan(c/2 + (d*x)/2)^4 + 4*b^4*tan(c/2 + (d*x)/2)^6 + b^4*tan(c/2 + (d*x)/2)^8 + b^4)) - (2*a^3*tan(c/2 + (d*x)/2)^6)/(d*(4*b^4*tan(c/2 + (d*x)/2)^2 + 6*b^4*tan(c/2 + (d*x)/2)^4 + 4*b^4*tan(c/2 + (d*x)/2)^6 + b^4*tan(c/2 + (d*x)/2)^8 + b^4)) - (2*a^3*atanh((a^5*(b^2 - a^2)^(1/2))/(a^5*b + (7*a^7)/b - (8*a^9)/b^3 + 14*a^6*tan(c/2 + (d*x)/2) + 2*a^4*b^2*tan(c/2 + (d*x)/2) - (16*a^8*tan(c/2 + (d*x)/2))/b^2) + (8*a^7*(b^2 - a^2)^(1/2))/(7*a^7*b + a^5*b^3 - (8*a^9)/b - 16*a^8*tan(c/2 + (d*x)/2) + 2*a^4*b^4*tan(c/2 + (d*x)/2) + 14*a^6*b^2*tan(c/2 + (d*x)/2)) + (2*a^4*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^5 + (7*a^7)/b^2 - (8*a^9)/b^4 + 2*a^4*b*tan(c/2 + (d*x)/2) + (14*a^6*tan(c/2 + (d*x)/2))/b - (16*a^8*tan(c/2 + (d*x)/2))/b^3) + (15*a^6*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(7*a^7 + a^5*b^2 - (8*a^9)/b^2 + 14*a^6*b*tan(c/2 + (d*x)/2) + 2*a^4*b^3*tan(c/2 + (d*x)/2) - (16*a^8*tan(c/2 + (d*x)/2))/b) - (8*a^8*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a^5*b^4 - 8*a^9 + 7*a^7*b^2 - 16*a^8*b*tan(c/2 + (d*x)/2) + 2*a^4*b^5*tan(c/2 + (d*x)/2) + 14*a^6*b^3*tan(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(b^5*d)","B"
1287,1,225,148,12.477548,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x)^2)/(a + b*sin(c + d*x)),x)","\frac{a^2\,\cos\left(c+d\,x\right)}{b^3\,d}-\frac{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{\frac{\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{12}}{b\,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\,a^2\,\mathrm{atanh}\left(\frac{-\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}{\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)\,\sqrt{b^2-a^2}}{b^4\,d}","Not used",1,"(a^2*cos(c + d*x))/(b^3*d) - (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) - (cos(c + d*x)/4 + cos(3*c + 3*d*x)/12)/(b*d) + (2*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^4*d) + (2*a^2*atanh((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))/((b^2 - a^2)^(1/2)*(a*cos(c/2 + (d*x)/2) + 2*b*sin(c/2 + (d*x)/2))))*(b^2 - a^2)^(1/2))/(b^4*d)","B"
1288,1,190,100,12.068586,"\text{Not used}","int((cos(c + d*x)^2*sin(c + d*x))/(a + b*sin(c + d*x)),x)","\frac{\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{\sin\left(2\,c+2\,d\,x\right)}{4}}{b\,d}-\frac{2\,a^2\,\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^3\,d}-\frac{a\,\cos\left(c+d\,x\right)}{b^2\,d}-\frac{2\,a\,\mathrm{atanh}\left(\frac{-\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}{\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)\,\sqrt{b^2-a^2}}{b^3\,d}","Not used",1,"(atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + sin(2*c + 2*d*x)/4)/(b*d) - (2*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^3*d) - (a*cos(c + d*x))/(b^2*d) - (2*a*atanh((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))/((b^2 - a^2)^(1/2)*(a*cos(c/2 + (d*x)/2) + 2*b*sin(c/2 + (d*x)/2))))*(b^2 - a^2)^(1/2))/(b^3*d)","B"
1289,1,896,75,11.974763,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{2\,\mathrm{atan}\left(\frac{64\,a^3}{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+64\,a^2\,b-64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-64\,b^3}-\frac{64\,a\,b^2}{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+64\,a^2\,b-64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-64\,b^3}+\frac{64\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+64\,a^2\,b-64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-64\,b^3}-\frac{64\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+64\,a^2\,b-64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-64\,b^3}\right)}{b\,d}-\frac{2\,\mathrm{atanh}\left(\frac{64\,a^2\,\sqrt{b^2-a^2}}{256\,a^2\,b-768\,b^3+\frac{512\,b^5}{a^2}-64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+832\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1792\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{1024\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}-\frac{512\,b^2\,\sqrt{b^2-a^2}}{256\,a^2\,b-768\,b^3+\frac{512\,b^5}{a^2}-64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+832\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1792\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{1024\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}+\frac{512\,b^4\,\sqrt{b^2-a^2}}{256\,a^4\,b+512\,b^5-768\,a^2\,b^3-64\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1792\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+832\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1024\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}}-\frac{1280\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{256\,a^3\,b-768\,a\,b^3+\frac{512\,b^5}{a}-64\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1792\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+832\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1024\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}}+\frac{1024\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{-64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6+256\,a^5\,b+832\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^2-768\,a^3\,b^3-1792\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^4+512\,a\,b^5+1024\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6}+\frac{320\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{256\,a^2\,b-768\,b^3+\frac{512\,b^5}{a^2}-64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+832\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1792\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{1024\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}}\right)\,\sqrt{b^2-a^2}}{a\,b\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a*d) + (2*atan((64*a^3)/(64*a^2*b - 64*b^3 + 64*a^3*tan(c/2 + (d*x)/2) - 64*a*b^2*tan(c/2 + (d*x)/2)) - (64*a*b^2)/(64*a^2*b - 64*b^3 + 64*a^3*tan(c/2 + (d*x)/2) - 64*a*b^2*tan(c/2 + (d*x)/2)) + (64*b^3*tan(c/2 + (d*x)/2))/(64*a^2*b - 64*b^3 + 64*a^3*tan(c/2 + (d*x)/2) - 64*a*b^2*tan(c/2 + (d*x)/2)) - (64*a^2*b*tan(c/2 + (d*x)/2))/(64*a^2*b - 64*b^3 + 64*a^3*tan(c/2 + (d*x)/2) - 64*a*b^2*tan(c/2 + (d*x)/2))))/(b*d) - (2*atanh((64*a^2*(b^2 - a^2)^(1/2))/(256*a^2*b - 768*b^3 + (512*b^5)/a^2 - 64*a^3*tan(c/2 + (d*x)/2) + 832*a*b^2*tan(c/2 + (d*x)/2) - (1792*b^4*tan(c/2 + (d*x)/2))/a + (1024*b^6*tan(c/2 + (d*x)/2))/a^3) - (512*b^2*(b^2 - a^2)^(1/2))/(256*a^2*b - 768*b^3 + (512*b^5)/a^2 - 64*a^3*tan(c/2 + (d*x)/2) + 832*a*b^2*tan(c/2 + (d*x)/2) - (1792*b^4*tan(c/2 + (d*x)/2))/a + (1024*b^6*tan(c/2 + (d*x)/2))/a^3) + (512*b^4*(b^2 - a^2)^(1/2))/(256*a^4*b + 512*b^5 - 768*a^2*b^3 - 64*a^5*tan(c/2 + (d*x)/2) - 1792*a*b^4*tan(c/2 + (d*x)/2) + 832*a^3*b^2*tan(c/2 + (d*x)/2) + (1024*b^6*tan(c/2 + (d*x)/2))/a) - (1280*b^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(256*a^3*b - 768*a*b^3 + (512*b^5)/a - 64*a^4*tan(c/2 + (d*x)/2) - 1792*b^4*tan(c/2 + (d*x)/2) + 832*a^2*b^2*tan(c/2 + (d*x)/2) + (1024*b^6*tan(c/2 + (d*x)/2))/a^2) + (1024*b^5*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(512*a*b^5 + 256*a^5*b - 768*a^3*b^3 - 64*a^6*tan(c/2 + (d*x)/2) + 1024*b^6*tan(c/2 + (d*x)/2) - 1792*a^2*b^4*tan(c/2 + (d*x)/2) + 832*a^4*b^2*tan(c/2 + (d*x)/2)) + (320*a*b*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(256*a^2*b - 768*b^3 + (512*b^5)/a^2 - 64*a^3*tan(c/2 + (d*x)/2) + 832*a*b^2*tan(c/2 + (d*x)/2) - (1792*b^4*tan(c/2 + (d*x)/2))/a + (1024*b^6*tan(c/2 + (d*x)/2))/a^3))*(b^2 - a^2)^(1/2))/(a*b*d)","B"
1290,1,204,80,11.939587,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","-\frac{\mathrm{cot}\left(c+d\,x\right)}{a\,d}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{\mathrm{atan}\left(\frac{a^3\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a\,b^2\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-2\,a^3\,b-5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+2\,a\,b^3+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^2\,d}","Not used",1,"(atan((a^3*(b^2 - a^2)^(1/2)*1i - a*b^2*(b^2 - a^2)^(1/2)*2i - b^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i)/(2*a*b^3 - 2*a^3*b + a^4*tan(c/2 + (d*x)/2) + 4*b^4*tan(c/2 + (d*x)/2) - 5*a^2*b^2*tan(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i)/(a^2*d) - cot(c + d*x)/(a*d) - (b*log(tan(c/2 + (d*x)/2)))/(a^2*d)","B"
1291,1,790,114,12.452991,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,\left(\frac{a^3\,d}{2}-\frac{a^3\,d\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}-\frac{a^2\,\left(\frac{\cos\left(c+d\,x\right)}{2}+\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}-\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{4}\right)}{\frac{a^3\,d}{2}-\frac{a^3\,d\,\cos\left(2\,c+2\,d\,x\right)}{2}}-\frac{b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2\,\left(\frac{a^3\,d}{2}-\frac{a^3\,d\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}+\frac{a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,\left(\frac{a^3\,d}{2}-\frac{a^3\,d\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}+\frac{b\,\mathrm{atan}\left(\frac{a^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a^2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}+a\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-a^3\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^2-12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{\frac{a^3\,d}{2}-\frac{a^3\,d\,\cos\left(2\,c+2\,d\,x\right)}{2}}-\frac{b\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{a^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a^2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}+a\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-a^3\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^2-12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{\frac{a^3\,d}{2}-\frac{a^3\,d\,\cos\left(2\,c+2\,d\,x\right)}{2}}","Not used",1,"(b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(2*((a^3*d)/2 - (a^3*d*cos(2*c + 2*d*x))/2)) - (a^2*(cos(c + d*x)/2 + log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/4 - (log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/4))/((a^3*d)/2 - (a^3*d*cos(2*c + 2*d*x))/2) - (b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/(2*((a^3*d)/2 - (a^3*d*cos(2*c + 2*d*x))/2)) + (a*b*sin(2*c + 2*d*x))/(2*((a^3*d)/2 - (a^3*d*cos(2*c + 2*d*x))/2)) + (b*atan((a^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a^2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i + a*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - a^3*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i)/(a^5*cos(c/2 + (d*x)/2) + 8*b^5*sin(c/2 + (d*x)/2) + 4*a*b^4*cos(c/2 + (d*x)/2) + 4*a^4*b*sin(c/2 + (d*x)/2) - 5*a^3*b^2*cos(c/2 + (d*x)/2) - 12*a^2*b^3*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*1i)/((a^3*d)/2 - (a^3*d*cos(2*c + 2*d*x))/2) - (b*cos(2*c + 2*d*x)*atan((a^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a^2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i + a*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - a^3*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i)/(a^5*cos(c/2 + (d*x)/2) + 8*b^5*sin(c/2 + (d*x)/2) + 4*a*b^4*cos(c/2 + (d*x)/2) + 4*a^4*b*sin(c/2 + (d*x)/2) - 5*a^3*b^2*cos(c/2 + (d*x)/2) - 12*a^2*b^3*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*1i)/((a^3*d)/2 - (a^3*d*cos(2*c + 2*d*x))/2)","B"
1292,1,749,153,13.512790,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{a^3\,\left(\frac{\cos\left(c+d\,x\right)}{8}+\frac{\cos\left(3\,c+3\,d\,x\right)}{24}\right)-a^2\,\left(\frac{b\,\sin\left(2\,c+2\,d\,x\right)}{8}-\frac{b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{16}+\frac{3\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{16}\right)+a\,\left(\frac{b^2\,\cos\left(c+d\,x\right)}{8}-\frac{b^2\,\cos\left(3\,c+3\,d\,x\right)}{8}\right)+\frac{3\,b^3\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}-\frac{b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{b^2\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{a^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a^2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}+a\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-a^3\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^2-12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}}{4}-\frac{b^2\,\sin\left(3\,c+3\,d\,x\right)\,\mathrm{atan}\left(\frac{a^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a^2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}+a\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-a^3\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^2-12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{4}}{\frac{a^4\,d\,\sin\left(3\,c+3\,d\,x\right)}{8}-\frac{3\,a^4\,d\,\sin\left(c+d\,x\right)}{8}}","Not used",1,"(a^3*(cos(c + d*x)/8 + cos(3*c + 3*d*x)/24) - a^2*((b*sin(2*c + 2*d*x))/8 - (b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/16 + (3*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/16) + a*((b^2*cos(c + d*x))/8 - (b^2*cos(3*c + 3*d*x))/8) + (3*b^3*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 - (b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/8 + (b^2*sin(c + d*x)*atan((a^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a^2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i + a*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - a^3*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i)/(a^5*cos(c/2 + (d*x)/2) + 8*b^5*sin(c/2 + (d*x)/2) + 4*a*b^4*cos(c/2 + (d*x)/2) + 4*a^4*b*sin(c/2 + (d*x)/2) - 5*a^3*b^2*cos(c/2 + (d*x)/2) - 12*a^2*b^3*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*3i)/4 - (b^2*sin(3*c + 3*d*x)*atan((a^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a^2*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i + a*b^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - a^3*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i)/(a^5*cos(c/2 + (d*x)/2) + 8*b^5*sin(c/2 + (d*x)/2) + 4*a*b^4*cos(c/2 + (d*x)/2) + 4*a^4*b*sin(c/2 + (d*x)/2) - 5*a^3*b^2*cos(c/2 + (d*x)/2) - 12*a^2*b^3*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*1i)/4)/((a^4*d*sin(3*c + 3*d*x))/8 - (3*a^4*d*sin(c + d*x))/8)","B"
1293,1,873,194,12.069369,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{8\,a^2}-\frac{b^3}{2\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^2\,b-8\,b^3\right)+\frac{a^3}{4}-\frac{2\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+2\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,a^4\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4+4\,a^2\,b^2-8\,b^4\right)}{8\,a^5\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}+\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^9+2\,a^7\,b^2-32\,a^5\,b^4+32\,a^3\,b^6\right)}{4\,a^7}-\frac{a^9\,b+12\,a^7\,b^3-16\,a^5\,b^5}{4\,a^8}+\frac{b^3\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{10}-32\,a^8\,b^2\right)}{4\,a^7}\right)\,\sqrt{b^2-a^2}}{a^5}\right)\,1{}\mathrm{i}}{a^5}-\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{a^9\,b+12\,a^7\,b^3-16\,a^5\,b^5}{4\,a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^9+2\,a^7\,b^2-32\,a^5\,b^4+32\,a^3\,b^6\right)}{4\,a^7}+\frac{b^3\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{10}-32\,a^8\,b^2\right)}{4\,a^7}\right)\,\sqrt{b^2-a^2}}{a^5}\right)\,1{}\mathrm{i}}{a^5}}{\frac{a^6\,b^3+3\,a^4\,b^5-12\,a^2\,b^7+8\,b^9}{2\,a^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4\,b^4-10\,a^2\,b^6+8\,b^8\right)}{2\,a^7}+\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^9+2\,a^7\,b^2-32\,a^5\,b^4+32\,a^3\,b^6\right)}{4\,a^7}-\frac{a^9\,b+12\,a^7\,b^3-16\,a^5\,b^5}{4\,a^8}+\frac{b^3\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{10}-32\,a^8\,b^2\right)}{4\,a^7}\right)\,\sqrt{b^2-a^2}}{a^5}\right)}{a^5}+\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{a^9\,b+12\,a^7\,b^3-16\,a^5\,b^5}{4\,a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^9+2\,a^7\,b^2-32\,a^5\,b^4+32\,a^3\,b^6\right)}{4\,a^7}+\frac{b^3\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{10}-32\,a^8\,b^2\right)}{4\,a^7}\right)\,\sqrt{b^2-a^2}}{a^5}\right)}{a^5}}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^5\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a*d) + (tan(c/2 + (d*x)/2)*(b/(8*a^2) - b^3/(2*a^4)))/d - (tan(c/2 + (d*x)/2)^3*(2*a^2*b - 8*b^3) + a^3/4 - (2*a^2*b*tan(c/2 + (d*x)/2))/3 + 2*a*b^2*tan(c/2 + (d*x)/2)^2)/(16*a^4*d*tan(c/2 + (d*x)/2)^4) - (log(tan(c/2 + (d*x)/2))*(a^4 - 8*b^4 + 4*a^2*b^2))/(8*a^5*d) - (b*tan(c/2 + (d*x)/2)^3)/(24*a^2*d) + (b^2*tan(c/2 + (d*x)/2)^2)/(8*a^3*d) + (b^3*atan(((b^3*(b^2 - a^2)^(1/2)*((tan(c/2 + (d*x)/2)*(a^9 + 32*a^3*b^6 - 32*a^5*b^4 + 2*a^7*b^2))/(4*a^7) - (a^9*b - 16*a^5*b^5 + 12*a^7*b^3)/(4*a^8) + (b^3*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^10 - 32*a^8*b^2))/(4*a^7))*(b^2 - a^2)^(1/2))/a^5)*1i)/a^5 - (b^3*(b^2 - a^2)^(1/2)*((a^9*b - 16*a^5*b^5 + 12*a^7*b^3)/(4*a^8) - (tan(c/2 + (d*x)/2)*(a^9 + 32*a^3*b^6 - 32*a^5*b^4 + 2*a^7*b^2))/(4*a^7) + (b^3*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^10 - 32*a^8*b^2))/(4*a^7))*(b^2 - a^2)^(1/2))/a^5)*1i)/a^5)/((8*b^9 - 12*a^2*b^7 + 3*a^4*b^5 + a^6*b^3)/(2*a^8) + (tan(c/2 + (d*x)/2)*(8*b^8 - 10*a^2*b^6 + 2*a^4*b^4))/(2*a^7) + (b^3*(b^2 - a^2)^(1/2)*((tan(c/2 + (d*x)/2)*(a^9 + 32*a^3*b^6 - 32*a^5*b^4 + 2*a^7*b^2))/(4*a^7) - (a^9*b - 16*a^5*b^5 + 12*a^7*b^3)/(4*a^8) + (b^3*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^10 - 32*a^8*b^2))/(4*a^7))*(b^2 - a^2)^(1/2))/a^5))/a^5 + (b^3*(b^2 - a^2)^(1/2)*((a^9*b - 16*a^5*b^5 + 12*a^7*b^3)/(4*a^8) - (tan(c/2 + (d*x)/2)*(a^9 + 32*a^3*b^6 - 32*a^5*b^4 + 2*a^7*b^2))/(4*a^7) + (b^3*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^10 - 32*a^8*b^2))/(4*a^7))*(b^2 - a^2)^(1/2))/a^5))/a^5))*(b^2 - a^2)^(1/2)*2i)/(a^5*d)","B"
1294,1,1007,238,12.081452,"\text{Not used}","int(cos(c + d*x)^2/(sin(c + d*x)^6*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b}{32\,a^2}-\frac{b\,\left(\frac{1}{32\,a}+\frac{b^2}{8\,a^3}\right)}{a}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1}{16\,a}+\frac{b^2}{8\,a^3}+\frac{2\,b\,\left(\frac{b}{16\,a^2}-\frac{2\,b\,\left(\frac{1}{32\,a}+\frac{b^2}{8\,a^3}\right)}{a}\right)}{a}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{1}{96\,a}+\frac{b^2}{24\,a^3}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{a^4\,b}{8}+\frac{a^2\,b^3}{2}-b^5\right)}{a^6\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^4+4\,a^2\,b^2-16\,b^4\right)-\frac{a^4}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^4}{3}+\frac{4\,a^2\,b^2}{3}\right)+\frac{a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+4\,a\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,a^5\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}-\frac{b^4\,\mathrm{atan}\left(\frac{\frac{b^4\,\sqrt{b^2-a^2}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}\,b+2\,a^8\,b^3-32\,a^6\,b^5+32\,a^4\,b^7\right)}{4\,a^9}-\frac{a^{10}\,b^2+12\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}+\frac{b^4\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{b^2-a^2}}{a^6}\right)\,1{}\mathrm{i}}{a^6}-\frac{b^4\,\sqrt{b^2-a^2}\,\left(\frac{a^{10}\,b^2+12\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}\,b+2\,a^8\,b^3-32\,a^6\,b^5+32\,a^4\,b^7\right)}{4\,a^9}+\frac{b^4\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{b^2-a^2}}{a^6}\right)\,1{}\mathrm{i}}{a^6}}{\frac{a^6\,b^5+3\,a^4\,b^7-12\,a^2\,b^9+8\,b^{11}}{2\,a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4\,b^6-10\,a^2\,b^8+8\,b^{10}\right)}{2\,a^9}+\frac{b^4\,\sqrt{b^2-a^2}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}\,b+2\,a^8\,b^3-32\,a^6\,b^5+32\,a^4\,b^7\right)}{4\,a^9}-\frac{a^{10}\,b^2+12\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}+\frac{b^4\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{b^2-a^2}}{a^6}\right)}{a^6}+\frac{b^4\,\sqrt{b^2-a^2}\,\left(\frac{a^{10}\,b^2+12\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}\,b+2\,a^8\,b^3-32\,a^6\,b^5+32\,a^4\,b^7\right)}{4\,a^9}+\frac{b^4\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{b^2-a^2}}{a^6}\right)}{a^6}}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^6\,d}","Not used",1,"tan(c/2 + (d*x)/2)^5/(160*a*d) + (tan(c/2 + (d*x)/2)^2*(b/(32*a^2) - (b*(1/(32*a) + b^2/(8*a^3)))/a))/d - (tan(c/2 + (d*x)/2)*(1/(16*a) + b^2/(8*a^3) + (2*b*(b/(16*a^2) - (2*b*(1/(32*a) + b^2/(8*a^3)))/a))/a))/d + (tan(c/2 + (d*x)/2)^3*(1/(96*a) + b^2/(24*a^3)))/d + (log(tan(c/2 + (d*x)/2))*((a^4*b)/8 - b^5 + (a^2*b^3)/2))/(a^6*d) - (b*tan(c/2 + (d*x)/2)^4)/(64*a^2*d) + (tan(c/2 + (d*x)/2)^4*(2*a^4 - 16*b^4 + 4*a^2*b^2) - a^4/5 - tan(c/2 + (d*x)/2)^2*(a^4/3 + (4*a^2*b^2)/3) + (a^3*b*tan(c/2 + (d*x)/2))/2 + 4*a*b^3*tan(c/2 + (d*x)/2)^3)/(32*a^5*d*tan(c/2 + (d*x)/2)^5) - (b^4*atan(((b^4*(b^2 - a^2)^(1/2)*((tan(c/2 + (d*x)/2)*(a^10*b + 32*a^4*b^7 - 32*a^6*b^5 + 2*a^8*b^3))/(4*a^9) - (12*a^8*b^4 - 16*a^6*b^6 + a^10*b^2)/(4*a^10) + (b^4*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(b^2 - a^2)^(1/2))/a^6)*1i)/a^6 - (b^4*(b^2 - a^2)^(1/2)*((12*a^8*b^4 - 16*a^6*b^6 + a^10*b^2)/(4*a^10) - (tan(c/2 + (d*x)/2)*(a^10*b + 32*a^4*b^7 - 32*a^6*b^5 + 2*a^8*b^3))/(4*a^9) + (b^4*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(b^2 - a^2)^(1/2))/a^6)*1i)/a^6)/((8*b^11 - 12*a^2*b^9 + 3*a^4*b^7 + a^6*b^5)/(2*a^10) + (tan(c/2 + (d*x)/2)*(8*b^10 - 10*a^2*b^8 + 2*a^4*b^6))/(2*a^9) + (b^4*(b^2 - a^2)^(1/2)*((tan(c/2 + (d*x)/2)*(a^10*b + 32*a^4*b^7 - 32*a^6*b^5 + 2*a^8*b^3))/(4*a^9) - (12*a^8*b^4 - 16*a^6*b^6 + a^10*b^2)/(4*a^10) + (b^4*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(b^2 - a^2)^(1/2))/a^6))/a^6 + (b^4*(b^2 - a^2)^(1/2)*((12*a^8*b^4 - 16*a^6*b^6 + a^10*b^2)/(4*a^10) - (tan(c/2 + (d*x)/2)*(a^10*b + 32*a^4*b^7 - 32*a^6*b^5 + 2*a^8*b^3))/(4*a^9) + (b^4*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(b^2 - a^2)^(1/2))/a^6))/a^6))*(b^2 - a^2)^(1/2)*2i)/(a^6*d)","B"
1295,1,133,149,0.082843,"\text{Not used}","int((cos(c + d*x)^3*sin(c + d*x)^3)/(a + b*sin(c + d*x)),x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{1}{3\,b}-\frac{a^2}{3\,b^3}\right)-\frac{{\sin\left(c+d\,x\right)}^5}{5\,b}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{4\,b^2}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(a^5-a^3\,b^2\right)}{b^6}-\frac{a\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{1}{b}-\frac{a^2}{b^3}\right)}{2\,b}+\frac{a^2\,\sin\left(c+d\,x\right)\,\left(\frac{1}{b}-\frac{a^2}{b^3}\right)}{b^2}}{d}","Not used",1,"(sin(c + d*x)^3*(1/(3*b) - a^2/(3*b^3)) - sin(c + d*x)^5/(5*b) + (a*sin(c + d*x)^4)/(4*b^2) + (log(a + b*sin(c + d*x))*(a^5 - a^3*b^2))/b^6 - (a*sin(c + d*x)^2*(1/b - a^2/b^3))/(2*b) + (a^2*sin(c + d*x)*(1/b - a^2/b^3))/b^2)/d","B"
1296,1,107,119,11.622684,"\text{Not used}","int((cos(c + d*x)^3*sin(c + d*x)^2)/(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}{2\,b}-\frac{a^2}{2\,b^3}\right)-\frac{a\,{\sin\left(c+d\,x\right)}^3}{3\,b^2}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(a^4-a^2\,b^2\right)}{b^5}+\frac{a\,\sin\left(c+d\,x\right)\,\left(\frac{1}{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/(2*b) - a^2/(2*b^3)) - (a*sin(c + d*x)^3)/(3*b^2) + (log(a + b*sin(c + d*x))*(a^4 - a^2*b^2))/b^5 + (a*sin(c + d*x)*(1/b - a^2/b^3))/b)/d","B"
1297,1,78,89,0.068187,"\text{Not used}","int((cos(c + d*x)^3*sin(c + d*x))/(a + b*sin(c + d*x)),x)","\frac{\sin\left(c+d\,x\right)\,\left(\frac{1}{b}-\frac{a^2}{b^3}\right)-\frac{{\sin\left(c+d\,x\right)}^3}{3\,b}+\frac{a\,{\sin\left(c+d\,x\right)}^2}{2\,b^2}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(a\,b^2-a^3\right)}{b^4}}{d}","Not used",1,"(sin(c + d*x)*(1/b - a^2/b^3) - sin(c + d*x)^3/(3*b) + (a*sin(c + d*x)^2)/(2*b^2) - (log(a + b*sin(c + d*x))*(a*b^2 - a^3))/b^4)/d","B"
1298,1,98,59,11.860990,"\text{Not used}","int(cos(c + d*x)^3/(sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{\sin\left(c+d\,x\right)}{b\,d}+\frac{\ln\left(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)\,\left(\frac{a}{b^2}-\frac{1}{a}\right)}{d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b^2\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a*d) - sin(c + d*x)/(b*d) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a/b^2 - 1/a))/d - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/(b^2*d)","B"
1299,1,118,60,11.857324,"\text{Not used}","int(cos(c + d*x)^3/(sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{\ln\left(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)\,\left(\frac{b}{a^2}-\frac{1}{b}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}-\frac{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b\,d}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}","Not used",1,"(log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(b/a^2 - 1/b))/d - tan(c/2 + (d*x)/2)/(2*a*d) - cot(c/2 + (d*x)/2)/(2*a*d) + log(tan(c/2 + (d*x)/2)^2 + 1)/(b*d) - (b*log(tan(c/2 + (d*x)/2)))/(a^2*d)","B"
1300,1,144,84,11.758325,"\text{Not used}","int(cos(c + d*x)^3/(sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-b^2\right)}{a^3\,d}-\frac{\frac{a}{2}-2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^2\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}+\frac{\ln\left(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)\,\left(a^2-b^2\right)}{a^3\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(2*a^2*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) - (log(tan(c/2 + (d*x)/2))*(a^2 - b^2))/(a^3*d) - (a/2 - 2*b*tan(c/2 + (d*x)/2))/(4*a^2*d*tan(c/2 + (d*x)/2)^2) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2))/(a^3*d)","B"
1301,1,600,282,14.636859,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^3)/(a + b*sin(c + d*x)),x)","\frac{\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)}{8\,b\,d}+\frac{\sin\left(2\,c+2\,d\,x\right)}{64\,b\,d}-\frac{\sin\left(4\,c+4\,d\,x\right)}{64\,b\,d}-\frac{\sin\left(6\,c+6\,d\,x\right)}{192\,b\,d}+\frac{a\,\cos\left(3\,c+3\,d\,x\right)}{16\,b^2\,d}+\frac{a\,\cos\left(5\,c+5\,d\,x\right)}{80\,b^2\,d}-\frac{5\,a^3\,\cos\left(c+d\,x\right)}{4\,b^4\,d}+\frac{a^5\,\cos\left(c+d\,x\right)}{b^6\,d}+\frac{3\,a^2\,\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)}{4\,b^3\,d}-\frac{3\,a^4\,\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^5\,d}+\frac{2\,a^6\,\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^7\,d}-\frac{a^3\,\cos\left(3\,c+3\,d\,x\right)}{12\,b^4\,d}+\frac{a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,b^3\,d}+\frac{a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,b^3\,d}-\frac{a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,b^5\,d}+\frac{a\,\cos\left(c+d\,x\right)}{8\,b^2\,d}-\frac{2\,a^3\,\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{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{b^7\,d}","Not used",1,"atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(8*b*d) + sin(2*c + 2*d*x)/(64*b*d) - sin(4*c + 4*d*x)/(64*b*d) - sin(6*c + 6*d*x)/(192*b*d) + (a*cos(3*c + 3*d*x))/(16*b^2*d) + (a*cos(5*c + 5*d*x))/(80*b^2*d) - (5*a^3*cos(c + d*x))/(4*b^4*d) + (a^5*cos(c + d*x))/(b^6*d) + (3*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*b^3*d) - (3*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^5*d) + (2*a^6*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^7*d) - (a^3*cos(3*c + 3*d*x))/(12*b^4*d) + (a^2*sin(2*c + 2*d*x))/(4*b^3*d) + (a^2*sin(4*c + 4*d*x))/(32*b^3*d) - (a^4*sin(2*c + 2*d*x))/(4*b^5*d) + (a*cos(c + d*x))/(8*b^2*d) - (2*a^3*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)))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(b^7*d)","B"
1302,1,511,235,13.368691,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x)^2)/(a + b*sin(c + d*x)),x)","\frac{5\,a^2\,\cos\left(c+d\,x\right)}{4\,b^3\,d}-\frac{\cos\left(3\,c+3\,d\,x\right)}{16\,b\,d}-\frac{\cos\left(5\,c+5\,d\,x\right)}{80\,b\,d}-\frac{\cos\left(c+d\,x\right)}{8\,b\,d}-\frac{a^4\,\cos\left(c+d\,x\right)}{b^5\,d}-\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4\,b^2\,d}-\frac{a\,\sin\left(4\,c+4\,d\,x\right)}{32\,b^2\,d}+\frac{3\,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\,a^5\,\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^6\,d}+\frac{a^2\,\cos\left(3\,c+3\,d\,x\right)}{12\,b^3\,d}+\frac{a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,b^4\,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)}{4\,b^2\,d}+\frac{2\,a^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{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{b^6\,d}","Not used",1,"(5*a^2*cos(c + d*x))/(4*b^3*d) - cos(3*c + 3*d*x)/(16*b*d) - cos(5*c + 5*d*x)/(80*b*d) - cos(c + d*x)/(8*b*d) - (a^4*cos(c + d*x))/(b^5*d) - (a*sin(2*c + 2*d*x))/(4*b^2*d) - (a*sin(4*c + 4*d*x))/(32*b^2*d) + (3*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^4*d) - (2*a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^6*d) + (a^2*cos(3*c + 3*d*x))/(12*b^3*d) + (a^3*sin(2*c + 2*d*x))/(4*b^4*d) - (3*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*b^2*d) + (2*a^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)))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(b^6*d)","B"
1303,1,453,159,12.949678,"\text{Not used}","int((cos(c + d*x)^4*sin(c + d*x))/(a + b*sin(c + d*x)),x)","\frac{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)}{4\,b\,d}+\frac{\sin\left(2\,c+2\,d\,x\right)}{4\,b\,d}+\frac{\sin\left(4\,c+4\,d\,x\right)}{32\,b\,d}-\frac{a\,\cos\left(3\,c+3\,d\,x\right)}{12\,b^2\,d}+\frac{a^3\,\cos\left(c+d\,x\right)}{b^4\,d}-\frac{3\,a^2\,\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^3\,d}+\frac{2\,a^4\,\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^5\,d}-\frac{a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,b^3\,d}-\frac{5\,a\,\cos\left(c+d\,x\right)}{4\,b^2\,d}-\frac{2\,a\,\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{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{b^5\,d}","Not used",1,"(3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*b*d) + sin(2*c + 2*d*x)/(4*b*d) + sin(4*c + 4*d*x)/(32*b*d) - (a*cos(3*c + 3*d*x))/(12*b^2*d) + (a^3*cos(c + d*x))/(b^4*d) - (3*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^3*d) + (2*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^5*d) - (a^2*sin(2*c + 2*d*x))/(4*b^3*d) - (5*a*cos(c + d*x))/(4*b^2*d) - (2*a*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)))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(b^5*d)","B"
1304,1,1320,124,14.031327,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{\sin\left(2\,c+2\,d\,x\right)}{4\,b\,d}-\frac{3\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}{-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)}{b\,d}+\frac{a\,\cos\left(c+d\,x\right)}{b^2\,d}+\frac{2\,a^2\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}{-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)}{b^3\,d}+\frac{\mathrm{atan}\left(\frac{-a^6\,\sin\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)}^{3/2}\,16{}\mathrm{i}-a^{12}\,\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}\,16{}\mathrm{i}+b^6\,\sin\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)}^{3/2}\,64{}\mathrm{i}-a^3\,b^3\,\cos\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)}^{3/2}\,42{}\mathrm{i}+a^3\,b^9\,\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}\,66{}\mathrm{i}-a^5\,b^7\,\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}\,176{}\mathrm{i}+a^7\,b^5\,\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}\,178{}\mathrm{i}-a^9\,b^3\,\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}\,81{}\mathrm{i}-a^2\,b^4\,\sin\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)}^{3/2}\,116{}\mathrm{i}+a^4\,b^2\,\sin\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)}^{3/2}\,72{}\mathrm{i}+a^2\,b^{10}\,\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}\,148{}\mathrm{i}-a^4\,b^8\,\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}\,460{}\mathrm{i}+a^6\,b^6\,\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}\,577{}\mathrm{i}-a^8\,b^4\,\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}\,368{}\mathrm{i}+a^{10}\,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}\,120{}\mathrm{i}+a\,b^5\,\cos\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)}^{3/2}\,32{}\mathrm{i}+a^5\,b\,\cos\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)}^{3/2}\,14{}\mathrm{i}+a^{11}\,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}\,14{}\mathrm{i}}{3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b^3-9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^4-37\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^5+54\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^6+161\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^7-137\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^8-351\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^9+180\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^{10}+416\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^{11}-120\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{12}-256\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{13}+32\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{14}+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{15}}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}\,2{}\mathrm{i}}{a\,b^3\,d}","Not used",1,"log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(a*d) - sin(2*c + 2*d*x)/(4*b*d) - (3*atan((2*a^3*cos(c/2 + (d*x)/2) + 2*b^3*sin(c/2 + (d*x)/2) - 3*a*b^2*cos(c/2 + (d*x)/2))/(2*b^3*cos(c/2 + (d*x)/2) - 2*a^3*sin(c/2 + (d*x)/2) + 3*a*b^2*sin(c/2 + (d*x)/2))))/(b*d) + (a*cos(c + d*x))/(b^2*d) + (2*a^2*atan((2*a^3*cos(c/2 + (d*x)/2) + 2*b^3*sin(c/2 + (d*x)/2) - 3*a*b^2*cos(c/2 + (d*x)/2))/(2*b^3*cos(c/2 + (d*x)/2) - 2*a^3*sin(c/2 + (d*x)/2) + 3*a*b^2*sin(c/2 + (d*x)/2))))/(b^3*d) + (atan((b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*64i - a^12*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*16i - a^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*16i - a^3*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*42i + a^3*b^9*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*66i - a^5*b^7*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*176i + a^7*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*178i - a^9*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*81i - a^2*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*116i + a^4*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*72i + a^2*b^10*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*148i - a^4*b^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*460i + a^6*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*577i - a^8*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*368i + a^10*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*120i + a*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*32i + a^5*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*14i + a^11*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*14i)/(64*b^15*sin(c/2 + (d*x)/2) + 32*a*b^14*cos(c/2 + (d*x)/2) - 120*a^3*b^12*cos(c/2 + (d*x)/2) + 180*a^5*b^10*cos(c/2 + (d*x)/2) - 137*a^7*b^8*cos(c/2 + (d*x)/2) + 54*a^9*b^6*cos(c/2 + (d*x)/2) - 9*a^11*b^4*cos(c/2 + (d*x)/2) - 256*a^2*b^13*sin(c/2 + (d*x)/2) + 416*a^4*b^11*sin(c/2 + (d*x)/2) - 351*a^6*b^9*sin(c/2 + (d*x)/2) + 161*a^8*b^7*sin(c/2 + (d*x)/2) - 37*a^10*b^5*sin(c/2 + (d*x)/2) + 3*a^12*b^3*sin(c/2 + (d*x)/2)))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*2i)/(a*b^3*d)","B"
1305,1,1167,104,13.780969,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","-\frac{\mathrm{cot}\left(c+d\,x\right)}{a\,d}-\frac{b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^2\,d}-\frac{\sin\left(2\,c+2\,d\,x\right)}{2\,b\,d\,\sin\left(c+d\,x\right)}-\frac{2\,a\,\mathrm{atan}\left(\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}{b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^2\,d}+\frac{\mathrm{atan}\left(\frac{16\,b^6\,\sin\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)}^{3/2}-4\,a^{12}\,\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}-4\,a^6\,\sin\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)}^{3/2}-12\,a^3\,b^3\,\cos\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)}^{3/2}+a^5\,b^7\,\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}+4\,a^7\,b^5\,\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}-6\,a^9\,b^3\,\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}-29\,a^2\,b^4\,\sin\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)}^{3/2}+18\,a^4\,b^2\,\sin\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)}^{3/2}+a^2\,b^{10}\,\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}-4\,a^4\,b^8\,\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}+22\,a^6\,b^6\,\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}-32\,a^8\,b^4\,\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}+18\,a^{10}\,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}+8\,a\,b^5\,\cos\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)}^{3/2}+5\,a^5\,b\,\cos\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)}^{3/2}+2\,a^{11}\,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}}{-3{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{14}\,b+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}\,b^2+36{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b^3-51{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^4-151{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^5+126{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^6+323{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^7-167{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^8-390{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^9+123{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^{10}+269{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^{11}-48{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{12}-100{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{13}+8{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{14}+16{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{15}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^2\,b^2\,d}","Not used",1,"(atan((16*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 4*a^12*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 4*a^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 12*a^3*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + a^5*b^7*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 4*a^7*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 6*a^9*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 29*a^2*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 18*a^4*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + a^2*b^10*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 4*a^4*b^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 22*a^6*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 32*a^8*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 18*a^10*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 8*a*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 5*a^5*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 2*a^11*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(b^15*sin(c/2 + (d*x)/2)*16i + a*b^14*cos(c/2 + (d*x)/2)*8i - a^14*b*sin(c/2 + (d*x)/2)*3i - a^3*b^12*cos(c/2 + (d*x)/2)*48i + a^5*b^10*cos(c/2 + (d*x)/2)*123i - a^7*b^8*cos(c/2 + (d*x)/2)*167i + a^9*b^6*cos(c/2 + (d*x)/2)*126i - a^11*b^4*cos(c/2 + (d*x)/2)*51i + a^13*b^2*cos(c/2 + (d*x)/2)*9i - a^2*b^13*sin(c/2 + (d*x)/2)*100i + a^4*b^11*sin(c/2 + (d*x)/2)*269i - a^6*b^9*sin(c/2 + (d*x)/2)*390i + a^8*b^7*sin(c/2 + (d*x)/2)*323i - a^10*b^5*sin(c/2 + (d*x)/2)*151i + a^12*b^3*sin(c/2 + (d*x)/2)*36i))*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^2*b^2*d) - (b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^2*d) - sin(2*c + 2*d*x)/(2*b*d*sin(c + d*x)) - (2*a*atan((a^3*cos(c/2 + (d*x)/2) + b^3*sin(c/2 + (d*x)/2))/(b^3*cos(c/2 + (d*x)/2) - a^3*sin(c/2 + (d*x)/2))))/(b^2*d) - cot(c + d*x)/(a*d)","B"
1306,1,2718,123,12.675914,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}-\frac{a^3\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,2{}\mathrm{i}}{a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}+\frac{2\,\mathrm{atan}\left(\frac{32\,b^6\,\sin\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)}^{3/2}-14\,a^{12}\,\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}-14\,a^6\,\sin\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)}^{3/2}-36\,a^3\,b^3\,\cos\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)}^{3/2}+2\,a^5\,b^7\,\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}+8\,a^7\,b^5\,\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}-24\,a^9\,b^3\,\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}-82\,a^2\,b^4\,\sin\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)}^{3/2}+63\,a^4\,b^2\,\sin\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)}^{3/2}+2\,a^2\,b^{10}\,\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}-11\,a^4\,b^8\,\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}+56\,a^6\,b^6\,\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}-106\,a^8\,b^4\,\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}+72\,a^{10}\,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}+16\,a\,b^5\,\cos\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)}^{3/2}+19\,a^5\,b\,\cos\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)}^{3/2}+13\,a^{11}\,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}}{-6{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{14}\,b+27{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}\,b^2+108{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b^3-165{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^4-482{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^5+390{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^6+982{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^7-469{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^8-1080{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^9+309{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^{10}+670{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^{11}-108{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{12}-224{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{13}+16{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{14}+32{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{15}}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}-\frac{a^2\,b\,\cos\left(c+d\,x\right)\,1{}\mathrm{i}}{a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}+\frac{a^3\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\cos\left(2\,c+2\,d\,x\right)\,2{}\mathrm{i}}{a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}-\frac{a^2\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}\right)}+\frac{a\,b^2\,\sin\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}-\frac{2\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{32\,b^6\,\sin\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)}^{3/2}-14\,a^{12}\,\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}-14\,a^6\,\sin\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)}^{3/2}-36\,a^3\,b^3\,\cos\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)}^{3/2}+2\,a^5\,b^7\,\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}+8\,a^7\,b^5\,\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}-24\,a^9\,b^3\,\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}-82\,a^2\,b^4\,\sin\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)}^{3/2}+63\,a^4\,b^2\,\sin\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)}^{3/2}+2\,a^2\,b^{10}\,\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}-11\,a^4\,b^8\,\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}+56\,a^6\,b^6\,\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}-106\,a^8\,b^4\,\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}+72\,a^{10}\,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}+16\,a\,b^5\,\cos\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)}^{3/2}+19\,a^5\,b\,\cos\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)}^{3/2}+13\,a^{11}\,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}}{-6{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{14}\,b+27{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}\,b^2+108{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b^3-165{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^4-482{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^5+390{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^6+982{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^7-469{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^8-1080{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^9+309{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^{10}+670{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^{11}-108{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{12}-224{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{13}+16{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{14}+32{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{15}}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}-\frac{b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}+\frac{a^2\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,3{}\mathrm{i}}{2\,\left(a^3\,b\,d\,1{}\mathrm{i}-a^3\,b\,d\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}\right)}","Not used",1,"(b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*1i)/(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i) - (a^3*atan((2*a^3*cos(c/2 + (d*x)/2) + 2*b^3*sin(c/2 + (d*x)/2) - 3*a^2*b*sin(c/2 + (d*x)/2))/(2*a^3*sin(c/2 + (d*x)/2) - 2*b^3*cos(c/2 + (d*x)/2) + 3*a^2*b*cos(c/2 + (d*x)/2)))*2i)/(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i) + (2*atan((32*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 14*a^12*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 14*a^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 36*a^3*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 2*a^5*b^7*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 8*a^7*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 24*a^9*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 82*a^2*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 63*a^4*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 2*a^2*b^10*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 11*a^4*b^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 56*a^6*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 106*a^8*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 72*a^10*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 16*a*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 19*a^5*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 13*a^11*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(b^15*sin(c/2 + (d*x)/2)*32i + a*b^14*cos(c/2 + (d*x)/2)*16i - a^14*b*sin(c/2 + (d*x)/2)*6i - a^3*b^12*cos(c/2 + (d*x)/2)*108i + a^5*b^10*cos(c/2 + (d*x)/2)*309i - a^7*b^8*cos(c/2 + (d*x)/2)*469i + a^9*b^6*cos(c/2 + (d*x)/2)*390i - a^11*b^4*cos(c/2 + (d*x)/2)*165i + a^13*b^2*cos(c/2 + (d*x)/2)*27i - a^2*b^13*sin(c/2 + (d*x)/2)*224i + a^4*b^11*sin(c/2 + (d*x)/2)*670i - a^6*b^9*sin(c/2 + (d*x)/2)*1080i + a^8*b^7*sin(c/2 + (d*x)/2)*982i - a^10*b^5*sin(c/2 + (d*x)/2)*482i + a^12*b^3*sin(c/2 + (d*x)/2)*108i))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i) - (a^2*b*cos(c + d*x)*1i)/(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i) + (a^3*atan((2*a^3*cos(c/2 + (d*x)/2) + 2*b^3*sin(c/2 + (d*x)/2) - 3*a^2*b*sin(c/2 + (d*x)/2))/(2*a^3*sin(c/2 + (d*x)/2) - 2*b^3*cos(c/2 + (d*x)/2) + 3*a^2*b*cos(c/2 + (d*x)/2)))*cos(2*c + 2*d*x)*2i)/(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i) - (a^2*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*3i)/(2*(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i)) + (a*b^2*sin(2*c + 2*d*x)*1i)/(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i) - (2*cos(2*c + 2*d*x)*atan((32*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 14*a^12*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 14*a^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 36*a^3*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 2*a^5*b^7*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 8*a^7*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 24*a^9*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 82*a^2*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 63*a^4*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 2*a^2*b^10*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 11*a^4*b^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 56*a^6*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 106*a^8*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 72*a^10*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 16*a*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 19*a^5*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + 13*a^11*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(b^15*sin(c/2 + (d*x)/2)*32i + a*b^14*cos(c/2 + (d*x)/2)*16i - a^14*b*sin(c/2 + (d*x)/2)*6i - a^3*b^12*cos(c/2 + (d*x)/2)*108i + a^5*b^10*cos(c/2 + (d*x)/2)*309i - a^7*b^8*cos(c/2 + (d*x)/2)*469i + a^9*b^6*cos(c/2 + (d*x)/2)*390i - a^11*b^4*cos(c/2 + (d*x)/2)*165i + a^13*b^2*cos(c/2 + (d*x)/2)*27i - a^2*b^13*sin(c/2 + (d*x)/2)*224i + a^4*b^11*sin(c/2 + (d*x)/2)*670i - a^6*b^9*sin(c/2 + (d*x)/2)*1080i + a^8*b^7*sin(c/2 + (d*x)/2)*982i - a^10*b^5*sin(c/2 + (d*x)/2)*482i + a^12*b^3*sin(c/2 + (d*x)/2)*108i))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i) - (b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i) + (a^2*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*3i)/(2*(a^3*b*d*1i - a^3*b*d*cos(2*c + 2*d*x)*1i))","B"
1307,1,654,154,12.424500,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}+\frac{5\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}+\frac{3\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,a^2\,d}-\frac{b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^4\,d}+\frac{b\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{b^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}+\frac{\mathrm{atan}\left(\frac{2\,a^5\,\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}+8\,b^5\,\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}-7\,a^3\,b^2\,\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}-16\,a^2\,b^3\,\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}+4\,a\,b^4\,\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}+7\,a^4\,b\,\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}}{2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8-5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b-16{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^2+14{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^3+34{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^4-13{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^5-28{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^6+4{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^7+8{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^4\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a*d) - cot(c/2 + (d*x)/2)^3/(24*a*d) + (5*cot(c/2 + (d*x)/2))/(8*a*d) - (5*tan(c/2 + (d*x)/2))/(8*a*d) + (3*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(2*a^2*d) - (b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^4*d) + (b*cot(c/2 + (d*x)/2)^2)/(8*a^2*d) - (b^2*cot(c/2 + (d*x)/2))/(2*a^3*d) - (b*tan(c/2 + (d*x)/2)^2)/(8*a^2*d) + (b^2*tan(c/2 + (d*x)/2))/(2*a^3*d) + (atan((2*a^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 8*b^5*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 7*a^3*b^2*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 16*a^2*b^3*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 4*a*b^4*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 7*a^4*b*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^8*sin(c/2 + (d*x)/2)*2i + b^8*sin(c/2 + (d*x)/2)*8i + a*b^7*cos(c/2 + (d*x)/2)*4i - a^7*b*cos(c/2 + (d*x)/2)*5i - a^3*b^5*cos(c/2 + (d*x)/2)*13i + a^5*b^3*cos(c/2 + (d*x)/2)*14i - a^2*b^6*sin(c/2 + (d*x)/2)*28i + a^4*b^4*sin(c/2 + (d*x)/2)*34i - a^6*b^2*sin(c/2 + (d*x)/2)*16i))*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^4*d)","B"
1308,1,953,198,12.155835,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{1}{8\,a}-\frac{b^2}{8\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{8\,a^2}+\frac{2\,b\,\left(\frac{1}{4\,a}-\frac{b^2}{4\,a^3}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a\,b^2-2\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(10\,a^2\,b-8\,b^3\right)+\frac{a^3}{4}-\frac{2\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{16\,a^4\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^4}{8}-\frac{3\,a^2\,b^2}{2}+b^4\right)}{a^5\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^9-34\,a^7\,b^2+64\,a^5\,b^4-32\,a^3\,b^6\right)}{4\,a^7}-\frac{11\,a^9\,b-28\,a^7\,b^3+16\,a^5\,b^5}{4\,a^8}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{10}-32\,a^8\,b^2\right)}{4\,a^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5}\right)\,1{}\mathrm{i}}{a^5}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{11\,a^9\,b-28\,a^7\,b^3+16\,a^5\,b^5}{4\,a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^9-34\,a^7\,b^2+64\,a^5\,b^4-32\,a^3\,b^6\right)}{4\,a^7}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{10}-32\,a^8\,b^2\right)}{4\,a^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5}\right)\,1{}\mathrm{i}}{a^5}}{\frac{3\,a^8\,b-18\,a^6\,b^3+35\,a^4\,b^5-28\,a^2\,b^7+8\,b^9}{2\,a^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-10\,a^6\,b^2+28\,a^4\,b^4-26\,a^2\,b^6+8\,b^8\right)}{2\,a^7}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^9-34\,a^7\,b^2+64\,a^5\,b^4-32\,a^3\,b^6\right)}{4\,a^7}-\frac{11\,a^9\,b-28\,a^7\,b^3+16\,a^5\,b^5}{4\,a^8}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{10}-32\,a^8\,b^2\right)}{4\,a^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5}\right)}{a^5}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{11\,a^9\,b-28\,a^7\,b^3+16\,a^5\,b^5}{4\,a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^9-34\,a^7\,b^2+64\,a^5\,b^4-32\,a^3\,b^6\right)}{4\,a^7}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{10}-32\,a^8\,b^2\right)}{4\,a^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5}\right)}{a^5}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^5\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a*d) - (tan(c/2 + (d*x)/2)^2*(1/(8*a) - b^2/(8*a^3)))/d + (tan(c/2 + (d*x)/2)*(b/(8*a^2) + (2*b*(1/(4*a) - b^2/(4*a^3)))/a))/d - (tan(c/2 + (d*x)/2)^2*(2*a*b^2 - 2*a^3) + tan(c/2 + (d*x)/2)^3*(10*a^2*b - 8*b^3) + a^3/4 - (2*a^2*b*tan(c/2 + (d*x)/2))/3)/(16*a^4*d*tan(c/2 + (d*x)/2)^4) + (log(tan(c/2 + (d*x)/2))*((3*a^4)/8 + b^4 - (3*a^2*b^2)/2))/(a^5*d) - (b*tan(c/2 + (d*x)/2)^3)/(24*a^2*d) - (b*atan(((b*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(c/2 + (d*x)/2)*(3*a^9 - 32*a^3*b^6 + 64*a^5*b^4 - 34*a^7*b^2))/(4*a^7) - (11*a^9*b + 16*a^5*b^5 - 28*a^7*b^3)/(4*a^8) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^10 - 32*a^8*b^2))/(4*a^7))*(-(a + b)^3*(a - b)^3)^(1/2))/a^5)*1i)/a^5 - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((11*a^9*b + 16*a^5*b^5 - 28*a^7*b^3)/(4*a^8) - (tan(c/2 + (d*x)/2)*(3*a^9 - 32*a^3*b^6 + 64*a^5*b^4 - 34*a^7*b^2))/(4*a^7) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^10 - 32*a^8*b^2))/(4*a^7))*(-(a + b)^3*(a - b)^3)^(1/2))/a^5)*1i)/a^5)/((3*a^8*b + 8*b^9 - 28*a^2*b^7 + 35*a^4*b^5 - 18*a^6*b^3)/(2*a^8) + (tan(c/2 + (d*x)/2)*(8*b^8 - 26*a^2*b^6 + 28*a^4*b^4 - 10*a^6*b^2))/(2*a^7) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(c/2 + (d*x)/2)*(3*a^9 - 32*a^3*b^6 + 64*a^5*b^4 - 34*a^7*b^2))/(4*a^7) - (11*a^9*b + 16*a^5*b^5 - 28*a^7*b^3)/(4*a^8) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^10 - 32*a^8*b^2))/(4*a^7))*(-(a + b)^3*(a - b)^3)^(1/2))/a^5))/a^5 + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((11*a^9*b + 16*a^5*b^5 - 28*a^7*b^3)/(4*a^8) - (tan(c/2 + (d*x)/2)*(3*a^9 - 32*a^3*b^6 + 64*a^5*b^4 - 34*a^7*b^2))/(4*a^7) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^10 - 32*a^8*b^2))/(4*a^7))*(-(a + b)^3*(a - b)^3)^(1/2))/a^5))/a^5))*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^5*d)","B"
1309,1,1082,244,12.180665,"\text{Not used}","int(cos(c + d*x)^4/(sin(c + d*x)^6*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b}{32\,a^2}+\frac{b\,\left(\frac{3}{32\,a}-\frac{b^2}{8\,a^3}\right)}{a}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b^2}{8\,a^3}-\frac{1}{16\,a}+\frac{2\,b\,\left(\frac{b}{16\,a^2}+\frac{2\,b\,\left(\frac{3}{32\,a}-\frac{b^2}{8\,a^3}\right)}{a}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{1}{32\,a}-\frac{b^2}{24\,a^3}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^4-\frac{4\,a^2\,b^2}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^4-20\,a^2\,b^2+16\,b^4\right)-\frac{a^4}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a\,b^3-4\,a^3\,b\right)+\frac{a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{32\,a^5\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^4\,b}{8}-\frac{3\,a^2\,b^3}{2}+b^5\right)}{a^6\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}\,b-34\,a^8\,b^3+64\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}-\frac{11\,a^{10}\,b^2-28\,a^8\,b^4+16\,a^6\,b^6}{4\,a^{10}}+\frac{b^2\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^6}\right)\,1{}\mathrm{i}}{a^6}-\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{11\,a^{10}\,b^2-28\,a^8\,b^4+16\,a^6\,b^6}{4\,a^{10}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}\,b-34\,a^8\,b^3+64\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}+\frac{b^2\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^6}\right)\,1{}\mathrm{i}}{a^6}}{\frac{3\,a^8\,b^3-18\,a^6\,b^5+35\,a^4\,b^7-28\,a^2\,b^9+8\,b^{11}}{2\,a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-10\,a^6\,b^4+28\,a^4\,b^6-26\,a^2\,b^8+8\,b^{10}\right)}{2\,a^9}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}\,b-34\,a^8\,b^3+64\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}-\frac{11\,a^{10}\,b^2-28\,a^8\,b^4+16\,a^6\,b^6}{4\,a^{10}}+\frac{b^2\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^6}\right)}{a^6}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{11\,a^{10}\,b^2-28\,a^8\,b^4+16\,a^6\,b^6}{4\,a^{10}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}\,b-34\,a^8\,b^3+64\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}+\frac{b^2\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^6}\right)}{a^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^6\,d}","Not used",1,"tan(c/2 + (d*x)/2)^5/(160*a*d) + (tan(c/2 + (d*x)/2)^2*(b/(32*a^2) + (b*(3/(32*a) - b^2/(8*a^3)))/a))/d - (tan(c/2 + (d*x)/2)*(b^2/(8*a^3) - 1/(16*a) + (2*b*(b/(16*a^2) + (2*b*(3/(32*a) - b^2/(8*a^3)))/a))/a))/d - (tan(c/2 + (d*x)/2)^3*(1/(32*a) - b^2/(24*a^3)))/d - (b*tan(c/2 + (d*x)/2)^4)/(64*a^2*d) + (tan(c/2 + (d*x)/2)^2*(a^4 - (4*a^2*b^2)/3) - tan(c/2 + (d*x)/2)^4*(2*a^4 + 16*b^4 - 20*a^2*b^2) - a^4/5 + tan(c/2 + (d*x)/2)^3*(4*a*b^3 - 4*a^3*b) + (a^3*b*tan(c/2 + (d*x)/2))/2)/(32*a^5*d*tan(c/2 + (d*x)/2)^5) - (log(tan(c/2 + (d*x)/2))*((3*a^4*b)/8 + b^5 - (3*a^2*b^3)/2))/(a^6*d) + (b^2*atan(((b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(c/2 + (d*x)/2)*(3*a^10*b - 32*a^4*b^7 + 64*a^6*b^5 - 34*a^8*b^3))/(4*a^9) - (16*a^6*b^6 - 28*a^8*b^4 + 11*a^10*b^2)/(4*a^10) + (b^2*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^3*(a - b)^3)^(1/2))/a^6)*1i)/a^6 - (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((16*a^6*b^6 - 28*a^8*b^4 + 11*a^10*b^2)/(4*a^10) - (tan(c/2 + (d*x)/2)*(3*a^10*b - 32*a^4*b^7 + 64*a^6*b^5 - 34*a^8*b^3))/(4*a^9) + (b^2*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^3*(a - b)^3)^(1/2))/a^6)*1i)/a^6)/((8*b^11 - 28*a^2*b^9 + 35*a^4*b^7 - 18*a^6*b^5 + 3*a^8*b^3)/(2*a^10) + (tan(c/2 + (d*x)/2)*(8*b^10 - 26*a^2*b^8 + 28*a^4*b^6 - 10*a^6*b^4))/(2*a^9) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(c/2 + (d*x)/2)*(3*a^10*b - 32*a^4*b^7 + 64*a^6*b^5 - 34*a^8*b^3))/(4*a^9) - (16*a^6*b^6 - 28*a^8*b^4 + 11*a^10*b^2)/(4*a^10) + (b^2*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^3*(a - b)^3)^(1/2))/a^6))/a^6 + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((16*a^6*b^6 - 28*a^8*b^4 + 11*a^10*b^2)/(4*a^10) - (tan(c/2 + (d*x)/2)*(3*a^10*b - 32*a^4*b^7 + 64*a^6*b^5 - 34*a^8*b^3))/(4*a^9) + (b^2*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^3*(a - b)^3)^(1/2))/a^6))/a^6))*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^6*d)","B"
1310,1,236,212,0.132133,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^3)/(a + b*sin(c + d*x)),x)","-\frac{{\sin\left(c+d\,x\right)}^5\,\left(\frac{2}{5\,b}-\frac{a^2}{5\,b^3}\right)-\frac{{\sin\left(c+d\,x\right)}^7}{7\,b}-{\sin\left(c+d\,x\right)}^3\,\left(\frac{1}{3\,b}-\frac{a^2\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{3\,b^2}\right)+\frac{a\,{\sin\left(c+d\,x\right)}^6}{6\,b^2}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}{b^8}-\frac{a\,{\sin\left(c+d\,x\right)}^4\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{4\,b}+\frac{a\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{1}{b}-\frac{a^2\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{b^2}\right)}{2\,b}-\frac{a^2\,\sin\left(c+d\,x\right)\,\left(\frac{1}{b}-\frac{a^2\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{b^2}\right)}{b^2}}{d}","Not used",1,"-(sin(c + d*x)^5*(2/(5*b) - a^2/(5*b^3)) - sin(c + d*x)^7/(7*b) - sin(c + d*x)^3*(1/(3*b) - (a^2*(2/b - a^2/b^3))/(3*b^2)) + (a*sin(c + d*x)^6)/(6*b^2) + (log(a + b*sin(c + d*x))*(a^7 + a^3*b^4 - 2*a^5*b^2))/b^8 - (a*sin(c + d*x)^4*(2/b - a^2/b^3))/(4*b) + (a*sin(c + d*x)^2*(1/b - (a^2*(2/b - a^2/b^3))/b^2))/(2*b) - (a^2*sin(c + d*x)*(1/b - (a^2*(2/b - a^2/b^3))/b^2))/b^2)/d","B"
1311,1,191,180,11.781688,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x)^2)/(a + b*sin(c + d*x)),x)","\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{1}{2\,b}-\frac{a^2\,\left(\frac{1}{b}-\frac{a^2}{2\,b^3}\right)}{b^2}\right)-{\sin\left(c+d\,x\right)}^4\,\left(\frac{1}{2\,b}-\frac{a^2}{4\,b^3}\right)+\frac{{\sin\left(c+d\,x\right)}^6}{6\,b}-\frac{a\,{\sin\left(c+d\,x\right)}^5}{5\,b^2}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(a^6-2\,a^4\,b^2+a^2\,b^4\right)}{b^7}-\frac{a\,\sin\left(c+d\,x\right)\,\left(\frac{1}{b}-\frac{a^2\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{b^2}\right)}{b}+\frac{a\,{\sin\left(c+d\,x\right)}^3\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{3\,b}}{d}","Not used",1,"(sin(c + d*x)^2*(1/(2*b) - (a^2*(1/b - a^2/(2*b^3)))/b^2) - sin(c + d*x)^4*(1/(2*b) - a^2/(4*b^3)) + sin(c + d*x)^6/(6*b) - (a*sin(c + d*x)^5)/(5*b^2) + (log(a + b*sin(c + d*x))*(a^6 + a^2*b^4 - 2*a^4*b^2))/b^7 - (a*sin(c + d*x)*(1/b - (a^2*(2/b - a^2/b^3))/b^2))/b + (a*sin(c + d*x)^3*(2/b - a^2/b^3))/(3*b))/d","B"
1312,1,150,148,0.074653,"\text{Not used}","int((cos(c + d*x)^5*sin(c + d*x))/(a + b*sin(c + d*x)),x)","\frac{\sin\left(c+d\,x\right)\,\left(\frac{1}{b}-\frac{a^2\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{b^2}\right)-{\sin\left(c+d\,x\right)}^3\,\left(\frac{2}{3\,b}-\frac{a^2}{3\,b^3}\right)+\frac{{\sin\left(c+d\,x\right)}^5}{5\,b}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(a^5-2\,a^3\,b^2+a\,b^4\right)}{b^6}-\frac{a\,{\sin\left(c+d\,x\right)}^4}{4\,b^2}+\frac{a\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{2\,b}}{d}","Not used",1,"(sin(c + d*x)*(1/b - (a^2*(2/b - a^2/b^3))/b^2) - sin(c + d*x)^3*(2/(3*b) - a^2/(3*b^3)) + sin(c + d*x)^5/(5*b) - (log(a + b*sin(c + d*x))*(a*b^4 + a^5 - 2*a^3*b^2))/b^6 - (a*sin(c + d*x)^4)/(4*b^2) + (a*sin(c + d*x)^2*(2/b - a^2/b^3))/(2*b))/d","B"
1313,1,254,107,12.097747,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-2\,b^2\right)}{b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^2-2\,b^2\right)}{b^3}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{b^2}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2-4\,b^2\right)}{3\,b^3}}{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{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2-2\,b^2\right)}{b^4\,d}-\frac{\ln\left(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)\,{\left(a^2-b^2\right)}^2}{a\,b^4\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a*d) + ((2*tan(c/2 + (d*x)/2)*(a^2 - 2*b^2))/b^3 + (2*tan(c/2 + (d*x)/2)^5*(a^2 - 2*b^2))/b^3 - (2*a*tan(c/2 + (d*x)/2)^2)/b^2 - (2*a*tan(c/2 + (d*x)/2)^4)/b^2 + (4*tan(c/2 + (d*x)/2)^3*(3*a^2 - 4*b^2))/(3*b^3))/(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)) + (a*log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 - 2*b^2))/(b^4*d) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2)^2)/(a*b^4*d)","B"
1314,1,233,96,12.028715,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{\ln\left(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)\,{\left(a^2-b^2\right)}^2}{a^2\,b^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2-2\,b^2\right)}{b^3\,d}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+b^2\right)}{b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,a^2+b^2\right)}{b^2}-\frac{4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b}+1}{d\,\left(2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,{\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)\right)}","Not used",1,"(log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2)^2)/(a^2*b^3*d) - tan(c/2 + (d*x)/2)/(2*a*d) - (log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 - 2*b^2))/(b^3*d) - (b*log(tan(c/2 + (d*x)/2)))/(a^2*d) - ((2*tan(c/2 + (d*x)/2)^2*(2*a^2 + b^2))/b^2 + (tan(c/2 + (d*x)/2)^4*(4*a^2 + b^2))/b^2 - (4*a*tan(c/2 + (d*x)/2)^3)/b + 1)/(d*(2*a*tan(c/2 + (d*x)/2) + 4*a*tan(c/2 + (d*x)/2)^3 + 2*a*tan(c/2 + (d*x)/2)^5))","B"
1315,1,238,105,11.979983,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{\frac{a}{2}-2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^2+b^2\right)}{b}}{d\,\left(4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2-b^2\right)}{a^3\,d}-\frac{\ln\left(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)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{a^3\,b^2\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(2*a^2*d) - (a/2 - 2*b*tan(c/2 + (d*x)/2) + (a*tan(c/2 + (d*x)/2)^2)/2 - (2*tan(c/2 + (d*x)/2)^3*(4*a^2 + b^2))/b)/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 + 4*a^2*tan(c/2 + (d*x)/2)^4)) - tan(c/2 + (d*x)/2)^2/(8*a*d) + (a*log(tan(c/2 + (d*x)/2)^2 + 1))/(b^2*d) - (log(tan(c/2 + (d*x)/2))*(2*a^2 - b^2))/(a^3*d) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 + b^4 - 2*a^2*b^2))/(a^3*b^2*d)","B"
1316,1,227,120,11.927530,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7}{8\,a}-\frac{b^2}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2\,b-b^3\right)}{a^4\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,a^2-4\,b^2\right)-\frac{a^2}{3}+a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}+\frac{\ln\left(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)\,{\left(a^2-b^2\right)}^2}{a^4\,b\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(7/(8*a) - b^2/(2*a^3)))/d - tan(c/2 + (d*x)/2)^3/(24*a*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(b*d) + (log(tan(c/2 + (d*x)/2))*(2*a^2*b - b^3))/(a^4*d) + (b*tan(c/2 + (d*x)/2)^2)/(8*a^2*d) + (tan(c/2 + (d*x)/2)^2*(7*a^2 - 4*b^2) - a^2/3 + a*b*tan(c/2 + (d*x)/2))/(8*a^3*d*tan(c/2 + (d*x)/2)^3) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2)^2)/(a^4*b*d)","B"
1317,1,281,148,11.827963,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3}{16\,a}-\frac{b^2}{8\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{8\,a^2}+\frac{2\,b\,\left(\frac{3}{8\,a}-\frac{b^2}{4\,a^3}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a\,b^2-3\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(14\,a^2\,b-8\,b^3\right)+\frac{a^3}{4}-\frac{2\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{16\,a^4\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}-\frac{\ln\left(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)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{a^5\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{a^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(3/(16*a) - b^2/(8*a^3)))/d - tan(c/2 + (d*x)/2)^4/(64*a*d) - (tan(c/2 + (d*x)/2)*(b/(8*a^2) + (2*b*(3/(8*a) - b^2/(4*a^3)))/a))/d - (tan(c/2 + (d*x)/2)^2*(2*a*b^2 - 3*a^3) + tan(c/2 + (d*x)/2)^3*(14*a^2*b - 8*b^3) + a^3/4 - (2*a^2*b*tan(c/2 + (d*x)/2))/3)/(16*a^4*d*tan(c/2 + (d*x)/2)^4) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 + b^4 - 2*a^2*b^2))/(a^5*d) + (b*tan(c/2 + (d*x)/2)^3)/(24*a^2*d) + (log(tan(c/2 + (d*x)/2))*(a^4 + b^4 - 2*a^2*b^2))/(a^5*d)","B"
1318,1,381,179,11.916667,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^6*(a + b*sin(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b^2}{8\,a^3}-\frac{5}{16\,a}+\frac{2\,b\,\left(\frac{b}{16\,a^2}+\frac{2\,b\,\left(\frac{5}{32\,a}-\frac{b^2}{8\,a^3}\right)}{a}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b}{32\,a^2}+\frac{b\,\left(\frac{5}{32\,a}-\frac{b^2}{8\,a^3}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5}{96\,a}-\frac{b^2}{24\,a^3}\right)}{d}+\frac{\ln\left(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)\,\left(a^4\,b-2\,a^2\,b^3+b^5\right)}{a^6\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4\,b-2\,a^2\,b^3+b^5\right)}{a^6\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{5\,a^4}{3}-\frac{4\,a^2\,b^2}{3}\right)-\frac{a^4}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(10\,a^4-28\,a^2\,b^2+16\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a\,b^3-6\,a^3\,b\right)+\frac{a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{32\,a^5\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(tan(c/2 + (d*x)/2)*(b^2/(8*a^3) - 5/(16*a) + (2*b*(b/(16*a^2) + (2*b*(5/(32*a) - b^2/(8*a^3)))/a))/a))/d - (tan(c/2 + (d*x)/2)^2*(b/(32*a^2) + (b*(5/(32*a) - b^2/(8*a^3)))/a))/d - tan(c/2 + (d*x)/2)^5/(160*a*d) + (tan(c/2 + (d*x)/2)^3*(5/(96*a) - b^2/(24*a^3)))/d + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4*b + b^5 - 2*a^2*b^3))/(a^6*d) + (b*tan(c/2 + (d*x)/2)^4)/(64*a^2*d) - (log(tan(c/2 + (d*x)/2))*(a^4*b + b^5 - 2*a^2*b^3))/(a^6*d) + (tan(c/2 + (d*x)/2)^2*((5*a^4)/3 - (4*a^2*b^2)/3) - a^4/5 - tan(c/2 + (d*x)/2)^4*(10*a^4 + 16*b^4 - 28*a^2*b^2) + tan(c/2 + (d*x)/2)^3*(4*a*b^3 - 6*a^3*b) + (a^3*b*tan(c/2 + (d*x)/2))/2)/(32*a^5*d*tan(c/2 + (d*x)/2)^5)","B"
1319,1,514,212,12.314133,"\text{Not used}","int(cos(c + d*x)^5/(sin(c + d*x)^7*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{b}{96\,a^2}+\frac{2\,b\,\left(\frac{1}{16\,a}-\frac{b^2}{16\,a^3}\right)}{3\,a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{32\,a^2}-\frac{2\,b\,\left(\frac{b^2}{16\,a^3}-\frac{5}{64\,a}+\frac{2\,b\,\left(\frac{b}{32\,a^2}+\frac{2\,b\,\left(\frac{1}{16\,a}-\frac{b^2}{16\,a^3}\right)}{a}\right)}{a}\right)}{a}+\frac{2\,b\,\left(\frac{1}{16\,a}-\frac{b^2}{16\,a^3}\right)}{a}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b^2}{32\,a^3}-\frac{5}{128\,a}+\frac{b\,\left(\frac{b}{32\,a^2}+\frac{2\,b\,\left(\frac{1}{16\,a}-\frac{b^2}{16\,a^3}\right)}{a}\right)}{a}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4\,b^2-2\,a^2\,b^4+b^6\right)}{a^7\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^2\,d}-\frac{\ln\left(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)\,\left(a^4\,b^2-2\,a^2\,b^4+b^6\right)}{a^7\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{10\,a^4\,b}{3}-\frac{8\,a^2\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{5\,a^5}{2}-12\,a^3\,b^2+8\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(20\,a^4\,b-56\,a^2\,b^3+32\,b^5\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^5-a^3\,b^2\right)+\frac{a^5}{6}-\frac{2\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}}{64\,a^6\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"(tan(c/2 + (d*x)/2)^4*(1/(64*a) - b^2/(64*a^3)))/d - (tan(c/2 + (d*x)/2)^3*(b/(96*a^2) + (2*b*(1/(16*a) - b^2/(16*a^3)))/(3*a)))/d - tan(c/2 + (d*x)/2)^6/(384*a*d) + (tan(c/2 + (d*x)/2)*(b/(32*a^2) - (2*b*(b^2/(16*a^3) - 5/(64*a) + (2*b*(b/(32*a^2) + (2*b*(1/(16*a) - b^2/(16*a^3)))/a))/a))/a + (2*b*(1/(16*a) - b^2/(16*a^3)))/a))/d + (tan(c/2 + (d*x)/2)^2*(b^2/(32*a^3) - 5/(128*a) + (b*(b/(32*a^2) + (2*b*(1/(16*a) - b^2/(16*a^3)))/a))/a))/d + (log(tan(c/2 + (d*x)/2))*(b^6 - 2*a^2*b^4 + a^4*b^2))/(a^7*d) + (b*tan(c/2 + (d*x)/2)^5)/(160*a^2*d) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(b^6 - 2*a^2*b^4 + a^4*b^2))/(a^7*d) - (tan(c/2 + (d*x)/2)^3*((10*a^4*b)/3 - (8*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^4*(8*a*b^4 + (5*a^5)/2 - 12*a^3*b^2) - tan(c/2 + (d*x)/2)^5*(20*a^4*b + 32*b^5 - 56*a^2*b^3) - tan(c/2 + (d*x)/2)^2*(a^5 - a^3*b^2) + a^5/6 - (2*a^4*b*tan(c/2 + (d*x)/2))/5)/(64*a^6*d*tan(c/2 + (d*x)/2)^6)","B"
1320,1,4505,467,15.077439,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^3)/(a + b*sin(c + d*x)),x)","\frac{\frac{2\,\left(-105\,a^7+245\,a^5\,b^2-161\,a^3\,b^4+15\,a\,b^6\right)}{105\,b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6\right)}{b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(-7\,a^7+19\,a^5\,b^2-15\,a^3\,b^4+a\,b^6\right)}{b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(-63\,a^7+157\,a^5\,b^2-109\,a^3\,b^4+15\,a\,b^6\right)}{3\,b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-105\,a^7+245\,a^5\,b^2-161\,a^3\,b^4+15\,a\,b^6\right)}{3\,b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-315\,a^7+695\,a^5\,b^2-419\,a^3\,b^4+45\,a\,b^6\right)}{15\,b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-525\,a^7+1175\,a^5\,b^2-743\,a^3\,b^4+45\,a\,b^6\right)}{15\,b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-735\,a^7+1645\,a^5\,b^2-973\,a^3\,b^4+15\,a\,b^6\right)}{105\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^6-144\,a^4\,b^2+88\,a^2\,b^4-5\,b^6\right)}{64\,b^7}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(64\,a^6-144\,a^4\,b^2+88\,a^2\,b^4-5\,b^6\right)}{64\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(960\,a^6-1776\,a^4\,b^2+488\,a^2\,b^4+397\,b^6\right)}{192\,b^7}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(960\,a^6-1776\,a^4\,b^2+488\,a^2\,b^4+397\,b^6\right)}{192\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(960\,a^6-1392\,a^4\,b^2+680\,a^2\,b^4+1765\,b^6\right)}{192\,b^7}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(960\,a^6-1392\,a^4\,b^2+680\,a^2\,b^4+1765\,b^6\right)}{192\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(1728\,a^6-2736\,a^4\,b^2+904\,a^2\,b^4-895\,b^6\right)}{192\,b^7}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(1728\,a^6-2736\,a^4\,b^2+904\,a^2\,b^4-895\,b^6\right)}{192\,b^7}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,a^{18}\,b^8-160\,a^{16}\,b^{10}+320\,a^{14}\,b^{12}-320\,a^{12}\,b^{14}+160\,a^{10}\,b^{16}-\frac{125\,a^8\,b^{18}}{4}-\frac{25\,a^6\,b^{20}}{16}+\frac{25\,a^4\,b^{22}}{32}+\frac{25\,a^2\,b^{24}}{512}}{b^{23}}-\frac{\left(\frac{-16\,a^9\,b^{18}+44\,a^7\,b^{20}-38\,a^5\,b^{22}+\frac{35\,a^3\,b^{24}}{4}+\frac{5\,a\,b^{26}}{4}}{b^{23}}-\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(49152\,a\,b^{28}-32768\,a^3\,b^{26}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{10}\,b^{18}+98304\,a^8\,b^{20}-98304\,a^6\,b^{22}+32768\,a^4\,b^{24}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{19}\,b^8+212992\,a^{17}\,b^{10}-573440\,a^{15}\,b^{12}+819200\,a^{13}\,b^{14}-655360\,a^{11}\,b^{16}+278144\,a^9\,b^{18}-47584\,a^7\,b^{20}-2000\,a^5\,b^{22}+775\,a^3\,b^{24}+50\,a\,b^{26}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{128\,b^9}+\frac{\left(\frac{32\,a^{18}\,b^8-160\,a^{16}\,b^{10}+320\,a^{14}\,b^{12}-320\,a^{12}\,b^{14}+160\,a^{10}\,b^{16}-\frac{125\,a^8\,b^{18}}{4}-\frac{25\,a^6\,b^{20}}{16}+\frac{25\,a^4\,b^{22}}{32}+\frac{25\,a^2\,b^{24}}{512}}{b^{23}}+\frac{\left(\frac{-16\,a^9\,b^{18}+44\,a^7\,b^{20}-38\,a^5\,b^{22}+\frac{35\,a^3\,b^{24}}{4}+\frac{5\,a\,b^{26}}{4}}{b^{23}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(49152\,a\,b^{28}-32768\,a^3\,b^{26}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{10}\,b^{18}+98304\,a^8\,b^{20}-98304\,a^6\,b^{22}+32768\,a^4\,b^{24}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{19}\,b^8+212992\,a^{17}\,b^{10}-573440\,a^{15}\,b^{12}+819200\,a^{13}\,b^{14}-655360\,a^{11}\,b^{16}+278144\,a^9\,b^{18}-47584\,a^7\,b^{20}-2000\,a^5\,b^{22}+775\,a^3\,b^{24}+50\,a\,b^{26}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{128\,b^9}}{\frac{32\,a^{25}-248\,a^{23}\,b^2+836\,a^{21}\,b^4-\frac{3195\,a^{19}\,b^6}{2}+\frac{3773\,a^{17}\,b^8}{2}-\frac{11217\,a^{15}\,b^{10}}{8}+\frac{10135\,a^{13}\,b^{12}}{16}-\frac{39415\,a^{11}\,b^{14}}{256}+\frac{3205\,a^9\,b^{16}}{256}+\frac{315\,a^7\,b^{18}}{256}-\frac{25\,a^5\,b^{20}}{256}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32768\,a^{26}-262144\,a^{24}\,b^2+917504\,a^{22}\,b^4-1835008\,a^{20}\,b^6+2293760\,a^{18}\,b^8-1834240\,a^{16}\,b^{10}+913600\,a^{14}\,b^{12}-254240\,a^{12}\,b^{14}+24850\,a^{10}\,b^{16}+3850\,a^8\,b^{18}-650\,a^6\,b^{20}-50\,a^4\,b^{22}\right)}{256\,b^{24}}+\frac{\left(\frac{32\,a^{18}\,b^8-160\,a^{16}\,b^{10}+320\,a^{14}\,b^{12}-320\,a^{12}\,b^{14}+160\,a^{10}\,b^{16}-\frac{125\,a^8\,b^{18}}{4}-\frac{25\,a^6\,b^{20}}{16}+\frac{25\,a^4\,b^{22}}{32}+\frac{25\,a^2\,b^{24}}{512}}{b^{23}}-\frac{\left(\frac{-16\,a^9\,b^{18}+44\,a^7\,b^{20}-38\,a^5\,b^{22}+\frac{35\,a^3\,b^{24}}{4}+\frac{5\,a\,b^{26}}{4}}{b^{23}}-\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(49152\,a\,b^{28}-32768\,a^3\,b^{26}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{10}\,b^{18}+98304\,a^8\,b^{20}-98304\,a^6\,b^{22}+32768\,a^4\,b^{24}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{19}\,b^8+212992\,a^{17}\,b^{10}-573440\,a^{15}\,b^{12}+819200\,a^{13}\,b^{14}-655360\,a^{11}\,b^{16}+278144\,a^9\,b^{18}-47584\,a^7\,b^{20}-2000\,a^5\,b^{22}+775\,a^3\,b^{24}+50\,a\,b^{26}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}-\frac{\left(\frac{32\,a^{18}\,b^8-160\,a^{16}\,b^{10}+320\,a^{14}\,b^{12}-320\,a^{12}\,b^{14}+160\,a^{10}\,b^{16}-\frac{125\,a^8\,b^{18}}{4}-\frac{25\,a^6\,b^{20}}{16}+\frac{25\,a^4\,b^{22}}{32}+\frac{25\,a^2\,b^{24}}{512}}{b^{23}}+\frac{\left(\frac{-16\,a^9\,b^{18}+44\,a^7\,b^{20}-38\,a^5\,b^{22}+\frac{35\,a^3\,b^{24}}{4}+\frac{5\,a\,b^{26}}{4}}{b^{23}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(49152\,a\,b^{28}-32768\,a^3\,b^{26}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{10}\,b^{18}+98304\,a^8\,b^{20}-98304\,a^6\,b^{22}+32768\,a^4\,b^{24}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{19}\,b^8+212992\,a^{17}\,b^{10}-573440\,a^{15}\,b^{12}+819200\,a^{13}\,b^{14}-655360\,a^{11}\,b^{16}+278144\,a^9\,b^{18}-47584\,a^7\,b^{20}-2000\,a^5\,b^{22}+775\,a^3\,b^{24}+50\,a\,b^{26}\right)}{512\,b^{24}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)}{128\,b^9}}\right)\,\left(-a^8\,128{}\mathrm{i}+a^6\,b^2\,320{}\mathrm{i}-a^4\,b^4\,240{}\mathrm{i}+a^2\,b^6\,40{}\mathrm{i}+b^8\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{64\,b^9\,d}-\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{18}\,b^8-160\,a^{16}\,b^{10}+320\,a^{14}\,b^{12}-320\,a^{12}\,b^{14}+160\,a^{10}\,b^{16}-\frac{125\,a^8\,b^{18}}{4}-\frac{25\,a^6\,b^{20}}{16}+\frac{25\,a^4\,b^{22}}{32}+\frac{25\,a^2\,b^{24}}{512}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{19}\,b^8+212992\,a^{17}\,b^{10}-573440\,a^{15}\,b^{12}+819200\,a^{13}\,b^{14}-655360\,a^{11}\,b^{16}+278144\,a^9\,b^{18}-47584\,a^7\,b^{20}-2000\,a^5\,b^{22}+775\,a^3\,b^{24}+50\,a\,b^{26}\right)}{512\,b^{24}}+\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^9\,b^{18}+44\,a^7\,b^{20}-38\,a^5\,b^{22}+\frac{35\,a^3\,b^{24}}{4}+\frac{5\,a\,b^{26}}{4}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{10}\,b^{18}+98304\,a^8\,b^{20}-98304\,a^6\,b^{22}+32768\,a^4\,b^{24}\right)}{512\,b^{24}}+\frac{a^3\,\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(49152\,a\,b^{28}-32768\,a^3\,b^{26}\right)}{512\,b^{24}}\right)}{b^9}\right)}{b^9}\right)\,1{}\mathrm{i}}{b^9}+\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{18}\,b^8-160\,a^{16}\,b^{10}+320\,a^{14}\,b^{12}-320\,a^{12}\,b^{14}+160\,a^{10}\,b^{16}-\frac{125\,a^8\,b^{18}}{4}-\frac{25\,a^6\,b^{20}}{16}+\frac{25\,a^4\,b^{22}}{32}+\frac{25\,a^2\,b^{24}}{512}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{19}\,b^8+212992\,a^{17}\,b^{10}-573440\,a^{15}\,b^{12}+819200\,a^{13}\,b^{14}-655360\,a^{11}\,b^{16}+278144\,a^9\,b^{18}-47584\,a^7\,b^{20}-2000\,a^5\,b^{22}+775\,a^3\,b^{24}+50\,a\,b^{26}\right)}{512\,b^{24}}-\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^9\,b^{18}+44\,a^7\,b^{20}-38\,a^5\,b^{22}+\frac{35\,a^3\,b^{24}}{4}+\frac{5\,a\,b^{26}}{4}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{10}\,b^{18}+98304\,a^8\,b^{20}-98304\,a^6\,b^{22}+32768\,a^4\,b^{24}\right)}{512\,b^{24}}-\frac{a^3\,\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(49152\,a\,b^{28}-32768\,a^3\,b^{26}\right)}{512\,b^{24}}\right)}{b^9}\right)}{b^9}\right)\,1{}\mathrm{i}}{b^9}}{\frac{32\,a^{25}-248\,a^{23}\,b^2+836\,a^{21}\,b^4-\frac{3195\,a^{19}\,b^6}{2}+\frac{3773\,a^{17}\,b^8}{2}-\frac{11217\,a^{15}\,b^{10}}{8}+\frac{10135\,a^{13}\,b^{12}}{16}-\frac{39415\,a^{11}\,b^{14}}{256}+\frac{3205\,a^9\,b^{16}}{256}+\frac{315\,a^7\,b^{18}}{256}-\frac{25\,a^5\,b^{20}}{256}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32768\,a^{26}-262144\,a^{24}\,b^2+917504\,a^{22}\,b^4-1835008\,a^{20}\,b^6+2293760\,a^{18}\,b^8-1834240\,a^{16}\,b^{10}+913600\,a^{14}\,b^{12}-254240\,a^{12}\,b^{14}+24850\,a^{10}\,b^{16}+3850\,a^8\,b^{18}-650\,a^6\,b^{20}-50\,a^4\,b^{22}\right)}{256\,b^{24}}-\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{18}\,b^8-160\,a^{16}\,b^{10}+320\,a^{14}\,b^{12}-320\,a^{12}\,b^{14}+160\,a^{10}\,b^{16}-\frac{125\,a^8\,b^{18}}{4}-\frac{25\,a^6\,b^{20}}{16}+\frac{25\,a^4\,b^{22}}{32}+\frac{25\,a^2\,b^{24}}{512}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{19}\,b^8+212992\,a^{17}\,b^{10}-573440\,a^{15}\,b^{12}+819200\,a^{13}\,b^{14}-655360\,a^{11}\,b^{16}+278144\,a^9\,b^{18}-47584\,a^7\,b^{20}-2000\,a^5\,b^{22}+775\,a^3\,b^{24}+50\,a\,b^{26}\right)}{512\,b^{24}}+\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^9\,b^{18}+44\,a^7\,b^{20}-38\,a^5\,b^{22}+\frac{35\,a^3\,b^{24}}{4}+\frac{5\,a\,b^{26}}{4}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{10}\,b^{18}+98304\,a^8\,b^{20}-98304\,a^6\,b^{22}+32768\,a^4\,b^{24}\right)}{512\,b^{24}}+\frac{a^3\,\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(49152\,a\,b^{28}-32768\,a^3\,b^{26}\right)}{512\,b^{24}}\right)}{b^9}\right)}{b^9}\right)}{b^9}+\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{18}\,b^8-160\,a^{16}\,b^{10}+320\,a^{14}\,b^{12}-320\,a^{12}\,b^{14}+160\,a^{10}\,b^{16}-\frac{125\,a^8\,b^{18}}{4}-\frac{25\,a^6\,b^{20}}{16}+\frac{25\,a^4\,b^{22}}{32}+\frac{25\,a^2\,b^{24}}{512}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{19}\,b^8+212992\,a^{17}\,b^{10}-573440\,a^{15}\,b^{12}+819200\,a^{13}\,b^{14}-655360\,a^{11}\,b^{16}+278144\,a^9\,b^{18}-47584\,a^7\,b^{20}-2000\,a^5\,b^{22}+775\,a^3\,b^{24}+50\,a\,b^{26}\right)}{512\,b^{24}}-\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^9\,b^{18}+44\,a^7\,b^{20}-38\,a^5\,b^{22}+\frac{35\,a^3\,b^{24}}{4}+\frac{5\,a\,b^{26}}{4}}{b^{23}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32768\,a^{10}\,b^{18}+98304\,a^8\,b^{20}-98304\,a^6\,b^{22}+32768\,a^4\,b^{24}\right)}{512\,b^{24}}-\frac{a^3\,\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(49152\,a\,b^{28}-32768\,a^3\,b^{26}\right)}{512\,b^{24}}\right)}{b^9}\right)}{b^9}\right)}{b^9}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{b^9\,d}","Not used",1,"((2*(15*a*b^6 - 105*a^7 - 161*a^3*b^4 + 245*a^5*b^2))/(105*b^8) + (2*tan(c/2 + (d*x)/2)^14*(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))/b^8 + (2*tan(c/2 + (d*x)/2)^12*(a*b^6 - 7*a^7 - 15*a^3*b^4 + 19*a^5*b^2))/b^8 + (2*tan(c/2 + (d*x)/2)^10*(15*a*b^6 - 63*a^7 - 109*a^3*b^4 + 157*a^5*b^2))/(3*b^8) + (2*tan(c/2 + (d*x)/2)^8*(15*a*b^6 - 105*a^7 - 161*a^3*b^4 + 245*a^5*b^2))/(3*b^8) + (2*tan(c/2 + (d*x)/2)^4*(45*a*b^6 - 315*a^7 - 419*a^3*b^4 + 695*a^5*b^2))/(15*b^8) + (2*tan(c/2 + (d*x)/2)^6*(45*a*b^6 - 525*a^7 - 743*a^3*b^4 + 1175*a^5*b^2))/(15*b^8) + (2*tan(c/2 + (d*x)/2)^2*(15*a*b^6 - 735*a^7 - 973*a^3*b^4 + 1645*a^5*b^2))/(105*b^8) + (tan(c/2 + (d*x)/2)*(64*a^6 - 5*b^6 + 88*a^2*b^4 - 144*a^4*b^2))/(64*b^7) - (tan(c/2 + (d*x)/2)^15*(64*a^6 - 5*b^6 + 88*a^2*b^4 - 144*a^4*b^2))/(64*b^7) + (tan(c/2 + (d*x)/2)^3*(960*a^6 + 397*b^6 + 488*a^2*b^4 - 1776*a^4*b^2))/(192*b^7) - (tan(c/2 + (d*x)/2)^13*(960*a^6 + 397*b^6 + 488*a^2*b^4 - 1776*a^4*b^2))/(192*b^7) + (tan(c/2 + (d*x)/2)^7*(960*a^6 + 1765*b^6 + 680*a^2*b^4 - 1392*a^4*b^2))/(192*b^7) - (tan(c/2 + (d*x)/2)^9*(960*a^6 + 1765*b^6 + 680*a^2*b^4 - 1392*a^4*b^2))/(192*b^7) + (tan(c/2 + (d*x)/2)^5*(1728*a^6 - 895*b^6 + 904*a^2*b^4 - 2736*a^4*b^2))/(192*b^7) - (tan(c/2 + (d*x)/2)^11*(1728*a^6 - 895*b^6 + 904*a^2*b^4 - 2736*a^4*b^2))/(192*b^7))/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) - (atan((((((25*a^2*b^24)/512 + (25*a^4*b^22)/32 - (25*a^6*b^20)/16 - (125*a^8*b^18)/4 + 160*a^10*b^16 - 320*a^12*b^14 + 320*a^14*b^12 - 160*a^16*b^10 + 32*a^18*b^8)/b^23 - ((((5*a*b^26)/4 + (35*a^3*b^24)/4 - 38*a^5*b^22 + 44*a^7*b^20 - 16*a^9*b^18)/b^23 - ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(49152*a*b^28 - 32768*a^3*b^26))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) + (tan(c/2 + (d*x)/2)*(32768*a^4*b^24 - 98304*a^6*b^22 + 98304*a^8*b^20 - 32768*a^10*b^18))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) + (tan(c/2 + (d*x)/2)*(50*a*b^26 + 775*a^3*b^24 - 2000*a^5*b^22 - 47584*a^7*b^20 + 278144*a^9*b^18 - 655360*a^11*b^16 + 819200*a^13*b^14 - 573440*a^15*b^12 + 212992*a^17*b^10 - 32768*a^19*b^8))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i)*1i)/(128*b^9) + ((((25*a^2*b^24)/512 + (25*a^4*b^22)/32 - (25*a^6*b^20)/16 - (125*a^8*b^18)/4 + 160*a^10*b^16 - 320*a^12*b^14 + 320*a^14*b^12 - 160*a^16*b^10 + 32*a^18*b^8)/b^23 + ((((5*a*b^26)/4 + (35*a^3*b^24)/4 - 38*a^5*b^22 + 44*a^7*b^20 - 16*a^9*b^18)/b^23 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(49152*a*b^28 - 32768*a^3*b^26))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) + (tan(c/2 + (d*x)/2)*(32768*a^4*b^24 - 98304*a^6*b^22 + 98304*a^8*b^20 - 32768*a^10*b^18))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) + (tan(c/2 + (d*x)/2)*(50*a*b^26 + 775*a^3*b^24 - 2000*a^5*b^22 - 47584*a^7*b^20 + 278144*a^9*b^18 - 655360*a^11*b^16 + 819200*a^13*b^14 - 573440*a^15*b^12 + 212992*a^17*b^10 - 32768*a^19*b^8))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i)*1i)/(128*b^9))/((32*a^25 - (25*a^5*b^20)/256 + (315*a^7*b^18)/256 + (3205*a^9*b^16)/256 - (39415*a^11*b^14)/256 + (10135*a^13*b^12)/16 - (11217*a^15*b^10)/8 + (3773*a^17*b^8)/2 - (3195*a^19*b^6)/2 + 836*a^21*b^4 - 248*a^23*b^2)/b^23 + (tan(c/2 + (d*x)/2)*(32768*a^26 - 50*a^4*b^22 - 650*a^6*b^20 + 3850*a^8*b^18 + 24850*a^10*b^16 - 254240*a^12*b^14 + 913600*a^14*b^12 - 1834240*a^16*b^10 + 2293760*a^18*b^8 - 1835008*a^20*b^6 + 917504*a^22*b^4 - 262144*a^24*b^2))/(256*b^24) + ((((25*a^2*b^24)/512 + (25*a^4*b^22)/32 - (25*a^6*b^20)/16 - (125*a^8*b^18)/4 + 160*a^10*b^16 - 320*a^12*b^14 + 320*a^14*b^12 - 160*a^16*b^10 + 32*a^18*b^8)/b^23 - ((((5*a*b^26)/4 + (35*a^3*b^24)/4 - 38*a^5*b^22 + 44*a^7*b^20 - 16*a^9*b^18)/b^23 - ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(49152*a*b^28 - 32768*a^3*b^26))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) + (tan(c/2 + (d*x)/2)*(32768*a^4*b^24 - 98304*a^6*b^22 + 98304*a^8*b^20 - 32768*a^10*b^18))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) + (tan(c/2 + (d*x)/2)*(50*a*b^26 + 775*a^3*b^24 - 2000*a^5*b^22 - 47584*a^7*b^20 + 278144*a^9*b^18 - 655360*a^11*b^16 + 819200*a^13*b^14 - 573440*a^15*b^12 + 212992*a^17*b^10 - 32768*a^19*b^8))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) - ((((25*a^2*b^24)/512 + (25*a^4*b^22)/32 - (25*a^6*b^20)/16 - (125*a^8*b^18)/4 + 160*a^10*b^16 - 320*a^12*b^14 + 320*a^14*b^12 - 160*a^16*b^10 + 32*a^18*b^8)/b^23 + ((((5*a*b^26)/4 + (35*a^3*b^24)/4 - 38*a^5*b^22 + 44*a^7*b^20 - 16*a^9*b^18)/b^23 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(49152*a*b^28 - 32768*a^3*b^26))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) + (tan(c/2 + (d*x)/2)*(32768*a^4*b^24 - 98304*a^6*b^22 + 98304*a^8*b^20 - 32768*a^10*b^18))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9) + (tan(c/2 + (d*x)/2)*(50*a*b^26 + 775*a^3*b^24 - 2000*a^5*b^22 - 47584*a^7*b^20 + 278144*a^9*b^18 - 655360*a^11*b^16 + 819200*a^13*b^14 - 573440*a^15*b^12 + 212992*a^17*b^10 - 32768*a^19*b^8))/(512*b^24))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i))/(128*b^9)))*(b^8*5i - a^8*128i + a^2*b^6*40i - a^4*b^4*240i + a^6*b^2*320i)*1i)/(64*b^9*d) - (a^3*atan(((a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^2*b^24)/512 + (25*a^4*b^22)/32 - (25*a^6*b^20)/16 - (125*a^8*b^18)/4 + 160*a^10*b^16 - 320*a^12*b^14 + 320*a^14*b^12 - 160*a^16*b^10 + 32*a^18*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a*b^26 + 775*a^3*b^24 - 2000*a^5*b^22 - 47584*a^7*b^20 + 278144*a^9*b^18 - 655360*a^11*b^16 + 819200*a^13*b^14 - 573440*a^15*b^12 + 212992*a^17*b^10 - 32768*a^19*b^8))/(512*b^24) + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(((5*a*b^26)/4 + (35*a^3*b^24)/4 - 38*a^5*b^22 + 44*a^7*b^20 - 16*a^9*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(32768*a^4*b^24 - 98304*a^6*b^22 + 98304*a^8*b^20 - 32768*a^10*b^18))/(512*b^24) + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(49152*a*b^28 - 32768*a^3*b^26))/(512*b^24)))/b^9))/b^9)*1i)/b^9 + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^2*b^24)/512 + (25*a^4*b^22)/32 - (25*a^6*b^20)/16 - (125*a^8*b^18)/4 + 160*a^10*b^16 - 320*a^12*b^14 + 320*a^14*b^12 - 160*a^16*b^10 + 32*a^18*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a*b^26 + 775*a^3*b^24 - 2000*a^5*b^22 - 47584*a^7*b^20 + 278144*a^9*b^18 - 655360*a^11*b^16 + 819200*a^13*b^14 - 573440*a^15*b^12 + 212992*a^17*b^10 - 32768*a^19*b^8))/(512*b^24) - (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(((5*a*b^26)/4 + (35*a^3*b^24)/4 - 38*a^5*b^22 + 44*a^7*b^20 - 16*a^9*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(32768*a^4*b^24 - 98304*a^6*b^22 + 98304*a^8*b^20 - 32768*a^10*b^18))/(512*b^24) - (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(49152*a*b^28 - 32768*a^3*b^26))/(512*b^24)))/b^9))/b^9)*1i)/b^9)/((32*a^25 - (25*a^5*b^20)/256 + (315*a^7*b^18)/256 + (3205*a^9*b^16)/256 - (39415*a^11*b^14)/256 + (10135*a^13*b^12)/16 - (11217*a^15*b^10)/8 + (3773*a^17*b^8)/2 - (3195*a^19*b^6)/2 + 836*a^21*b^4 - 248*a^23*b^2)/b^23 + (tan(c/2 + (d*x)/2)*(32768*a^26 - 50*a^4*b^22 - 650*a^6*b^20 + 3850*a^8*b^18 + 24850*a^10*b^16 - 254240*a^12*b^14 + 913600*a^14*b^12 - 1834240*a^16*b^10 + 2293760*a^18*b^8 - 1835008*a^20*b^6 + 917504*a^22*b^4 - 262144*a^24*b^2))/(256*b^24) - (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^2*b^24)/512 + (25*a^4*b^22)/32 - (25*a^6*b^20)/16 - (125*a^8*b^18)/4 + 160*a^10*b^16 - 320*a^12*b^14 + 320*a^14*b^12 - 160*a^16*b^10 + 32*a^18*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a*b^26 + 775*a^3*b^24 - 2000*a^5*b^22 - 47584*a^7*b^20 + 278144*a^9*b^18 - 655360*a^11*b^16 + 819200*a^13*b^14 - 573440*a^15*b^12 + 212992*a^17*b^10 - 32768*a^19*b^8))/(512*b^24) + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(((5*a*b^26)/4 + (35*a^3*b^24)/4 - 38*a^5*b^22 + 44*a^7*b^20 - 16*a^9*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(32768*a^4*b^24 - 98304*a^6*b^22 + 98304*a^8*b^20 - 32768*a^10*b^18))/(512*b^24) + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(49152*a*b^28 - 32768*a^3*b^26))/(512*b^24)))/b^9))/b^9))/b^9 + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^2*b^24)/512 + (25*a^4*b^22)/32 - (25*a^6*b^20)/16 - (125*a^8*b^18)/4 + 160*a^10*b^16 - 320*a^12*b^14 + 320*a^14*b^12 - 160*a^16*b^10 + 32*a^18*b^8)/b^23 + (tan(c/2 + (d*x)/2)*(50*a*b^26 + 775*a^3*b^24 - 2000*a^5*b^22 - 47584*a^7*b^20 + 278144*a^9*b^18 - 655360*a^11*b^16 + 819200*a^13*b^14 - 573440*a^15*b^12 + 212992*a^17*b^10 - 32768*a^19*b^8))/(512*b^24) - (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(((5*a*b^26)/4 + (35*a^3*b^24)/4 - 38*a^5*b^22 + 44*a^7*b^20 - 16*a^9*b^18)/b^23 + (tan(c/2 + (d*x)/2)*(32768*a^4*b^24 - 98304*a^6*b^22 + 98304*a^8*b^20 - 32768*a^10*b^18))/(512*b^24) - (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(49152*a*b^28 - 32768*a^3*b^26))/(512*b^24)))/b^9))/b^9))/b^9))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(b^9*d)","B"
1321,1,3797,408,14.463250,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x)^2)/(a + b*sin(c + d*x)),x)","\frac{\frac{2\,\left(105\,a^6-245\,a^4\,b^2+161\,a^2\,b^4-15\,b^6\right)}{105\,b^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(8\,a^5-18\,a^3\,b^2+11\,a\,b^4\right)}{8\,b^6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(24\,a^5-42\,a^3\,b^2+7\,a\,b^4\right)}{6\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(24\,a^5-42\,a^3\,b^2+7\,a\,b^4\right)}{6\,b^6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(120\,a^5-174\,a^3\,b^2+85\,a\,b^4\right)}{24\,b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(120\,a^5-174\,a^3\,b^2+85\,a\,b^4\right)}{24\,b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}{b^7}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(3\,a^6-8\,a^4\,b^2+6\,a^2\,b^4\right)}{b^7}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(15\,a^6-34\,a^4\,b^2+22\,a^2\,b^4\right)}{3\,b^7}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(45\,a^6-100\,a^4\,b^2+58\,a^2\,b^4\right)}{15\,b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(45\,a^6-109\,a^4\,b^2+73\,a^2\,b^4-15\,b^6\right)}{3\,b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(75\,a^6-165\,a^4\,b^2+101\,a^2\,b^4-15\,b^6\right)}{5\,b^7}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^4-18\,a^2\,b^2+11\,b^4\right)}{8\,b^6}}{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{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{16}\,b^7-160\,a^{14}\,b^9+320\,a^{12}\,b^{11}-320\,a^{10}\,b^{13}+\frac{325\,a^8\,b^{15}}{2}-\frac{75\,a^6\,b^{17}}{2}+\frac{25\,a^4\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{17}\,b^7+3328\,a^{15}\,b^9-8960\,a^{13}\,b^{11}+12800\,a^{11}\,b^{13}-10260\,a^9\,b^{15}+4436\,a^7\,b^{17}-881\,a^5\,b^{19}+50\,a^3\,b^{21}\right)}{8\,b^{21}}+\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^8\,b^{16}+44\,a^6\,b^{18}-38\,a^4\,b^{20}+10\,a^2\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^9\,b^{16}+1536\,a^7\,b^{18}-1536\,a^5\,b^{20}+512\,a^3\,b^{22}\right)}{8\,b^{21}}+\frac{a^2\,\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(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)}{b^8}\right)}{b^8}\right)\,1{}\mathrm{i}}{b^8}+\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{16}\,b^7-160\,a^{14}\,b^9+320\,a^{12}\,b^{11}-320\,a^{10}\,b^{13}+\frac{325\,a^8\,b^{15}}{2}-\frac{75\,a^6\,b^{17}}{2}+\frac{25\,a^4\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{17}\,b^7+3328\,a^{15}\,b^9-8960\,a^{13}\,b^{11}+12800\,a^{11}\,b^{13}-10260\,a^9\,b^{15}+4436\,a^7\,b^{17}-881\,a^5\,b^{19}+50\,a^3\,b^{21}\right)}{8\,b^{21}}-\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^8\,b^{16}+44\,a^6\,b^{18}-38\,a^4\,b^{20}+10\,a^2\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^9\,b^{16}+1536\,a^7\,b^{18}-1536\,a^5\,b^{20}+512\,a^3\,b^{22}\right)}{8\,b^{21}}-\frac{a^2\,\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(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)}{b^8}\right)}{b^8}\right)\,1{}\mathrm{i}}{b^8}}{\frac{32\,a^{22}-248\,a^{20}\,b^2+836\,a^{18}\,b^4-1595\,a^{16}\,b^6+1874\,a^{14}\,b^8-\frac{5511\,a^{12}\,b^{10}}{4}+\frac{2445\,a^{10}\,b^{12}}{4}-\frac{585\,a^8\,b^{14}}{4}+\frac{55\,a^6\,b^{16}}{4}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{23}-4096\,a^{21}\,b^2+14336\,a^{19}\,b^4-28672\,a^{17}\,b^6+35880\,a^{15}\,b^8-28880\,a^{13}\,b^{10}+14770\,a^{11}\,b^{12}-4550\,a^9\,b^{14}+750\,a^7\,b^{16}-50\,a^5\,b^{18}\right)}{4\,b^{21}}-\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{16}\,b^7-160\,a^{14}\,b^9+320\,a^{12}\,b^{11}-320\,a^{10}\,b^{13}+\frac{325\,a^8\,b^{15}}{2}-\frac{75\,a^6\,b^{17}}{2}+\frac{25\,a^4\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{17}\,b^7+3328\,a^{15}\,b^9-8960\,a^{13}\,b^{11}+12800\,a^{11}\,b^{13}-10260\,a^9\,b^{15}+4436\,a^7\,b^{17}-881\,a^5\,b^{19}+50\,a^3\,b^{21}\right)}{8\,b^{21}}+\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^8\,b^{16}+44\,a^6\,b^{18}-38\,a^4\,b^{20}+10\,a^2\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^9\,b^{16}+1536\,a^7\,b^{18}-1536\,a^5\,b^{20}+512\,a^3\,b^{22}\right)}{8\,b^{21}}+\frac{a^2\,\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(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)}{b^8}\right)}{b^8}\right)}{b^8}+\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{16}\,b^7-160\,a^{14}\,b^9+320\,a^{12}\,b^{11}-320\,a^{10}\,b^{13}+\frac{325\,a^8\,b^{15}}{2}-\frac{75\,a^6\,b^{17}}{2}+\frac{25\,a^4\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{17}\,b^7+3328\,a^{15}\,b^9-8960\,a^{13}\,b^{11}+12800\,a^{11}\,b^{13}-10260\,a^9\,b^{15}+4436\,a^7\,b^{17}-881\,a^5\,b^{19}+50\,a^3\,b^{21}\right)}{8\,b^{21}}-\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^8\,b^{16}+44\,a^6\,b^{18}-38\,a^4\,b^{20}+10\,a^2\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^9\,b^{16}+1536\,a^7\,b^{18}-1536\,a^5\,b^{20}+512\,a^3\,b^{22}\right)}{8\,b^{21}}-\frac{a^2\,\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(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)}{b^8}\right)}{b^8}\right)}{b^8}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{b^8\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{32\,a^{16}\,b^7-160\,a^{14}\,b^9+320\,a^{12}\,b^{11}-320\,a^{10}\,b^{13}+\frac{325\,a^8\,b^{15}}{2}-\frac{75\,a^6\,b^{17}}{2}+\frac{25\,a^4\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{17}\,b^7+3328\,a^{15}\,b^9-8960\,a^{13}\,b^{11}+12800\,a^{11}\,b^{13}-10260\,a^9\,b^{15}+4436\,a^7\,b^{17}-881\,a^5\,b^{19}+50\,a^3\,b^{21}\right)}{8\,b^{21}}-\frac{a\,\left(\frac{-16\,a^8\,b^{16}+44\,a^6\,b^{18}-38\,a^4\,b^{20}+10\,a^2\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^9\,b^{16}+1536\,a^7\,b^{18}-1536\,a^5\,b^{20}+512\,a^3\,b^{22}\right)}{8\,b^{21}}-\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)}{16\,b^8}+\frac{a\,\left(\frac{32\,a^{16}\,b^7-160\,a^{14}\,b^9+320\,a^{12}\,b^{11}-320\,a^{10}\,b^{13}+\frac{325\,a^8\,b^{15}}{2}-\frac{75\,a^6\,b^{17}}{2}+\frac{25\,a^4\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{17}\,b^7+3328\,a^{15}\,b^9-8960\,a^{13}\,b^{11}+12800\,a^{11}\,b^{13}-10260\,a^9\,b^{15}+4436\,a^7\,b^{17}-881\,a^5\,b^{19}+50\,a^3\,b^{21}\right)}{8\,b^{21}}+\frac{a\,\left(\frac{-16\,a^8\,b^{16}+44\,a^6\,b^{18}-38\,a^4\,b^{20}+10\,a^2\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^9\,b^{16}+1536\,a^7\,b^{18}-1536\,a^5\,b^{20}+512\,a^3\,b^{22}\right)}{8\,b^{21}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)}{16\,b^8}}{\frac{32\,a^{22}-248\,a^{20}\,b^2+836\,a^{18}\,b^4-1595\,a^{16}\,b^6+1874\,a^{14}\,b^8-\frac{5511\,a^{12}\,b^{10}}{4}+\frac{2445\,a^{10}\,b^{12}}{4}-\frac{585\,a^8\,b^{14}}{4}+\frac{55\,a^6\,b^{16}}{4}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{23}-4096\,a^{21}\,b^2+14336\,a^{19}\,b^4-28672\,a^{17}\,b^6+35880\,a^{15}\,b^8-28880\,a^{13}\,b^{10}+14770\,a^{11}\,b^{12}-4550\,a^9\,b^{14}+750\,a^7\,b^{16}-50\,a^5\,b^{18}\right)}{4\,b^{21}}+\frac{a\,\left(\frac{32\,a^{16}\,b^7-160\,a^{14}\,b^9+320\,a^{12}\,b^{11}-320\,a^{10}\,b^{13}+\frac{325\,a^8\,b^{15}}{2}-\frac{75\,a^6\,b^{17}}{2}+\frac{25\,a^4\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{17}\,b^7+3328\,a^{15}\,b^9-8960\,a^{13}\,b^{11}+12800\,a^{11}\,b^{13}-10260\,a^9\,b^{15}+4436\,a^7\,b^{17}-881\,a^5\,b^{19}+50\,a^3\,b^{21}\right)}{8\,b^{21}}-\frac{a\,\left(\frac{-16\,a^8\,b^{16}+44\,a^6\,b^{18}-38\,a^4\,b^{20}+10\,a^2\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^9\,b^{16}+1536\,a^7\,b^{18}-1536\,a^5\,b^{20}+512\,a^3\,b^{22}\right)}{8\,b^{21}}-\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}-\frac{a\,\left(\frac{32\,a^{16}\,b^7-160\,a^{14}\,b^9+320\,a^{12}\,b^{11}-320\,a^{10}\,b^{13}+\frac{325\,a^8\,b^{15}}{2}-\frac{75\,a^6\,b^{17}}{2}+\frac{25\,a^4\,b^{19}}{8}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{17}\,b^7+3328\,a^{15}\,b^9-8960\,a^{13}\,b^{11}+12800\,a^{11}\,b^{13}-10260\,a^9\,b^{15}+4436\,a^7\,b^{17}-881\,a^5\,b^{19}+50\,a^3\,b^{21}\right)}{8\,b^{21}}+\frac{a\,\left(\frac{-16\,a^8\,b^{16}+44\,a^6\,b^{18}-38\,a^4\,b^{20}+10\,a^2\,b^{22}}{b^{20}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^9\,b^{16}+1536\,a^7\,b^{18}-1536\,a^5\,b^{20}+512\,a^3\,b^{22}\right)}{8\,b^{21}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{25}-512\,a^3\,b^{23}\right)}{8\,b^{21}}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)\,1{}\mathrm{i}}{16\,b^8}}\right)\,\left(16\,a^6-40\,a^4\,b^2+30\,a^2\,b^4-5\,b^6\right)}{8\,b^8\,d}","Not used",1,"((2*(105*a^6 - 15*b^6 + 161*a^2*b^4 - 245*a^4*b^2))/(105*b^7) + (tan(c/2 + (d*x)/2)^13*(11*a*b^4 + 8*a^5 - 18*a^3*b^2))/(8*b^6) - (tan(c/2 + (d*x)/2)^3*(7*a*b^4 + 24*a^5 - 42*a^3*b^2))/(6*b^6) + (tan(c/2 + (d*x)/2)^11*(7*a*b^4 + 24*a^5 - 42*a^3*b^2))/(6*b^6) - (tan(c/2 + (d*x)/2)^5*(85*a*b^4 + 120*a^5 - 174*a^3*b^2))/(24*b^6) + (tan(c/2 + (d*x)/2)^9*(85*a*b^4 + 120*a^5 - 174*a^3*b^2))/(24*b^6) + (2*tan(c/2 + (d*x)/2)^12*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/b^7 + (4*tan(c/2 + (d*x)/2)^10*(3*a^6 + 6*a^2*b^4 - 8*a^4*b^2))/b^7 + (8*tan(c/2 + (d*x)/2)^6*(15*a^6 + 22*a^2*b^4 - 34*a^4*b^2))/(3*b^7) + (4*tan(c/2 + (d*x)/2)^2*(45*a^6 + 58*a^2*b^4 - 100*a^4*b^2))/(15*b^7) + (2*tan(c/2 + (d*x)/2)^8*(45*a^6 - 15*b^6 + 73*a^2*b^4 - 109*a^4*b^2))/(3*b^7) + (2*tan(c/2 + (d*x)/2)^4*(75*a^6 - 15*b^6 + 101*a^2*b^4 - 165*a^4*b^2))/(5*b^7) - (a*tan(c/2 + (d*x)/2)*(8*a^4 + 11*b^4 - 18*a^2*b^2))/(8*b^6))/(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)) + (a^2*atan(((a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^4*b^19)/8 - (75*a^6*b^17)/2 + (325*a^8*b^15)/2 - 320*a^10*b^13 + 320*a^12*b^11 - 160*a^14*b^9 + 32*a^16*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a^3*b^21 - 881*a^5*b^19 + 4436*a^7*b^17 - 10260*a^9*b^15 + 12800*a^11*b^13 - 8960*a^13*b^11 + 3328*a^15*b^9 - 512*a^17*b^7))/(8*b^21) + (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((10*a^2*b^22 - 38*a^4*b^20 + 44*a^6*b^18 - 16*a^8*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^3*b^22 - 1536*a^5*b^20 + 1536*a^7*b^18 - 512*a^9*b^16))/(8*b^21) + (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21)))/b^8))/b^8)*1i)/b^8 + (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^4*b^19)/8 - (75*a^6*b^17)/2 + (325*a^8*b^15)/2 - 320*a^10*b^13 + 320*a^12*b^11 - 160*a^14*b^9 + 32*a^16*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a^3*b^21 - 881*a^5*b^19 + 4436*a^7*b^17 - 10260*a^9*b^15 + 12800*a^11*b^13 - 8960*a^13*b^11 + 3328*a^15*b^9 - 512*a^17*b^7))/(8*b^21) - (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((10*a^2*b^22 - 38*a^4*b^20 + 44*a^6*b^18 - 16*a^8*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^3*b^22 - 1536*a^5*b^20 + 1536*a^7*b^18 - 512*a^9*b^16))/(8*b^21) - (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21)))/b^8))/b^8)*1i)/b^8)/((32*a^22 + (55*a^6*b^16)/4 - (585*a^8*b^14)/4 + (2445*a^10*b^12)/4 - (5511*a^12*b^10)/4 + 1874*a^14*b^8 - 1595*a^16*b^6 + 836*a^18*b^4 - 248*a^20*b^2)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^23 - 50*a^5*b^18 + 750*a^7*b^16 - 4550*a^9*b^14 + 14770*a^11*b^12 - 28880*a^13*b^10 + 35880*a^15*b^8 - 28672*a^17*b^6 + 14336*a^19*b^4 - 4096*a^21*b^2))/(4*b^21) - (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^4*b^19)/8 - (75*a^6*b^17)/2 + (325*a^8*b^15)/2 - 320*a^10*b^13 + 320*a^12*b^11 - 160*a^14*b^9 + 32*a^16*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a^3*b^21 - 881*a^5*b^19 + 4436*a^7*b^17 - 10260*a^9*b^15 + 12800*a^11*b^13 - 8960*a^13*b^11 + 3328*a^15*b^9 - 512*a^17*b^7))/(8*b^21) + (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((10*a^2*b^22 - 38*a^4*b^20 + 44*a^6*b^18 - 16*a^8*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^3*b^22 - 1536*a^5*b^20 + 1536*a^7*b^18 - 512*a^9*b^16))/(8*b^21) + (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21)))/b^8))/b^8))/b^8 + (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^4*b^19)/8 - (75*a^6*b^17)/2 + (325*a^8*b^15)/2 - 320*a^10*b^13 + 320*a^12*b^11 - 160*a^14*b^9 + 32*a^16*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a^3*b^21 - 881*a^5*b^19 + 4436*a^7*b^17 - 10260*a^9*b^15 + 12800*a^11*b^13 - 8960*a^13*b^11 + 3328*a^15*b^9 - 512*a^17*b^7))/(8*b^21) - (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((10*a^2*b^22 - 38*a^4*b^20 + 44*a^6*b^18 - 16*a^8*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^3*b^22 - 1536*a^5*b^20 + 1536*a^7*b^18 - 512*a^9*b^16))/(8*b^21) - (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21)))/b^8))/b^8))/b^8))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(b^8*d) + (a*atan(((a*(((25*a^4*b^19)/8 - (75*a^6*b^17)/2 + (325*a^8*b^15)/2 - 320*a^10*b^13 + 320*a^12*b^11 - 160*a^14*b^9 + 32*a^16*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a^3*b^21 - 881*a^5*b^19 + 4436*a^7*b^17 - 10260*a^9*b^15 + 12800*a^11*b^13 - 8960*a^13*b^11 + 3328*a^15*b^9 - 512*a^17*b^7))/(8*b^21) - (a*((10*a^2*b^22 - 38*a^4*b^20 + 44*a^6*b^18 - 16*a^8*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^3*b^22 - 1536*a^5*b^20 + 1536*a^7*b^18 - 512*a^9*b^16))/(8*b^21) - (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2))/(16*b^8) + (a*(((25*a^4*b^19)/8 - (75*a^6*b^17)/2 + (325*a^8*b^15)/2 - 320*a^10*b^13 + 320*a^12*b^11 - 160*a^14*b^9 + 32*a^16*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a^3*b^21 - 881*a^5*b^19 + 4436*a^7*b^17 - 10260*a^9*b^15 + 12800*a^11*b^13 - 8960*a^13*b^11 + 3328*a^15*b^9 - 512*a^17*b^7))/(8*b^21) + (a*((10*a^2*b^22 - 38*a^4*b^20 + 44*a^6*b^18 - 16*a^8*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^3*b^22 - 1536*a^5*b^20 + 1536*a^7*b^18 - 512*a^9*b^16))/(8*b^21) + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2))/(16*b^8))/((32*a^22 + (55*a^6*b^16)/4 - (585*a^8*b^14)/4 + (2445*a^10*b^12)/4 - (5511*a^12*b^10)/4 + 1874*a^14*b^8 - 1595*a^16*b^6 + 836*a^18*b^4 - 248*a^20*b^2)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^23 - 50*a^5*b^18 + 750*a^7*b^16 - 4550*a^9*b^14 + 14770*a^11*b^12 - 28880*a^13*b^10 + 35880*a^15*b^8 - 28672*a^17*b^6 + 14336*a^19*b^4 - 4096*a^21*b^2))/(4*b^21) + (a*(((25*a^4*b^19)/8 - (75*a^6*b^17)/2 + (325*a^8*b^15)/2 - 320*a^10*b^13 + 320*a^12*b^11 - 160*a^14*b^9 + 32*a^16*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a^3*b^21 - 881*a^5*b^19 + 4436*a^7*b^17 - 10260*a^9*b^15 + 12800*a^11*b^13 - 8960*a^13*b^11 + 3328*a^15*b^9 - 512*a^17*b^7))/(8*b^21) - (a*((10*a^2*b^22 - 38*a^4*b^20 + 44*a^6*b^18 - 16*a^8*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^3*b^22 - 1536*a^5*b^20 + 1536*a^7*b^18 - 512*a^9*b^16))/(8*b^21) - (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8) - (a*(((25*a^4*b^19)/8 - (75*a^6*b^17)/2 + (325*a^8*b^15)/2 - 320*a^10*b^13 + 320*a^12*b^11 - 160*a^14*b^9 + 32*a^16*b^7)/b^20 + (tan(c/2 + (d*x)/2)*(50*a^3*b^21 - 881*a^5*b^19 + 4436*a^7*b^17 - 10260*a^9*b^15 + 12800*a^11*b^13 - 8960*a^13*b^11 + 3328*a^15*b^9 - 512*a^17*b^7))/(8*b^21) + (a*((10*a^2*b^22 - 38*a^4*b^20 + 44*a^6*b^18 - 16*a^8*b^16)/b^20 + (tan(c/2 + (d*x)/2)*(512*a^3*b^22 - 1536*a^5*b^20 + 1536*a^7*b^18 - 512*a^9*b^16))/(8*b^21) + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^25 - 512*a^3*b^23))/(8*b^21))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2)*1i)/(16*b^8)))*(16*a^6 - 5*b^6 + 30*a^2*b^4 - 40*a^4*b^2))/(8*b^8*d)","B"
1322,1,3683,228,14.382749,"\text{Not used}","int((cos(c + d*x)^6*sin(c + d*x))/(a + b*sin(c + d*x)),x)","-\frac{\frac{2\,\left(15\,a^5-35\,a^3\,b^2+23\,a\,b^4\right)}{15\,b^6}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(5\,a^5-11\,a^3\,b^2+7\,a\,b^4\right)}{b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^5-13\,a^3\,b^2+9\,a\,b^4\right)}{b^6}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(15\,a^5-35\,a^3\,b^2+23\,a\,b^4\right)}{3\,b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(25\,a^5-55\,a^3\,b^2+31\,a\,b^4\right)}{5\,b^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^4-18\,a^2\,b^2+11\,b^4\right)}{8\,b^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(8\,a^4-10\,a^2\,b^2+15\,b^4\right)}{4\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(8\,a^4-10\,a^2\,b^2+15\,b^4\right)}{4\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(8\,a^4-18\,a^2\,b^2+11\,b^4\right)}{8\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-72\,a^4+114\,a^2\,b^2+5\,b^4\right)}{24\,b^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-72\,a^4+114\,a^2\,b^2+5\,b^4\right)}{24\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^5-3\,a^3\,b^2+3\,a\,b^4\right)}{b^6}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,a^{14}\,b^6-160\,a^{12}\,b^8+320\,a^{10}\,b^{10}-320\,a^8\,b^{12}+\frac{325\,a^6\,b^{14}}{2}-\frac{75\,a^4\,b^{16}}{2}+\frac{25\,a^2\,b^{18}}{8}}{b^{17}}-\frac{\left(\frac{-16\,a^7\,b^{14}+44\,a^5\,b^{16}-38\,a^3\,b^{18}+10\,a\,b^{20}}{b^{17}}-\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{22}-512\,a^3\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^8\,b^{14}+1536\,a^6\,b^{16}-1536\,a^4\,b^{18}+512\,a^2\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^6+3328\,a^{13}\,b^8-8960\,a^{11}\,b^{10}+12800\,a^9\,b^{12}-10260\,a^7\,b^{14}+4436\,a^5\,b^{16}-881\,a^3\,b^{18}+50\,a\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^7}+\frac{\left(\frac{32\,a^{14}\,b^6-160\,a^{12}\,b^8+320\,a^{10}\,b^{10}-320\,a^8\,b^{12}+\frac{325\,a^6\,b^{14}}{2}-\frac{75\,a^4\,b^{16}}{2}+\frac{25\,a^2\,b^{18}}{8}}{b^{17}}+\frac{\left(\frac{-16\,a^7\,b^{14}+44\,a^5\,b^{16}-38\,a^3\,b^{18}+10\,a\,b^{20}}{b^{17}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{22}-512\,a^3\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^8\,b^{14}+1536\,a^6\,b^{16}-1536\,a^4\,b^{18}+512\,a^2\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^6+3328\,a^{13}\,b^8-8960\,a^{11}\,b^{10}+12800\,a^9\,b^{12}-10260\,a^7\,b^{14}+4436\,a^5\,b^{16}-881\,a^3\,b^{18}+50\,a\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^7}}{\frac{32\,a^{19}-248\,a^{17}\,b^2+836\,a^{15}\,b^4-1595\,a^{13}\,b^6+1874\,a^{11}\,b^8-\frac{5511\,a^9\,b^{10}}{4}+\frac{2445\,a^7\,b^{12}}{4}-\frac{585\,a^5\,b^{14}}{4}+\frac{55\,a^3\,b^{16}}{4}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{20}-4096\,a^{18}\,b^2+14336\,a^{16}\,b^4-28672\,a^{14}\,b^6+35880\,a^{12}\,b^8-28880\,a^{10}\,b^{10}+14770\,a^8\,b^{12}-4550\,a^6\,b^{14}+750\,a^4\,b^{16}-50\,a^2\,b^{18}\right)}{4\,b^{18}}+\frac{\left(\frac{32\,a^{14}\,b^6-160\,a^{12}\,b^8+320\,a^{10}\,b^{10}-320\,a^8\,b^{12}+\frac{325\,a^6\,b^{14}}{2}-\frac{75\,a^4\,b^{16}}{2}+\frac{25\,a^2\,b^{18}}{8}}{b^{17}}-\frac{\left(\frac{-16\,a^7\,b^{14}+44\,a^5\,b^{16}-38\,a^3\,b^{18}+10\,a\,b^{20}}{b^{17}}-\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{22}-512\,a^3\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^8\,b^{14}+1536\,a^6\,b^{16}-1536\,a^4\,b^{18}+512\,a^2\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^6+3328\,a^{13}\,b^8-8960\,a^{11}\,b^{10}+12800\,a^9\,b^{12}-10260\,a^7\,b^{14}+4436\,a^5\,b^{16}-881\,a^3\,b^{18}+50\,a\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}-\frac{\left(\frac{32\,a^{14}\,b^6-160\,a^{12}\,b^8+320\,a^{10}\,b^{10}-320\,a^8\,b^{12}+\frac{325\,a^6\,b^{14}}{2}-\frac{75\,a^4\,b^{16}}{2}+\frac{25\,a^2\,b^{18}}{8}}{b^{17}}+\frac{\left(\frac{-16\,a^7\,b^{14}+44\,a^5\,b^{16}-38\,a^3\,b^{18}+10\,a\,b^{20}}{b^{17}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(768\,a\,b^{22}-512\,a^3\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^8\,b^{14}+1536\,a^6\,b^{16}-1536\,a^4\,b^{18}+512\,a^2\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^6+3328\,a^{13}\,b^8-8960\,a^{11}\,b^{10}+12800\,a^9\,b^{12}-10260\,a^7\,b^{14}+4436\,a^5\,b^{16}-881\,a^3\,b^{18}+50\,a\,b^{20}\right)}{8\,b^{18}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)}{16\,b^7}}\right)\,\left(a^6\,16{}\mathrm{i}-a^4\,b^2\,40{}\mathrm{i}+a^2\,b^4\,30{}\mathrm{i}-b^6\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^7\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{14}\,b^6-160\,a^{12}\,b^8+320\,a^{10}\,b^{10}-320\,a^8\,b^{12}+\frac{325\,a^6\,b^{14}}{2}-\frac{75\,a^4\,b^{16}}{2}+\frac{25\,a^2\,b^{18}}{8}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^6+3328\,a^{13}\,b^8-8960\,a^{11}\,b^{10}+12800\,a^9\,b^{12}-10260\,a^7\,b^{14}+4436\,a^5\,b^{16}-881\,a^3\,b^{18}+50\,a\,b^{20}\right)}{8\,b^{18}}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^7\,b^{14}+44\,a^5\,b^{16}-38\,a^3\,b^{18}+10\,a\,b^{20}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^8\,b^{14}+1536\,a^6\,b^{16}-1536\,a^4\,b^{18}+512\,a^2\,b^{20}\right)}{8\,b^{18}}+\frac{a\,\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(768\,a\,b^{22}-512\,a^3\,b^{20}\right)}{8\,b^{18}}\right)}{b^7}\right)}{b^7}\right)\,1{}\mathrm{i}}{b^7}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{14}\,b^6-160\,a^{12}\,b^8+320\,a^{10}\,b^{10}-320\,a^8\,b^{12}+\frac{325\,a^6\,b^{14}}{2}-\frac{75\,a^4\,b^{16}}{2}+\frac{25\,a^2\,b^{18}}{8}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^6+3328\,a^{13}\,b^8-8960\,a^{11}\,b^{10}+12800\,a^9\,b^{12}-10260\,a^7\,b^{14}+4436\,a^5\,b^{16}-881\,a^3\,b^{18}+50\,a\,b^{20}\right)}{8\,b^{18}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^7\,b^{14}+44\,a^5\,b^{16}-38\,a^3\,b^{18}+10\,a\,b^{20}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^8\,b^{14}+1536\,a^6\,b^{16}-1536\,a^4\,b^{18}+512\,a^2\,b^{20}\right)}{8\,b^{18}}-\frac{a\,\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(768\,a\,b^{22}-512\,a^3\,b^{20}\right)}{8\,b^{18}}\right)}{b^7}\right)}{b^7}\right)\,1{}\mathrm{i}}{b^7}}{\frac{32\,a^{19}-248\,a^{17}\,b^2+836\,a^{15}\,b^4-1595\,a^{13}\,b^6+1874\,a^{11}\,b^8-\frac{5511\,a^9\,b^{10}}{4}+\frac{2445\,a^7\,b^{12}}{4}-\frac{585\,a^5\,b^{14}}{4}+\frac{55\,a^3\,b^{16}}{4}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{20}-4096\,a^{18}\,b^2+14336\,a^{16}\,b^4-28672\,a^{14}\,b^6+35880\,a^{12}\,b^8-28880\,a^{10}\,b^{10}+14770\,a^8\,b^{12}-4550\,a^6\,b^{14}+750\,a^4\,b^{16}-50\,a^2\,b^{18}\right)}{4\,b^{18}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{14}\,b^6-160\,a^{12}\,b^8+320\,a^{10}\,b^{10}-320\,a^8\,b^{12}+\frac{325\,a^6\,b^{14}}{2}-\frac{75\,a^4\,b^{16}}{2}+\frac{25\,a^2\,b^{18}}{8}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^6+3328\,a^{13}\,b^8-8960\,a^{11}\,b^{10}+12800\,a^9\,b^{12}-10260\,a^7\,b^{14}+4436\,a^5\,b^{16}-881\,a^3\,b^{18}+50\,a\,b^{20}\right)}{8\,b^{18}}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^7\,b^{14}+44\,a^5\,b^{16}-38\,a^3\,b^{18}+10\,a\,b^{20}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^8\,b^{14}+1536\,a^6\,b^{16}-1536\,a^4\,b^{18}+512\,a^2\,b^{20}\right)}{8\,b^{18}}+\frac{a\,\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(768\,a\,b^{22}-512\,a^3\,b^{20}\right)}{8\,b^{18}}\right)}{b^7}\right)}{b^7}\right)}{b^7}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{14}\,b^6-160\,a^{12}\,b^8+320\,a^{10}\,b^{10}-320\,a^8\,b^{12}+\frac{325\,a^6\,b^{14}}{2}-\frac{75\,a^4\,b^{16}}{2}+\frac{25\,a^2\,b^{18}}{8}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^6+3328\,a^{13}\,b^8-8960\,a^{11}\,b^{10}+12800\,a^9\,b^{12}-10260\,a^7\,b^{14}+4436\,a^5\,b^{16}-881\,a^3\,b^{18}+50\,a\,b^{20}\right)}{8\,b^{18}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-16\,a^7\,b^{14}+44\,a^5\,b^{16}-38\,a^3\,b^{18}+10\,a\,b^{20}}{b^{17}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^8\,b^{14}+1536\,a^6\,b^{16}-1536\,a^4\,b^{18}+512\,a^2\,b^{20}\right)}{8\,b^{18}}-\frac{a\,\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(768\,a\,b^{22}-512\,a^3\,b^{20}\right)}{8\,b^{18}}\right)}{b^7}\right)}{b^7}\right)}{b^7}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{b^7\,d}","Not used",1,"- ((2*(23*a*b^4 + 15*a^5 - 35*a^3*b^2))/(15*b^6) + (4*tan(c/2 + (d*x)/2)^4*(7*a*b^4 + 5*a^5 - 11*a^3*b^2))/b^6 + (2*tan(c/2 + (d*x)/2)^8*(9*a*b^4 + 5*a^5 - 13*a^3*b^2))/b^6 + (4*tan(c/2 + (d*x)/2)^6*(23*a*b^4 + 15*a^5 - 35*a^3*b^2))/(3*b^6) + (2*tan(c/2 + (d*x)/2)^2*(31*a*b^4 + 25*a^5 - 55*a^3*b^2))/(5*b^6) - (tan(c/2 + (d*x)/2)*(8*a^4 + 11*b^4 - 18*a^2*b^2))/(8*b^5) - (tan(c/2 + (d*x)/2)^5*(8*a^4 + 15*b^4 - 10*a^2*b^2))/(4*b^5) + (tan(c/2 + (d*x)/2)^7*(8*a^4 + 15*b^4 - 10*a^2*b^2))/(4*b^5) + (tan(c/2 + (d*x)/2)^11*(8*a^4 + 11*b^4 - 18*a^2*b^2))/(8*b^5) + (tan(c/2 + (d*x)/2)^3*(5*b^4 - 72*a^4 + 114*a^2*b^2))/(24*b^5) - (tan(c/2 + (d*x)/2)^9*(5*b^4 - 72*a^4 + 114*a^2*b^2))/(24*b^5) + (2*tan(c/2 + (d*x)/2)^10*(3*a*b^4 + a^5 - 3*a^3*b^2))/b^6)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - (atan((((((25*a^2*b^18)/8 - (75*a^4*b^16)/2 + (325*a^6*b^14)/2 - 320*a^8*b^12 + 320*a^10*b^10 - 160*a^12*b^8 + 32*a^14*b^6)/b^17 - (((10*a*b^20 - 38*a^3*b^18 + 44*a^5*b^16 - 16*a^7*b^14)/b^17 - ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^22 - 512*a^3*b^20))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) + (tan(c/2 + (d*x)/2)*(512*a^2*b^20 - 1536*a^4*b^18 + 1536*a^6*b^16 - 512*a^8*b^14))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) + (tan(c/2 + (d*x)/2)*(50*a*b^20 - 881*a^3*b^18 + 4436*a^5*b^16 - 10260*a^7*b^14 + 12800*a^9*b^12 - 8960*a^11*b^10 + 3328*a^13*b^8 - 512*a^15*b^6))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i)*1i)/(16*b^7) + ((((25*a^2*b^18)/8 - (75*a^4*b^16)/2 + (325*a^6*b^14)/2 - 320*a^8*b^12 + 320*a^10*b^10 - 160*a^12*b^8 + 32*a^14*b^6)/b^17 + (((10*a*b^20 - 38*a^3*b^18 + 44*a^5*b^16 - 16*a^7*b^14)/b^17 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^22 - 512*a^3*b^20))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) + (tan(c/2 + (d*x)/2)*(512*a^2*b^20 - 1536*a^4*b^18 + 1536*a^6*b^16 - 512*a^8*b^14))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) + (tan(c/2 + (d*x)/2)*(50*a*b^20 - 881*a^3*b^18 + 4436*a^5*b^16 - 10260*a^7*b^14 + 12800*a^9*b^12 - 8960*a^11*b^10 + 3328*a^13*b^8 - 512*a^15*b^6))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i)*1i)/(16*b^7))/((32*a^19 + (55*a^3*b^16)/4 - (585*a^5*b^14)/4 + (2445*a^7*b^12)/4 - (5511*a^9*b^10)/4 + 1874*a^11*b^8 - 1595*a^13*b^6 + 836*a^15*b^4 - 248*a^17*b^2)/b^17 + (tan(c/2 + (d*x)/2)*(512*a^20 - 50*a^2*b^18 + 750*a^4*b^16 - 4550*a^6*b^14 + 14770*a^8*b^12 - 28880*a^10*b^10 + 35880*a^12*b^8 - 28672*a^14*b^6 + 14336*a^16*b^4 - 4096*a^18*b^2))/(4*b^18) + ((((25*a^2*b^18)/8 - (75*a^4*b^16)/2 + (325*a^6*b^14)/2 - 320*a^8*b^12 + 320*a^10*b^10 - 160*a^12*b^8 + 32*a^14*b^6)/b^17 - (((10*a*b^20 - 38*a^3*b^18 + 44*a^5*b^16 - 16*a^7*b^14)/b^17 - ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^22 - 512*a^3*b^20))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) + (tan(c/2 + (d*x)/2)*(512*a^2*b^20 - 1536*a^4*b^18 + 1536*a^6*b^16 - 512*a^8*b^14))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) + (tan(c/2 + (d*x)/2)*(50*a*b^20 - 881*a^3*b^18 + 4436*a^5*b^16 - 10260*a^7*b^14 + 12800*a^9*b^12 - 8960*a^11*b^10 + 3328*a^13*b^8 - 512*a^15*b^6))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) - ((((25*a^2*b^18)/8 - (75*a^4*b^16)/2 + (325*a^6*b^14)/2 - 320*a^8*b^12 + 320*a^10*b^10 - 160*a^12*b^8 + 32*a^14*b^6)/b^17 + (((10*a*b^20 - 38*a^3*b^18 + 44*a^5*b^16 - 16*a^7*b^14)/b^17 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^22 - 512*a^3*b^20))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) + (tan(c/2 + (d*x)/2)*(512*a^2*b^20 - 1536*a^4*b^18 + 1536*a^6*b^16 - 512*a^8*b^14))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7) + (tan(c/2 + (d*x)/2)*(50*a*b^20 - 881*a^3*b^18 + 4436*a^5*b^16 - 10260*a^7*b^14 + 12800*a^9*b^12 - 8960*a^11*b^10 + 3328*a^13*b^8 - 512*a^15*b^6))/(8*b^18))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i))/(16*b^7)))*(a^6*16i - b^6*5i + a^2*b^4*30i - a^4*b^2*40i)*1i)/(8*b^7*d) - (a*atan(((a*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^2*b^18)/8 - (75*a^4*b^16)/2 + (325*a^6*b^14)/2 - 320*a^8*b^12 + 320*a^10*b^10 - 160*a^12*b^8 + 32*a^14*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(50*a*b^20 - 881*a^3*b^18 + 4436*a^5*b^16 - 10260*a^7*b^14 + 12800*a^9*b^12 - 8960*a^11*b^10 + 3328*a^13*b^8 - 512*a^15*b^6))/(8*b^18) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((10*a*b^20 - 38*a^3*b^18 + 44*a^5*b^16 - 16*a^7*b^14)/b^17 + (tan(c/2 + (d*x)/2)*(512*a^2*b^20 - 1536*a^4*b^18 + 1536*a^6*b^16 - 512*a^8*b^14))/(8*b^18) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^22 - 512*a^3*b^20))/(8*b^18)))/b^7))/b^7)*1i)/b^7 + (a*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^2*b^18)/8 - (75*a^4*b^16)/2 + (325*a^6*b^14)/2 - 320*a^8*b^12 + 320*a^10*b^10 - 160*a^12*b^8 + 32*a^14*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(50*a*b^20 - 881*a^3*b^18 + 4436*a^5*b^16 - 10260*a^7*b^14 + 12800*a^9*b^12 - 8960*a^11*b^10 + 3328*a^13*b^8 - 512*a^15*b^6))/(8*b^18) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*((10*a*b^20 - 38*a^3*b^18 + 44*a^5*b^16 - 16*a^7*b^14)/b^17 + (tan(c/2 + (d*x)/2)*(512*a^2*b^20 - 1536*a^4*b^18 + 1536*a^6*b^16 - 512*a^8*b^14))/(8*b^18) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^22 - 512*a^3*b^20))/(8*b^18)))/b^7))/b^7)*1i)/b^7)/((32*a^19 + (55*a^3*b^16)/4 - (585*a^5*b^14)/4 + (2445*a^7*b^12)/4 - (5511*a^9*b^10)/4 + 1874*a^11*b^8 - 1595*a^13*b^6 + 836*a^15*b^4 - 248*a^17*b^2)/b^17 + (tan(c/2 + (d*x)/2)*(512*a^20 - 50*a^2*b^18 + 750*a^4*b^16 - 4550*a^6*b^14 + 14770*a^8*b^12 - 28880*a^10*b^10 + 35880*a^12*b^8 - 28672*a^14*b^6 + 14336*a^16*b^4 - 4096*a^18*b^2))/(4*b^18) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^2*b^18)/8 - (75*a^4*b^16)/2 + (325*a^6*b^14)/2 - 320*a^8*b^12 + 320*a^10*b^10 - 160*a^12*b^8 + 32*a^14*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(50*a*b^20 - 881*a^3*b^18 + 4436*a^5*b^16 - 10260*a^7*b^14 + 12800*a^9*b^12 - 8960*a^11*b^10 + 3328*a^13*b^8 - 512*a^15*b^6))/(8*b^18) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((10*a*b^20 - 38*a^3*b^18 + 44*a^5*b^16 - 16*a^7*b^14)/b^17 + (tan(c/2 + (d*x)/2)*(512*a^2*b^20 - 1536*a^4*b^18 + 1536*a^6*b^16 - 512*a^8*b^14))/(8*b^18) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^22 - 512*a^3*b^20))/(8*b^18)))/b^7))/b^7))/b^7 + (a*(-(a + b)^5*(a - b)^5)^(1/2)*(((25*a^2*b^18)/8 - (75*a^4*b^16)/2 + (325*a^6*b^14)/2 - 320*a^8*b^12 + 320*a^10*b^10 - 160*a^12*b^8 + 32*a^14*b^6)/b^17 + (tan(c/2 + (d*x)/2)*(50*a*b^20 - 881*a^3*b^18 + 4436*a^5*b^16 - 10260*a^7*b^14 + 12800*a^9*b^12 - 8960*a^11*b^10 + 3328*a^13*b^8 - 512*a^15*b^6))/(8*b^18) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*((10*a*b^20 - 38*a^3*b^18 + 44*a^5*b^16 - 16*a^7*b^14)/b^17 + (tan(c/2 + (d*x)/2)*(512*a^2*b^20 - 1536*a^4*b^18 + 1536*a^6*b^16 - 512*a^8*b^14))/(8*b^18) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(768*a*b^22 - 512*a^3*b^20))/(8*b^18)))/b^7))/b^7))/b^7))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(b^7*d)","B"
1323,1,4866,252,13.399249,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\frac{2\,\left(7\,a\,b^2-3\,a^3\right)}{3\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a\,b^2-a^3\right)}{b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(7\,a\,b^2-3\,a^3\right)}{b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(19\,a\,b^2-9\,a^3\right)}{3\,b^4}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-9\,b^2\right)}{4\,b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^2-b^2\right)}{4\,b^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(4\,a^2-b^2\right)}{4\,b^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,a^2-9\,b^2\right)}{4\,b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-112\,a^{15}+900\,a^{13}\,b^2-3252\,a^{11}\,b^4+\frac{13697\,a^9\,b^6}{2}-\frac{18191\,a^7\,b^8}{2}+\frac{15271\,a^5\,b^{10}}{2}-3760\,a^3\,b^{12}+840\,a\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{16}\,b^4-2560\,a^{14}\,b^6+11392\,a^{12}\,b^8-29728\,a^{10}\,b^{10}+50084\,a^8\,b^{12}-56140\,a^6\,b^{14}+41125\,a^4\,b^{16}-18084\,a^2\,b^{18}+3664\,b^{20}\right)}{2\,b^{16}}-\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-96\,a^{12}\,b^4+608\,a^{10}\,b^6-1600\,a^8\,b^8+2068\,a^6\,b^{10}-\frac{2395\,a^4\,b^{12}}{2}+94\,a^2\,b^{14}+128\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^8-2240\,a^{11}\,b^{10}+10816\,a^9\,b^{12}-24664\,a^7\,b^{14}+29985\,a^5\,b^{16}-18960\,a^3\,b^{18}+4944\,a\,b^{20}\right)}{2\,b^{16}}-\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-112\,a^7\,b^{10}+340\,a^5\,b^{12}-452\,a^3\,b^{14}+256\,a\,b^{16}}{b^{11}}-\frac{\left(\frac{128\,a^2\,b^{16}-96\,a^4\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^5\,b^{18}-1088\,a^3\,b^{20}+1024\,a\,b^{22}\right)}{2\,b^{16}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)}{8\,b^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^8\,b^{14}-1280\,a^6\,b^{16}+2432\,a^4\,b^{18}-2368\,a^2\,b^{20}+1024\,b^{22}\right)}{2\,b^{16}}\right)}{8\,b^5}\right)}{8\,b^5}\right)\,1{}\mathrm{i}}{8\,b^5}+\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-112\,a^{15}+900\,a^{13}\,b^2-3252\,a^{11}\,b^4+\frac{13697\,a^9\,b^6}{2}-\frac{18191\,a^7\,b^8}{2}+\frac{15271\,a^5\,b^{10}}{2}-3760\,a^3\,b^{12}+840\,a\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{16}\,b^4-2560\,a^{14}\,b^6+11392\,a^{12}\,b^8-29728\,a^{10}\,b^{10}+50084\,a^8\,b^{12}-56140\,a^6\,b^{14}+41125\,a^4\,b^{16}-18084\,a^2\,b^{18}+3664\,b^{20}\right)}{2\,b^{16}}+\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-96\,a^{12}\,b^4+608\,a^{10}\,b^6-1600\,a^8\,b^8+2068\,a^6\,b^{10}-\frac{2395\,a^4\,b^{12}}{2}+94\,a^2\,b^{14}+128\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^8-2240\,a^{11}\,b^{10}+10816\,a^9\,b^{12}-24664\,a^7\,b^{14}+29985\,a^5\,b^{16}-18960\,a^3\,b^{18}+4944\,a\,b^{20}\right)}{2\,b^{16}}+\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-112\,a^7\,b^{10}+340\,a^5\,b^{12}-452\,a^3\,b^{14}+256\,a\,b^{16}}{b^{11}}+\frac{\left(\frac{128\,a^2\,b^{16}-96\,a^4\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^5\,b^{18}-1088\,a^3\,b^{20}+1024\,a\,b^{22}\right)}{2\,b^{16}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)}{8\,b^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^8\,b^{14}-1280\,a^6\,b^{16}+2432\,a^4\,b^{18}-2368\,a^2\,b^{20}+1024\,b^{22}\right)}{2\,b^{16}}\right)}{8\,b^5}\right)}{8\,b^5}\right)\,1{}\mathrm{i}}{8\,b^5}}{\frac{224\,a^{14}-1800\,a^{12}\,b^2+6312\,a^{10}\,b^4-12481\,a^8\,b^6+14991\,a^6\,b^8-10911\,a^4\,b^{10}+4445\,a^2\,b^{12}-780\,b^{14}}{b^{11}}+\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-112\,a^{15}+900\,a^{13}\,b^2-3252\,a^{11}\,b^4+\frac{13697\,a^9\,b^6}{2}-\frac{18191\,a^7\,b^8}{2}+\frac{15271\,a^5\,b^{10}}{2}-3760\,a^3\,b^{12}+840\,a\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{16}\,b^4-2560\,a^{14}\,b^6+11392\,a^{12}\,b^8-29728\,a^{10}\,b^{10}+50084\,a^8\,b^{12}-56140\,a^6\,b^{14}+41125\,a^4\,b^{16}-18084\,a^2\,b^{18}+3664\,b^{20}\right)}{2\,b^{16}}-\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-96\,a^{12}\,b^4+608\,a^{10}\,b^6-1600\,a^8\,b^8+2068\,a^6\,b^{10}-\frac{2395\,a^4\,b^{12}}{2}+94\,a^2\,b^{14}+128\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^8-2240\,a^{11}\,b^{10}+10816\,a^9\,b^{12}-24664\,a^7\,b^{14}+29985\,a^5\,b^{16}-18960\,a^3\,b^{18}+4944\,a\,b^{20}\right)}{2\,b^{16}}-\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-112\,a^7\,b^{10}+340\,a^5\,b^{12}-452\,a^3\,b^{14}+256\,a\,b^{16}}{b^{11}}-\frac{\left(\frac{128\,a^2\,b^{16}-96\,a^4\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^5\,b^{18}-1088\,a^3\,b^{20}+1024\,a\,b^{22}\right)}{2\,b^{16}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)}{8\,b^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^8\,b^{14}-1280\,a^6\,b^{16}+2432\,a^4\,b^{18}-2368\,a^2\,b^{20}+1024\,b^{22}\right)}{2\,b^{16}}\right)}{8\,b^5}\right)}{8\,b^5}\right)}{8\,b^5}-\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-112\,a^{15}+900\,a^{13}\,b^2-3252\,a^{11}\,b^4+\frac{13697\,a^9\,b^6}{2}-\frac{18191\,a^7\,b^8}{2}+\frac{15271\,a^5\,b^{10}}{2}-3760\,a^3\,b^{12}+840\,a\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{16}\,b^4-2560\,a^{14}\,b^6+11392\,a^{12}\,b^8-29728\,a^{10}\,b^{10}+50084\,a^8\,b^{12}-56140\,a^6\,b^{14}+41125\,a^4\,b^{16}-18084\,a^2\,b^{18}+3664\,b^{20}\right)}{2\,b^{16}}+\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-96\,a^{12}\,b^4+608\,a^{10}\,b^6-1600\,a^8\,b^8+2068\,a^6\,b^{10}-\frac{2395\,a^4\,b^{12}}{2}+94\,a^2\,b^{14}+128\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^8-2240\,a^{11}\,b^{10}+10816\,a^9\,b^{12}-24664\,a^7\,b^{14}+29985\,a^5\,b^{16}-18960\,a^3\,b^{18}+4944\,a\,b^{20}\right)}{2\,b^{16}}+\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,\left(\frac{-112\,a^7\,b^{10}+340\,a^5\,b^{12}-452\,a^3\,b^{14}+256\,a\,b^{16}}{b^{11}}+\frac{\left(\frac{128\,a^2\,b^{16}-96\,a^4\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^5\,b^{18}-1088\,a^3\,b^{20}+1024\,a\,b^{22}\right)}{2\,b^{16}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)}{8\,b^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^8\,b^{14}-1280\,a^6\,b^{16}+2432\,a^4\,b^{18}-2368\,a^2\,b^{20}+1024\,b^{22}\right)}{2\,b^{16}}\right)}{8\,b^5}\right)}{8\,b^5}\right)}{8\,b^5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{19}+5632\,a^{17}\,b^2-27904\,a^{15}\,b^4+81600\,a^{13}\,b^6-155016\,a^{11}\,b^8+198160\,a^9\,b^{10}-170260\,a^7\,b^{12}+94700\,a^5\,b^{14}-30900\,a^3\,b^{16}+4500\,a\,b^{18}\right)}{b^{16}}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,20{}\mathrm{i}+b^4\,15{}\mathrm{i}\right)\,1{}\mathrm{i}}{4\,b^5\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-112\,a^{15}+900\,a^{13}\,b^2-3252\,a^{11}\,b^4+\frac{13697\,a^9\,b^6}{2}-\frac{18191\,a^7\,b^8}{2}+\frac{15271\,a^5\,b^{10}}{2}-3760\,a^3\,b^{12}+840\,a\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{16}\,b^4-2560\,a^{14}\,b^6+11392\,a^{12}\,b^8-29728\,a^{10}\,b^{10}+50084\,a^8\,b^{12}-56140\,a^6\,b^{14}+41125\,a^4\,b^{16}-18084\,a^2\,b^{18}+3664\,b^{20}\right)}{2\,b^{16}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-96\,a^{12}\,b^4+608\,a^{10}\,b^6-1600\,a^8\,b^8+2068\,a^6\,b^{10}-\frac{2395\,a^4\,b^{12}}{2}+94\,a^2\,b^{14}+128\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^8-2240\,a^{11}\,b^{10}+10816\,a^9\,b^{12}-24664\,a^7\,b^{14}+29985\,a^5\,b^{16}-18960\,a^3\,b^{18}+4944\,a\,b^{20}\right)}{2\,b^{16}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-112\,a^7\,b^{10}+340\,a^5\,b^{12}-452\,a^3\,b^{14}+256\,a\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^8\,b^{14}-1280\,a^6\,b^{16}+2432\,a^4\,b^{18}-2368\,a^2\,b^{20}+1024\,b^{22}\right)}{2\,b^{16}}+\frac{\left(\frac{128\,a^2\,b^{16}-96\,a^4\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^5\,b^{18}-1088\,a^3\,b^{20}+1024\,a\,b^{22}\right)}{2\,b^{16}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}\right)\,1{}\mathrm{i}}{a\,b^5}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-112\,a^{15}+900\,a^{13}\,b^2-3252\,a^{11}\,b^4+\frac{13697\,a^9\,b^6}{2}-\frac{18191\,a^7\,b^8}{2}+\frac{15271\,a^5\,b^{10}}{2}-3760\,a^3\,b^{12}+840\,a\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{16}\,b^4-2560\,a^{14}\,b^6+11392\,a^{12}\,b^8-29728\,a^{10}\,b^{10}+50084\,a^8\,b^{12}-56140\,a^6\,b^{14}+41125\,a^4\,b^{16}-18084\,a^2\,b^{18}+3664\,b^{20}\right)}{2\,b^{16}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-96\,a^{12}\,b^4+608\,a^{10}\,b^6-1600\,a^8\,b^8+2068\,a^6\,b^{10}-\frac{2395\,a^4\,b^{12}}{2}+94\,a^2\,b^{14}+128\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^8-2240\,a^{11}\,b^{10}+10816\,a^9\,b^{12}-24664\,a^7\,b^{14}+29985\,a^5\,b^{16}-18960\,a^3\,b^{18}+4944\,a\,b^{20}\right)}{2\,b^{16}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-112\,a^7\,b^{10}+340\,a^5\,b^{12}-452\,a^3\,b^{14}+256\,a\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^8\,b^{14}-1280\,a^6\,b^{16}+2432\,a^4\,b^{18}-2368\,a^2\,b^{20}+1024\,b^{22}\right)}{2\,b^{16}}-\frac{\left(\frac{128\,a^2\,b^{16}-96\,a^4\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^5\,b^{18}-1088\,a^3\,b^{20}+1024\,a\,b^{22}\right)}{2\,b^{16}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}\right)\,1{}\mathrm{i}}{a\,b^5}}{\frac{224\,a^{14}-1800\,a^{12}\,b^2+6312\,a^{10}\,b^4-12481\,a^8\,b^6+14991\,a^6\,b^8-10911\,a^4\,b^{10}+4445\,a^2\,b^{12}-780\,b^{14}}{b^{11}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{19}+5632\,a^{17}\,b^2-27904\,a^{15}\,b^4+81600\,a^{13}\,b^6-155016\,a^{11}\,b^8+198160\,a^9\,b^{10}-170260\,a^7\,b^{12}+94700\,a^5\,b^{14}-30900\,a^3\,b^{16}+4500\,a\,b^{18}\right)}{b^{16}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-112\,a^{15}+900\,a^{13}\,b^2-3252\,a^{11}\,b^4+\frac{13697\,a^9\,b^6}{2}-\frac{18191\,a^7\,b^8}{2}+\frac{15271\,a^5\,b^{10}}{2}-3760\,a^3\,b^{12}+840\,a\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{16}\,b^4-2560\,a^{14}\,b^6+11392\,a^{12}\,b^8-29728\,a^{10}\,b^{10}+50084\,a^8\,b^{12}-56140\,a^6\,b^{14}+41125\,a^4\,b^{16}-18084\,a^2\,b^{18}+3664\,b^{20}\right)}{2\,b^{16}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-96\,a^{12}\,b^4+608\,a^{10}\,b^6-1600\,a^8\,b^8+2068\,a^6\,b^{10}-\frac{2395\,a^4\,b^{12}}{2}+94\,a^2\,b^{14}+128\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^8-2240\,a^{11}\,b^{10}+10816\,a^9\,b^{12}-24664\,a^7\,b^{14}+29985\,a^5\,b^{16}-18960\,a^3\,b^{18}+4944\,a\,b^{20}\right)}{2\,b^{16}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-112\,a^7\,b^{10}+340\,a^5\,b^{12}-452\,a^3\,b^{14}+256\,a\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^8\,b^{14}-1280\,a^6\,b^{16}+2432\,a^4\,b^{18}-2368\,a^2\,b^{20}+1024\,b^{22}\right)}{2\,b^{16}}+\frac{\left(\frac{128\,a^2\,b^{16}-96\,a^4\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^5\,b^{18}-1088\,a^3\,b^{20}+1024\,a\,b^{22}\right)}{2\,b^{16}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-112\,a^{15}+900\,a^{13}\,b^2-3252\,a^{11}\,b^4+\frac{13697\,a^9\,b^6}{2}-\frac{18191\,a^7\,b^8}{2}+\frac{15271\,a^5\,b^{10}}{2}-3760\,a^3\,b^{12}+840\,a\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{16}\,b^4-2560\,a^{14}\,b^6+11392\,a^{12}\,b^8-29728\,a^{10}\,b^{10}+50084\,a^8\,b^{12}-56140\,a^6\,b^{14}+41125\,a^4\,b^{16}-18084\,a^2\,b^{18}+3664\,b^{20}\right)}{2\,b^{16}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-96\,a^{12}\,b^4+608\,a^{10}\,b^6-1600\,a^8\,b^8+2068\,a^6\,b^{10}-\frac{2395\,a^4\,b^{12}}{2}+94\,a^2\,b^{14}+128\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^8-2240\,a^{11}\,b^{10}+10816\,a^9\,b^{12}-24664\,a^7\,b^{14}+29985\,a^5\,b^{16}-18960\,a^3\,b^{18}+4944\,a\,b^{20}\right)}{2\,b^{16}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-112\,a^7\,b^{10}+340\,a^5\,b^{12}-452\,a^3\,b^{14}+256\,a\,b^{16}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^8\,b^{14}-1280\,a^6\,b^{16}+2432\,a^4\,b^{18}-2368\,a^2\,b^{20}+1024\,b^{22}\right)}{2\,b^{16}}-\frac{\left(\frac{128\,a^2\,b^{16}-96\,a^4\,b^{14}}{b^{11}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^5\,b^{18}-1088\,a^3\,b^{20}+1024\,a\,b^{22}\right)}{2\,b^{16}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a\,b^5\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a*d) + ((2*(7*a*b^2 - 3*a^3))/(3*b^4) + (2*tan(c/2 + (d*x)/2)^6*(3*a*b^2 - a^3))/b^4 + (2*tan(c/2 + (d*x)/2)^4*(7*a*b^2 - 3*a^3))/b^4 + (2*tan(c/2 + (d*x)/2)^2*(19*a*b^2 - 9*a^3))/(3*b^4) + (tan(c/2 + (d*x)/2)*(4*a^2 - 9*b^2))/(4*b^3) + (tan(c/2 + (d*x)/2)^3*(4*a^2 - b^2))/(4*b^3) - (tan(c/2 + (d*x)/2)^5*(4*a^2 - b^2))/(4*b^3) - (tan(c/2 + (d*x)/2)^7*(4*a^2 - 9*b^2))/(4*b^3))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (atan((((a^4*8i + b^4*15i - a^2*b^2*20i)*((840*a*b^14 - 112*a^15 - 3760*a^3*b^12 + (15271*a^5*b^10)/2 - (18191*a^7*b^8)/2 + (13697*a^9*b^6)/2 - 3252*a^11*b^4 + 900*a^13*b^2)/b^11 + (tan(c/2 + (d*x)/2)*(3664*b^20 - 18084*a^2*b^18 + 41125*a^4*b^16 - 56140*a^6*b^14 + 50084*a^8*b^12 - 29728*a^10*b^10 + 11392*a^12*b^8 - 2560*a^14*b^6 + 256*a^16*b^4))/(2*b^16) - ((a^4*8i + b^4*15i - a^2*b^2*20i)*((128*b^16 + 94*a^2*b^14 - (2395*a^4*b^12)/2 + 2068*a^6*b^10 - 1600*a^8*b^8 + 608*a^10*b^6 - 96*a^12*b^4)/b^11 + (tan(c/2 + (d*x)/2)*(4944*a*b^20 - 18960*a^3*b^18 + 29985*a^5*b^16 - 24664*a^7*b^14 + 10816*a^9*b^12 - 2240*a^11*b^10 + 128*a^13*b^8))/(2*b^16) - ((a^4*8i + b^4*15i - a^2*b^2*20i)*((256*a*b^16 - 452*a^3*b^14 + 340*a^5*b^12 - 112*a^7*b^10)/b^11 - (((128*a^2*b^16 - 96*a^4*b^14)/b^11 + (tan(c/2 + (d*x)/2)*(1024*a*b^22 - 1088*a^3*b^20 + 128*a^5*b^18))/(2*b^16))*(a^4*8i + b^4*15i - a^2*b^2*20i))/(8*b^5) + (tan(c/2 + (d*x)/2)*(1024*b^22 - 2368*a^2*b^20 + 2432*a^4*b^18 - 1280*a^6*b^16 + 256*a^8*b^14))/(2*b^16)))/(8*b^5)))/(8*b^5))*1i)/(8*b^5) + ((a^4*8i + b^4*15i - a^2*b^2*20i)*((840*a*b^14 - 112*a^15 - 3760*a^3*b^12 + (15271*a^5*b^10)/2 - (18191*a^7*b^8)/2 + (13697*a^9*b^6)/2 - 3252*a^11*b^4 + 900*a^13*b^2)/b^11 + (tan(c/2 + (d*x)/2)*(3664*b^20 - 18084*a^2*b^18 + 41125*a^4*b^16 - 56140*a^6*b^14 + 50084*a^8*b^12 - 29728*a^10*b^10 + 11392*a^12*b^8 - 2560*a^14*b^6 + 256*a^16*b^4))/(2*b^16) + ((a^4*8i + b^4*15i - a^2*b^2*20i)*((128*b^16 + 94*a^2*b^14 - (2395*a^4*b^12)/2 + 2068*a^6*b^10 - 1600*a^8*b^8 + 608*a^10*b^6 - 96*a^12*b^4)/b^11 + (tan(c/2 + (d*x)/2)*(4944*a*b^20 - 18960*a^3*b^18 + 29985*a^5*b^16 - 24664*a^7*b^14 + 10816*a^9*b^12 - 2240*a^11*b^10 + 128*a^13*b^8))/(2*b^16) + ((a^4*8i + b^4*15i - a^2*b^2*20i)*((256*a*b^16 - 452*a^3*b^14 + 340*a^5*b^12 - 112*a^7*b^10)/b^11 + (((128*a^2*b^16 - 96*a^4*b^14)/b^11 + (tan(c/2 + (d*x)/2)*(1024*a*b^22 - 1088*a^3*b^20 + 128*a^5*b^18))/(2*b^16))*(a^4*8i + b^4*15i - a^2*b^2*20i))/(8*b^5) + (tan(c/2 + (d*x)/2)*(1024*b^22 - 2368*a^2*b^20 + 2432*a^4*b^18 - 1280*a^6*b^16 + 256*a^8*b^14))/(2*b^16)))/(8*b^5)))/(8*b^5))*1i)/(8*b^5))/((224*a^14 - 780*b^14 + 4445*a^2*b^12 - 10911*a^4*b^10 + 14991*a^6*b^8 - 12481*a^8*b^6 + 6312*a^10*b^4 - 1800*a^12*b^2)/b^11 + ((a^4*8i + b^4*15i - a^2*b^2*20i)*((840*a*b^14 - 112*a^15 - 3760*a^3*b^12 + (15271*a^5*b^10)/2 - (18191*a^7*b^8)/2 + (13697*a^9*b^6)/2 - 3252*a^11*b^4 + 900*a^13*b^2)/b^11 + (tan(c/2 + (d*x)/2)*(3664*b^20 - 18084*a^2*b^18 + 41125*a^4*b^16 - 56140*a^6*b^14 + 50084*a^8*b^12 - 29728*a^10*b^10 + 11392*a^12*b^8 - 2560*a^14*b^6 + 256*a^16*b^4))/(2*b^16) - ((a^4*8i + b^4*15i - a^2*b^2*20i)*((128*b^16 + 94*a^2*b^14 - (2395*a^4*b^12)/2 + 2068*a^6*b^10 - 1600*a^8*b^8 + 608*a^10*b^6 - 96*a^12*b^4)/b^11 + (tan(c/2 + (d*x)/2)*(4944*a*b^20 - 18960*a^3*b^18 + 29985*a^5*b^16 - 24664*a^7*b^14 + 10816*a^9*b^12 - 2240*a^11*b^10 + 128*a^13*b^8))/(2*b^16) - ((a^4*8i + b^4*15i - a^2*b^2*20i)*((256*a*b^16 - 452*a^3*b^14 + 340*a^5*b^12 - 112*a^7*b^10)/b^11 - (((128*a^2*b^16 - 96*a^4*b^14)/b^11 + (tan(c/2 + (d*x)/2)*(1024*a*b^22 - 1088*a^3*b^20 + 128*a^5*b^18))/(2*b^16))*(a^4*8i + b^4*15i - a^2*b^2*20i))/(8*b^5) + (tan(c/2 + (d*x)/2)*(1024*b^22 - 2368*a^2*b^20 + 2432*a^4*b^18 - 1280*a^6*b^16 + 256*a^8*b^14))/(2*b^16)))/(8*b^5)))/(8*b^5)))/(8*b^5) - ((a^4*8i + b^4*15i - a^2*b^2*20i)*((840*a*b^14 - 112*a^15 - 3760*a^3*b^12 + (15271*a^5*b^10)/2 - (18191*a^7*b^8)/2 + (13697*a^9*b^6)/2 - 3252*a^11*b^4 + 900*a^13*b^2)/b^11 + (tan(c/2 + (d*x)/2)*(3664*b^20 - 18084*a^2*b^18 + 41125*a^4*b^16 - 56140*a^6*b^14 + 50084*a^8*b^12 - 29728*a^10*b^10 + 11392*a^12*b^8 - 2560*a^14*b^6 + 256*a^16*b^4))/(2*b^16) + ((a^4*8i + b^4*15i - a^2*b^2*20i)*((128*b^16 + 94*a^2*b^14 - (2395*a^4*b^12)/2 + 2068*a^6*b^10 - 1600*a^8*b^8 + 608*a^10*b^6 - 96*a^12*b^4)/b^11 + (tan(c/2 + (d*x)/2)*(4944*a*b^20 - 18960*a^3*b^18 + 29985*a^5*b^16 - 24664*a^7*b^14 + 10816*a^9*b^12 - 2240*a^11*b^10 + 128*a^13*b^8))/(2*b^16) + ((a^4*8i + b^4*15i - a^2*b^2*20i)*((256*a*b^16 - 452*a^3*b^14 + 340*a^5*b^12 - 112*a^7*b^10)/b^11 + (((128*a^2*b^16 - 96*a^4*b^14)/b^11 + (tan(c/2 + (d*x)/2)*(1024*a*b^22 - 1088*a^3*b^20 + 128*a^5*b^18))/(2*b^16))*(a^4*8i + b^4*15i - a^2*b^2*20i))/(8*b^5) + (tan(c/2 + (d*x)/2)*(1024*b^22 - 2368*a^2*b^20 + 2432*a^4*b^18 - 1280*a^6*b^16 + 256*a^8*b^14))/(2*b^16)))/(8*b^5)))/(8*b^5)))/(8*b^5) - (tan(c/2 + (d*x)/2)*(4500*a*b^18 - 512*a^19 - 30900*a^3*b^16 + 94700*a^5*b^14 - 170260*a^7*b^12 + 198160*a^9*b^10 - 155016*a^11*b^8 + 81600*a^13*b^6 - 27904*a^15*b^4 + 5632*a^17*b^2))/b^16))*(a^4*8i + b^4*15i - a^2*b^2*20i)*1i)/(4*b^5*d) - (atan((((-(a + b)^5*(a - b)^5)^(1/2)*((840*a*b^14 - 112*a^15 - 3760*a^3*b^12 + (15271*a^5*b^10)/2 - (18191*a^7*b^8)/2 + (13697*a^9*b^6)/2 - 3252*a^11*b^4 + 900*a^13*b^2)/b^11 + (tan(c/2 + (d*x)/2)*(3664*b^20 - 18084*a^2*b^18 + 41125*a^4*b^16 - 56140*a^6*b^14 + 50084*a^8*b^12 - 29728*a^10*b^10 + 11392*a^12*b^8 - 2560*a^14*b^6 + 256*a^16*b^4))/(2*b^16) + ((-(a + b)^5*(a - b)^5)^(1/2)*((128*b^16 + 94*a^2*b^14 - (2395*a^4*b^12)/2 + 2068*a^6*b^10 - 1600*a^8*b^8 + 608*a^10*b^6 - 96*a^12*b^4)/b^11 + (tan(c/2 + (d*x)/2)*(4944*a*b^20 - 18960*a^3*b^18 + 29985*a^5*b^16 - 24664*a^7*b^14 + 10816*a^9*b^12 - 2240*a^11*b^10 + 128*a^13*b^8))/(2*b^16) + ((-(a + b)^5*(a - b)^5)^(1/2)*((256*a*b^16 - 452*a^3*b^14 + 340*a^5*b^12 - 112*a^7*b^10)/b^11 + (tan(c/2 + (d*x)/2)*(1024*b^22 - 2368*a^2*b^20 + 2432*a^4*b^18 - 1280*a^6*b^16 + 256*a^8*b^14))/(2*b^16) + (((128*a^2*b^16 - 96*a^4*b^14)/b^11 + (tan(c/2 + (d*x)/2)*(1024*a*b^22 - 1088*a^3*b^20 + 128*a^5*b^18))/(2*b^16))*(-(a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5)))/(a*b^5))*1i)/(a*b^5) + ((-(a + b)^5*(a - b)^5)^(1/2)*((840*a*b^14 - 112*a^15 - 3760*a^3*b^12 + (15271*a^5*b^10)/2 - (18191*a^7*b^8)/2 + (13697*a^9*b^6)/2 - 3252*a^11*b^4 + 900*a^13*b^2)/b^11 + (tan(c/2 + (d*x)/2)*(3664*b^20 - 18084*a^2*b^18 + 41125*a^4*b^16 - 56140*a^6*b^14 + 50084*a^8*b^12 - 29728*a^10*b^10 + 11392*a^12*b^8 - 2560*a^14*b^6 + 256*a^16*b^4))/(2*b^16) - ((-(a + b)^5*(a - b)^5)^(1/2)*((128*b^16 + 94*a^2*b^14 - (2395*a^4*b^12)/2 + 2068*a^6*b^10 - 1600*a^8*b^8 + 608*a^10*b^6 - 96*a^12*b^4)/b^11 + (tan(c/2 + (d*x)/2)*(4944*a*b^20 - 18960*a^3*b^18 + 29985*a^5*b^16 - 24664*a^7*b^14 + 10816*a^9*b^12 - 2240*a^11*b^10 + 128*a^13*b^8))/(2*b^16) - ((-(a + b)^5*(a - b)^5)^(1/2)*((256*a*b^16 - 452*a^3*b^14 + 340*a^5*b^12 - 112*a^7*b^10)/b^11 + (tan(c/2 + (d*x)/2)*(1024*b^22 - 2368*a^2*b^20 + 2432*a^4*b^18 - 1280*a^6*b^16 + 256*a^8*b^14))/(2*b^16) - (((128*a^2*b^16 - 96*a^4*b^14)/b^11 + (tan(c/2 + (d*x)/2)*(1024*a*b^22 - 1088*a^3*b^20 + 128*a^5*b^18))/(2*b^16))*(-(a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5)))/(a*b^5))*1i)/(a*b^5))/((224*a^14 - 780*b^14 + 4445*a^2*b^12 - 10911*a^4*b^10 + 14991*a^6*b^8 - 12481*a^8*b^6 + 6312*a^10*b^4 - 1800*a^12*b^2)/b^11 - (tan(c/2 + (d*x)/2)*(4500*a*b^18 - 512*a^19 - 30900*a^3*b^16 + 94700*a^5*b^14 - 170260*a^7*b^12 + 198160*a^9*b^10 - 155016*a^11*b^8 + 81600*a^13*b^6 - 27904*a^15*b^4 + 5632*a^17*b^2))/b^16 - ((-(a + b)^5*(a - b)^5)^(1/2)*((840*a*b^14 - 112*a^15 - 3760*a^3*b^12 + (15271*a^5*b^10)/2 - (18191*a^7*b^8)/2 + (13697*a^9*b^6)/2 - 3252*a^11*b^4 + 900*a^13*b^2)/b^11 + (tan(c/2 + (d*x)/2)*(3664*b^20 - 18084*a^2*b^18 + 41125*a^4*b^16 - 56140*a^6*b^14 + 50084*a^8*b^12 - 29728*a^10*b^10 + 11392*a^12*b^8 - 2560*a^14*b^6 + 256*a^16*b^4))/(2*b^16) + ((-(a + b)^5*(a - b)^5)^(1/2)*((128*b^16 + 94*a^2*b^14 - (2395*a^4*b^12)/2 + 2068*a^6*b^10 - 1600*a^8*b^8 + 608*a^10*b^6 - 96*a^12*b^4)/b^11 + (tan(c/2 + (d*x)/2)*(4944*a*b^20 - 18960*a^3*b^18 + 29985*a^5*b^16 - 24664*a^7*b^14 + 10816*a^9*b^12 - 2240*a^11*b^10 + 128*a^13*b^8))/(2*b^16) + ((-(a + b)^5*(a - b)^5)^(1/2)*((256*a*b^16 - 452*a^3*b^14 + 340*a^5*b^12 - 112*a^7*b^10)/b^11 + (tan(c/2 + (d*x)/2)*(1024*b^22 - 2368*a^2*b^20 + 2432*a^4*b^18 - 1280*a^6*b^16 + 256*a^8*b^14))/(2*b^16) + (((128*a^2*b^16 - 96*a^4*b^14)/b^11 + (tan(c/2 + (d*x)/2)*(1024*a*b^22 - 1088*a^3*b^20 + 128*a^5*b^18))/(2*b^16))*(-(a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5)))/(a*b^5)))/(a*b^5) + ((-(a + b)^5*(a - b)^5)^(1/2)*((840*a*b^14 - 112*a^15 - 3760*a^3*b^12 + (15271*a^5*b^10)/2 - (18191*a^7*b^8)/2 + (13697*a^9*b^6)/2 - 3252*a^11*b^4 + 900*a^13*b^2)/b^11 + (tan(c/2 + (d*x)/2)*(3664*b^20 - 18084*a^2*b^18 + 41125*a^4*b^16 - 56140*a^6*b^14 + 50084*a^8*b^12 - 29728*a^10*b^10 + 11392*a^12*b^8 - 2560*a^14*b^6 + 256*a^16*b^4))/(2*b^16) - ((-(a + b)^5*(a - b)^5)^(1/2)*((128*b^16 + 94*a^2*b^14 - (2395*a^4*b^12)/2 + 2068*a^6*b^10 - 1600*a^8*b^8 + 608*a^10*b^6 - 96*a^12*b^4)/b^11 + (tan(c/2 + (d*x)/2)*(4944*a*b^20 - 18960*a^3*b^18 + 29985*a^5*b^16 - 24664*a^7*b^14 + 10816*a^9*b^12 - 2240*a^11*b^10 + 128*a^13*b^8))/(2*b^16) - ((-(a + b)^5*(a - b)^5)^(1/2)*((256*a*b^16 - 452*a^3*b^14 + 340*a^5*b^12 - 112*a^7*b^10)/b^11 + (tan(c/2 + (d*x)/2)*(1024*b^22 - 2368*a^2*b^20 + 2432*a^4*b^18 - 1280*a^6*b^16 + 256*a^8*b^14))/(2*b^16) - (((128*a^2*b^16 - 96*a^4*b^14)/b^11 + (tan(c/2 + (d*x)/2)*(1024*a*b^22 - 1088*a^3*b^20 + 128*a^5*b^18))/(2*b^16))*(-(a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5)))/(a*b^5)))/(a*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a*b^5*d)","B"
1324,1,4892,183,13.098907,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a\,d}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a\,b^2-a^3\right)}{b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a\,b^2-a^3\right)}{b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+3\,b^2\right)}{b^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2-b^2\right)}{b^2}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a\,b^2-3\,a^3\right)}{3\,b^3}+1}{d\,\left(2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,a\,{\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)\right)}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-14\,a^{14}+105\,a^{12}\,b^2-309\,a^{10}\,b^4+467\,a^8\,b^6-386\,a^6\,b^8+136\,a^4\,b^{10}+10\,a^2\,b^{12}\right)}{a^2\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-12\,a^{12}\,b^3+76\,a^{10}\,b^5-155\,a^8\,b^7+86\,a^6\,b^9+50\,a^4\,b^{11}-52\,a^2\,b^{13}+16\,b^{15}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^6-140\,a^{12}\,b^8+661\,a^{10}\,b^{10}-1264\,a^8\,b^{12}+1020\,a^6\,b^{14}-360\,a^4\,b^{16}+84\,a^2\,b^{18}\right)}{a^3\,b^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-14\,a^8\,b^8+50\,a^6\,b^{10}-64\,a^4\,b^{12}+32\,a^2\,b^{14}\right)}{a^2\,b^8}+\frac{\left(\frac{8\,\left(16\,a^4\,b^{13}-12\,a^6\,b^{11}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^{14}-68\,a^6\,b^{16}+64\,a^4\,b^{18}\right)}{a^3\,b^{12}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}\,b^{11}-80\,a^8\,b^{13}+152\,a^6\,b^{15}-148\,a^4\,b^{17}+64\,a^2\,b^{19}\right)}{a^3\,b^{12}}\right)}{a^2\,b^4}\right)}{a^2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^3-160\,a^{14}\,b^5+652\,a^{12}\,b^7-1408\,a^{10}\,b^9+1769\,a^8\,b^{11}-1300\,a^6\,b^{13}+460\,a^4\,b^{15}-24\,a^2\,b^{17}+4\,b^{19}\right)}{a^3\,b^{12}}\right)\,1{}\mathrm{i}}{a^2\,b^4}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-14\,a^{14}+105\,a^{12}\,b^2-309\,a^{10}\,b^4+467\,a^8\,b^6-386\,a^6\,b^8+136\,a^4\,b^{10}+10\,a^2\,b^{12}\right)}{a^2\,b^8}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-12\,a^{12}\,b^3+76\,a^{10}\,b^5-155\,a^8\,b^7+86\,a^6\,b^9+50\,a^4\,b^{11}-52\,a^2\,b^{13}+16\,b^{15}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^6-140\,a^{12}\,b^8+661\,a^{10}\,b^{10}-1264\,a^8\,b^{12}+1020\,a^6\,b^{14}-360\,a^4\,b^{16}+84\,a^2\,b^{18}\right)}{a^3\,b^{12}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-14\,a^8\,b^8+50\,a^6\,b^{10}-64\,a^4\,b^{12}+32\,a^2\,b^{14}\right)}{a^2\,b^8}-\frac{\left(\frac{8\,\left(16\,a^4\,b^{13}-12\,a^6\,b^{11}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^{14}-68\,a^6\,b^{16}+64\,a^4\,b^{18}\right)}{a^3\,b^{12}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}\,b^{11}-80\,a^8\,b^{13}+152\,a^6\,b^{15}-148\,a^4\,b^{17}+64\,a^2\,b^{19}\right)}{a^3\,b^{12}}\right)}{a^2\,b^4}\right)}{a^2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^3-160\,a^{14}\,b^5+652\,a^{12}\,b^7-1408\,a^{10}\,b^9+1769\,a^8\,b^{11}-1300\,a^6\,b^{13}+460\,a^4\,b^{15}-24\,a^2\,b^{17}+4\,b^{19}\right)}{a^3\,b^{12}}\right)\,1{}\mathrm{i}}{a^2\,b^4}}{\frac{16\,\left(-14\,a^{12}\,b+105\,a^{10}\,b^3-297\,a^8\,b^5+391\,a^6\,b^7-231\,a^4\,b^9+36\,a^2\,b^{11}+10\,b^{13}\right)}{a^2\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-14\,a^{14}+105\,a^{12}\,b^2-309\,a^{10}\,b^4+467\,a^8\,b^6-386\,a^6\,b^8+136\,a^4\,b^{10}+10\,a^2\,b^{12}\right)}{a^2\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-12\,a^{12}\,b^3+76\,a^{10}\,b^5-155\,a^8\,b^7+86\,a^6\,b^9+50\,a^4\,b^{11}-52\,a^2\,b^{13}+16\,b^{15}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^6-140\,a^{12}\,b^8+661\,a^{10}\,b^{10}-1264\,a^8\,b^{12}+1020\,a^6\,b^{14}-360\,a^4\,b^{16}+84\,a^2\,b^{18}\right)}{a^3\,b^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-14\,a^8\,b^8+50\,a^6\,b^{10}-64\,a^4\,b^{12}+32\,a^2\,b^{14}\right)}{a^2\,b^8}+\frac{\left(\frac{8\,\left(16\,a^4\,b^{13}-12\,a^6\,b^{11}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^{14}-68\,a^6\,b^{16}+64\,a^4\,b^{18}\right)}{a^3\,b^{12}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}\,b^{11}-80\,a^8\,b^{13}+152\,a^6\,b^{15}-148\,a^4\,b^{17}+64\,a^2\,b^{19}\right)}{a^3\,b^{12}}\right)}{a^2\,b^4}\right)}{a^2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^3-160\,a^{14}\,b^5+652\,a^{12}\,b^7-1408\,a^{10}\,b^9+1769\,a^8\,b^{11}-1300\,a^6\,b^{13}+460\,a^4\,b^{15}-24\,a^2\,b^{17}+4\,b^{19}\right)}{a^3\,b^{12}}\right)}{a^2\,b^4}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-14\,a^{14}+105\,a^{12}\,b^2-309\,a^{10}\,b^4+467\,a^8\,b^6-386\,a^6\,b^8+136\,a^4\,b^{10}+10\,a^2\,b^{12}\right)}{a^2\,b^8}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-12\,a^{12}\,b^3+76\,a^{10}\,b^5-155\,a^8\,b^7+86\,a^6\,b^9+50\,a^4\,b^{11}-52\,a^2\,b^{13}+16\,b^{15}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^6-140\,a^{12}\,b^8+661\,a^{10}\,b^{10}-1264\,a^8\,b^{12}+1020\,a^6\,b^{14}-360\,a^4\,b^{16}+84\,a^2\,b^{18}\right)}{a^3\,b^{12}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-14\,a^8\,b^8+50\,a^6\,b^{10}-64\,a^4\,b^{12}+32\,a^2\,b^{14}\right)}{a^2\,b^8}-\frac{\left(\frac{8\,\left(16\,a^4\,b^{13}-12\,a^6\,b^{11}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^{14}-68\,a^6\,b^{16}+64\,a^4\,b^{18}\right)}{a^3\,b^{12}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}\,b^{11}-80\,a^8\,b^{13}+152\,a^6\,b^{15}-148\,a^4\,b^{17}+64\,a^2\,b^{19}\right)}{a^3\,b^{12}}\right)}{a^2\,b^4}\right)}{a^2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^3-160\,a^{14}\,b^5+652\,a^{12}\,b^7-1408\,a^{10}\,b^9+1769\,a^8\,b^{11}-1300\,a^6\,b^{13}+460\,a^4\,b^{15}-24\,a^2\,b^{17}+4\,b^{19}\right)}{a^3\,b^{12}}\right)}{a^2\,b^4}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{18}-352\,a^{16}\,b^2+1624\,a^{14}\,b^4-4080\,a^{12}\,b^6+6036\,a^{10}\,b^8-5260\,a^8\,b^{10}+2500\,a^6\,b^{12}-500\,a^4\,b^{14}\right)}{a^3\,b^{12}}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^2\,b^4\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-14\,a^{14}+105\,a^{12}\,b^2-309\,a^{10}\,b^4+467\,a^8\,b^6-386\,a^6\,b^8+136\,a^4\,b^{10}+10\,a^2\,b^{12}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^3-160\,a^{14}\,b^5+652\,a^{12}\,b^7-1408\,a^{10}\,b^9+1769\,a^8\,b^{11}-1300\,a^6\,b^{13}+460\,a^4\,b^{15}-24\,a^2\,b^{17}+4\,b^{19}\right)}{a^3\,b^{12}}-\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-12\,a^{12}\,b^3+76\,a^{10}\,b^5-155\,a^8\,b^7+86\,a^6\,b^9+50\,a^4\,b^{11}-52\,a^2\,b^{13}+16\,b^{15}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^6-140\,a^{12}\,b^8+661\,a^{10}\,b^{10}-1264\,a^8\,b^{12}+1020\,a^6\,b^{14}-360\,a^4\,b^{16}+84\,a^2\,b^{18}\right)}{a^3\,b^{12}}-\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-14\,a^8\,b^8+50\,a^6\,b^{10}-64\,a^4\,b^{12}+32\,a^2\,b^{14}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}\,b^{11}-80\,a^8\,b^{13}+152\,a^6\,b^{15}-148\,a^4\,b^{17}+64\,a^2\,b^{19}\right)}{a^3\,b^{12}}-\frac{a\,\left(\frac{8\,\left(16\,a^4\,b^{13}-12\,a^6\,b^{11}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^{14}-68\,a^6\,b^{16}+64\,a^4\,b^{18}\right)}{a^3\,b^{12}}\right)\,\left(2\,a^2-5\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}\right)}{2\,b^4}+\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-14\,a^{14}+105\,a^{12}\,b^2-309\,a^{10}\,b^4+467\,a^8\,b^6-386\,a^6\,b^8+136\,a^4\,b^{10}+10\,a^2\,b^{12}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^3-160\,a^{14}\,b^5+652\,a^{12}\,b^7-1408\,a^{10}\,b^9+1769\,a^8\,b^{11}-1300\,a^6\,b^{13}+460\,a^4\,b^{15}-24\,a^2\,b^{17}+4\,b^{19}\right)}{a^3\,b^{12}}+\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-12\,a^{12}\,b^3+76\,a^{10}\,b^5-155\,a^8\,b^7+86\,a^6\,b^9+50\,a^4\,b^{11}-52\,a^2\,b^{13}+16\,b^{15}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^6-140\,a^{12}\,b^8+661\,a^{10}\,b^{10}-1264\,a^8\,b^{12}+1020\,a^6\,b^{14}-360\,a^4\,b^{16}+84\,a^2\,b^{18}\right)}{a^3\,b^{12}}+\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-14\,a^8\,b^8+50\,a^6\,b^{10}-64\,a^4\,b^{12}+32\,a^2\,b^{14}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}\,b^{11}-80\,a^8\,b^{13}+152\,a^6\,b^{15}-148\,a^4\,b^{17}+64\,a^2\,b^{19}\right)}{a^3\,b^{12}}+\frac{a\,\left(\frac{8\,\left(16\,a^4\,b^{13}-12\,a^6\,b^{11}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^{14}-68\,a^6\,b^{16}+64\,a^4\,b^{18}\right)}{a^3\,b^{12}}\right)\,\left(2\,a^2-5\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}\right)}{2\,b^4}}{\frac{16\,\left(-14\,a^{12}\,b+105\,a^{10}\,b^3-297\,a^8\,b^5+391\,a^6\,b^7-231\,a^4\,b^9+36\,a^2\,b^{11}+10\,b^{13}\right)}{a^2\,b^8}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{18}-352\,a^{16}\,b^2+1624\,a^{14}\,b^4-4080\,a^{12}\,b^6+6036\,a^{10}\,b^8-5260\,a^8\,b^{10}+2500\,a^6\,b^{12}-500\,a^4\,b^{14}\right)}{a^3\,b^{12}}-\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-14\,a^{14}+105\,a^{12}\,b^2-309\,a^{10}\,b^4+467\,a^8\,b^6-386\,a^6\,b^8+136\,a^4\,b^{10}+10\,a^2\,b^{12}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^3-160\,a^{14}\,b^5+652\,a^{12}\,b^7-1408\,a^{10}\,b^9+1769\,a^8\,b^{11}-1300\,a^6\,b^{13}+460\,a^4\,b^{15}-24\,a^2\,b^{17}+4\,b^{19}\right)}{a^3\,b^{12}}-\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-12\,a^{12}\,b^3+76\,a^{10}\,b^5-155\,a^8\,b^7+86\,a^6\,b^9+50\,a^4\,b^{11}-52\,a^2\,b^{13}+16\,b^{15}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^6-140\,a^{12}\,b^8+661\,a^{10}\,b^{10}-1264\,a^8\,b^{12}+1020\,a^6\,b^{14}-360\,a^4\,b^{16}+84\,a^2\,b^{18}\right)}{a^3\,b^{12}}-\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-14\,a^8\,b^8+50\,a^6\,b^{10}-64\,a^4\,b^{12}+32\,a^2\,b^{14}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}\,b^{11}-80\,a^8\,b^{13}+152\,a^6\,b^{15}-148\,a^4\,b^{17}+64\,a^2\,b^{19}\right)}{a^3\,b^{12}}-\frac{a\,\left(\frac{8\,\left(16\,a^4\,b^{13}-12\,a^6\,b^{11}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^{14}-68\,a^6\,b^{16}+64\,a^4\,b^{18}\right)}{a^3\,b^{12}}\right)\,\left(2\,a^2-5\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-14\,a^{14}+105\,a^{12}\,b^2-309\,a^{10}\,b^4+467\,a^8\,b^6-386\,a^6\,b^8+136\,a^4\,b^{10}+10\,a^2\,b^{12}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{16}\,b^3-160\,a^{14}\,b^5+652\,a^{12}\,b^7-1408\,a^{10}\,b^9+1769\,a^8\,b^{11}-1300\,a^6\,b^{13}+460\,a^4\,b^{15}-24\,a^2\,b^{17}+4\,b^{19}\right)}{a^3\,b^{12}}+\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-12\,a^{12}\,b^3+76\,a^{10}\,b^5-155\,a^8\,b^7+86\,a^6\,b^9+50\,a^4\,b^{11}-52\,a^2\,b^{13}+16\,b^{15}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}\,b^6-140\,a^{12}\,b^8+661\,a^{10}\,b^{10}-1264\,a^8\,b^{12}+1020\,a^6\,b^{14}-360\,a^4\,b^{16}+84\,a^2\,b^{18}\right)}{a^3\,b^{12}}+\frac{a\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{8\,\left(-14\,a^8\,b^8+50\,a^6\,b^{10}-64\,a^4\,b^{12}+32\,a^2\,b^{14}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}\,b^{11}-80\,a^8\,b^{13}+152\,a^6\,b^{15}-148\,a^4\,b^{17}+64\,a^2\,b^{19}\right)}{a^3\,b^{12}}+\frac{a\,\left(\frac{8\,\left(16\,a^4\,b^{13}-12\,a^6\,b^{11}\right)}{a^2\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b^{14}-68\,a^6\,b^{16}+64\,a^4\,b^{18}\right)}{a^3\,b^{12}}\right)\,\left(2\,a^2-5\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}}\right)\,\left(2\,a^2-5\,b^2\right)}{b^4\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a*d) - (3*tan(c/2 + (d*x)/2)^4 + (8*tan(c/2 + (d*x)/2)^3*(2*a*b^2 - a^3))/b^3 + (4*tan(c/2 + (d*x)/2)^5*(3*a*b^2 - a^3))/b^3 + (tan(c/2 + (d*x)/2)^2*(2*a^2 + 3*b^2))/b^2 - (tan(c/2 + (d*x)/2)^6*(2*a^2 - b^2))/b^2 + (4*tan(c/2 + (d*x)/2)*(7*a*b^2 - 3*a^3))/(3*b^3) + 1)/(d*(2*a*tan(c/2 + (d*x)/2) + 6*a*tan(c/2 + (d*x)/2)^3 + 6*a*tan(c/2 + (d*x)/2)^5 + 2*a*tan(c/2 + (d*x)/2)^7)) - (b*log(tan(c/2 + (d*x)/2)))/(a^2*d) - (atan((((-(a + b)^5*(a - b)^5)^(1/2)*((8*(10*a^2*b^12 - 14*a^14 + 136*a^4*b^10 - 386*a^6*b^8 + 467*a^8*b^6 - 309*a^10*b^4 + 105*a^12*b^2))/(a^2*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(16*b^15 - 52*a^2*b^13 + 50*a^4*b^11 + 86*a^6*b^9 - 155*a^8*b^7 + 76*a^10*b^5 - 12*a^12*b^3))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(84*a^2*b^18 - 360*a^4*b^16 + 1020*a^6*b^14 - 1264*a^8*b^12 + 661*a^10*b^10 - 140*a^12*b^8 + 8*a^14*b^6))/(a^3*b^12) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(32*a^2*b^14 - 64*a^4*b^12 + 50*a^6*b^10 - 14*a^8*b^8))/(a^2*b^8) + (((8*(16*a^4*b^13 - 12*a^6*b^11))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^18 - 68*a^6*b^16 + 8*a^8*b^14))/(a^3*b^12))*(-(a + b)^5*(a - b)^5)^(1/2))/(a^2*b^4) + (8*tan(c/2 + (d*x)/2)*(64*a^2*b^19 - 148*a^4*b^17 + 152*a^6*b^15 - 80*a^8*b^13 + 16*a^10*b^11))/(a^3*b^12)))/(a^2*b^4)))/(a^2*b^4) + (8*tan(c/2 + (d*x)/2)*(4*b^19 - 24*a^2*b^17 + 460*a^4*b^15 - 1300*a^6*b^13 + 1769*a^8*b^11 - 1408*a^10*b^9 + 652*a^12*b^7 - 160*a^14*b^5 + 16*a^16*b^3))/(a^3*b^12))*1i)/(a^2*b^4) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(10*a^2*b^12 - 14*a^14 + 136*a^4*b^10 - 386*a^6*b^8 + 467*a^8*b^6 - 309*a^10*b^4 + 105*a^12*b^2))/(a^2*b^8) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(16*b^15 - 52*a^2*b^13 + 50*a^4*b^11 + 86*a^6*b^9 - 155*a^8*b^7 + 76*a^10*b^5 - 12*a^12*b^3))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(84*a^2*b^18 - 360*a^4*b^16 + 1020*a^6*b^14 - 1264*a^8*b^12 + 661*a^10*b^10 - 140*a^12*b^8 + 8*a^14*b^6))/(a^3*b^12) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(32*a^2*b^14 - 64*a^4*b^12 + 50*a^6*b^10 - 14*a^8*b^8))/(a^2*b^8) - (((8*(16*a^4*b^13 - 12*a^6*b^11))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^18 - 68*a^6*b^16 + 8*a^8*b^14))/(a^3*b^12))*(-(a + b)^5*(a - b)^5)^(1/2))/(a^2*b^4) + (8*tan(c/2 + (d*x)/2)*(64*a^2*b^19 - 148*a^4*b^17 + 152*a^6*b^15 - 80*a^8*b^13 + 16*a^10*b^11))/(a^3*b^12)))/(a^2*b^4)))/(a^2*b^4) + (8*tan(c/2 + (d*x)/2)*(4*b^19 - 24*a^2*b^17 + 460*a^4*b^15 - 1300*a^6*b^13 + 1769*a^8*b^11 - 1408*a^10*b^9 + 652*a^12*b^7 - 160*a^14*b^5 + 16*a^16*b^3))/(a^3*b^12))*1i)/(a^2*b^4))/((16*(10*b^13 - 14*a^12*b + 36*a^2*b^11 - 231*a^4*b^9 + 391*a^6*b^7 - 297*a^8*b^5 + 105*a^10*b^3))/(a^2*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(10*a^2*b^12 - 14*a^14 + 136*a^4*b^10 - 386*a^6*b^8 + 467*a^8*b^6 - 309*a^10*b^4 + 105*a^12*b^2))/(a^2*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(16*b^15 - 52*a^2*b^13 + 50*a^4*b^11 + 86*a^6*b^9 - 155*a^8*b^7 + 76*a^10*b^5 - 12*a^12*b^3))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(84*a^2*b^18 - 360*a^4*b^16 + 1020*a^6*b^14 - 1264*a^8*b^12 + 661*a^10*b^10 - 140*a^12*b^8 + 8*a^14*b^6))/(a^3*b^12) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(32*a^2*b^14 - 64*a^4*b^12 + 50*a^6*b^10 - 14*a^8*b^8))/(a^2*b^8) + (((8*(16*a^4*b^13 - 12*a^6*b^11))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^18 - 68*a^6*b^16 + 8*a^8*b^14))/(a^3*b^12))*(-(a + b)^5*(a - b)^5)^(1/2))/(a^2*b^4) + (8*tan(c/2 + (d*x)/2)*(64*a^2*b^19 - 148*a^4*b^17 + 152*a^6*b^15 - 80*a^8*b^13 + 16*a^10*b^11))/(a^3*b^12)))/(a^2*b^4)))/(a^2*b^4) + (8*tan(c/2 + (d*x)/2)*(4*b^19 - 24*a^2*b^17 + 460*a^4*b^15 - 1300*a^6*b^13 + 1769*a^8*b^11 - 1408*a^10*b^9 + 652*a^12*b^7 - 160*a^14*b^5 + 16*a^16*b^3))/(a^3*b^12)))/(a^2*b^4) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(10*a^2*b^12 - 14*a^14 + 136*a^4*b^10 - 386*a^6*b^8 + 467*a^8*b^6 - 309*a^10*b^4 + 105*a^12*b^2))/(a^2*b^8) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(16*b^15 - 52*a^2*b^13 + 50*a^4*b^11 + 86*a^6*b^9 - 155*a^8*b^7 + 76*a^10*b^5 - 12*a^12*b^3))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(84*a^2*b^18 - 360*a^4*b^16 + 1020*a^6*b^14 - 1264*a^8*b^12 + 661*a^10*b^10 - 140*a^12*b^8 + 8*a^14*b^6))/(a^3*b^12) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(32*a^2*b^14 - 64*a^4*b^12 + 50*a^6*b^10 - 14*a^8*b^8))/(a^2*b^8) - (((8*(16*a^4*b^13 - 12*a^6*b^11))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^18 - 68*a^6*b^16 + 8*a^8*b^14))/(a^3*b^12))*(-(a + b)^5*(a - b)^5)^(1/2))/(a^2*b^4) + (8*tan(c/2 + (d*x)/2)*(64*a^2*b^19 - 148*a^4*b^17 + 152*a^6*b^15 - 80*a^8*b^13 + 16*a^10*b^11))/(a^3*b^12)))/(a^2*b^4)))/(a^2*b^4) + (8*tan(c/2 + (d*x)/2)*(4*b^19 - 24*a^2*b^17 + 460*a^4*b^15 - 1300*a^6*b^13 + 1769*a^8*b^11 - 1408*a^10*b^9 + 652*a^12*b^7 - 160*a^14*b^5 + 16*a^16*b^3))/(a^3*b^12)))/(a^2*b^4) - (16*tan(c/2 + (d*x)/2)*(32*a^18 - 500*a^4*b^14 + 2500*a^6*b^12 - 5260*a^8*b^10 + 6036*a^10*b^8 - 4080*a^12*b^6 + 1624*a^14*b^4 - 352*a^16*b^2))/(a^3*b^12)))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a^2*b^4*d) - (a*atan(((a*(2*a^2 - 5*b^2)*((8*(10*a^2*b^12 - 14*a^14 + 136*a^4*b^10 - 386*a^6*b^8 + 467*a^8*b^6 - 309*a^10*b^4 + 105*a^12*b^2))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(4*b^19 - 24*a^2*b^17 + 460*a^4*b^15 - 1300*a^6*b^13 + 1769*a^8*b^11 - 1408*a^10*b^9 + 652*a^12*b^7 - 160*a^14*b^5 + 16*a^16*b^3))/(a^3*b^12) - (a*(2*a^2 - 5*b^2)*((8*(16*b^15 - 52*a^2*b^13 + 50*a^4*b^11 + 86*a^6*b^9 - 155*a^8*b^7 + 76*a^10*b^5 - 12*a^12*b^3))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(84*a^2*b^18 - 360*a^4*b^16 + 1020*a^6*b^14 - 1264*a^8*b^12 + 661*a^10*b^10 - 140*a^12*b^8 + 8*a^14*b^6))/(a^3*b^12) - (a*(2*a^2 - 5*b^2)*((8*(32*a^2*b^14 - 64*a^4*b^12 + 50*a^6*b^10 - 14*a^8*b^8))/(a^2*b^8) - (a*((8*(16*a^4*b^13 - 12*a^6*b^11))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^18 - 68*a^6*b^16 + 8*a^8*b^14))/(a^3*b^12))*(2*a^2 - 5*b^2)*1i)/(2*b^4) + (8*tan(c/2 + (d*x)/2)*(64*a^2*b^19 - 148*a^4*b^17 + 152*a^6*b^15 - 80*a^8*b^13 + 16*a^10*b^11))/(a^3*b^12))*1i)/(2*b^4))*1i)/(2*b^4)))/(2*b^4) + (a*(2*a^2 - 5*b^2)*((8*(10*a^2*b^12 - 14*a^14 + 136*a^4*b^10 - 386*a^6*b^8 + 467*a^8*b^6 - 309*a^10*b^4 + 105*a^12*b^2))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(4*b^19 - 24*a^2*b^17 + 460*a^4*b^15 - 1300*a^6*b^13 + 1769*a^8*b^11 - 1408*a^10*b^9 + 652*a^12*b^7 - 160*a^14*b^5 + 16*a^16*b^3))/(a^3*b^12) + (a*(2*a^2 - 5*b^2)*((8*(16*b^15 - 52*a^2*b^13 + 50*a^4*b^11 + 86*a^6*b^9 - 155*a^8*b^7 + 76*a^10*b^5 - 12*a^12*b^3))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(84*a^2*b^18 - 360*a^4*b^16 + 1020*a^6*b^14 - 1264*a^8*b^12 + 661*a^10*b^10 - 140*a^12*b^8 + 8*a^14*b^6))/(a^3*b^12) + (a*(2*a^2 - 5*b^2)*((8*(32*a^2*b^14 - 64*a^4*b^12 + 50*a^6*b^10 - 14*a^8*b^8))/(a^2*b^8) + (a*((8*(16*a^4*b^13 - 12*a^6*b^11))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^18 - 68*a^6*b^16 + 8*a^8*b^14))/(a^3*b^12))*(2*a^2 - 5*b^2)*1i)/(2*b^4) + (8*tan(c/2 + (d*x)/2)*(64*a^2*b^19 - 148*a^4*b^17 + 152*a^6*b^15 - 80*a^8*b^13 + 16*a^10*b^11))/(a^3*b^12))*1i)/(2*b^4))*1i)/(2*b^4)))/(2*b^4))/((16*(10*b^13 - 14*a^12*b + 36*a^2*b^11 - 231*a^4*b^9 + 391*a^6*b^7 - 297*a^8*b^5 + 105*a^10*b^3))/(a^2*b^8) - (16*tan(c/2 + (d*x)/2)*(32*a^18 - 500*a^4*b^14 + 2500*a^6*b^12 - 5260*a^8*b^10 + 6036*a^10*b^8 - 4080*a^12*b^6 + 1624*a^14*b^4 - 352*a^16*b^2))/(a^3*b^12) - (a*(2*a^2 - 5*b^2)*((8*(10*a^2*b^12 - 14*a^14 + 136*a^4*b^10 - 386*a^6*b^8 + 467*a^8*b^6 - 309*a^10*b^4 + 105*a^12*b^2))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(4*b^19 - 24*a^2*b^17 + 460*a^4*b^15 - 1300*a^6*b^13 + 1769*a^8*b^11 - 1408*a^10*b^9 + 652*a^12*b^7 - 160*a^14*b^5 + 16*a^16*b^3))/(a^3*b^12) - (a*(2*a^2 - 5*b^2)*((8*(16*b^15 - 52*a^2*b^13 + 50*a^4*b^11 + 86*a^6*b^9 - 155*a^8*b^7 + 76*a^10*b^5 - 12*a^12*b^3))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(84*a^2*b^18 - 360*a^4*b^16 + 1020*a^6*b^14 - 1264*a^8*b^12 + 661*a^10*b^10 - 140*a^12*b^8 + 8*a^14*b^6))/(a^3*b^12) - (a*(2*a^2 - 5*b^2)*((8*(32*a^2*b^14 - 64*a^4*b^12 + 50*a^6*b^10 - 14*a^8*b^8))/(a^2*b^8) - (a*((8*(16*a^4*b^13 - 12*a^6*b^11))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^18 - 68*a^6*b^16 + 8*a^8*b^14))/(a^3*b^12))*(2*a^2 - 5*b^2)*1i)/(2*b^4) + (8*tan(c/2 + (d*x)/2)*(64*a^2*b^19 - 148*a^4*b^17 + 152*a^6*b^15 - 80*a^8*b^13 + 16*a^10*b^11))/(a^3*b^12))*1i)/(2*b^4))*1i)/(2*b^4))*1i)/(2*b^4) + (a*(2*a^2 - 5*b^2)*((8*(10*a^2*b^12 - 14*a^14 + 136*a^4*b^10 - 386*a^6*b^8 + 467*a^8*b^6 - 309*a^10*b^4 + 105*a^12*b^2))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(4*b^19 - 24*a^2*b^17 + 460*a^4*b^15 - 1300*a^6*b^13 + 1769*a^8*b^11 - 1408*a^10*b^9 + 652*a^12*b^7 - 160*a^14*b^5 + 16*a^16*b^3))/(a^3*b^12) + (a*(2*a^2 - 5*b^2)*((8*(16*b^15 - 52*a^2*b^13 + 50*a^4*b^11 + 86*a^6*b^9 - 155*a^8*b^7 + 76*a^10*b^5 - 12*a^12*b^3))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(84*a^2*b^18 - 360*a^4*b^16 + 1020*a^6*b^14 - 1264*a^8*b^12 + 661*a^10*b^10 - 140*a^12*b^8 + 8*a^14*b^6))/(a^3*b^12) + (a*(2*a^2 - 5*b^2)*((8*(32*a^2*b^14 - 64*a^4*b^12 + 50*a^6*b^10 - 14*a^8*b^8))/(a^2*b^8) + (a*((8*(16*a^4*b^13 - 12*a^6*b^11))/(a^2*b^8) + (8*tan(c/2 + (d*x)/2)*(64*a^4*b^18 - 68*a^6*b^16 + 8*a^8*b^14))/(a^3*b^12))*(2*a^2 - 5*b^2)*1i)/(2*b^4) + (8*tan(c/2 + (d*x)/2)*(64*a^2*b^19 - 148*a^4*b^17 + 152*a^6*b^15 - 80*a^8*b^13 + 16*a^10*b^11))/(a^3*b^12))*1i)/(2*b^4))*1i)/(2*b^4))*1i)/(2*b^4)))*(2*a^2 - 5*b^2))/(b^4*d)","B"
1325,1,4898,174,13.090764,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{\frac{a}{2}-2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+b^2\right)}{b}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^3+a\,b^2\right)}{b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(16\,a^3+a\,b^2\right)}{2\,b^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^2-b^2\right)}{b}}{d\,\left(4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{4\,\left(-28\,a^{15}+270\,a^{13}\,b^2-998\,a^{11}\,b^4+1709\,a^9\,b^6-1272\,a^7\,b^8+272\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^5}+\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{4\,\left(-28\,a^{11}\,b^6+160\,a^9\,b^8-208\,a^7\,b^{10}+64\,a^5\,b^{12}\right)}{a^6\,b^5}+\frac{\left(\frac{4\,\left(32\,a^8\,b^{10}-24\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{11}\,b^{10}-136\,a^9\,b^{12}+128\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)}{b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^8-200\,a^{10}\,b^{10}+484\,a^8\,b^{12}-456\,a^6\,b^{14}+128\,a^4\,b^{16}\right)}{a^6\,b^8}\right)}{b^3}-\frac{4\,\left(24\,a^{14}\,b^2-152\,a^{12}\,b^4+240\,a^{10}\,b^6+78\,a^8\,b^8-360\,a^6\,b^{10}+184\,a^4\,b^{12}-32\,a^2\,b^{14}\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{15}\,b^4-280\,a^{13}\,b^6+1242\,a^{11}\,b^8-2128\,a^9\,b^{10}+1320\,a^7\,b^{12}-160\,a^5\,b^{14}+8\,a^3\,b^{16}\right)}{a^6\,b^8}\right)}{b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-360\,a^{14}\,b^4+1684\,a^{12}\,b^6-4201\,a^{10}\,b^8+5738\,a^8\,b^{10}-3900\,a^6\,b^{12}+1040\,a^4\,b^{14}-68\,a^2\,b^{16}+8\,b^{18}\right)}{a^6\,b^8}\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{4\,\left(-28\,a^{15}+270\,a^{13}\,b^2-998\,a^{11}\,b^4+1709\,a^9\,b^6-1272\,a^7\,b^8+272\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^5}+\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{4\,\left(-28\,a^{11}\,b^6+160\,a^9\,b^8-208\,a^7\,b^{10}+64\,a^5\,b^{12}\right)}{a^6\,b^5}-\frac{\left(\frac{4\,\left(32\,a^8\,b^{10}-24\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{11}\,b^{10}-136\,a^9\,b^{12}+128\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)}{b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^8-200\,a^{10}\,b^{10}+484\,a^8\,b^{12}-456\,a^6\,b^{14}+128\,a^4\,b^{16}\right)}{a^6\,b^8}\right)}{b^3}+\frac{4\,\left(24\,a^{14}\,b^2-152\,a^{12}\,b^4+240\,a^{10}\,b^6+78\,a^8\,b^8-360\,a^6\,b^{10}+184\,a^4\,b^{12}-32\,a^2\,b^{14}\right)}{a^6\,b^5}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{15}\,b^4-280\,a^{13}\,b^6+1242\,a^{11}\,b^8-2128\,a^9\,b^{10}+1320\,a^7\,b^{12}-160\,a^5\,b^{14}+8\,a^3\,b^{16}\right)}{a^6\,b^8}\right)}{b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-360\,a^{14}\,b^4+1684\,a^{12}\,b^6-4201\,a^{10}\,b^8+5738\,a^8\,b^{10}-3900\,a^6\,b^{12}+1040\,a^4\,b^{14}-68\,a^2\,b^{16}+8\,b^{18}\right)}{a^6\,b^8}\right)\,1{}\mathrm{i}}{b^3}}{\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{4\,\left(-28\,a^{15}+270\,a^{13}\,b^2-998\,a^{11}\,b^4+1709\,a^9\,b^6-1272\,a^7\,b^8+272\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^5}+\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{4\,\left(-28\,a^{11}\,b^6+160\,a^9\,b^8-208\,a^7\,b^{10}+64\,a^5\,b^{12}\right)}{a^6\,b^5}+\frac{\left(\frac{4\,\left(32\,a^8\,b^{10}-24\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{11}\,b^{10}-136\,a^9\,b^{12}+128\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)}{b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^8-200\,a^{10}\,b^{10}+484\,a^8\,b^{12}-456\,a^6\,b^{14}+128\,a^4\,b^{16}\right)}{a^6\,b^8}\right)}{b^3}-\frac{4\,\left(24\,a^{14}\,b^2-152\,a^{12}\,b^4+240\,a^{10}\,b^6+78\,a^8\,b^8-360\,a^6\,b^{10}+184\,a^4\,b^{12}-32\,a^2\,b^{14}\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{15}\,b^4-280\,a^{13}\,b^6+1242\,a^{11}\,b^8-2128\,a^9\,b^{10}+1320\,a^7\,b^{12}-160\,a^5\,b^{14}+8\,a^3\,b^{16}\right)}{a^6\,b^8}\right)}{b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-360\,a^{14}\,b^4+1684\,a^{12}\,b^6-4201\,a^{10}\,b^8+5738\,a^8\,b^{10}-3900\,a^6\,b^{12}+1040\,a^4\,b^{14}-68\,a^2\,b^{16}+8\,b^{18}\right)}{a^6\,b^8}\right)}{b^3}-\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{4\,\left(-28\,a^{15}+270\,a^{13}\,b^2-998\,a^{11}\,b^4+1709\,a^9\,b^6-1272\,a^7\,b^8+272\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^5}+\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,\left(\frac{4\,\left(-28\,a^{11}\,b^6+160\,a^9\,b^8-208\,a^7\,b^{10}+64\,a^5\,b^{12}\right)}{a^6\,b^5}-\frac{\left(\frac{4\,\left(32\,a^8\,b^{10}-24\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{11}\,b^{10}-136\,a^9\,b^{12}+128\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)}{b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^8-200\,a^{10}\,b^{10}+484\,a^8\,b^{12}-456\,a^6\,b^{14}+128\,a^4\,b^{16}\right)}{a^6\,b^8}\right)}{b^3}+\frac{4\,\left(24\,a^{14}\,b^2-152\,a^{12}\,b^4+240\,a^{10}\,b^6+78\,a^8\,b^8-360\,a^6\,b^{10}+184\,a^4\,b^{12}-32\,a^2\,b^{14}\right)}{a^6\,b^5}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{15}\,b^4-280\,a^{13}\,b^6+1242\,a^{11}\,b^8-2128\,a^9\,b^{10}+1320\,a^7\,b^{12}-160\,a^5\,b^{14}+8\,a^3\,b^{16}\right)}{a^6\,b^8}\right)}{b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-360\,a^{14}\,b^4+1684\,a^{12}\,b^6-4201\,a^{10}\,b^8+5738\,a^8\,b^{10}-3900\,a^6\,b^{12}+1040\,a^4\,b^{14}-68\,a^2\,b^{16}+8\,b^{18}\right)}{a^6\,b^8}\right)}{b^3}+\frac{8\,\left(70\,a^{14}-553\,a^{12}\,b^2+1695\,a^{10}\,b^4-2549\,a^8\,b^6+1937\,a^6\,b^8-642\,a^4\,b^{10}+22\,a^2\,b^{12}+20\,b^{14}\right)}{a^6\,b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{17}-624\,a^{15}\,b^2+2448\,a^{13}\,b^4-4940\,a^{11}\,b^6+5412\,a^9\,b^8-3060\,a^7\,b^{10}+700\,a^5\,b^{12}\right)}{a^6\,b^8}}\right)\,\left(a^2\,1{}\mathrm{i}-\frac{b^2\,5{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{b^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{5\,a^2}{2}-b^2\right)}{a^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-28\,a^{15}+270\,a^{13}\,b^2-998\,a^{11}\,b^4+1709\,a^9\,b^6-1272\,a^7\,b^8+272\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-360\,a^{14}\,b^4+1684\,a^{12}\,b^6-4201\,a^{10}\,b^8+5738\,a^8\,b^{10}-3900\,a^6\,b^{12}+1040\,a^4\,b^{14}-68\,a^2\,b^{16}+8\,b^{18}\right)}{a^6\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{15}\,b^4-280\,a^{13}\,b^6+1242\,a^{11}\,b^8-2128\,a^9\,b^{10}+1320\,a^7\,b^{12}-160\,a^5\,b^{14}+8\,a^3\,b^{16}\right)}{a^6\,b^8}-\frac{4\,\left(24\,a^{14}\,b^2-152\,a^{12}\,b^4+240\,a^{10}\,b^6+78\,a^8\,b^8-360\,a^6\,b^{10}+184\,a^4\,b^{12}-32\,a^2\,b^{14}\right)}{a^6\,b^5}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-28\,a^{11}\,b^6+160\,a^9\,b^8-208\,a^7\,b^{10}+64\,a^5\,b^{12}\right)}{a^6\,b^5}+\frac{\left(\frac{4\,\left(32\,a^8\,b^{10}-24\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{11}\,b^{10}-136\,a^9\,b^{12}+128\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^3\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^8-200\,a^{10}\,b^{10}+484\,a^8\,b^{12}-456\,a^6\,b^{14}+128\,a^4\,b^{16}\right)}{a^6\,b^8}\right)}{a^3\,b^3}\right)}{a^3\,b^3}\right)\,1{}\mathrm{i}}{a^3\,b^3}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-28\,a^{15}+270\,a^{13}\,b^2-998\,a^{11}\,b^4+1709\,a^9\,b^6-1272\,a^7\,b^8+272\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-360\,a^{14}\,b^4+1684\,a^{12}\,b^6-4201\,a^{10}\,b^8+5738\,a^8\,b^{10}-3900\,a^6\,b^{12}+1040\,a^4\,b^{14}-68\,a^2\,b^{16}+8\,b^{18}\right)}{a^6\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(24\,a^{14}\,b^2-152\,a^{12}\,b^4+240\,a^{10}\,b^6+78\,a^8\,b^8-360\,a^6\,b^{10}+184\,a^4\,b^{12}-32\,a^2\,b^{14}\right)}{a^6\,b^5}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{15}\,b^4-280\,a^{13}\,b^6+1242\,a^{11}\,b^8-2128\,a^9\,b^{10}+1320\,a^7\,b^{12}-160\,a^5\,b^{14}+8\,a^3\,b^{16}\right)}{a^6\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-28\,a^{11}\,b^6+160\,a^9\,b^8-208\,a^7\,b^{10}+64\,a^5\,b^{12}\right)}{a^6\,b^5}-\frac{\left(\frac{4\,\left(32\,a^8\,b^{10}-24\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{11}\,b^{10}-136\,a^9\,b^{12}+128\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^3\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^8-200\,a^{10}\,b^{10}+484\,a^8\,b^{12}-456\,a^6\,b^{14}+128\,a^4\,b^{16}\right)}{a^6\,b^8}\right)}{a^3\,b^3}\right)}{a^3\,b^3}\right)\,1{}\mathrm{i}}{a^3\,b^3}}{\frac{8\,\left(70\,a^{14}-553\,a^{12}\,b^2+1695\,a^{10}\,b^4-2549\,a^8\,b^6+1937\,a^6\,b^8-642\,a^4\,b^{10}+22\,a^2\,b^{12}+20\,b^{14}\right)}{a^6\,b^5}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-28\,a^{15}+270\,a^{13}\,b^2-998\,a^{11}\,b^4+1709\,a^9\,b^6-1272\,a^7\,b^8+272\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-360\,a^{14}\,b^4+1684\,a^{12}\,b^6-4201\,a^{10}\,b^8+5738\,a^8\,b^{10}-3900\,a^6\,b^{12}+1040\,a^4\,b^{14}-68\,a^2\,b^{16}+8\,b^{18}\right)}{a^6\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{15}\,b^4-280\,a^{13}\,b^6+1242\,a^{11}\,b^8-2128\,a^9\,b^{10}+1320\,a^7\,b^{12}-160\,a^5\,b^{14}+8\,a^3\,b^{16}\right)}{a^6\,b^8}-\frac{4\,\left(24\,a^{14}\,b^2-152\,a^{12}\,b^4+240\,a^{10}\,b^6+78\,a^8\,b^8-360\,a^6\,b^{10}+184\,a^4\,b^{12}-32\,a^2\,b^{14}\right)}{a^6\,b^5}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-28\,a^{11}\,b^6+160\,a^9\,b^8-208\,a^7\,b^{10}+64\,a^5\,b^{12}\right)}{a^6\,b^5}+\frac{\left(\frac{4\,\left(32\,a^8\,b^{10}-24\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{11}\,b^{10}-136\,a^9\,b^{12}+128\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^3\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^8-200\,a^{10}\,b^{10}+484\,a^8\,b^{12}-456\,a^6\,b^{14}+128\,a^4\,b^{16}\right)}{a^6\,b^8}\right)}{a^3\,b^3}\right)}{a^3\,b^3}\right)}{a^3\,b^3}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-28\,a^{15}+270\,a^{13}\,b^2-998\,a^{11}\,b^4+1709\,a^9\,b^6-1272\,a^7\,b^8+272\,a^5\,b^{10}+20\,a^3\,b^{12}\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{16}\,b^2-360\,a^{14}\,b^4+1684\,a^{12}\,b^6-4201\,a^{10}\,b^8+5738\,a^8\,b^{10}-3900\,a^6\,b^{12}+1040\,a^4\,b^{14}-68\,a^2\,b^{16}+8\,b^{18}\right)}{a^6\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(24\,a^{14}\,b^2-152\,a^{12}\,b^4+240\,a^{10}\,b^6+78\,a^8\,b^8-360\,a^6\,b^{10}+184\,a^4\,b^{12}-32\,a^2\,b^{14}\right)}{a^6\,b^5}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{15}\,b^4-280\,a^{13}\,b^6+1242\,a^{11}\,b^8-2128\,a^9\,b^{10}+1320\,a^7\,b^{12}-160\,a^5\,b^{14}+8\,a^3\,b^{16}\right)}{a^6\,b^8}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-28\,a^{11}\,b^6+160\,a^9\,b^8-208\,a^7\,b^{10}+64\,a^5\,b^{12}\right)}{a^6\,b^5}-\frac{\left(\frac{4\,\left(32\,a^8\,b^{10}-24\,a^{10}\,b^8\right)}{a^6\,b^5}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{11}\,b^{10}-136\,a^9\,b^{12}+128\,a^7\,b^{14}\right)}{a^6\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^3\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^8-200\,a^{10}\,b^{10}+484\,a^8\,b^{12}-456\,a^6\,b^{14}+128\,a^4\,b^{16}\right)}{a^6\,b^8}\right)}{a^3\,b^3}\right)}{a^3\,b^3}\right)}{a^3\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{17}-624\,a^{15}\,b^2+2448\,a^{13}\,b^4-4940\,a^{11}\,b^6+5412\,a^9\,b^8-3060\,a^7\,b^{10}+700\,a^5\,b^{12}\right)}{a^6\,b^8}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^3\,b^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - (a/2 - 2*b*tan(c/2 + (d*x)/2) - (4*tan(c/2 + (d*x)/2)^3*(a^2 + b^2))/b + (tan(c/2 + (d*x)/2)^2*(a*b^2 + 8*a^3))/b^2 + (tan(c/2 + (d*x)/2)^4*(a*b^2 + 16*a^3))/(2*b^2) + (2*tan(c/2 + (d*x)/2)^5*(2*a^2 - b^2))/b)/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 + 8*a^2*tan(c/2 + (d*x)/2)^4 + 4*a^2*tan(c/2 + (d*x)/2)^6)) - (b*tan(c/2 + (d*x)/2))/(2*a^2*d) + (atan((((a^2*1i - (b^2*5i)/2)*((4*(20*a^3*b^12 - 28*a^15 + 272*a^5*b^10 - 1272*a^7*b^8 + 1709*a^9*b^6 - 998*a^11*b^4 + 270*a^13*b^2))/(a^6*b^5) + ((a^2*1i - (b^2*5i)/2)*(((a^2*1i - (b^2*5i)/2)*((4*(64*a^5*b^12 - 208*a^7*b^10 + 160*a^9*b^8 - 28*a^11*b^6))/(a^6*b^5) + (((4*(32*a^8*b^10 - 24*a^10*b^8))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^7*b^14 - 136*a^9*b^12 + 16*a^11*b^10))/(a^6*b^8))*(a^2*1i - (b^2*5i)/2))/b^3 + (4*tan(c/2 + (d*x)/2)*(128*a^4*b^16 - 456*a^6*b^14 + 484*a^8*b^12 - 200*a^10*b^10 + 32*a^12*b^8))/(a^6*b^8)))/b^3 - (4*(184*a^4*b^12 - 32*a^2*b^14 - 360*a^6*b^10 + 78*a^8*b^8 + 240*a^10*b^6 - 152*a^12*b^4 + 24*a^14*b^2))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(8*a^3*b^16 - 160*a^5*b^14 + 1320*a^7*b^12 - 2128*a^9*b^10 + 1242*a^11*b^8 - 280*a^13*b^6 + 16*a^15*b^4))/(a^6*b^8)))/b^3 + (4*tan(c/2 + (d*x)/2)*(8*b^18 - 68*a^2*b^16 + 1040*a^4*b^14 - 3900*a^6*b^12 + 5738*a^8*b^10 - 4201*a^10*b^8 + 1684*a^12*b^6 - 360*a^14*b^4 + 32*a^16*b^2))/(a^6*b^8))*1i)/b^3 + ((a^2*1i - (b^2*5i)/2)*((4*(20*a^3*b^12 - 28*a^15 + 272*a^5*b^10 - 1272*a^7*b^8 + 1709*a^9*b^6 - 998*a^11*b^4 + 270*a^13*b^2))/(a^6*b^5) + ((a^2*1i - (b^2*5i)/2)*(((a^2*1i - (b^2*5i)/2)*((4*(64*a^5*b^12 - 208*a^7*b^10 + 160*a^9*b^8 - 28*a^11*b^6))/(a^6*b^5) - (((4*(32*a^8*b^10 - 24*a^10*b^8))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^7*b^14 - 136*a^9*b^12 + 16*a^11*b^10))/(a^6*b^8))*(a^2*1i - (b^2*5i)/2))/b^3 + (4*tan(c/2 + (d*x)/2)*(128*a^4*b^16 - 456*a^6*b^14 + 484*a^8*b^12 - 200*a^10*b^10 + 32*a^12*b^8))/(a^6*b^8)))/b^3 + (4*(184*a^4*b^12 - 32*a^2*b^14 - 360*a^6*b^10 + 78*a^8*b^8 + 240*a^10*b^6 - 152*a^12*b^4 + 24*a^14*b^2))/(a^6*b^5) - (4*tan(c/2 + (d*x)/2)*(8*a^3*b^16 - 160*a^5*b^14 + 1320*a^7*b^12 - 2128*a^9*b^10 + 1242*a^11*b^8 - 280*a^13*b^6 + 16*a^15*b^4))/(a^6*b^8)))/b^3 + (4*tan(c/2 + (d*x)/2)*(8*b^18 - 68*a^2*b^16 + 1040*a^4*b^14 - 3900*a^6*b^12 + 5738*a^8*b^10 - 4201*a^10*b^8 + 1684*a^12*b^6 - 360*a^14*b^4 + 32*a^16*b^2))/(a^6*b^8))*1i)/b^3)/(((a^2*1i - (b^2*5i)/2)*((4*(20*a^3*b^12 - 28*a^15 + 272*a^5*b^10 - 1272*a^7*b^8 + 1709*a^9*b^6 - 998*a^11*b^4 + 270*a^13*b^2))/(a^6*b^5) + ((a^2*1i - (b^2*5i)/2)*(((a^2*1i - (b^2*5i)/2)*((4*(64*a^5*b^12 - 208*a^7*b^10 + 160*a^9*b^8 - 28*a^11*b^6))/(a^6*b^5) + (((4*(32*a^8*b^10 - 24*a^10*b^8))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^7*b^14 - 136*a^9*b^12 + 16*a^11*b^10))/(a^6*b^8))*(a^2*1i - (b^2*5i)/2))/b^3 + (4*tan(c/2 + (d*x)/2)*(128*a^4*b^16 - 456*a^6*b^14 + 484*a^8*b^12 - 200*a^10*b^10 + 32*a^12*b^8))/(a^6*b^8)))/b^3 - (4*(184*a^4*b^12 - 32*a^2*b^14 - 360*a^6*b^10 + 78*a^8*b^8 + 240*a^10*b^6 - 152*a^12*b^4 + 24*a^14*b^2))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(8*a^3*b^16 - 160*a^5*b^14 + 1320*a^7*b^12 - 2128*a^9*b^10 + 1242*a^11*b^8 - 280*a^13*b^6 + 16*a^15*b^4))/(a^6*b^8)))/b^3 + (4*tan(c/2 + (d*x)/2)*(8*b^18 - 68*a^2*b^16 + 1040*a^4*b^14 - 3900*a^6*b^12 + 5738*a^8*b^10 - 4201*a^10*b^8 + 1684*a^12*b^6 - 360*a^14*b^4 + 32*a^16*b^2))/(a^6*b^8)))/b^3 - ((a^2*1i - (b^2*5i)/2)*((4*(20*a^3*b^12 - 28*a^15 + 272*a^5*b^10 - 1272*a^7*b^8 + 1709*a^9*b^6 - 998*a^11*b^4 + 270*a^13*b^2))/(a^6*b^5) + ((a^2*1i - (b^2*5i)/2)*(((a^2*1i - (b^2*5i)/2)*((4*(64*a^5*b^12 - 208*a^7*b^10 + 160*a^9*b^8 - 28*a^11*b^6))/(a^6*b^5) - (((4*(32*a^8*b^10 - 24*a^10*b^8))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^7*b^14 - 136*a^9*b^12 + 16*a^11*b^10))/(a^6*b^8))*(a^2*1i - (b^2*5i)/2))/b^3 + (4*tan(c/2 + (d*x)/2)*(128*a^4*b^16 - 456*a^6*b^14 + 484*a^8*b^12 - 200*a^10*b^10 + 32*a^12*b^8))/(a^6*b^8)))/b^3 + (4*(184*a^4*b^12 - 32*a^2*b^14 - 360*a^6*b^10 + 78*a^8*b^8 + 240*a^10*b^6 - 152*a^12*b^4 + 24*a^14*b^2))/(a^6*b^5) - (4*tan(c/2 + (d*x)/2)*(8*a^3*b^16 - 160*a^5*b^14 + 1320*a^7*b^12 - 2128*a^9*b^10 + 1242*a^11*b^8 - 280*a^13*b^6 + 16*a^15*b^4))/(a^6*b^8)))/b^3 + (4*tan(c/2 + (d*x)/2)*(8*b^18 - 68*a^2*b^16 + 1040*a^4*b^14 - 3900*a^6*b^12 + 5738*a^8*b^10 - 4201*a^10*b^8 + 1684*a^12*b^6 - 360*a^14*b^4 + 32*a^16*b^2))/(a^6*b^8)))/b^3 + (8*(70*a^14 + 20*b^14 + 22*a^2*b^12 - 642*a^4*b^10 + 1937*a^6*b^8 - 2549*a^8*b^6 + 1695*a^10*b^4 - 553*a^12*b^2))/(a^6*b^5) - (8*tan(c/2 + (d*x)/2)*(64*a^17 + 700*a^5*b^12 - 3060*a^7*b^10 + 5412*a^9*b^8 - 4940*a^11*b^6 + 2448*a^13*b^4 - 624*a^15*b^2))/(a^6*b^8)))*(a^2*1i - (b^2*5i)/2)*2i)/(b^3*d) - (log(tan(c/2 + (d*x)/2))*((5*a^2)/2 - b^2))/(a^3*d) + (atan((((-(a + b)^5*(a - b)^5)^(1/2)*((4*(20*a^3*b^12 - 28*a^15 + 272*a^5*b^10 - 1272*a^7*b^8 + 1709*a^9*b^6 - 998*a^11*b^4 + 270*a^13*b^2))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(8*b^18 - 68*a^2*b^16 + 1040*a^4*b^14 - 3900*a^6*b^12 + 5738*a^8*b^10 - 4201*a^10*b^8 + 1684*a^12*b^6 - 360*a^14*b^4 + 32*a^16*b^2))/(a^6*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*tan(c/2 + (d*x)/2)*(8*a^3*b^16 - 160*a^5*b^14 + 1320*a^7*b^12 - 2128*a^9*b^10 + 1242*a^11*b^8 - 280*a^13*b^6 + 16*a^15*b^4))/(a^6*b^8) - (4*(184*a^4*b^12 - 32*a^2*b^14 - 360*a^6*b^10 + 78*a^8*b^8 + 240*a^10*b^6 - 152*a^12*b^4 + 24*a^14*b^2))/(a^6*b^5) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(64*a^5*b^12 - 208*a^7*b^10 + 160*a^9*b^8 - 28*a^11*b^6))/(a^6*b^5) + (((4*(32*a^8*b^10 - 24*a^10*b^8))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^7*b^14 - 136*a^9*b^12 + 16*a^11*b^10))/(a^6*b^8))*(-(a + b)^5*(a - b)^5)^(1/2))/(a^3*b^3) + (4*tan(c/2 + (d*x)/2)*(128*a^4*b^16 - 456*a^6*b^14 + 484*a^8*b^12 - 200*a^10*b^10 + 32*a^12*b^8))/(a^6*b^8)))/(a^3*b^3)))/(a^3*b^3))*1i)/(a^3*b^3) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(20*a^3*b^12 - 28*a^15 + 272*a^5*b^10 - 1272*a^7*b^8 + 1709*a^9*b^6 - 998*a^11*b^4 + 270*a^13*b^2))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(8*b^18 - 68*a^2*b^16 + 1040*a^4*b^14 - 3900*a^6*b^12 + 5738*a^8*b^10 - 4201*a^10*b^8 + 1684*a^12*b^6 - 360*a^14*b^4 + 32*a^16*b^2))/(a^6*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(184*a^4*b^12 - 32*a^2*b^14 - 360*a^6*b^10 + 78*a^8*b^8 + 240*a^10*b^6 - 152*a^12*b^4 + 24*a^14*b^2))/(a^6*b^5) - (4*tan(c/2 + (d*x)/2)*(8*a^3*b^16 - 160*a^5*b^14 + 1320*a^7*b^12 - 2128*a^9*b^10 + 1242*a^11*b^8 - 280*a^13*b^6 + 16*a^15*b^4))/(a^6*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(64*a^5*b^12 - 208*a^7*b^10 + 160*a^9*b^8 - 28*a^11*b^6))/(a^6*b^5) - (((4*(32*a^8*b^10 - 24*a^10*b^8))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^7*b^14 - 136*a^9*b^12 + 16*a^11*b^10))/(a^6*b^8))*(-(a + b)^5*(a - b)^5)^(1/2))/(a^3*b^3) + (4*tan(c/2 + (d*x)/2)*(128*a^4*b^16 - 456*a^6*b^14 + 484*a^8*b^12 - 200*a^10*b^10 + 32*a^12*b^8))/(a^6*b^8)))/(a^3*b^3)))/(a^3*b^3))*1i)/(a^3*b^3))/((8*(70*a^14 + 20*b^14 + 22*a^2*b^12 - 642*a^4*b^10 + 1937*a^6*b^8 - 2549*a^8*b^6 + 1695*a^10*b^4 - 553*a^12*b^2))/(a^6*b^5) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(20*a^3*b^12 - 28*a^15 + 272*a^5*b^10 - 1272*a^7*b^8 + 1709*a^9*b^6 - 998*a^11*b^4 + 270*a^13*b^2))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(8*b^18 - 68*a^2*b^16 + 1040*a^4*b^14 - 3900*a^6*b^12 + 5738*a^8*b^10 - 4201*a^10*b^8 + 1684*a^12*b^6 - 360*a^14*b^4 + 32*a^16*b^2))/(a^6*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*tan(c/2 + (d*x)/2)*(8*a^3*b^16 - 160*a^5*b^14 + 1320*a^7*b^12 - 2128*a^9*b^10 + 1242*a^11*b^8 - 280*a^13*b^6 + 16*a^15*b^4))/(a^6*b^8) - (4*(184*a^4*b^12 - 32*a^2*b^14 - 360*a^6*b^10 + 78*a^8*b^8 + 240*a^10*b^6 - 152*a^12*b^4 + 24*a^14*b^2))/(a^6*b^5) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(64*a^5*b^12 - 208*a^7*b^10 + 160*a^9*b^8 - 28*a^11*b^6))/(a^6*b^5) + (((4*(32*a^8*b^10 - 24*a^10*b^8))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^7*b^14 - 136*a^9*b^12 + 16*a^11*b^10))/(a^6*b^8))*(-(a + b)^5*(a - b)^5)^(1/2))/(a^3*b^3) + (4*tan(c/2 + (d*x)/2)*(128*a^4*b^16 - 456*a^6*b^14 + 484*a^8*b^12 - 200*a^10*b^10 + 32*a^12*b^8))/(a^6*b^8)))/(a^3*b^3)))/(a^3*b^3)))/(a^3*b^3) - ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(20*a^3*b^12 - 28*a^15 + 272*a^5*b^10 - 1272*a^7*b^8 + 1709*a^9*b^6 - 998*a^11*b^4 + 270*a^13*b^2))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(8*b^18 - 68*a^2*b^16 + 1040*a^4*b^14 - 3900*a^6*b^12 + 5738*a^8*b^10 - 4201*a^10*b^8 + 1684*a^12*b^6 - 360*a^14*b^4 + 32*a^16*b^2))/(a^6*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(184*a^4*b^12 - 32*a^2*b^14 - 360*a^6*b^10 + 78*a^8*b^8 + 240*a^10*b^6 - 152*a^12*b^4 + 24*a^14*b^2))/(a^6*b^5) - (4*tan(c/2 + (d*x)/2)*(8*a^3*b^16 - 160*a^5*b^14 + 1320*a^7*b^12 - 2128*a^9*b^10 + 1242*a^11*b^8 - 280*a^13*b^6 + 16*a^15*b^4))/(a^6*b^8) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(64*a^5*b^12 - 208*a^7*b^10 + 160*a^9*b^8 - 28*a^11*b^6))/(a^6*b^5) - (((4*(32*a^8*b^10 - 24*a^10*b^8))/(a^6*b^5) + (4*tan(c/2 + (d*x)/2)*(128*a^7*b^14 - 136*a^9*b^12 + 16*a^11*b^10))/(a^6*b^8))*(-(a + b)^5*(a - b)^5)^(1/2))/(a^3*b^3) + (4*tan(c/2 + (d*x)/2)*(128*a^4*b^16 - 456*a^6*b^14 + 484*a^8*b^12 - 200*a^10*b^10 + 32*a^12*b^8))/(a^6*b^8)))/(a^3*b^3)))/(a^3*b^3)))/(a^3*b^3) - (8*tan(c/2 + (d*x)/2)*(64*a^17 + 700*a^5*b^12 - 3060*a^7*b^10 + 5412*a^9*b^8 - 4940*a^11*b^6 + 2448*a^13*b^4 - 624*a^15*b^2))/(a^6*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a^3*b^3*d)","B"
1326,1,4712,197,15.568422,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{\cos\left(c+d\,x\right)}{32\,a\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}+\frac{3\,\sin\left(c+d\,x\right)}{32\,b\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}-\frac{7\,\cos\left(3\,c+3\,d\,x\right)}{96\,a\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}+\frac{\sin\left(2\,c+2\,d\,x\right)}{32\,b\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32\,b\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}-\frac{\sin\left(4\,c+4\,d\,x\right)}{64\,b\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}+\frac{b^2\,\cos\left(3\,c+3\,d\,x\right)}{32\,a^3\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}-\frac{b^2\,\cos\left(c+d\,x\right)}{32\,a^3\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}+\frac{b\,\sin\left(2\,c+2\,d\,x\right)}{32\,a^2\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}+\frac{15\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{64\,a^2\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}-\frac{3\,a\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)}{16\,b^2\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}-\frac{5\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{64\,a^2\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}-\frac{3\,b^3\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{32\,a^4\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}+\frac{a\,\sin\left(3\,c+3\,d\,x\right)\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)}{16\,b^2\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}+\frac{b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{32\,a^4\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}+\frac{\sin\left(3\,c+3\,d\,x\right)\,\mathrm{atan}\left(\frac{a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,8{}\mathrm{i}+a^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,8{}\mathrm{i}+b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,32{}\mathrm{i}+a\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,16{}\mathrm{i}-a^7\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,12{}\mathrm{i}-a^{17}\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,2{}\mathrm{i}-a^3\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,52{}\mathrm{i}+a^5\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,45{}\mathrm{i}-a^7\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,2{}\mathrm{i}+a^9\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,12{}\mathrm{i}-a^{11}\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,14{}\mathrm{i}-a^{13}\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,12{}\mathrm{i}+a^{15}\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,15{}\mathrm{i}-a^2\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,114{}\mathrm{i}+a^4\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,121{}\mathrm{i}-a^6\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,50{}\mathrm{i}+a^2\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,2{}\mathrm{i}-a^4\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,17{}\mathrm{i}+a^6\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,60{}\mathrm{i}-a^8\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,115{}\mathrm{i}+a^{10}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,162{}\mathrm{i}-a^{12}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,199{}\mathrm{i}+a^{14}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,146{}\mathrm{i}-a^{16}\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,50{}\mathrm{i}}{-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{22}\,b+30\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{21}\,b^2+150\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{20}\,b^3-275\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{19}\,b^4-960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{18}\,b^5+1175\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{17}\,b^6+3470\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{16}\,b^7-2975\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{15}\,b^8-7922\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{14}\,b^9+4906\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}\,b^{10}+12156\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b^{11}-5528\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^{12}-12976\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^{13}+4332\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^{14}+9738\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^{15}-2334\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^{16}-5060\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^{17}+825\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^{18}+1734\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^{19}-172\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{20}-352\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{21}+16\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{22}+32\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{23}}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,1{}\mathrm{i}}{16\,a^4\,b^2\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}-\frac{\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,8{}\mathrm{i}+a^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,8{}\mathrm{i}+b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,32{}\mathrm{i}+a\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,16{}\mathrm{i}-a^7\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,12{}\mathrm{i}-a^{17}\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,2{}\mathrm{i}-a^3\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,52{}\mathrm{i}+a^5\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,45{}\mathrm{i}-a^7\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,2{}\mathrm{i}+a^9\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,12{}\mathrm{i}-a^{11}\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,14{}\mathrm{i}-a^{13}\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,12{}\mathrm{i}+a^{15}\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,15{}\mathrm{i}-a^2\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,114{}\mathrm{i}+a^4\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,121{}\mathrm{i}-a^6\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\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)}^{3/2}\,50{}\mathrm{i}+a^2\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,2{}\mathrm{i}-a^4\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,17{}\mathrm{i}+a^6\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,60{}\mathrm{i}-a^8\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,115{}\mathrm{i}+a^{10}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,162{}\mathrm{i}-a^{12}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,199{}\mathrm{i}+a^{14}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,146{}\mathrm{i}-a^{16}\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,50{}\mathrm{i}}{-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{22}\,b+30\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{21}\,b^2+150\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{20}\,b^3-275\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{19}\,b^4-960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{18}\,b^5+1175\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{17}\,b^6+3470\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{16}\,b^7-2975\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{15}\,b^8-7922\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{14}\,b^9+4906\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}\,b^{10}+12156\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b^{11}-5528\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^{12}-12976\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^{13}+4332\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^{14}+9738\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^{15}-2334\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^{16}-5060\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^{17}+825\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^{18}+1734\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^{19}-172\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{20}-352\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{21}+16\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{22}+32\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{23}}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}\,3{}\mathrm{i}}{16\,a^4\,b^2\,d\,\left(\frac{3\,\sin\left(c+d\,x\right)}{32}-\frac{\sin\left(3\,c+3\,d\,x\right)}{32}\right)}","Not used",1,"cos(c + d*x)/(32*a*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) + (3*sin(c + d*x))/(32*b*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) - (7*cos(3*c + 3*d*x))/(96*a*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) + sin(2*c + 2*d*x)/(32*b*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) - sin(3*c + 3*d*x)/(32*b*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) - sin(4*c + 4*d*x)/(64*b*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) + (b^2*cos(3*c + 3*d*x))/(32*a^3*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) - (b^2*cos(c + d*x))/(32*a^3*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) + (b*sin(2*c + 2*d*x))/(32*a^2*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) + (15*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(64*a^2*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) - (3*a*sin(c + d*x)*atan((2*a^5*cos(c/2 + (d*x)/2) - 2*b^5*sin(c/2 + (d*x)/2) + 5*a^2*b^3*sin(c/2 + (d*x)/2))/(2*b^5*cos(c/2 + (d*x)/2) + 2*a^5*sin(c/2 + (d*x)/2) - 5*a^2*b^3*cos(c/2 + (d*x)/2))))/(16*b^2*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) - (5*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/(64*a^2*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) - (3*b^3*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(32*a^4*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) + (a*sin(3*c + 3*d*x)*atan((2*a^5*cos(c/2 + (d*x)/2) - 2*b^5*sin(c/2 + (d*x)/2) + 5*a^2*b^3*sin(c/2 + (d*x)/2))/(2*b^5*cos(c/2 + (d*x)/2) + 2*a^5*sin(c/2 + (d*x)/2) - 5*a^2*b^3*cos(c/2 + (d*x)/2))))/(16*b^2*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) + (b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/(32*a^4*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) + (sin(3*c + 3*d*x)*atan((a^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*8i + a^18*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*8i + b^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*32i + a*b^7*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*16i - a^7*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*12i - a^17*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*2i - a^3*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*52i + a^5*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*45i - a^7*b^11*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*2i + a^9*b^9*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*12i - a^11*b^7*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*14i - a^13*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*12i + a^15*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*15i - a^2*b^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*114i + a^4*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*121i - a^6*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*50i + a^2*b^16*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*2i - a^4*b^14*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*17i + a^6*b^12*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*60i - a^8*b^10*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*115i + a^10*b^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*162i - a^12*b^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*199i + a^14*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*146i - a^16*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*50i)/(32*b^23*sin(c/2 + (d*x)/2) + 16*a*b^22*cos(c/2 + (d*x)/2) - 10*a^22*b*sin(c/2 + (d*x)/2) - 172*a^3*b^20*cos(c/2 + (d*x)/2) + 825*a^5*b^18*cos(c/2 + (d*x)/2) - 2334*a^7*b^16*cos(c/2 + (d*x)/2) + 4332*a^9*b^14*cos(c/2 + (d*x)/2) - 5528*a^11*b^12*cos(c/2 + (d*x)/2) + 4906*a^13*b^10*cos(c/2 + (d*x)/2) - 2975*a^15*b^8*cos(c/2 + (d*x)/2) + 1175*a^17*b^6*cos(c/2 + (d*x)/2) - 275*a^19*b^4*cos(c/2 + (d*x)/2) + 30*a^21*b^2*cos(c/2 + (d*x)/2) - 352*a^2*b^21*sin(c/2 + (d*x)/2) + 1734*a^4*b^19*sin(c/2 + (d*x)/2) - 5060*a^6*b^17*sin(c/2 + (d*x)/2) + 9738*a^8*b^15*sin(c/2 + (d*x)/2) - 12976*a^10*b^13*sin(c/2 + (d*x)/2) + 12156*a^12*b^11*sin(c/2 + (d*x)/2) - 7922*a^14*b^9*sin(c/2 + (d*x)/2) + 3470*a^16*b^7*sin(c/2 + (d*x)/2) - 960*a^18*b^5*sin(c/2 + (d*x)/2) + 150*a^20*b^3*sin(c/2 + (d*x)/2)))*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*1i)/(16*a^4*b^2*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32)) - (sin(c + d*x)*atan((a^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*8i + a^18*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*8i + b^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*32i + a*b^7*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*16i - a^7*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*12i - a^17*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*2i - a^3*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*52i + a^5*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*45i - a^7*b^11*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*2i + a^9*b^9*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*12i - a^11*b^7*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*14i - a^13*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*12i + a^15*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*15i - a^2*b^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*114i + a^4*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*121i - a^6*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(3/2)*50i + a^2*b^16*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*2i - a^4*b^14*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*17i + a^6*b^12*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*60i - a^8*b^10*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*115i + a^10*b^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*162i - a^12*b^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*199i + a^14*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*146i - a^16*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*50i)/(32*b^23*sin(c/2 + (d*x)/2) + 16*a*b^22*cos(c/2 + (d*x)/2) - 10*a^22*b*sin(c/2 + (d*x)/2) - 172*a^3*b^20*cos(c/2 + (d*x)/2) + 825*a^5*b^18*cos(c/2 + (d*x)/2) - 2334*a^7*b^16*cos(c/2 + (d*x)/2) + 4332*a^9*b^14*cos(c/2 + (d*x)/2) - 5528*a^11*b^12*cos(c/2 + (d*x)/2) + 4906*a^13*b^10*cos(c/2 + (d*x)/2) - 2975*a^15*b^8*cos(c/2 + (d*x)/2) + 1175*a^17*b^6*cos(c/2 + (d*x)/2) - 275*a^19*b^4*cos(c/2 + (d*x)/2) + 30*a^21*b^2*cos(c/2 + (d*x)/2) - 352*a^2*b^21*sin(c/2 + (d*x)/2) + 1734*a^4*b^19*sin(c/2 + (d*x)/2) - 5060*a^6*b^17*sin(c/2 + (d*x)/2) + 9738*a^8*b^15*sin(c/2 + (d*x)/2) - 12976*a^10*b^13*sin(c/2 + (d*x)/2) + 12156*a^12*b^11*sin(c/2 + (d*x)/2) - 7922*a^14*b^9*sin(c/2 + (d*x)/2) + 3470*a^16*b^7*sin(c/2 + (d*x)/2) - 960*a^18*b^5*sin(c/2 + (d*x)/2) + 150*a^20*b^3*sin(c/2 + (d*x)/2)))*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2)*3i)/(16*a^4*b^2*d*((3*sin(c + d*x))/32 - sin(3*c + 3*d*x)/32))","B"
1327,1,4334,195,13.397914,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}-\frac{2\,\mathrm{atan}\left(-\frac{\frac{\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}-410\,a^{14}\,b^2+929\,a^{12}\,b^4-1096\,a^{10}\,b^6+873\,a^8\,b^8-550\,a^6\,b^{10}+255\,a^4\,b^{12}-68\,a^2\,b^{14}+8\,b^{16}\right)}{a^{12}}-\frac{4\,\left(53\,a^{15}\,b-120\,a^{13}\,b^3+48\,a^{11}\,b^5+56\,a^9\,b^7-48\,a^7\,b^9+8\,a^5\,b^{11}\right)}{a^{12}}+\frac{\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}-180\,a^{15}\,b^2+252\,a^{13}\,b^4-148\,a^{11}\,b^6+100\,a^9\,b^8-40\,a^7\,b^{10}+8\,a^5\,b^{12}\right)}{a^{12}}-\frac{4\,\left(24\,a^{16}\,b+58\,a^{14}\,b^3-345\,a^{12}\,b^5+543\,a^{10}\,b^7-440\,a^8\,b^9+184\,a^6\,b^{11}-32\,a^4\,b^{13}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(-93\,a^{15}\,b^3+240\,a^{13}\,b^5-208\,a^{11}\,b^7+64\,a^9\,b^9\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}\,b^2-335\,a^{14}\,b^4+604\,a^{12}\,b^6-456\,a^{10}\,b^8+128\,a^8\,b^{10}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(32\,a^{14}\,b^5-24\,a^{16}\,b^3\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^2-136\,a^{15}\,b^4+128\,a^{13}\,b^6\right)}{a^{12}}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}}{b}+\frac{\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}-410\,a^{14}\,b^2+929\,a^{12}\,b^4-1096\,a^{10}\,b^6+873\,a^8\,b^8-550\,a^6\,b^{10}+255\,a^4\,b^{12}-68\,a^2\,b^{14}+8\,b^{16}\right)}{a^{12}}-\frac{4\,\left(53\,a^{15}\,b-120\,a^{13}\,b^3+48\,a^{11}\,b^5+56\,a^9\,b^7-48\,a^7\,b^9+8\,a^5\,b^{11}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(24\,a^{16}\,b+58\,a^{14}\,b^3-345\,a^{12}\,b^5+543\,a^{10}\,b^7-440\,a^8\,b^9+184\,a^6\,b^{11}-32\,a^4\,b^{13}\right)}{a^{12}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}-180\,a^{15}\,b^2+252\,a^{13}\,b^4-148\,a^{11}\,b^6+100\,a^9\,b^8-40\,a^7\,b^{10}+8\,a^5\,b^{12}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(-93\,a^{15}\,b^3+240\,a^{13}\,b^5-208\,a^{11}\,b^7+64\,a^9\,b^9\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}\,b^2-335\,a^{14}\,b^4+604\,a^{12}\,b^6-456\,a^{10}\,b^8+128\,a^8\,b^{10}\right)}{a^{12}}-\frac{\left(\frac{4\,\left(32\,a^{14}\,b^5-24\,a^{16}\,b^3\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^2-136\,a^{15}\,b^4+128\,a^{13}\,b^6\right)}{a^{12}}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}}{b}}{\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-4\,a^{15}+4\,a^{13}\,b^2+12\,a^{11}\,b^4-20\,a^9\,b^6+8\,a^7\,b^8\right)}{a^{12}}-\frac{8\,\left(15\,a^{14}\,b-20\,a^{12}\,b^3-97\,a^{10}\,b^5+305\,a^8\,b^7-366\,a^6\,b^9+223\,a^4\,b^{11}-68\,a^2\,b^{13}+8\,b^{15}\right)}{a^{12}}+\frac{\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}-410\,a^{14}\,b^2+929\,a^{12}\,b^4-1096\,a^{10}\,b^6+873\,a^8\,b^8-550\,a^6\,b^{10}+255\,a^4\,b^{12}-68\,a^2\,b^{14}+8\,b^{16}\right)}{a^{12}}-\frac{4\,\left(53\,a^{15}\,b-120\,a^{13}\,b^3+48\,a^{11}\,b^5+56\,a^9\,b^7-48\,a^7\,b^9+8\,a^5\,b^{11}\right)}{a^{12}}+\frac{\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}-180\,a^{15}\,b^2+252\,a^{13}\,b^4-148\,a^{11}\,b^6+100\,a^9\,b^8-40\,a^7\,b^{10}+8\,a^5\,b^{12}\right)}{a^{12}}-\frac{4\,\left(24\,a^{16}\,b+58\,a^{14}\,b^3-345\,a^{12}\,b^5+543\,a^{10}\,b^7-440\,a^8\,b^9+184\,a^6\,b^{11}-32\,a^4\,b^{13}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(-93\,a^{15}\,b^3+240\,a^{13}\,b^5-208\,a^{11}\,b^7+64\,a^9\,b^9\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}\,b^2-335\,a^{14}\,b^4+604\,a^{12}\,b^6-456\,a^{10}\,b^8+128\,a^8\,b^{10}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(32\,a^{14}\,b^5-24\,a^{16}\,b^3\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^2-136\,a^{15}\,b^4+128\,a^{13}\,b^6\right)}{a^{12}}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}-\frac{\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}-410\,a^{14}\,b^2+929\,a^{12}\,b^4-1096\,a^{10}\,b^6+873\,a^8\,b^8-550\,a^6\,b^{10}+255\,a^4\,b^{12}-68\,a^2\,b^{14}+8\,b^{16}\right)}{a^{12}}-\frac{4\,\left(53\,a^{15}\,b-120\,a^{13}\,b^3+48\,a^{11}\,b^5+56\,a^9\,b^7-48\,a^7\,b^9+8\,a^5\,b^{11}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(24\,a^{16}\,b+58\,a^{14}\,b^3-345\,a^{12}\,b^5+543\,a^{10}\,b^7-440\,a^8\,b^9+184\,a^6\,b^{11}-32\,a^4\,b^{13}\right)}{a^{12}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}-180\,a^{15}\,b^2+252\,a^{13}\,b^4-148\,a^{11}\,b^6+100\,a^9\,b^8-40\,a^7\,b^{10}+8\,a^5\,b^{12}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(-93\,a^{15}\,b^3+240\,a^{13}\,b^5-208\,a^{11}\,b^7+64\,a^9\,b^9\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}\,b^2-335\,a^{14}\,b^4+604\,a^{12}\,b^6-456\,a^{10}\,b^8+128\,a^8\,b^{10}\right)}{a^{12}}-\frac{\left(\frac{4\,\left(32\,a^{14}\,b^5-24\,a^{16}\,b^3\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^2-136\,a^{15}\,b^4+128\,a^{13}\,b^6\right)}{a^{12}}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}\right)\,1{}\mathrm{i}}{b}}\right)}{b\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{1}{4\,a}-\frac{b^2}{8\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{8\,a^2}+\frac{2\,b\,\left(\frac{1}{2\,a}-\frac{b^2}{4\,a^3}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a\,b^2-4\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(18\,a^2\,b-8\,b^3\right)+\frac{a^3}{4}-\frac{2\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{16\,a^4\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{15\,a^4}{8}-\frac{5\,a^2\,b^2}{2}+b^4\right)}{a^5\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}-410\,a^{14}\,b^2+929\,a^{12}\,b^4-1096\,a^{10}\,b^6+873\,a^8\,b^8-550\,a^6\,b^{10}+255\,a^4\,b^{12}-68\,a^2\,b^{14}+8\,b^{16}\right)}{a^{12}}-\frac{4\,\left(53\,a^{15}\,b-120\,a^{13}\,b^3+48\,a^{11}\,b^5+56\,a^9\,b^7-48\,a^7\,b^9+8\,a^5\,b^{11}\right)}{a^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}-180\,a^{15}\,b^2+252\,a^{13}\,b^4-148\,a^{11}\,b^6+100\,a^9\,b^8-40\,a^7\,b^{10}+8\,a^5\,b^{12}\right)}{a^{12}}-\frac{4\,\left(24\,a^{16}\,b+58\,a^{14}\,b^3-345\,a^{12}\,b^5+543\,a^{10}\,b^7-440\,a^8\,b^9+184\,a^6\,b^{11}-32\,a^4\,b^{13}\right)}{a^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-93\,a^{15}\,b^3+240\,a^{13}\,b^5-208\,a^{11}\,b^7+64\,a^9\,b^9\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}\,b^2-335\,a^{14}\,b^4+604\,a^{12}\,b^6-456\,a^{10}\,b^8+128\,a^8\,b^{10}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(32\,a^{14}\,b^5-24\,a^{16}\,b^3\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^2-136\,a^{15}\,b^4+128\,a^{13}\,b^6\right)}{a^{12}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^5\,b}\right)}{a^5\,b}\right)}{a^5\,b}\right)\,1{}\mathrm{i}}{a^5\,b}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}-410\,a^{14}\,b^2+929\,a^{12}\,b^4-1096\,a^{10}\,b^6+873\,a^8\,b^8-550\,a^6\,b^{10}+255\,a^4\,b^{12}-68\,a^2\,b^{14}+8\,b^{16}\right)}{a^{12}}-\frac{4\,\left(53\,a^{15}\,b-120\,a^{13}\,b^3+48\,a^{11}\,b^5+56\,a^9\,b^7-48\,a^7\,b^9+8\,a^5\,b^{11}\right)}{a^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(24\,a^{16}\,b+58\,a^{14}\,b^3-345\,a^{12}\,b^5+543\,a^{10}\,b^7-440\,a^8\,b^9+184\,a^6\,b^{11}-32\,a^4\,b^{13}\right)}{a^{12}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}-180\,a^{15}\,b^2+252\,a^{13}\,b^4-148\,a^{11}\,b^6+100\,a^9\,b^8-40\,a^7\,b^{10}+8\,a^5\,b^{12}\right)}{a^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-93\,a^{15}\,b^3+240\,a^{13}\,b^5-208\,a^{11}\,b^7+64\,a^9\,b^9\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}\,b^2-335\,a^{14}\,b^4+604\,a^{12}\,b^6-456\,a^{10}\,b^8+128\,a^8\,b^{10}\right)}{a^{12}}-\frac{\left(\frac{4\,\left(32\,a^{14}\,b^5-24\,a^{16}\,b^3\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^2-136\,a^{15}\,b^4+128\,a^{13}\,b^6\right)}{a^{12}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^5\,b}\right)}{a^5\,b}\right)}{a^5\,b}\right)\,1{}\mathrm{i}}{a^5\,b}}{\frac{8\,\left(15\,a^{14}\,b-20\,a^{12}\,b^3-97\,a^{10}\,b^5+305\,a^8\,b^7-366\,a^6\,b^9+223\,a^4\,b^{11}-68\,a^2\,b^{13}+8\,b^{15}\right)}{a^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-4\,a^{15}+4\,a^{13}\,b^2+12\,a^{11}\,b^4-20\,a^9\,b^6+8\,a^7\,b^8\right)}{a^{12}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}-410\,a^{14}\,b^2+929\,a^{12}\,b^4-1096\,a^{10}\,b^6+873\,a^8\,b^8-550\,a^6\,b^{10}+255\,a^4\,b^{12}-68\,a^2\,b^{14}+8\,b^{16}\right)}{a^{12}}-\frac{4\,\left(53\,a^{15}\,b-120\,a^{13}\,b^3+48\,a^{11}\,b^5+56\,a^9\,b^7-48\,a^7\,b^9+8\,a^5\,b^{11}\right)}{a^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}-180\,a^{15}\,b^2+252\,a^{13}\,b^4-148\,a^{11}\,b^6+100\,a^9\,b^8-40\,a^7\,b^{10}+8\,a^5\,b^{12}\right)}{a^{12}}-\frac{4\,\left(24\,a^{16}\,b+58\,a^{14}\,b^3-345\,a^{12}\,b^5+543\,a^{10}\,b^7-440\,a^8\,b^9+184\,a^6\,b^{11}-32\,a^4\,b^{13}\right)}{a^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-93\,a^{15}\,b^3+240\,a^{13}\,b^5-208\,a^{11}\,b^7+64\,a^9\,b^9\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}\,b^2-335\,a^{14}\,b^4+604\,a^{12}\,b^6-456\,a^{10}\,b^8+128\,a^8\,b^{10}\right)}{a^{12}}+\frac{\left(\frac{4\,\left(32\,a^{14}\,b^5-24\,a^{16}\,b^3\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^2-136\,a^{15}\,b^4+128\,a^{13}\,b^6\right)}{a^{12}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^5\,b}\right)}{a^5\,b}\right)}{a^5\,b}\right)}{a^5\,b}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}-410\,a^{14}\,b^2+929\,a^{12}\,b^4-1096\,a^{10}\,b^6+873\,a^8\,b^8-550\,a^6\,b^{10}+255\,a^4\,b^{12}-68\,a^2\,b^{14}+8\,b^{16}\right)}{a^{12}}-\frac{4\,\left(53\,a^{15}\,b-120\,a^{13}\,b^3+48\,a^{11}\,b^5+56\,a^9\,b^7-48\,a^7\,b^9+8\,a^5\,b^{11}\right)}{a^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(24\,a^{16}\,b+58\,a^{14}\,b^3-345\,a^{12}\,b^5+543\,a^{10}\,b^7-440\,a^8\,b^9+184\,a^6\,b^{11}-32\,a^4\,b^{13}\right)}{a^{12}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}-180\,a^{15}\,b^2+252\,a^{13}\,b^4-148\,a^{11}\,b^6+100\,a^9\,b^8-40\,a^7\,b^{10}+8\,a^5\,b^{12}\right)}{a^{12}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-93\,a^{15}\,b^3+240\,a^{13}\,b^5-208\,a^{11}\,b^7+64\,a^9\,b^9\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(62\,a^{16}\,b^2-335\,a^{14}\,b^4+604\,a^{12}\,b^6-456\,a^{10}\,b^8+128\,a^8\,b^{10}\right)}{a^{12}}-\frac{\left(\frac{4\,\left(32\,a^{14}\,b^5-24\,a^{16}\,b^3\right)}{a^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{17}\,b^2-136\,a^{15}\,b^4+128\,a^{13}\,b^6\right)}{a^{12}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^5\,b}\right)}{a^5\,b}\right)}{a^5\,b}\right)}{a^5\,b}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^5\,b\,d}","Not used",1,"tan(c/2 + (d*x)/2)^4/(64*a*d) - (2*atan(-(((((((4*(64*a^9*b^9 - 208*a^11*b^7 + 240*a^13*b^5 - 93*a^15*b^3))/a^12 + (((4*(32*a^14*b^5 - 24*a^16*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^6 - 136*a^15*b^4 + 16*a^17*b^2))/a^12)*1i)/b + (4*tan(c/2 + (d*x)/2)*(128*a^8*b^10 - 456*a^10*b^8 + 604*a^12*b^6 - 335*a^14*b^4 + 62*a^16*b^2))/a^12)*1i)/b - (4*(24*a^16*b - 32*a^4*b^13 + 184*a^6*b^11 - 440*a^8*b^9 + 543*a^10*b^7 - 345*a^12*b^5 + 58*a^14*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(16*a^17 + 8*a^5*b^12 - 40*a^7*b^10 + 100*a^9*b^8 - 148*a^11*b^6 + 252*a^13*b^4 - 180*a^15*b^2))/a^12)*1i)/b - (4*(53*a^15*b + 8*a^5*b^11 - 48*a^7*b^9 + 56*a^9*b^7 + 48*a^11*b^5 - 120*a^13*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(62*a^16 + 8*b^16 - 68*a^2*b^14 + 255*a^4*b^12 - 550*a^6*b^10 + 873*a^8*b^8 - 1096*a^10*b^6 + 929*a^12*b^4 - 410*a^14*b^2))/a^12)/b + ((((4*(24*a^16*b - 32*a^4*b^13 + 184*a^6*b^11 - 440*a^8*b^9 + 543*a^10*b^7 - 345*a^12*b^5 + 58*a^14*b^3))/a^12 + (((4*(64*a^9*b^9 - 208*a^11*b^7 + 240*a^13*b^5 - 93*a^15*b^3))/a^12 - (((4*(32*a^14*b^5 - 24*a^16*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^6 - 136*a^15*b^4 + 16*a^17*b^2))/a^12)*1i)/b + (4*tan(c/2 + (d*x)/2)*(128*a^8*b^10 - 456*a^10*b^8 + 604*a^12*b^6 - 335*a^14*b^4 + 62*a^16*b^2))/a^12)*1i)/b - (4*tan(c/2 + (d*x)/2)*(16*a^17 + 8*a^5*b^12 - 40*a^7*b^10 + 100*a^9*b^8 - 148*a^11*b^6 + 252*a^13*b^4 - 180*a^15*b^2))/a^12)*1i)/b - (4*(53*a^15*b + 8*a^5*b^11 - 48*a^7*b^9 + 56*a^9*b^7 + 48*a^11*b^5 - 120*a^13*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(62*a^16 + 8*b^16 - 68*a^2*b^14 + 255*a^4*b^12 - 550*a^6*b^10 + 873*a^8*b^8 - 1096*a^10*b^6 + 929*a^12*b^4 - 410*a^14*b^2))/a^12)/b)/((((((((4*(64*a^9*b^9 - 208*a^11*b^7 + 240*a^13*b^5 - 93*a^15*b^3))/a^12 + (((4*(32*a^14*b^5 - 24*a^16*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^6 - 136*a^15*b^4 + 16*a^17*b^2))/a^12)*1i)/b + (4*tan(c/2 + (d*x)/2)*(128*a^8*b^10 - 456*a^10*b^8 + 604*a^12*b^6 - 335*a^14*b^4 + 62*a^16*b^2))/a^12)*1i)/b - (4*(24*a^16*b - 32*a^4*b^13 + 184*a^6*b^11 - 440*a^8*b^9 + 543*a^10*b^7 - 345*a^12*b^5 + 58*a^14*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(16*a^17 + 8*a^5*b^12 - 40*a^7*b^10 + 100*a^9*b^8 - 148*a^11*b^6 + 252*a^13*b^4 - 180*a^15*b^2))/a^12)*1i)/b - (4*(53*a^15*b + 8*a^5*b^11 - 48*a^7*b^9 + 56*a^9*b^7 + 48*a^11*b^5 - 120*a^13*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(62*a^16 + 8*b^16 - 68*a^2*b^14 + 255*a^4*b^12 - 550*a^6*b^10 + 873*a^8*b^8 - 1096*a^10*b^6 + 929*a^12*b^4 - 410*a^14*b^2))/a^12)*1i)/b - (((((4*(24*a^16*b - 32*a^4*b^13 + 184*a^6*b^11 - 440*a^8*b^9 + 543*a^10*b^7 - 345*a^12*b^5 + 58*a^14*b^3))/a^12 + (((4*(64*a^9*b^9 - 208*a^11*b^7 + 240*a^13*b^5 - 93*a^15*b^3))/a^12 - (((4*(32*a^14*b^5 - 24*a^16*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^6 - 136*a^15*b^4 + 16*a^17*b^2))/a^12)*1i)/b + (4*tan(c/2 + (d*x)/2)*(128*a^8*b^10 - 456*a^10*b^8 + 604*a^12*b^6 - 335*a^14*b^4 + 62*a^16*b^2))/a^12)*1i)/b - (4*tan(c/2 + (d*x)/2)*(16*a^17 + 8*a^5*b^12 - 40*a^7*b^10 + 100*a^9*b^8 - 148*a^11*b^6 + 252*a^13*b^4 - 180*a^15*b^2))/a^12)*1i)/b - (4*(53*a^15*b + 8*a^5*b^11 - 48*a^7*b^9 + 56*a^9*b^7 + 48*a^11*b^5 - 120*a^13*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(62*a^16 + 8*b^16 - 68*a^2*b^14 + 255*a^4*b^12 - 550*a^6*b^10 + 873*a^8*b^8 - 1096*a^10*b^6 + 929*a^12*b^4 - 410*a^14*b^2))/a^12)*1i)/b - (8*(15*a^14*b + 8*b^15 - 68*a^2*b^13 + 223*a^4*b^11 - 366*a^6*b^9 + 305*a^8*b^7 - 97*a^10*b^5 - 20*a^12*b^3))/a^12 + (8*tan(c/2 + (d*x)/2)*(8*a^7*b^8 - 4*a^15 - 20*a^9*b^6 + 12*a^11*b^4 + 4*a^13*b^2))/a^12)))/(b*d) - (tan(c/2 + (d*x)/2)^2*(1/(4*a) - b^2/(8*a^3)))/d + (tan(c/2 + (d*x)/2)*(b/(8*a^2) + (2*b*(1/(2*a) - b^2/(4*a^3)))/a))/d - (tan(c/2 + (d*x)/2)^2*(2*a*b^2 - 4*a^3) + tan(c/2 + (d*x)/2)^3*(18*a^2*b - 8*b^3) + a^3/4 - (2*a^2*b*tan(c/2 + (d*x)/2))/3)/(16*a^4*d*tan(c/2 + (d*x)/2)^4) + (log(tan(c/2 + (d*x)/2))*((15*a^4)/8 + b^4 - (5*a^2*b^2)/2))/(a^5*d) - (b*tan(c/2 + (d*x)/2)^3)/(24*a^2*d) - (atan((((-(a + b)^5*(a - b)^5)^(1/2)*((4*tan(c/2 + (d*x)/2)*(62*a^16 + 8*b^16 - 68*a^2*b^14 + 255*a^4*b^12 - 550*a^6*b^10 + 873*a^8*b^8 - 1096*a^10*b^6 + 929*a^12*b^4 - 410*a^14*b^2))/a^12 - (4*(53*a^15*b + 8*a^5*b^11 - 48*a^7*b^9 + 56*a^9*b^7 + 48*a^11*b^5 - 120*a^13*b^3))/a^12 + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*tan(c/2 + (d*x)/2)*(16*a^17 + 8*a^5*b^12 - 40*a^7*b^10 + 100*a^9*b^8 - 148*a^11*b^6 + 252*a^13*b^4 - 180*a^15*b^2))/a^12 - (4*(24*a^16*b - 32*a^4*b^13 + 184*a^6*b^11 - 440*a^8*b^9 + 543*a^10*b^7 - 345*a^12*b^5 + 58*a^14*b^3))/a^12 + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(64*a^9*b^9 - 208*a^11*b^7 + 240*a^13*b^5 - 93*a^15*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^8*b^10 - 456*a^10*b^8 + 604*a^12*b^6 - 335*a^14*b^4 + 62*a^16*b^2))/a^12 + (((4*(32*a^14*b^5 - 24*a^16*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^6 - 136*a^15*b^4 + 16*a^17*b^2))/a^12)*(-(a + b)^5*(a - b)^5)^(1/2))/(a^5*b)))/(a^5*b)))/(a^5*b))*1i)/(a^5*b) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*tan(c/2 + (d*x)/2)*(62*a^16 + 8*b^16 - 68*a^2*b^14 + 255*a^4*b^12 - 550*a^6*b^10 + 873*a^8*b^8 - 1096*a^10*b^6 + 929*a^12*b^4 - 410*a^14*b^2))/a^12 - (4*(53*a^15*b + 8*a^5*b^11 - 48*a^7*b^9 + 56*a^9*b^7 + 48*a^11*b^5 - 120*a^13*b^3))/a^12 + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(24*a^16*b - 32*a^4*b^13 + 184*a^6*b^11 - 440*a^8*b^9 + 543*a^10*b^7 - 345*a^12*b^5 + 58*a^14*b^3))/a^12 - (4*tan(c/2 + (d*x)/2)*(16*a^17 + 8*a^5*b^12 - 40*a^7*b^10 + 100*a^9*b^8 - 148*a^11*b^6 + 252*a^13*b^4 - 180*a^15*b^2))/a^12 + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(64*a^9*b^9 - 208*a^11*b^7 + 240*a^13*b^5 - 93*a^15*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^8*b^10 - 456*a^10*b^8 + 604*a^12*b^6 - 335*a^14*b^4 + 62*a^16*b^2))/a^12 - (((4*(32*a^14*b^5 - 24*a^16*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^6 - 136*a^15*b^4 + 16*a^17*b^2))/a^12)*(-(a + b)^5*(a - b)^5)^(1/2))/(a^5*b)))/(a^5*b)))/(a^5*b))*1i)/(a^5*b))/((8*(15*a^14*b + 8*b^15 - 68*a^2*b^13 + 223*a^4*b^11 - 366*a^6*b^9 + 305*a^8*b^7 - 97*a^10*b^5 - 20*a^12*b^3))/a^12 - (8*tan(c/2 + (d*x)/2)*(8*a^7*b^8 - 4*a^15 - 20*a^9*b^6 + 12*a^11*b^4 + 4*a^13*b^2))/a^12 - ((-(a + b)^5*(a - b)^5)^(1/2)*((4*tan(c/2 + (d*x)/2)*(62*a^16 + 8*b^16 - 68*a^2*b^14 + 255*a^4*b^12 - 550*a^6*b^10 + 873*a^8*b^8 - 1096*a^10*b^6 + 929*a^12*b^4 - 410*a^14*b^2))/a^12 - (4*(53*a^15*b + 8*a^5*b^11 - 48*a^7*b^9 + 56*a^9*b^7 + 48*a^11*b^5 - 120*a^13*b^3))/a^12 + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*tan(c/2 + (d*x)/2)*(16*a^17 + 8*a^5*b^12 - 40*a^7*b^10 + 100*a^9*b^8 - 148*a^11*b^6 + 252*a^13*b^4 - 180*a^15*b^2))/a^12 - (4*(24*a^16*b - 32*a^4*b^13 + 184*a^6*b^11 - 440*a^8*b^9 + 543*a^10*b^7 - 345*a^12*b^5 + 58*a^14*b^3))/a^12 + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(64*a^9*b^9 - 208*a^11*b^7 + 240*a^13*b^5 - 93*a^15*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^8*b^10 - 456*a^10*b^8 + 604*a^12*b^6 - 335*a^14*b^4 + 62*a^16*b^2))/a^12 + (((4*(32*a^14*b^5 - 24*a^16*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^6 - 136*a^15*b^4 + 16*a^17*b^2))/a^12)*(-(a + b)^5*(a - b)^5)^(1/2))/(a^5*b)))/(a^5*b)))/(a^5*b)))/(a^5*b) + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*tan(c/2 + (d*x)/2)*(62*a^16 + 8*b^16 - 68*a^2*b^14 + 255*a^4*b^12 - 550*a^6*b^10 + 873*a^8*b^8 - 1096*a^10*b^6 + 929*a^12*b^4 - 410*a^14*b^2))/a^12 - (4*(53*a^15*b + 8*a^5*b^11 - 48*a^7*b^9 + 56*a^9*b^7 + 48*a^11*b^5 - 120*a^13*b^3))/a^12 + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(24*a^16*b - 32*a^4*b^13 + 184*a^6*b^11 - 440*a^8*b^9 + 543*a^10*b^7 - 345*a^12*b^5 + 58*a^14*b^3))/a^12 - (4*tan(c/2 + (d*x)/2)*(16*a^17 + 8*a^5*b^12 - 40*a^7*b^10 + 100*a^9*b^8 - 148*a^11*b^6 + 252*a^13*b^4 - 180*a^15*b^2))/a^12 + ((-(a + b)^5*(a - b)^5)^(1/2)*((4*(64*a^9*b^9 - 208*a^11*b^7 + 240*a^13*b^5 - 93*a^15*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^8*b^10 - 456*a^10*b^8 + 604*a^12*b^6 - 335*a^14*b^4 + 62*a^16*b^2))/a^12 - (((4*(32*a^14*b^5 - 24*a^16*b^3))/a^12 + (4*tan(c/2 + (d*x)/2)*(128*a^13*b^6 - 136*a^15*b^4 + 16*a^17*b^2))/a^12)*(-(a + b)^5*(a - b)^5)^(1/2))/(a^5*b)))/(a^5*b)))/(a^5*b)))/(a^5*b)))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a^5*b*d)","B"
1328,1,1099,241,12.389251,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^6*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b}{32\,a^2}+\frac{b\,\left(\frac{7}{32\,a}-\frac{b^2}{8\,a^3}\right)}{a}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b^2}{8\,a^3}-\frac{11}{16\,a}+\frac{2\,b\,\left(\frac{b}{16\,a^2}+\frac{2\,b\,\left(\frac{7}{32\,a}-\frac{b^2}{8\,a^3}\right)}{a}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{7}{96\,a}-\frac{b^2}{24\,a^3}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{15\,a^4\,b}{8}-\frac{5\,a^2\,b^3}{2}+b^5\right)}{a^6\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{7\,a^4}{3}-\frac{4\,a^2\,b^2}{3}\right)-\frac{a^4}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(22\,a^4-36\,a^2\,b^2+16\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a\,b^3-8\,a^3\,b\right)+\frac{a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{32\,a^5\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^{12}-39\,a^{10}\,b^2+44\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}+\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a^{10}\,b-98\,a^8\,b^3+96\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}\right)\,1{}\mathrm{i}}{a^6}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^{12}-39\,a^{10}\,b^2+44\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}-\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a^{10}\,b-98\,a^8\,b^3+96\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}\right)\,1{}\mathrm{i}}{a^6}}{\frac{15\,a^{10}\,b-65\,a^8\,b^3+113\,a^6\,b^5-99\,a^4\,b^7+44\,a^2\,b^9-8\,b^{11}}{2\,a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}-66\,a^8\,b^2+110\,a^6\,b^4-94\,a^4\,b^6+42\,a^2\,b^8-8\,b^{10}\right)}{2\,a^9}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^{12}-39\,a^{10}\,b^2+44\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}+\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a^{10}\,b-98\,a^8\,b^3+96\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}\right)}{a^6}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^{12}-39\,a^{10}\,b^2+44\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}-\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a^{10}\,b-98\,a^8\,b^3+96\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}\right)}{a^6}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^6\,d}","Not used",1,"tan(c/2 + (d*x)/2)^5/(160*a*d) + (tan(c/2 + (d*x)/2)^2*(b/(32*a^2) + (b*(7/(32*a) - b^2/(8*a^3)))/a))/d - (tan(c/2 + (d*x)/2)*(b^2/(8*a^3) - 11/(16*a) + (2*b*(b/(16*a^2) + (2*b*(7/(32*a) - b^2/(8*a^3)))/a))/a))/d - (tan(c/2 + (d*x)/2)^3*(7/(96*a) - b^2/(24*a^3)))/d - (b*tan(c/2 + (d*x)/2)^4)/(64*a^2*d) - (log(tan(c/2 + (d*x)/2))*((15*a^4*b)/8 + b^5 - (5*a^2*b^3)/2))/(a^6*d) + (tan(c/2 + (d*x)/2)^2*((7*a^4)/3 - (4*a^2*b^2)/3) - a^4/5 - tan(c/2 + (d*x)/2)^4*(22*a^4 + 16*b^4 - 36*a^2*b^2) + tan(c/2 + (d*x)/2)^3*(4*a*b^3 - 8*a^3*b) + (a^3*b*tan(c/2 + (d*x)/2))/2)/(32*a^5*d*tan(c/2 + (d*x)/2)^5) - (atan((((-(a + b)^5*(a - b)^5)^(1/2)*((8*a^12 - 16*a^6*b^6 + 44*a^8*b^4 - 39*a^10*b^2)/(4*a^10) + ((2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^5*(a - b)^5)^(1/2))/a^6 + (tan(c/2 + (d*x)/2)*(31*a^10*b - 32*a^4*b^7 + 96*a^6*b^5 - 98*a^8*b^3))/(4*a^9))*1i)/a^6 + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*a^12 - 16*a^6*b^6 + 44*a^8*b^4 - 39*a^10*b^2)/(4*a^10) - ((2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^5*(a - b)^5)^(1/2))/a^6 + (tan(c/2 + (d*x)/2)*(31*a^10*b - 32*a^4*b^7 + 96*a^6*b^5 - 98*a^8*b^3))/(4*a^9))*1i)/a^6)/((15*a^10*b - 8*b^11 + 44*a^2*b^9 - 99*a^4*b^7 + 113*a^6*b^5 - 65*a^8*b^3)/(2*a^10) + (tan(c/2 + (d*x)/2)*(16*a^10 - 8*b^10 + 42*a^2*b^8 - 94*a^4*b^6 + 110*a^6*b^4 - 66*a^8*b^2))/(2*a^9) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*a^12 - 16*a^6*b^6 + 44*a^8*b^4 - 39*a^10*b^2)/(4*a^10) + ((2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^5*(a - b)^5)^(1/2))/a^6 + (tan(c/2 + (d*x)/2)*(31*a^10*b - 32*a^4*b^7 + 96*a^6*b^5 - 98*a^8*b^3))/(4*a^9)))/a^6 + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*a^12 - 16*a^6*b^6 + 44*a^8*b^4 - 39*a^10*b^2)/(4*a^10) - ((2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^5*(a - b)^5)^(1/2))/a^6 + (tan(c/2 + (d*x)/2)*(31*a^10*b - 32*a^4*b^7 + 96*a^6*b^5 - 98*a^8*b^3))/(4*a^9)))/a^6))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a^6*d)","B"
1329,1,1289,363,12.337204,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^7*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{b}{96\,a^2}+\frac{2\,b\,\left(\frac{3}{32\,a}-\frac{b^2}{16\,a^3}\right)}{3\,a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{3}{128\,a}-\frac{b^2}{64\,a^3}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{32\,a^2}-\frac{2\,b\,\left(\frac{b^2}{16\,a^3}-\frac{15}{64\,a}+\frac{2\,b\,\left(\frac{b}{32\,a^2}+\frac{2\,b\,\left(\frac{3}{32\,a}-\frac{b^2}{16\,a^3}\right)}{a}\right)}{a}\right)}{a}+\frac{2\,b\,\left(\frac{3}{32\,a}-\frac{b^2}{16\,a^3}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b^2}{32\,a^3}-\frac{15}{128\,a}+\frac{b\,\left(\frac{b}{32\,a^2}+\frac{2\,b\,\left(\frac{3}{32\,a}-\frac{b^2}{16\,a^3}\right)}{a}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{14\,a^4\,b}{3}-\frac{8\,a^2\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{15\,a^5}{2}-16\,a^3\,b^2+8\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(44\,a^4\,b-72\,a^2\,b^3+32\,b^5\right)+\frac{a^5}{6}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a^5}{2}-a^3\,b^2\right)-\frac{2\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}}{64\,a^6\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,a^6-30\,a^4\,b^2+40\,a^2\,b^4-16\,b^6\right)}{16\,a^7\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{13}-72\,a^{11}\,b^2+196\,a^9\,b^4-192\,a^7\,b^6+64\,a^5\,b^8\right)}{8\,a^{11}}-\frac{21\,a^{13}\,b-78\,a^{11}\,b^3+88\,a^9\,b^5-32\,a^7\,b^7}{8\,a^{12}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{14}-64\,a^{12}\,b^2\right)}{8\,a^{11}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^7}\right)\,1{}\mathrm{i}}{a^7}-\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{21\,a^{13}\,b-78\,a^{11}\,b^3+88\,a^9\,b^5-32\,a^7\,b^7}{8\,a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{13}-72\,a^{11}\,b^2+196\,a^9\,b^4-192\,a^7\,b^6+64\,a^5\,b^8\right)}{8\,a^{11}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{14}-64\,a^{12}\,b^2\right)}{8\,a^{11}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^7}\right)\,1{}\mathrm{i}}{a^7}}{\frac{5\,a^{12}\,b-45\,a^{10}\,b^3+145\,a^8\,b^5-231\,a^6\,b^7+198\,a^4\,b^9-88\,a^2\,b^{11}+16\,b^{13}}{4\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-22\,a^{10}\,b^2+102\,a^8\,b^4-190\,a^6\,b^6+178\,a^4\,b^8-84\,a^2\,b^{10}+16\,b^{12}\right)}{4\,a^{11}}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{13}-72\,a^{11}\,b^2+196\,a^9\,b^4-192\,a^7\,b^6+64\,a^5\,b^8\right)}{8\,a^{11}}-\frac{21\,a^{13}\,b-78\,a^{11}\,b^3+88\,a^9\,b^5-32\,a^7\,b^7}{8\,a^{12}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{14}-64\,a^{12}\,b^2\right)}{8\,a^{11}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^7}\right)}{a^7}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{21\,a^{13}\,b-78\,a^{11}\,b^3+88\,a^9\,b^5-32\,a^7\,b^7}{8\,a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{13}-72\,a^{11}\,b^2+196\,a^9\,b^4-192\,a^7\,b^6+64\,a^5\,b^8\right)}{8\,a^{11}}+\frac{b\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{14}-64\,a^{12}\,b^2\right)}{8\,a^{11}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^7}\right)}{a^7}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^7\,d}","Not used",1,"tan(c/2 + (d*x)/2)^6/(384*a*d) + (tan(c/2 + (d*x)/2)^3*(b/(96*a^2) + (2*b*(3/(32*a) - b^2/(16*a^3)))/(3*a)))/d - (tan(c/2 + (d*x)/2)^4*(3/(128*a) - b^2/(64*a^3)))/d - (tan(c/2 + (d*x)/2)*(b/(32*a^2) - (2*b*(b^2/(16*a^3) - 15/(64*a) + (2*b*(b/(32*a^2) + (2*b*(3/(32*a) - b^2/(16*a^3)))/a))/a))/a + (2*b*(3/(32*a) - b^2/(16*a^3)))/a))/d - (tan(c/2 + (d*x)/2)^2*(b^2/(32*a^3) - 15/(128*a) + (b*(b/(32*a^2) + (2*b*(3/(32*a) - b^2/(16*a^3)))/a))/a))/d - (tan(c/2 + (d*x)/2)^3*((14*a^4*b)/3 - (8*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^4*(8*a*b^4 + (15*a^5)/2 - 16*a^3*b^2) - tan(c/2 + (d*x)/2)^5*(44*a^4*b + 32*b^5 - 72*a^2*b^3) + a^5/6 - tan(c/2 + (d*x)/2)^2*((3*a^5)/2 - a^3*b^2) - (2*a^4*b*tan(c/2 + (d*x)/2))/5)/(64*a^6*d*tan(c/2 + (d*x)/2)^6) - (b*tan(c/2 + (d*x)/2)^5)/(160*a^2*d) - (log(tan(c/2 + (d*x)/2))*(5*a^6 - 16*b^6 + 40*a^2*b^4 - 30*a^4*b^2))/(16*a^7*d) + (b*atan(((b*(-(a + b)^5*(a - b)^5)^(1/2)*((tan(c/2 + (d*x)/2)*(5*a^13 + 64*a^5*b^8 - 192*a^7*b^6 + 196*a^9*b^4 - 72*a^11*b^2))/(8*a^11) - (21*a^13*b - 32*a^7*b^7 + 88*a^9*b^5 - 78*a^11*b^3)/(8*a^12) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^14 - 64*a^12*b^2))/(8*a^11))*(-(a + b)^5*(a - b)^5)^(1/2))/a^7)*1i)/a^7 - (b*(-(a + b)^5*(a - b)^5)^(1/2)*((21*a^13*b - 32*a^7*b^7 + 88*a^9*b^5 - 78*a^11*b^3)/(8*a^12) - (tan(c/2 + (d*x)/2)*(5*a^13 + 64*a^5*b^8 - 192*a^7*b^6 + 196*a^9*b^4 - 72*a^11*b^2))/(8*a^11) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^14 - 64*a^12*b^2))/(8*a^11))*(-(a + b)^5*(a - b)^5)^(1/2))/a^7)*1i)/a^7)/((5*a^12*b + 16*b^13 - 88*a^2*b^11 + 198*a^4*b^9 - 231*a^6*b^7 + 145*a^8*b^5 - 45*a^10*b^3)/(4*a^12) + (tan(c/2 + (d*x)/2)*(16*b^12 - 84*a^2*b^10 + 178*a^4*b^8 - 190*a^6*b^6 + 102*a^8*b^4 - 22*a^10*b^2))/(4*a^11) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((tan(c/2 + (d*x)/2)*(5*a^13 + 64*a^5*b^8 - 192*a^7*b^6 + 196*a^9*b^4 - 72*a^11*b^2))/(8*a^11) - (21*a^13*b - 32*a^7*b^7 + 88*a^9*b^5 - 78*a^11*b^3)/(8*a^12) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^14 - 64*a^12*b^2))/(8*a^11))*(-(a + b)^5*(a - b)^5)^(1/2))/a^7))/a^7 + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((21*a^13*b - 32*a^7*b^7 + 88*a^9*b^5 - 78*a^11*b^3)/(8*a^12) - (tan(c/2 + (d*x)/2)*(5*a^13 + 64*a^5*b^8 - 192*a^7*b^6 + 196*a^9*b^4 - 72*a^11*b^2))/(8*a^11) + (b*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^14 - 64*a^12*b^2))/(8*a^11))*(-(a + b)^5*(a - b)^5)^(1/2))/a^7))/a^7))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a^7*d)","B"
1330,1,1513,417,12.384578,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^8*(a + b*sin(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b^2}{32\,a^3}-\frac{5}{128\,a}+\frac{2\,b\,\left(\frac{b}{64\,a^2}+\frac{2\,b\,\left(\frac{5}{128\,a}-\frac{b^2}{32\,a^3}\right)}{a}\right)}{a}+\frac{2\,b\,\left(\frac{b}{64\,a^2}-\frac{2\,b\,\left(\frac{b^2}{32\,a^3}-\frac{9}{128\,a}+\frac{2\,b\,\left(\frac{b}{64\,a^2}+\frac{2\,b\,\left(\frac{5}{128\,a}-\frac{b^2}{32\,a^3}\right)}{a}\right)}{a}\right)}{a}+\frac{2\,b\,\left(\frac{5}{128\,a}-\frac{b^2}{32\,a^3}\right)}{a}\right)}{a}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{b}{256\,a^2}+\frac{b\,\left(\frac{5}{128\,a}-\frac{b^2}{32\,a^3}\right)}{2\,a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b}{128\,a^2}-\frac{b\,\left(\frac{b^2}{32\,a^3}-\frac{9}{128\,a}+\frac{2\,b\,\left(\frac{b}{64\,a^2}+\frac{2\,b\,\left(\frac{5}{128\,a}-\frac{b^2}{32\,a^3}\right)}{a}\right)}{a}\right)}{a}+\frac{b\,\left(\frac{5}{128\,a}-\frac{b^2}{32\,a^3}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{1}{128\,a}-\frac{b^2}{160\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{b^2}{96\,a^3}-\frac{3}{128\,a}+\frac{2\,b\,\left(\frac{b}{64\,a^2}+\frac{2\,b\,\left(\frac{5}{128\,a}-\frac{b^2}{32\,a^3}\right)}{a}\right)}{3\,a}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^6-\frac{4\,a^4\,b^2}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^5\,b-2\,a^3\,b^3\right)-\frac{a^6}{7}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^6-\frac{28\,a^4\,b^2}{3}+\frac{16\,a^2\,b^4}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(15\,a^5\,b-32\,a^3\,b^3+16\,a\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5\,a^6-88\,a^4\,b^2+144\,a^2\,b^4-64\,b^6\right)+\frac{a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{128\,a^7\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,a^2\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,a^6\,b-30\,a^4\,b^3+40\,a^2\,b^5-16\,b^7\right)}{16\,a^8\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-21\,a^{14}\,b^2+78\,a^{12}\,b^4-88\,a^{10}\,b^6+32\,a^8\,b^8}{8\,a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{14}\,b-72\,a^{12}\,b^3+196\,a^{10}\,b^5-192\,a^8\,b^7+64\,a^6\,b^9\right)}{8\,a^{13}}+\frac{b^2\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{16}-64\,a^{14}\,b^2\right)}{8\,a^{13}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^8}\right)\,1{}\mathrm{i}}{a^8}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-21\,a^{14}\,b^2+78\,a^{12}\,b^4-88\,a^{10}\,b^6+32\,a^8\,b^8}{8\,a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{14}\,b-72\,a^{12}\,b^3+196\,a^{10}\,b^5-192\,a^8\,b^7+64\,a^6\,b^9\right)}{8\,a^{13}}-\frac{b^2\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{16}-64\,a^{14}\,b^2\right)}{8\,a^{13}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^8}\right)\,1{}\mathrm{i}}{a^8}}{\frac{5\,a^{12}\,b^3-45\,a^{10}\,b^5+145\,a^8\,b^7-231\,a^6\,b^9+198\,a^4\,b^{11}-88\,a^2\,b^{13}+16\,b^{15}}{4\,a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-22\,a^{10}\,b^4+102\,a^8\,b^6-190\,a^6\,b^8+178\,a^4\,b^{10}-84\,a^2\,b^{12}+16\,b^{14}\right)}{4\,a^{13}}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-21\,a^{14}\,b^2+78\,a^{12}\,b^4-88\,a^{10}\,b^6+32\,a^8\,b^8}{8\,a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{14}\,b-72\,a^{12}\,b^3+196\,a^{10}\,b^5-192\,a^8\,b^7+64\,a^6\,b^9\right)}{8\,a^{13}}+\frac{b^2\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{16}-64\,a^{14}\,b^2\right)}{8\,a^{13}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^8}\right)}{a^8}-\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-21\,a^{14}\,b^2+78\,a^{12}\,b^4-88\,a^{10}\,b^6+32\,a^8\,b^8}{8\,a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{14}\,b-72\,a^{12}\,b^3+196\,a^{10}\,b^5-192\,a^8\,b^7+64\,a^6\,b^9\right)}{8\,a^{13}}-\frac{b^2\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{16}-64\,a^{14}\,b^2\right)}{8\,a^{13}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^8}\right)}{a^8}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(b^2/(32*a^3) - 5/(128*a) + (2*b*(b/(64*a^2) + (2*b*(5/(128*a) - b^2/(32*a^3)))/a))/a + (2*b*(b/(64*a^2) - (2*b*(b^2/(32*a^3) - 9/(128*a) + (2*b*(b/(64*a^2) + (2*b*(5/(128*a) - b^2/(32*a^3)))/a))/a))/a + (2*b*(5/(128*a) - b^2/(32*a^3)))/a))/a))/d + tan(c/2 + (d*x)/2)^7/(896*a*d) + (tan(c/2 + (d*x)/2)^4*(b/(256*a^2) + (b*(5/(128*a) - b^2/(32*a^3)))/(2*a)))/d - (tan(c/2 + (d*x)/2)^2*(b/(128*a^2) - (b*(b^2/(32*a^3) - 9/(128*a) + (2*b*(b/(64*a^2) + (2*b*(5/(128*a) - b^2/(32*a^3)))/a))/a))/a + (b*(5/(128*a) - b^2/(32*a^3)))/a))/d - (tan(c/2 + (d*x)/2)^5*(1/(128*a) - b^2/(160*a^3)))/d - (tan(c/2 + (d*x)/2)^3*(b^2/(96*a^3) - 3/(128*a) + (2*b*(b/(64*a^2) + (2*b*(5/(128*a) - b^2/(32*a^3)))/a))/(3*a)))/d + (tan(c/2 + (d*x)/2)^2*(a^6 - (4*a^4*b^2)/5) - tan(c/2 + (d*x)/2)^3*(3*a^5*b - 2*a^3*b^3) - a^6/7 - tan(c/2 + (d*x)/2)^4*(3*a^6 + (16*a^2*b^4)/3 - (28*a^4*b^2)/3) + tan(c/2 + (d*x)/2)^5*(16*a*b^5 + 15*a^5*b - 32*a^3*b^3) + tan(c/2 + (d*x)/2)^6*(5*a^6 - 64*b^6 + 144*a^2*b^4 - 88*a^4*b^2) + (a^5*b*tan(c/2 + (d*x)/2))/3)/(128*a^7*d*tan(c/2 + (d*x)/2)^7) - (b*tan(c/2 + (d*x)/2)^6)/(384*a^2*d) + (log(tan(c/2 + (d*x)/2))*(5*a^6*b - 16*b^7 + 40*a^2*b^5 - 30*a^4*b^3))/(16*a^8*d) - (b^2*atan(((b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((32*a^8*b^8 - 88*a^10*b^6 + 78*a^12*b^4 - 21*a^14*b^2)/(8*a^14) + (tan(c/2 + (d*x)/2)*(5*a^14*b + 64*a^6*b^9 - 192*a^8*b^7 + 196*a^10*b^5 - 72*a^12*b^3))/(8*a^13) + (b^2*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^16 - 64*a^14*b^2))/(8*a^13))*(-(a + b)^5*(a - b)^5)^(1/2))/a^8)*1i)/a^8 + (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((32*a^8*b^8 - 88*a^10*b^6 + 78*a^12*b^4 - 21*a^14*b^2)/(8*a^14) + (tan(c/2 + (d*x)/2)*(5*a^14*b + 64*a^6*b^9 - 192*a^8*b^7 + 196*a^10*b^5 - 72*a^12*b^3))/(8*a^13) - (b^2*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^16 - 64*a^14*b^2))/(8*a^13))*(-(a + b)^5*(a - b)^5)^(1/2))/a^8)*1i)/a^8)/((16*b^15 - 88*a^2*b^13 + 198*a^4*b^11 - 231*a^6*b^9 + 145*a^8*b^7 - 45*a^10*b^5 + 5*a^12*b^3)/(4*a^14) + (tan(c/2 + (d*x)/2)*(16*b^14 - 84*a^2*b^12 + 178*a^4*b^10 - 190*a^6*b^8 + 102*a^8*b^6 - 22*a^10*b^4))/(4*a^13) + (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((32*a^8*b^8 - 88*a^10*b^6 + 78*a^12*b^4 - 21*a^14*b^2)/(8*a^14) + (tan(c/2 + (d*x)/2)*(5*a^14*b + 64*a^6*b^9 - 192*a^8*b^7 + 196*a^10*b^5 - 72*a^12*b^3))/(8*a^13) + (b^2*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^16 - 64*a^14*b^2))/(8*a^13))*(-(a + b)^5*(a - b)^5)^(1/2))/a^8))/a^8 - (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((32*a^8*b^8 - 88*a^10*b^6 + 78*a^12*b^4 - 21*a^14*b^2)/(8*a^14) + (tan(c/2 + (d*x)/2)*(5*a^14*b + 64*a^6*b^9 - 192*a^8*b^7 + 196*a^10*b^5 - 72*a^12*b^3))/(8*a^13) - (b^2*(2*a^2*b - (tan(c/2 + (d*x)/2)*(48*a^16 - 64*a^14*b^2))/(8*a^13))*(-(a + b)^5*(a - b)^5)^(1/2))/a^8))/a^8))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a^8*d)","B"
1331,1,1861,476,12.665417,"\text{Not used}","int(cos(c + d*x)^6/(sin(c + d*x)^9*(a + b*sin(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2048\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{b}{640\,a^2}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{5\,a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{b}{384\,a^2}-\frac{2\,b\,\left(\frac{b^2}{64\,a^3}-\frac{1}{64\,a}+\frac{2\,b\,\left(\frac{b}{128\,a^2}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{a}\right)}{3\,a}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{3\,a}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{1}{128\,a}+\frac{b^2}{128\,a^3}+\frac{b\,\left(\frac{b}{128\,a^2}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{a}+\frac{b\,\left(\frac{b}{128\,a^2}-\frac{2\,b\,\left(\frac{b^2}{64\,a^3}-\frac{1}{64\,a}+\frac{2\,b\,\left(\frac{b}{128\,a^2}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{a}\right)}{a}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{a}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{128\,a^2}-\frac{2\,b\,\left(\frac{b^2}{64\,a^3}-\frac{1}{64\,a}+\frac{2\,b\,\left(\frac{b}{128\,a^2}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{a}\right)}{a}-\frac{2\,b\,\left(\frac{1}{64\,a}+\frac{b^2}{64\,a^3}+\frac{2\,b\,\left(\frac{b}{128\,a^2}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{a}+\frac{2\,b\,\left(\frac{b}{128\,a^2}-\frac{2\,b\,\left(\frac{b^2}{64\,a^3}-\frac{1}{64\,a}+\frac{2\,b\,\left(\frac{b}{128\,a^2}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{a}\right)}{a}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{a}\right)}{a}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{1}{384\,a}-\frac{b^2}{384\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{b^2}{256\,a^3}-\frac{1}{256\,a}+\frac{b\,\left(\frac{b}{128\,a^2}+\frac{2\,b\,\left(\frac{1}{64\,a}-\frac{b^2}{64\,a^3}\right)}{a}\right)}{2\,a}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,a^8+40\,a^6\,b^2-240\,a^4\,b^4+320\,a^2\,b^6-128\,b^8\right)}{128\,a^9\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^6\,b-\frac{8\,a^4\,b^3}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^6\,b-\frac{56\,a^4\,b^3}{3}+\frac{32\,a^2\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^7+30\,a^5\,b^2-64\,a^3\,b^4+32\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(10\,a^6\,b-176\,a^4\,b^3+288\,a^2\,b^5-128\,b^7\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^7-6\,a^5\,b^2+4\,a^3\,b^4\right)+\frac{a^7}{8}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{2\,a^7}{3}-\frac{2\,a^5\,b^2}{3}\right)-\frac{2\,a^6\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{7}\right)}{256\,a^8\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{896\,a^2\,d}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{17}+30\,a^{15}\,b^2-576\,a^{13}\,b^4+1568\,a^{11}\,b^6-1536\,a^9\,b^8+512\,a^7\,b^{10}\right)}{64\,a^{15}}-\frac{5\,a^{17}\,b+168\,a^{15}\,b^3-624\,a^{13}\,b^5+704\,a^{11}\,b^7-256\,a^9\,b^9}{64\,a^{16}}+\frac{b^3\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(384\,a^{18}-512\,a^{16}\,b^2\right)}{64\,a^{15}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^9}\right)\,1{}\mathrm{i}}{a^9}-\frac{b^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{5\,a^{17}\,b+168\,a^{15}\,b^3-624\,a^{13}\,b^5+704\,a^{11}\,b^7-256\,a^9\,b^9}{64\,a^{16}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{17}+30\,a^{15}\,b^2-576\,a^{13}\,b^4+1568\,a^{11}\,b^6-1536\,a^9\,b^8+512\,a^7\,b^{10}\right)}{64\,a^{15}}+\frac{b^3\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(384\,a^{18}-512\,a^{16}\,b^2\right)}{64\,a^{15}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^9}\right)\,1{}\mathrm{i}}{a^9}}{\frac{5\,a^{14}\,b^3+25\,a^{12}\,b^5-345\,a^{10}\,b^7+1155\,a^8\,b^9-1848\,a^6\,b^{11}+1584\,a^4\,b^{13}-704\,a^2\,b^{15}+128\,b^{17}}{32\,a^{16}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^{12}\,b^4-206\,a^{10}\,b^6+846\,a^8\,b^8-1530\,a^6\,b^{10}+1424\,a^4\,b^{12}-672\,a^2\,b^{14}+128\,b^{16}\right)}{32\,a^{15}}+\frac{b^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{17}+30\,a^{15}\,b^2-576\,a^{13}\,b^4+1568\,a^{11}\,b^6-1536\,a^9\,b^8+512\,a^7\,b^{10}\right)}{64\,a^{15}}-\frac{5\,a^{17}\,b+168\,a^{15}\,b^3-624\,a^{13}\,b^5+704\,a^{11}\,b^7-256\,a^9\,b^9}{64\,a^{16}}+\frac{b^3\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(384\,a^{18}-512\,a^{16}\,b^2\right)}{64\,a^{15}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^9}\right)}{a^9}+\frac{b^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{5\,a^{17}\,b+168\,a^{15}\,b^3-624\,a^{13}\,b^5+704\,a^{11}\,b^7-256\,a^9\,b^9}{64\,a^{16}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^{17}+30\,a^{15}\,b^2-576\,a^{13}\,b^4+1568\,a^{11}\,b^6-1536\,a^9\,b^8+512\,a^7\,b^{10}\right)}{64\,a^{15}}+\frac{b^3\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(384\,a^{18}-512\,a^{16}\,b^2\right)}{64\,a^{15}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^9}\right)}{a^9}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^9\,d}","Not used",1,"tan(c/2 + (d*x)/2)^8/(2048*a*d) + (tan(c/2 + (d*x)/2)^5*(b/(640*a^2) + (2*b*(1/(64*a) - b^2/(64*a^3)))/(5*a)))/d - (tan(c/2 + (d*x)/2)^3*(b/(384*a^2) - (2*b*(b^2/(64*a^3) - 1/(64*a) + (2*b*(b/(128*a^2) + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/a))/(3*a) + (2*b*(1/(64*a) - b^2/(64*a^3)))/(3*a)))/d + (tan(c/2 + (d*x)/2)^2*(1/(128*a) + b^2/(128*a^3) + (b*(b/(128*a^2) + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/a + (b*(b/(128*a^2) - (2*b*(b^2/(64*a^3) - 1/(64*a) + (2*b*(b/(128*a^2) + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/a))/a + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/a))/d + (tan(c/2 + (d*x)/2)*(b/(128*a^2) - (2*b*(b^2/(64*a^3) - 1/(64*a) + (2*b*(b/(128*a^2) + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/a))/a - (2*b*(1/(64*a) + b^2/(64*a^3) + (2*b*(b/(128*a^2) + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/a + (2*b*(b/(128*a^2) - (2*b*(b^2/(64*a^3) - 1/(64*a) + (2*b*(b/(128*a^2) + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/a))/a + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/a))/a + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/d - (tan(c/2 + (d*x)/2)^6*(1/(384*a) - b^2/(384*a^3)))/d - (tan(c/2 + (d*x)/2)^4*(b^2/(256*a^3) - 1/(256*a) + (b*(b/(128*a^2) + (2*b*(1/(64*a) - b^2/(64*a^3)))/a))/(2*a)))/d - (log(tan(c/2 + (d*x)/2))*(5*a^8 - 128*b^8 + 320*a^2*b^6 - 240*a^4*b^4 + 40*a^6*b^2))/(128*a^9*d) - (cot(c/2 + (d*x)/2)^8*(tan(c/2 + (d*x)/2)^3*(2*a^6*b - (8*a^4*b^3)/5) - tan(c/2 + (d*x)/2)^5*(6*a^6*b + (32*a^2*b^5)/3 - (56*a^4*b^3)/3) + tan(c/2 + (d*x)/2)^6*(32*a*b^6 + 2*a^7 - 64*a^3*b^4 + 30*a^5*b^2) + tan(c/2 + (d*x)/2)^7*(10*a^6*b - 128*b^7 + 288*a^2*b^5 - 176*a^4*b^3) + tan(c/2 + (d*x)/2)^4*(a^7 + 4*a^3*b^4 - 6*a^5*b^2) + a^7/8 - tan(c/2 + (d*x)/2)^2*((2*a^7)/3 - (2*a^5*b^2)/3) - (2*a^6*b*tan(c/2 + (d*x)/2))/7))/(256*a^8*d) - (b*tan(c/2 + (d*x)/2)^7)/(896*a^2*d) + (b^3*atan(((b^3*(-(a + b)^5*(a - b)^5)^(1/2)*((tan(c/2 + (d*x)/2)*(5*a^17 + 512*a^7*b^10 - 1536*a^9*b^8 + 1568*a^11*b^6 - 576*a^13*b^4 + 30*a^15*b^2))/(64*a^15) - (5*a^17*b - 256*a^9*b^9 + 704*a^11*b^7 - 624*a^13*b^5 + 168*a^15*b^3)/(64*a^16) + (b^3*(2*a^2*b - (tan(c/2 + (d*x)/2)*(384*a^18 - 512*a^16*b^2))/(64*a^15))*(-(a + b)^5*(a - b)^5)^(1/2))/a^9)*1i)/a^9 - (b^3*(-(a + b)^5*(a - b)^5)^(1/2)*((5*a^17*b - 256*a^9*b^9 + 704*a^11*b^7 - 624*a^13*b^5 + 168*a^15*b^3)/(64*a^16) - (tan(c/2 + (d*x)/2)*(5*a^17 + 512*a^7*b^10 - 1536*a^9*b^8 + 1568*a^11*b^6 - 576*a^13*b^4 + 30*a^15*b^2))/(64*a^15) + (b^3*(2*a^2*b - (tan(c/2 + (d*x)/2)*(384*a^18 - 512*a^16*b^2))/(64*a^15))*(-(a + b)^5*(a - b)^5)^(1/2))/a^9)*1i)/a^9)/((128*b^17 - 704*a^2*b^15 + 1584*a^4*b^13 - 1848*a^6*b^11 + 1155*a^8*b^9 - 345*a^10*b^7 + 25*a^12*b^5 + 5*a^14*b^3)/(32*a^16) + (tan(c/2 + (d*x)/2)*(128*b^16 - 672*a^2*b^14 + 1424*a^4*b^12 - 1530*a^6*b^10 + 846*a^8*b^8 - 206*a^10*b^6 + 10*a^12*b^4))/(32*a^15) + (b^3*(-(a + b)^5*(a - b)^5)^(1/2)*((tan(c/2 + (d*x)/2)*(5*a^17 + 512*a^7*b^10 - 1536*a^9*b^8 + 1568*a^11*b^6 - 576*a^13*b^4 + 30*a^15*b^2))/(64*a^15) - (5*a^17*b - 256*a^9*b^9 + 704*a^11*b^7 - 624*a^13*b^5 + 168*a^15*b^3)/(64*a^16) + (b^3*(2*a^2*b - (tan(c/2 + (d*x)/2)*(384*a^18 - 512*a^16*b^2))/(64*a^15))*(-(a + b)^5*(a - b)^5)^(1/2))/a^9))/a^9 + (b^3*(-(a + b)^5*(a - b)^5)^(1/2)*((5*a^17*b - 256*a^9*b^9 + 704*a^11*b^7 - 624*a^13*b^5 + 168*a^15*b^3)/(64*a^16) - (tan(c/2 + (d*x)/2)*(5*a^17 + 512*a^7*b^10 - 1536*a^9*b^8 + 1568*a^11*b^6 - 576*a^13*b^4 + 30*a^15*b^2))/(64*a^15) + (b^3*(2*a^2*b - (tan(c/2 + (d*x)/2)*(384*a^18 - 512*a^16*b^2))/(64*a^15))*(-(a + b)^5*(a - b)^5)^(1/2))/a^9))/a^9))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a^9*d)","B"
1332,1,134,93,12.271979,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)*(a + b*sin(c + d*x))),x)","-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d\,\left(a+b\right)}-\frac{\sin\left(c+d\,x\right)}{b\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{d\,\left(a-b\right)}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b^2\,d}-\frac{a^3\,\ln\left(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)}{d\,\left(b^4-a^2\,b^2\right)}","Not used",1,"- log(tan(c/2 + (d*x)/2) - 1)/(d*(a + b)) - sin(c + d*x)/(b*d) - log(tan(c/2 + (d*x)/2) + 1)/(d*(a - b)) - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/(b^2*d) - (a^3*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(b^4 - a^2*b^2))","B"
1333,1,117,80,11.939652,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{d\,\left(a-b\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d\,\left(a+b\right)}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b\,d}-\frac{a^2\,\ln\left(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)}{b\,d\,\left(a^2-b^2\right)}","Not used",1,"log(tan(c/2 + (d*x)/2) + 1)/(d*(a - b)) - log(tan(c/2 + (d*x)/2) - 1)/(d*(a + b)) + log(tan(c/2 + (d*x)/2)^2 + 1)/(b*d) - (a^2*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(b*d*(a^2 - b^2))","B"
1334,1,91,74,12.020388,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{a\,\ln\left(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)}{d\,\left(a^2-b^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{d\,\left(a-b\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d\,\left(a+b\right)}","Not used",1,"(a*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^2 - b^2)) - log(tan(c/2 + (d*x)/2) + 1)/(d*(a - b)) - log(tan(c/2 + (d*x)/2) - 1)/(d*(a + b))","B"
1335,1,87,93,0.171329,"\text{Not used}","int(1/(cos(c + d*x)*sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}-\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^2\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{a\,d\,\left(a^2-b^2\right)}","Not used",1,"log(sin(c + d*x))/(a*d) - log(sin(c + d*x) + 1)/(2*d*(a - b)) - log(sin(c + d*x) - 1)/(2*d*(a + b)) + (b^2*log(a + b*sin(c + d*x)))/(a*d*(a^2 - b^2))","B"
1336,1,98,110,11.918520,"\text{Not used}","int(1/(cos(c + d*x)*sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","-\frac{\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)}{2\,\left(a+b\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{2\,\left(a-b\right)}+\frac{1}{a\,\sin\left(c+d\,x\right)}+\frac{b\,\ln\left(\sin\left(c+d\,x\right)\right)}{a^2}+\frac{b^3\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{a^4-a^2\,b^2}}{d}","Not used",1,"-(log(sin(c + d*x) - 1)/(2*(a + b)) - log(sin(c + d*x) + 1)/(2*(a - b)) + 1/(a*sin(c + d*x)) + (b*log(sin(c + d*x)))/a^2 + (b^3*log(a + b*sin(c + d*x)))/(a^4 - a^2*b^2))/d","B"
1337,1,125,132,11.854721,"\text{Not used}","int(1/(cos(c + d*x)*sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)\right)\,\left(a^2+b^2\right)}{a^3\,d}-\frac{\frac{1}{2\,a}-\frac{b\,\sin\left(c+d\,x\right)}{a^2}}{d\,{\sin\left(c+d\,x\right)}^2}-\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^4\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^5-a^3\,b^2\right)}","Not used",1,"(log(sin(c + d*x))*(a^2 + b^2))/(a^3*d) - (1/(2*a) - (b*sin(c + d*x))/a^2)/(d*sin(c + d*x)^2) - log(sin(c + d*x) - 1)/(2*d*(a + b)) - log(sin(c + d*x) + 1)/(2*d*(a - b)) + (b^4*log(a + b*sin(c + d*x)))/(d*(a^5 - a^3*b^2))","B"
1338,1,2098,268,16.814591,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{4\,a^5\,\cos\left(c+d\,x\right)+\frac{5\,a^5}{2}+\frac{3\,a^5\,\cos\left(2\,c+2\,d\,x\right)}{2}}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,a^8\,\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^3\,d\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b\,\left(\frac{11\,a^4\,\sin\left(c+d\,x\right)}{8}+\frac{3\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{8}-3\,a^4\,\cos\left(c+d\,x\right)\,\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)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b^4\,\left(\frac{3\,a}{2}+2\,a\,\cos\left(c+d\,x\right)+\frac{a\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b^5\,\left(\frac{9\,\sin\left(c+d\,x\right)}{8}+\frac{\sin\left(3\,c+3\,d\,x\right)}{8}-3\,\cos\left(c+d\,x\right)\,\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)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{a^7\,\cos\left(c+d\,x\right)+\frac{a^7}{2}+\frac{a^7\,\cos\left(2\,c+2\,d\,x\right)}{2}}{b^2\,d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b^2\,\left(5\,a^3\,\cos\left(c+d\,x\right)+\frac{7\,a^3}{2}+\frac{3\,a^3\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\frac{a^6\,\sin\left(c+d\,x\right)}{8}+\frac{a^6\,\sin\left(3\,c+3\,d\,x\right)}{8}+3\,a^6\,\cos\left(c+d\,x\right)\,\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\,d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b^3\,\left(\frac{19\,a^2\,\sin\left(c+d\,x\right)}{8}+\frac{3\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{8}-7\,a^2\,\cos\left(c+d\,x\right)\,\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)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a^5\,\mathrm{atan}\left(\frac{a^{12}\,\sin\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)}^{3/2}\,8{}\mathrm{i}+a^{18}\,\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}\,8{}\mathrm{i}-b^{18}\,\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}\,18{}\mathrm{i}+a^3\,b^{15}\,\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}\,42{}\mathrm{i}-a^5\,b^{13}\,\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}\,67{}\mathrm{i}+a^7\,b^{11}\,\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}\,24{}\mathrm{i}+a^9\,b^9\,\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}\,45{}\mathrm{i}-a^{11}\,b^7\,\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}\,46{}\mathrm{i}+a^{13}\,b^5\,\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}\,3{}\mathrm{i}+a^{15}\,b^3\,\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}\,12{}\mathrm{i}-a^{10}\,b^2\,\sin\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)}^{3/2}\,12{}\mathrm{i}+a^2\,b^{16}\,\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}\,93{}\mathrm{i}-a^4\,b^{14}\,\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}\,176{}\mathrm{i}+a^6\,b^{12}\,\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}\,115{}\mathrm{i}+a^8\,b^{10}\,\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}\,66{}\mathrm{i}-a^{10}\,b^8\,\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}\,133{}\mathrm{i}+a^{12}\,b^6\,\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}\,36{}\mathrm{i}+a^{14}\,b^4\,\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}\,45{}\mathrm{i}-a^{16}\,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}\,36{}\mathrm{i}-a^{11}\,b\,\cos\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)}^{3/2}\,4{}\mathrm{i}-a\,b^{17}\,\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}\,9{}\mathrm{i}-a^{17}\,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}\,4{}\mathrm{i}}{-15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{17}\,b^4-30\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{16}\,b^5+80\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{15}\,b^6+160\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{14}\,b^7-160\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}\,b^8-320\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b^9+116\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^{10}+232\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^{11}+70\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^{12}+140\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^{13}-200\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^{14}-400\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^{15}+160\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^{16}+320\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^{17}-60\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{18}-120\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{19}+9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{20}+18\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{21}}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}\,2{}\mathrm{i}}{b^3\,d\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}","Not used",1,"(4*a^5*cos(c + d*x) + (5*a^5)/2 + (3*a^5*cos(2*c + 2*d*x))/2)/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (2*a^8*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^3*d*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b*((11*a^4*sin(c + d*x))/8 + (3*a^4*sin(3*c + 3*d*x))/8 - 3*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (b^4*((3*a)/2 + 2*a*cos(c + d*x) + (a*cos(2*c + 2*d*x))/2))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b^5*((9*sin(c + d*x))/8 + sin(3*c + 3*d*x)/8 - 3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (a^7*cos(c + d*x) + a^7/2 + (a^7*cos(2*c + 2*d*x))/2)/(b^2*d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b^2*(5*a^3*cos(c + d*x) + (7*a^3)/2 + (3*a^3*cos(2*c + 2*d*x))/2))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + ((a^6*sin(c + d*x))/8 + (a^6*sin(3*c + 3*d*x))/8 + 3*a^6*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (b^3*((19*a^2*sin(c + d*x))/8 + (3*a^2*sin(3*c + 3*d*x))/8 - 7*a^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (a^5*atan((a^12*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*8i + a^18*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*8i - b^18*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*18i + a^3*b^15*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*42i - a^5*b^13*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*67i + a^7*b^11*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*24i + a^9*b^9*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*45i - a^11*b^7*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*46i + a^13*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*3i + a^15*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*12i - a^10*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*12i + a^2*b^16*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*93i - a^4*b^14*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*176i + a^6*b^12*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*115i + a^8*b^10*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*66i - a^10*b^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*133i + a^12*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*36i + a^14*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*45i - a^16*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*36i - a^11*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2)*4i - a*b^17*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*9i - a^17*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*4i)/(18*b^21*sin(c/2 + (d*x)/2) + 9*a*b^20*cos(c/2 + (d*x)/2) - 60*a^3*b^18*cos(c/2 + (d*x)/2) + 160*a^5*b^16*cos(c/2 + (d*x)/2) - 200*a^7*b^14*cos(c/2 + (d*x)/2) + 70*a^9*b^12*cos(c/2 + (d*x)/2) + 116*a^11*b^10*cos(c/2 + (d*x)/2) - 160*a^13*b^8*cos(c/2 + (d*x)/2) + 80*a^15*b^6*cos(c/2 + (d*x)/2) - 15*a^17*b^4*cos(c/2 + (d*x)/2) - 120*a^2*b^19*sin(c/2 + (d*x)/2) + 320*a^4*b^17*sin(c/2 + (d*x)/2) - 400*a^6*b^15*sin(c/2 + (d*x)/2) + 140*a^8*b^13*sin(c/2 + (d*x)/2) + 232*a^10*b^11*sin(c/2 + (d*x)/2) - 320*a^12*b^9*sin(c/2 + (d*x)/2) + 160*a^14*b^7*sin(c/2 + (d*x)/2) - 30*a^16*b^5*sin(c/2 + (d*x)/2)))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*2i)/(b^3*d*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2))","B"
1339,1,1656,183,14.277611,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{a^5\,\sin\left(c+d\,x\right)-6\,a^5\,\cos\left(c+d\,x\right)\,\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)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,a^7\,\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^2\,d\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a^6\,\cos\left(c+d\,x\right)+\frac{a^6}{2}+\frac{a^6\,\cos\left(2\,c+2\,d\,x\right)}{2}}{b\,d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b^3\,\left(5\,a^2\,\cos\left(c+d\,x\right)+\frac{7\,a^2}{2}+\frac{3\,a^2\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b^2\,\left(2\,a^3\,\sin\left(c+d\,x\right)-6\,a^3\,\cos\left(c+d\,x\right)\,\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)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b^5\,\left(2\,\cos\left(c+d\,x\right)+\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{3}{2}\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b^4\,\left(a\,\sin\left(c+d\,x\right)-2\,a\,\cos\left(c+d\,x\right)\,\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)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b\,\left(4\,a^4\,\cos\left(c+d\,x\right)+\frac{5\,a^4}{2}+\frac{3\,a^4\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a^4\,\mathrm{atan}\left(\frac{\left(2\,b^{14}\,\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}-2\,a^{14}\,\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}-2\,a^8\,\sin\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)}^{3/2}-6\,a^3\,b^{11}\,\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}+15\,a^5\,b^9\,\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}-20\,a^7\,b^7\,\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}+15\,a^9\,b^5\,\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}-6\,a^{11}\,b^3\,\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}+3\,a^6\,b^2\,\sin\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)}^{3/2}-13\,a^2\,b^{12}\,\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}+36\,a^4\,b^{10}\,\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}-56\,a^6\,b^8\,\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}+54\,a^8\,b^6\,\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}-33\,a^{10}\,b^4\,\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}+12\,a^{12}\,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^7\,b\,\cos\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)}^{3/2}+a\,b^{13}\,\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}+a^{13}\,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}\right)\,1{}\mathrm{i}}{\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2-6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+12\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-19\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-38\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+30\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9-6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}-12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{b^2\,d\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}","Not used",1,"(a^5*sin(c + d*x) - 6*a^5*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (2*a^7*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (a^6*cos(c + d*x) + a^6/2 + (a^6*cos(2*c + 2*d*x))/2)/(b*d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (b^3*(5*a^2*cos(c + d*x) + (7*a^2)/2 + (3*a^2*cos(2*c + 2*d*x))/2))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b^2*(2*a^3*sin(c + d*x) - 6*a^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b^5*(2*cos(c + d*x) + cos(2*c + 2*d*x)/2 + 3/2))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (b^4*(a*sin(c + d*x) - 2*a*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b*(4*a^4*cos(c + d*x) + (5*a^4)/2 + (3*a^4*cos(2*c + 2*d*x))/2))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (a^4*atan(((2*b^14*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 2*a^14*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 2*a^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 6*a^3*b^11*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 15*a^5*b^9*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 20*a^7*b^7*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 15*a^9*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 6*a^11*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 3*a^6*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 13*a^2*b^12*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 36*a^4*b^10*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 56*a^6*b^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 54*a^8*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 33*a^10*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 12*a^12*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^7*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + a*b^13*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + a^13*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))*1i)/((a^4 + b^4 - 2*a^2*b^2)*(2*b^13*sin(c/2 + (d*x)/2) + a*b^12*cos(c/2 + (d*x)/2) - 6*a^3*b^10*cos(c/2 + (d*x)/2) + 15*a^5*b^8*cos(c/2 + (d*x)/2) - 19*a^7*b^6*cos(c/2 + (d*x)/2) + 12*a^9*b^4*cos(c/2 + (d*x)/2) - 3*a^11*b^2*cos(c/2 + (d*x)/2) - 12*a^2*b^11*sin(c/2 + (d*x)/2) + 30*a^4*b^9*sin(c/2 + (d*x)/2) - 38*a^6*b^7*sin(c/2 + (d*x)/2) + 24*a^8*b^5*sin(c/2 + (d*x)/2) - 6*a^10*b^3*sin(c/2 + (d*x)/2))))*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(b^2*d*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2))","B"
1340,1,1538,133,14.046336,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{a^5\,\cos\left(c+d\,x\right)+a^5}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,a^6\,\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\,d\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b\,\left(a^4\,\sin\left(c+d\,x\right)-6\,a^4\,\cos\left(c+d\,x\right)\,\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)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b^4\,\left(a+a\,\cos\left(c+d\,x\right)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b^2\,\left(2\,a^3\,\cos\left(c+d\,x\right)+2\,a^3\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b^3\,\left(2\,a^2\,\sin\left(c+d\,x\right)-6\,a^2\,\cos\left(c+d\,x\right)\,\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)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b^5\,\left(\sin\left(c+d\,x\right)-2\,\cos\left(c+d\,x\right)\,\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)\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{a^3\,\mathrm{atan}\left(\frac{\left(2\,b^{14}\,\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}-2\,a^{14}\,\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}-2\,a^8\,\sin\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)}^{3/2}-6\,a^3\,b^{11}\,\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}+15\,a^5\,b^9\,\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}-20\,a^7\,b^7\,\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}+15\,a^9\,b^5\,\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}-6\,a^{11}\,b^3\,\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}+3\,a^6\,b^2\,\sin\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)}^{3/2}-13\,a^2\,b^{12}\,\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}+36\,a^4\,b^{10}\,\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}-56\,a^6\,b^8\,\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}+54\,a^8\,b^6\,\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}-33\,a^{10}\,b^4\,\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}+12\,a^{12}\,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^7\,b\,\cos\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)}^{3/2}+a\,b^{13}\,\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}+a^{13}\,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}\right)\,1{}\mathrm{i}}{\left(a^4\,b-2\,a^2\,b^3+b^5\right)\,\left(-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b-6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^2+12\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^3+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^4-19\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^5-38\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^6+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^7+30\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^8-6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^9-12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{10}+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{11}+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{b\,d\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}","Not used",1,"(a^5*cos(c + d*x) + a^5)/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (2*a^6*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b*(a^4*sin(c + d*x) - 6*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (b^4*(a + a*cos(c + d*x)))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b^2*(2*a^3*cos(c + d*x) + 2*a^3))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (b^3*(2*a^2*sin(c + d*x) - 6*a^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b^5*(sin(c + d*x) - 2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/(d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (a^3*atan(((2*b^14*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 2*a^14*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 2*a^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 6*a^3*b^11*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 15*a^5*b^9*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 20*a^7*b^7*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 15*a^9*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 6*a^11*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 3*a^6*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) - 13*a^2*b^12*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 36*a^4*b^10*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 56*a^6*b^8*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 54*a^8*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 33*a^10*b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 12*a^12*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^7*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(3/2) + a*b^13*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + a^13*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))*1i)/((a^4*b + b^5 - 2*a^2*b^3)*(2*b^12*sin(c/2 + (d*x)/2) + a*b^11*cos(c/2 + (d*x)/2) - 3*a^11*b*cos(c/2 + (d*x)/2) - 6*a^3*b^9*cos(c/2 + (d*x)/2) + 15*a^5*b^7*cos(c/2 + (d*x)/2) - 19*a^7*b^5*cos(c/2 + (d*x)/2) + 12*a^9*b^3*cos(c/2 + (d*x)/2) - 12*a^2*b^10*sin(c/2 + (d*x)/2) + 30*a^4*b^8*sin(c/2 + (d*x)/2) - 38*a^6*b^6*sin(c/2 + (d*x)/2) + 24*a^8*b^4*sin(c/2 + (d*x)/2) - 6*a^10*b^2*sin(c/2 + (d*x)/2))))*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(b*d*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2))","B"
1341,1,148,96,11.964435,"\text{Not used}","int(sin(c + d*x)^2/(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\,a^2\,\mathrm{atan}\left(\frac{\frac{a^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^3\,\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\,a^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*a^2*atan(((a^2*(2*a^2*b - 2*b^3))/((a + b)^(3/2)*(a - b)^(3/2)) + (2*a^3*tan(c/2 + (d*x)/2)*(a^2 - b^2))/((a + b)^(3/2)*(a - b)^(3/2)))/(2*a^2)))/(d*(a + b)^(3/2)*(a - b)^(3/2))","B"
1342,1,151,82,12.018793,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{2\,a\,b\,\mathrm{atan}\left(\frac{\frac{a\,b\,\left(2\,a^2\,b-2\,b^3\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}+\frac{2\,a^2\,b\,\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\,a\,b}\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{\frac{2\,a}{a^2-b^2}-\frac{2\,b\,\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)}","Not used",1,"(2*a*b*atan(((a*b*(2*a^2*b - 2*b^3))/((a + b)^(3/2)*(a - b)^(3/2)) + (2*a^2*b*tan(c/2 + (d*x)/2)*(a^2 - b^2))/((a + b)^(3/2)*(a - b)^(3/2)))/(2*a*b)))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - ((2*a)/(a^2 - b^2) - (2*b*tan(c/2 + (d*x)/2))/(a^2 - b^2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
1343,1,659,118,12.882671,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{a^6\,\cos\left(c+d\,x\right)+a^6+a^2\,b^4-2\,a^4\,b^2+a^6\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-b^6\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+a^2\,b^4\,\cos\left(c+d\,x\right)-2\,a^4\,b^2\,\cos\left(c+d\,x\right)+2\,a^3\,b^3\,\sin\left(c+d\,x\right)-a\,b^5\,\sin\left(c+d\,x\right)-a^5\,b\,\sin\left(c+d\,x\right)+3\,a^2\,b^4\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-3\,a^4\,b^2\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+b^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{a^4\,\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}\,1{}\mathrm{i}+b^4\,\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}\,4{}\mathrm{i}-a^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}\,3{}\mathrm{i}+a\,b^3\,\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}\,2{}\mathrm{i}-a^3\,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}\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^2-7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^4+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^5-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^6-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^7}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}\,2{}\mathrm{i}}{a\,d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}","Not used",1,"(a^6*cos(c + d*x) + a^6 + a^2*b^4 - 2*a^4*b^2 + a^6*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - b^6*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + a^2*b^4*cos(c + d*x) - 2*a^4*b^2*cos(c + d*x) + 2*a^3*b^3*sin(c + d*x) - a*b^5*sin(c + d*x) - a^5*b*sin(c + d*x) + b^3*cos(c + d*x)*atan((a^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*1i + b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*4i - a^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)*3i + a*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*2i - a^3*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*1i)/(a^7*cos(c/2 + (d*x)/2) - 4*b^7*sin(c/2 + (d*x)/2) - 2*a*b^6*cos(c/2 + (d*x)/2) + 2*a^6*b*sin(c/2 + (d*x)/2) + 4*a^3*b^4*cos(c/2 + (d*x)/2) - 3*a^5*b^2*cos(c/2 + (d*x)/2) + 9*a^2*b^5*sin(c/2 + (d*x)/2) - 7*a^4*b^3*sin(c/2 + (d*x)/2)))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*2i + 3*a^2*b^4*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - 3*a^4*b^2*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d*cos(c + d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2))","B"
1344,1,778,128,13.681578,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","-\frac{\left(a\,b^6\,1{}\mathrm{i}-a^7\,\cos\left(2\,c+2\,d\,x\right)\,2{}\mathrm{i}-a^3\,b^4\,2{}\mathrm{i}+a^5\,b^2\,1{}\mathrm{i}+a\,b^6\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}-a^6\,b\,\sin\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}-a^2\,b^5\,\sin\left(c+d\,x\right)\,2{}\mathrm{i}+a^4\,b^3\,\sin\left(c+d\,x\right)\,4{}\mathrm{i}-a^3\,b^4\,\cos\left(2\,c+2\,d\,x\right)\,4{}\mathrm{i}+a^5\,b^2\,\cos\left(2\,c+2\,d\,x\right)\,5{}\mathrm{i}+b^7\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}-a^2\,b^5\,\sin\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}+a^4\,b^3\,\sin\left(2\,c+2\,d\,x\right)\,2{}\mathrm{i}-a^6\,b\,\sin\left(c+d\,x\right)\,2{}\mathrm{i}-a^6\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}+2\,b^4\,\sin\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{a^4\,\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}\,1{}\mathrm{i}+b^4\,\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}\,4{}\mathrm{i}-a^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}\,3{}\mathrm{i}+a\,b^3\,\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}\,2{}\mathrm{i}-a^3\,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}\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^2-7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^4+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^5-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^6-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^7}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}-a^2\,b^5\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)\,3{}\mathrm{i}+a^4\,b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^2\,d\,\sin\left(2\,c+2\,d\,x\right)\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}","Not used",1,"-((a*b^6*1i - a^7*cos(2*c + 2*d*x)*2i - a^3*b^4*2i + a^5*b^2*1i + a*b^6*cos(2*c + 2*d*x)*1i - a^6*b*sin(2*c + 2*d*x)*1i - a^2*b^5*sin(c + d*x)*2i + a^4*b^3*sin(c + d*x)*4i - a^3*b^4*cos(2*c + 2*d*x)*4i + a^5*b^2*cos(2*c + 2*d*x)*5i + b^7*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x)*1i - a^2*b^5*sin(2*c + 2*d*x)*1i + a^4*b^3*sin(2*c + 2*d*x)*2i - a^6*b*sin(c + d*x)*2i - a^6*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x)*1i + 2*b^4*sin(2*c + 2*d*x)*atan((a^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*1i + b^4*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*4i - a^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)*3i + a*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*2i - a^3*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2)*1i)/(a^7*cos(c/2 + (d*x)/2) - 4*b^7*sin(c/2 + (d*x)/2) - 2*a*b^6*cos(c/2 + (d*x)/2) + 2*a^6*b*sin(c/2 + (d*x)/2) + 4*a^3*b^4*cos(c/2 + (d*x)/2) - 3*a^5*b^2*cos(c/2 + (d*x)/2) + 9*a^2*b^5*sin(c/2 + (d*x)/2) - 7*a^4*b^3*sin(c/2 + (d*x)/2)))*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - a^2*b^5*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x)*3i + a^4*b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x)*3i)*1i)/(a^2*d*sin(2*c + 2*d*x)*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2))","B"
1345,1,1570,181,15.347666,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{a^5\,\left(\frac{3\,b^3\,\sin\left(c+d\,x\right)}{4}-\frac{5\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{4}\right)-a^7\,\left(\frac{b\,\sin\left(c+d\,x\right)}{2}-\frac{b\,\sin\left(3\,c+3\,d\,x\right)}{2}\right)+a^2\,\left(\frac{b^6}{4}+\frac{b^6\,\cos\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,b^6\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}-\frac{3\,b^6\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{8}\right)-a\,\left(\frac{b^7\,\sin\left(c+d\,x\right)}{4}+\frac{b^7\,\sin\left(3\,c+3\,d\,x\right)}{4}\right)-a^6\,\left(\frac{b^2\,\cos\left(c+d\,x\right)}{2}+\frac{b^2}{4}-\frac{7\,b^2\,\cos\left(2\,c+2\,d\,x\right)}{4}-\frac{b^2\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{7\,b^2\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}-\frac{7\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{8}\right)-a^4\,\left(\frac{b^4}{4}-\frac{b^4\,\cos\left(c+d\,x\right)}{4}+\frac{5\,b^4\,\cos\left(2\,c+2\,d\,x\right)}{4}+\frac{b^4\,\cos\left(3\,c+3\,d\,x\right)}{4}-\frac{3\,b^4\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{3\,b^4\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{8}\right)+a^8\,\left(\frac{\cos\left(c+d\,x\right)}{4}-\frac{3\,\cos\left(2\,c+2\,d\,x\right)}{4}-\frac{\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}-\frac{3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{8}+\frac{1}{4}\right)-\frac{b^8\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{b^8\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+a^3\,b^5\,\sin\left(3\,c+3\,d\,x\right)+\frac{b^5\,\mathrm{atan}\left(\frac{3\,a^6\,\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}+8\,b^6\,\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^3\,b^3\,\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}-7\,a^4\,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}+4\,a\,b^5\,\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}-3\,a^5\,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}}{3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9+6{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b-7{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^2-14{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^3+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^4+4{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^5+5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^6+12{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^7-4{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^8-8{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^9}\right)\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{2}-\frac{b^5\,\mathrm{atan}\left(\frac{3\,a^6\,\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}+8\,b^6\,\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^3\,b^3\,\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}-7\,a^4\,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}+4\,a\,b^5\,\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}-3\,a^5\,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}}{3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9+6{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b-7{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^2-14{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^3+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^4+4{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^5+5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^6+12{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^7-4{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^8-8{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^9}\right)\,\cos\left(c+d\,x\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{2}}{a^3\,d\,\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^2\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}","Not used",1,"(a^5*((3*b^3*sin(c + d*x))/4 - (5*b^3*sin(3*c + 3*d*x))/4) - a^7*((b*sin(c + d*x))/2 - (b*sin(3*c + 3*d*x))/2) + a^2*(b^6/4 + (b^6*cos(2*c + 2*d*x))/4 + (3*b^6*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 - (3*b^6*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/8) - a*((b^7*sin(c + d*x))/4 + (b^7*sin(3*c + 3*d*x))/4) - a^6*((b^2*cos(c + d*x))/2 + b^2/4 - (7*b^2*cos(2*c + 2*d*x))/4 - (b^2*cos(3*c + 3*d*x))/2 + (7*b^2*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 - (7*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/8) - a^4*(b^4/4 - (b^4*cos(c + d*x))/4 + (5*b^4*cos(2*c + 2*d*x))/4 + (b^4*cos(3*c + 3*d*x))/4 - (3*b^4*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (3*b^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/8) + a^8*(cos(c + d*x)/4 - (3*cos(2*c + 2*d*x))/4 - cos(3*c + 3*d*x)/4 + (3*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 - (3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/8 + 1/4) - (b^8*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (b^8*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + a^3*b^5*sin(3*c + 3*d*x) + (b^5*atan((3*a^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 8*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + a^3*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 7*a^4*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 4*a*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 3*a^5*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^9*cos(c/2 + (d*x)/2)*3i - b^9*sin(c/2 + (d*x)/2)*8i - a*b^8*cos(c/2 + (d*x)/2)*4i + a^8*b*sin(c/2 + (d*x)/2)*6i + a^3*b^6*cos(c/2 + (d*x)/2)*5i + a^5*b^4*cos(c/2 + (d*x)/2)*3i - a^7*b^2*cos(c/2 + (d*x)/2)*7i + a^2*b^7*sin(c/2 + (d*x)/2)*12i + a^4*b^5*sin(c/2 + (d*x)/2)*4i - a^6*b^3*sin(c/2 + (d*x)/2)*14i))*cos(3*c + 3*d*x)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/2 - (b^5*atan((3*a^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 8*b^6*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + a^3*b^3*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 7*a^4*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 4*a*b^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 3*a^5*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^9*cos(c/2 + (d*x)/2)*3i - b^9*sin(c/2 + (d*x)/2)*8i - a*b^8*cos(c/2 + (d*x)/2)*4i + a^8*b*sin(c/2 + (d*x)/2)*6i + a^3*b^6*cos(c/2 + (d*x)/2)*5i + a^5*b^4*cos(c/2 + (d*x)/2)*3i - a^7*b^2*cos(c/2 + (d*x)/2)*7i + a^2*b^7*sin(c/2 + (d*x)/2)*12i + a^4*b^5*sin(c/2 + (d*x)/2)*4i - a^6*b^3*sin(c/2 + (d*x)/2)*14i))*cos(c + d*x)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/2)/(a^3*d*cos(c + d*x)*sin(c + d*x)^2*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2))","B"
1346,1,217,126,12.290536,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(2\,a-b\right)}{2\,d\,{\left(a-b\right)}^2}-\frac{\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2-b^2}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2-b^2}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{a^2-b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^3\,\ln\left(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)}{d\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(2\,a+b\right)}{2\,d\,{\left(a+b\right)}^2}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*(2*a - b))/(2*d*(a - b)^2) - ((b*tan(c/2 + (d*x)/2))/(a^2 - b^2) - (2*a*tan(c/2 + (d*x)/2)^2)/(a^2 - b^2) + (b*tan(c/2 + (d*x)/2)^3)/(a^2 - b^2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) - (a^3*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^4 + b^4 - 2*a^2*b^2)) + (log(tan(c/2 + (d*x)/2) - 1)*(2*a + b))/(2*d*(a + b)^2)","B"
1347,1,206,116,12.215805,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2-b^2}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{a^2-b^2}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2-b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{2\,d\,{\left(a+b\right)}^2}+\frac{a^2\,b\,\ln\left(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)}{d\,\left(a^4-2\,a^2\,b^2+b^4\right)}","Not used",1,"((a*tan(c/2 + (d*x)/2))/(a^2 - b^2) + (a*tan(c/2 + (d*x)/2)^3)/(a^2 - b^2) - (2*b*tan(c/2 + (d*x)/2)^2)/(a^2 - b^2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) - (a*log(tan(c/2 + (d*x)/2) + 1))/(2*d*(a - b)^2) + (a*log(tan(c/2 + (d*x)/2) - 1))/(2*d*(a + b)^2) + (a^2*b*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^4 + b^4 - 2*a^2*b^2))","B"
1348,1,208,117,12.114376,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{2\,d\,{\left(a-b\right)}^2}-\frac{\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2-b^2}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2-b^2}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{a^2-b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{2\,d\,{\left(a+b\right)}^2}-\frac{a\,b^2\,\ln\left(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)}{d\,\left(a^4-2\,a^2\,b^2+b^4\right)}","Not used",1,"(b*log(tan(c/2 + (d*x)/2) + 1))/(2*d*(a - b)^2) - ((b*tan(c/2 + (d*x)/2))/(a^2 - b^2) - (2*a*tan(c/2 + (d*x)/2)^2)/(a^2 - b^2) + (b*tan(c/2 + (d*x)/2)^3)/(a^2 - b^2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) - (b*log(tan(c/2 + (d*x)/2) - 1))/(2*d*(a + b)^2) - (a*b^2*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^4 + b^4 - 2*a^2*b^2))","B"
1349,1,170,156,12.416523,"\text{Not used}","int(1/(cos(c + d*x)^3*sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{b}{4\,{\left(a-b\right)}^2}-\frac{1}{2\,\left(a-b\right)}\right)}{d}-\frac{\frac{a}{2\,\left(a^2-b^2\right)}-\frac{b\,\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)\right)}{a\,d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{b}{4\,{\left(a+b\right)}^2}+\frac{1}{2\,\left(a+b\right)}\right)}{d}-\frac{b^4\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{a\,d\,{\left(a^2-b^2\right)}^2}","Not used",1,"(log(sin(c + d*x) + 1)*(b/(4*(a - b)^2) - 1/(2*(a - b))))/d - (a/(2*(a^2 - b^2)) - (b*sin(c + d*x))/(2*(a^2 - b^2)))/(d*(sin(c + d*x)^2 - 1)) + log(sin(c + d*x))/(a*d) - (log(sin(c + d*x) - 1)*(b/(4*(a + b)^2) + 1/(2*(a + b))))/d - (b^4*log(a + b*sin(c + d*x)))/(a*d*(a^2 - b^2)^2)","B"
1350,1,195,171,12.403045,"\text{Not used}","int(1/(cos(c + d*x)^3*sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(3\,a-4\,b\right)}{4\,d\,{\left(a-b\right)}^2}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{b}{4\,{\left(a+b\right)}^2}+\frac{3}{4\,\left(a+b\right)}\right)}{d}-\frac{\frac{1}{a}+\frac{b\,\sin\left(c+d\,x\right)}{2\,\left(a^2-b^2\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(3\,a^2-2\,b^2\right)}{2\,a\,\left(a^2-b^2\right)}}{d\,\left(\sin\left(c+d\,x\right)-{\sin\left(c+d\,x\right)}^3\right)}-\frac{b\,\ln\left(\sin\left(c+d\,x\right)\right)}{a^2\,d}+\frac{b^5\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{a^2\,d\,{\left(a^2-b^2\right)}^2}","Not used",1,"(log(sin(c + d*x) + 1)*(3*a - 4*b))/(4*d*(a - b)^2) - (log(sin(c + d*x) - 1)*(b/(4*(a + b)^2) + 3/(4*(a + b))))/d - (1/a + (b*sin(c + d*x))/(2*(a^2 - b^2)) - (sin(c + d*x)^2*(3*a^2 - 2*b^2))/(2*a*(a^2 - b^2)))/(d*(sin(c + d*x) - sin(c + d*x)^3)) - (b*log(sin(c + d*x)))/(a^2*d) + (b^5*log(a + b*sin(c + d*x)))/(a^2*d*(a^2 - b^2)^2)","B"
1351,1,240,197,12.479274,"\text{Not used}","int(1/(cos(c + d*x)^3*sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{b}{4\,{\left(a-b\right)}^2}-\frac{1}{a-b}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{b}{4\,{\left(a+b\right)}^2}+\frac{1}{a+b}\right)}{d}-\frac{\frac{1}{2\,a}-\frac{b\,\sin\left(c+d\,x\right)}{a^2}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(2\,a^2-b^2\right)}{2\,a\,\left(a^2-b^2\right)}+\frac{b\,{\sin\left(c+d\,x\right)}^3\,\left(3\,a^2-2\,b^2\right)}{2\,a^2\,\left(a^2-b^2\right)}}{d\,\left({\sin\left(c+d\,x\right)}^2-{\sin\left(c+d\,x\right)}^4\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)\right)\,\left(2\,a^2+b^2\right)}{a^3\,d}-\frac{b^6\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}","Not used",1,"(log(sin(c + d*x) + 1)*(b/(4*(a - b)^2) - 1/(a - b)))/d - (log(sin(c + d*x) - 1)*(b/(4*(a + b)^2) + 1/(a + b)))/d - (1/(2*a) - (b*sin(c + d*x))/a^2 - (sin(c + d*x)^2*(2*a^2 - b^2))/(2*a*(a^2 - b^2)) + (b*sin(c + d*x)^3*(3*a^2 - 2*b^2))/(2*a^2*(a^2 - b^2)))/(d*(sin(c + d*x)^2 - sin(c + d*x)^4)) + (log(sin(c + d*x))*(2*a^2 + b^2))/(a^3*d) - (b^6*log(a + b*sin(c + d*x)))/(d*(a^7 + a^3*b^4 - 2*a^5*b^2))","B"
1352,1,372,177,17.427685,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{\frac{2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,\left(5\,a^2\,b-2\,b^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a\,b^2-5\,a^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2\,b-b^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{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\,a^4\,\mathrm{atan}\left(\frac{\frac{a^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^5\,\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\,a^4}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((2*a^3*tan(c/2 + (d*x)/2))/(a^4 + b^4 - 2*a^2*b^2) - (2*(5*a^2*b - 2*b^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (2*a^3*tan(c/2 + (d*x)/2)^5)/(a^4 + b^4 - 2*a^2*b^2) + (4*tan(c/2 + (d*x)/2)^3*(2*a*b^2 - 5*a^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (4*tan(c/2 + (d*x)/2)^2*(2*a^2*b - b^3))/(a^4 + b^4 - 2*a^2*b^2) - (2*a^2*b*tan(c/2 + (d*x)/2)^4)/(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*a^4*atan(((a^4*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a^5*tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(2*a^4)))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
1353,1,370,142,17.158125,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{\frac{2\,\left(2\,a^3+a\,b^2\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{4\,a^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(5\,a^2\,b-2\,b^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{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\,a^3\,b\,\mathrm{atan}\left(\frac{\frac{a^3\,b\,\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^4\,b\,\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\,a^3\,b}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((2*(a*b^2 + 2*a^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) - (4*a^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*(5*a^2*b - 2*b^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) - (2*a^2*b*tan(c/2 + (d*x)/2))/(a^4 + b^4 - 2*a^2*b^2) + (2*a*b^2*tan(c/2 + (d*x)/2)^4)/(a^4 + b^4 - 2*a^2*b^2) - (2*a^2*b*tan(c/2 + (d*x)/2)^5)/(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*a^3*b*atan(((a^3*b*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a^4*b*tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(2*a^3*b)))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
1354,1,375,165,17.402161,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{2\,a^2\,b^2\,\mathrm{atan}\left(\frac{\frac{a^2\,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{2\,a^3\,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}}}{2\,a^2\,b^2}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{2\,\left(2\,a^2\,b+b^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^3+a\,b^2\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{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)}","Not used",1,"(2*a^2*b^2*atan(((a^2*b^2*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a^3*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)))/(2*a^2*b^2)))/(d*(a + b)^(5/2)*(a - b)^(5/2)) - ((2*(2*a^2*b + b^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (2*b^3*tan(c/2 + (d*x)/2)^4)/(a^4 + b^4 - 2*a^2*b^2) + (4*tan(c/2 + (d*x)/2)^3*(a*b^2 + 2*a^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) - (2*a*b^2*tan(c/2 + (d*x)/2))/(a^4 + b^4 - 2*a^2*b^2) - (4*a^2*b*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^2) - (2*a*b^2*tan(c/2 + (d*x)/2)^5)/(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))","B"
1355,1,378,138,17.060871,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{\frac{2\,\left(4\,a\,b^2-a^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a\,b^2-a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^2+b^2\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{4\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{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\,a\,b^3\,\mathrm{atan}\left(\frac{\frac{a\,b^3\,\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^2\,b^3\,\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\,a\,b^3}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((2*(4*a*b^2 - a^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) - (2*b^3*tan(c/2 + (d*x)/2))/(a^4 + b^4 - 2*a^2*b^2) - (2*b^3*tan(c/2 + (d*x)/2)^5)/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(c/2 + (d*x)/2)^4*(2*a*b^2 - a^3))/(a^4 + b^4 - 2*a^2*b^2) + (4*b*tan(c/2 + (d*x)/2)^3*(2*a^2 + b^2))/(3*(a^4 + b^4 - 2*a^2*b^2)) - (4*a*b^2*tan(c/2 + (d*x)/2)^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*a*b^3*atan(((a*b^3*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a^2*b^3*tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(2*a*b^3)))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
1356,1,2162,194,16.202994,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)*(a + b*sin(c + d*x))),x)","-\frac{a^5\,\left(\frac{15\,b^5\,\sin\left(c+d\,x\right)}{4}+\frac{7\,b^5\,\sin\left(3\,c+3\,d\,x\right)}{4}\right)-a^7\,\left(\frac{9\,b^3\,\sin\left(c+d\,x\right)}{4}+\frac{11\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12}\right)-a^3\,\left(\frac{11\,b^7\,\sin\left(c+d\,x\right)}{4}+\frac{17\,b^7\,\sin\left(3\,c+3\,d\,x\right)}{12}\right)+a^9\,\left(\frac{b\,\sin\left(c+d\,x\right)}{2}+\frac{b\,\sin\left(3\,c+3\,d\,x\right)}{6}\right)-a^{10}\,\left(\cos\left(c+d\,x\right)+\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(3\,c+3\,d\,x\right)}{3}+\frac{3\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{5}{6}\right)+a\,\left(\frac{3\,b^9\,\sin\left(c+d\,x\right)}{4}+\frac{5\,b^9\,\sin\left(3\,c+3\,d\,x\right)}{12}\right)-a^2\,\left(\frac{7\,b^8\,\cos\left(c+d\,x\right)}{4}+\frac{4\,b^8}{3}+b^8\,\cos\left(2\,c+2\,d\,x\right)+\frac{7\,b^8\,\cos\left(3\,c+3\,d\,x\right)}{12}+\frac{15\,b^8\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{5\,b^8\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}\right)-a^6\,\left(\frac{33\,b^4\,\cos\left(c+d\,x\right)}{4}+\frac{13\,b^4}{2}+\frac{9\,b^4\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{11\,b^4\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{15\,b^4\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{5\,b^4\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}\right)+a^8\,\left(\frac{19\,b^2\,\cos\left(c+d\,x\right)}{4}+\frac{23\,b^2}{6}+\frac{5\,b^2\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{19\,b^2\,\cos\left(3\,c+3\,d\,x\right)}{12}+\frac{15\,b^2\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{5\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}\right)+a^4\,\left(\frac{25\,b^6\,\cos\left(c+d\,x\right)}{4}+\frac{29\,b^6}{6}+\frac{7\,b^6\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{25\,b^6\,\cos\left(3\,c+3\,d\,x\right)}{12}+\frac{15\,b^6\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{5\,b^6\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}\right)+\frac{3\,b^{10}\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{b^{10}\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{b^5\,\mathrm{atan}\left(\frac{4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-a^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+2\,a\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+a^5\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-2\,a^3\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-5\,a^2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+4\,a^4\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}}{1{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b-5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^2-10{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^3+10{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^4+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^5-11{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^6-24{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^7+7{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^8+15{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^9-2{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{10}-4{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{11}}\right)\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{2}+\frac{b^5\,\mathrm{atan}\left(\frac{4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-a^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+2\,a\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+a^5\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-2\,a^3\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-5\,a^2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+4\,a^4\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}}{1{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b-5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^2-10{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^3+10{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^4+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^5-11{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^6-24{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^7+7{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^8+15{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^9-2{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{10}-4{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{11}}\right)\,\cos\left(c+d\,x\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,3{}\mathrm{i}}{2}}{a\,d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"-(a^5*((15*b^5*sin(c + d*x))/4 + (7*b^5*sin(3*c + 3*d*x))/4) - a^7*((9*b^3*sin(c + d*x))/4 + (11*b^3*sin(3*c + 3*d*x))/12) - a^3*((11*b^7*sin(c + d*x))/4 + (17*b^7*sin(3*c + 3*d*x))/12) + a^9*((b*sin(c + d*x))/2 + (b*sin(3*c + 3*d*x))/6) - a^10*(cos(c + d*x) + cos(2*c + 2*d*x)/2 + cos(3*c + 3*d*x)/3 + (3*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + 5/6) + a*((3*b^9*sin(c + d*x))/4 + (5*b^9*sin(3*c + 3*d*x))/12) - a^2*((7*b^8*cos(c + d*x))/4 + (4*b^8)/3 + b^8*cos(2*c + 2*d*x) + (7*b^8*cos(3*c + 3*d*x))/12 + (15*b^8*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (5*b^8*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4) - a^6*((33*b^4*cos(c + d*x))/4 + (13*b^4)/2 + (9*b^4*cos(2*c + 2*d*x))/2 + (11*b^4*cos(3*c + 3*d*x))/4 + (15*b^4*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (5*b^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2) + a^8*((19*b^2*cos(c + d*x))/4 + (23*b^2)/6 + (5*b^2*cos(2*c + 2*d*x))/2 + (19*b^2*cos(3*c + 3*d*x))/12 + (15*b^2*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (5*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4) + a^4*((25*b^6*cos(c + d*x))/4 + (29*b^6)/6 + (7*b^6*cos(2*c + 2*d*x))/2 + (25*b^6*cos(3*c + 3*d*x))/12 + (15*b^6*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (5*b^6*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2) + (3*b^10*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (b^10*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (b^5*atan((4*b^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - a^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 2*a*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + a^5*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 2*a^3*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 5*a^2*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 4*a^4*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2))/(a^11*cos(c/2 + (d*x)/2)*1i - b^11*sin(c/2 + (d*x)/2)*4i - a*b^10*cos(c/2 + (d*x)/2)*2i + a^10*b*sin(c/2 + (d*x)/2)*2i + a^3*b^8*cos(c/2 + (d*x)/2)*7i - a^5*b^6*cos(c/2 + (d*x)/2)*11i + a^7*b^4*cos(c/2 + (d*x)/2)*10i - a^9*b^2*cos(c/2 + (d*x)/2)*5i + a^2*b^9*sin(c/2 + (d*x)/2)*15i - a^4*b^7*sin(c/2 + (d*x)/2)*24i + a^6*b^5*sin(c/2 + (d*x)/2)*21i - a^8*b^3*sin(c/2 + (d*x)/2)*10i))*cos(3*c + 3*d*x)*(-(a + b)^5*(a - b)^5)^(1/2)*1i)/2 + (b^5*atan((4*b^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - a^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 2*a*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + a^5*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 2*a^3*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 5*a^2*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 4*a^4*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2))/(a^11*cos(c/2 + (d*x)/2)*1i - b^11*sin(c/2 + (d*x)/2)*4i - a*b^10*cos(c/2 + (d*x)/2)*2i + a^10*b*sin(c/2 + (d*x)/2)*2i + a^3*b^8*cos(c/2 + (d*x)/2)*7i - a^5*b^6*cos(c/2 + (d*x)/2)*11i + a^7*b^4*cos(c/2 + (d*x)/2)*10i - a^9*b^2*cos(c/2 + (d*x)/2)*5i + a^2*b^9*sin(c/2 + (d*x)/2)*15i - a^4*b^7*sin(c/2 + (d*x)/2)*24i + a^6*b^5*sin(c/2 + (d*x)/2)*21i - a^8*b^3*sin(c/2 + (d*x)/2)*10i))*cos(c + d*x)*(-(a + b)^5*(a - b)^5)^(1/2)*3i)/2)/(a*d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
1357,1,2317,220,17.384156,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{a\,\left(\frac{3\,b^{10}}{8}+\frac{b^{10}\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{b^{10}\,\cos\left(4\,c+4\,d\,x\right)}{8}\right)-a^{10}\,\left(\frac{7\,b\,\sin\left(c+d\,x\right)}{12}+\frac{b\,\sin\left(2\,c+2\,d\,x\right)}{3}+\frac{b\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{b\,\sin\left(4\,c+4\,d\,x\right)}{6}+\frac{b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(4\,c+4\,d\,x\right)}{8}\right)-a^6\,\left(\frac{17\,b^5\,\sin\left(c+d\,x\right)}{4}+\frac{11\,b^5\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{9\,b^5\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{11\,b^5\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{5\,b^5\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{5\,b^5\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(4\,c+4\,d\,x\right)}{4}\right)-a^2\,\left(\frac{5\,b^9\,\sin\left(c+d\,x\right)}{6}+\frac{7\,b^9\,\sin\left(2\,c+2\,d\,x\right)}{12}+\frac{b^9\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{7\,b^9\,\sin\left(4\,c+4\,d\,x\right)}{24}+\frac{5\,b^9\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{5\,b^9\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(4\,c+4\,d\,x\right)}{8}\right)+a^8\,\left(\frac{31\,b^3\,\sin\left(c+d\,x\right)}{12}+\frac{19\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{12}+\frac{5\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{19\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{24}+\frac{5\,b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{5\,b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(4\,c+4\,d\,x\right)}{8}\right)+a^4\,\left(\frac{37\,b^7\,\sin\left(c+d\,x\right)}{12}+\frac{25\,b^7\,\sin\left(2\,c+2\,d\,x\right)}{12}+\frac{7\,b^7\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{25\,b^7\,\sin\left(4\,c+4\,d\,x\right)}{24}+\frac{5\,b^7\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{5\,b^7\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(4\,c+4\,d\,x\right)}{4}\right)-a^7\,\left(\frac{9\,b^4}{8}+6\,b^4\,\cos\left(2\,c+2\,d\,x\right)+\frac{23\,b^4\,\cos\left(4\,c+4\,d\,x\right)}{8}\right)+a^9\,\left(\frac{b^2}{4}+\frac{19\,b^2\,\cos\left(2\,c+2\,d\,x\right)}{6}+\frac{19\,b^2\,\cos\left(4\,c+4\,d\,x\right)}{12}\right)-a^3\,\left(\frac{11\,b^8}{8}+\frac{8\,b^8\,\cos\left(2\,c+2\,d\,x\right)}{3}+\frac{23\,b^8\,\cos\left(4\,c+4\,d\,x\right)}{24}\right)+a^5\,\left(\frac{15\,b^6}{8}+\frac{17\,b^6\,\cos\left(2\,c+2\,d\,x\right)}{3}+\frac{59\,b^6\,\cos\left(4\,c+4\,d\,x\right)}{24}\right)-a^{11}\,\left(\frac{2\,\cos\left(2\,c+2\,d\,x\right)}{3}+\frac{\cos\left(4\,c+4\,d\,x\right)}{3}\right)+\frac{b^{11}\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{b^{11}\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{b^6\,\mathrm{atan}\left(\frac{4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-a^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+2\,a\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+a^5\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-2\,a^3\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-5\,a^2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+4\,a^4\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}}{1{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b-5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^2-10{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^3+10{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^4+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^5-11{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^6-24{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^7+7{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^8+15{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^9-2{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{10}-4{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{11}}\right)\,\sin\left(2\,c+2\,d\,x\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{2}+\frac{b^6\,\mathrm{atan}\left(\frac{4\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-a^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+2\,a\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+a^5\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-2\,a^3\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-5\,a^2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+4\,a^4\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}}{1{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b-5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^2-10{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^3+10{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^4+21{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^5-11{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^6-24{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^7+7{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^8+15{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^9-2{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{10}-4{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{11}}\right)\,\sin\left(4\,c+4\,d\,x\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{4}}{a^2\,d\,\sin\left(c+d\,x\right)\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"(a*((3*b^10)/8 + (b^10*cos(2*c + 2*d*x))/2 + (b^10*cos(4*c + 4*d*x))/8) - a^10*((7*b*sin(c + d*x))/12 + (b*sin(2*c + 2*d*x))/3 + (b*sin(3*c + 3*d*x))/4 + (b*sin(4*c + 4*d*x))/6 + (b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x))/4 + (b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(4*c + 4*d*x))/8) - a^6*((17*b^5*sin(c + d*x))/4 + (11*b^5*sin(2*c + 2*d*x))/4 + (9*b^5*sin(3*c + 3*d*x))/4 + (11*b^5*sin(4*c + 4*d*x))/8 + (5*b^5*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x))/2 + (5*b^5*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(4*c + 4*d*x))/4) - a^2*((5*b^9*sin(c + d*x))/6 + (7*b^9*sin(2*c + 2*d*x))/12 + (b^9*sin(3*c + 3*d*x))/2 + (7*b^9*sin(4*c + 4*d*x))/24 + (5*b^9*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x))/4 + (5*b^9*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(4*c + 4*d*x))/8) + a^8*((31*b^3*sin(c + d*x))/12 + (19*b^3*sin(2*c + 2*d*x))/12 + (5*b^3*sin(3*c + 3*d*x))/4 + (19*b^3*sin(4*c + 4*d*x))/24 + (5*b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x))/4 + (5*b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(4*c + 4*d*x))/8) + a^4*((37*b^7*sin(c + d*x))/12 + (25*b^7*sin(2*c + 2*d*x))/12 + (7*b^7*sin(3*c + 3*d*x))/4 + (25*b^7*sin(4*c + 4*d*x))/24 + (5*b^7*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x))/2 + (5*b^7*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(4*c + 4*d*x))/4) - a^7*((9*b^4)/8 + 6*b^4*cos(2*c + 2*d*x) + (23*b^4*cos(4*c + 4*d*x))/8) + a^9*(b^2/4 + (19*b^2*cos(2*c + 2*d*x))/6 + (19*b^2*cos(4*c + 4*d*x))/12) - a^3*((11*b^8)/8 + (8*b^8*cos(2*c + 2*d*x))/3 + (23*b^8*cos(4*c + 4*d*x))/24) + a^5*((15*b^6)/8 + (17*b^6*cos(2*c + 2*d*x))/3 + (59*b^6*cos(4*c + 4*d*x))/24) - a^11*((2*cos(2*c + 2*d*x))/3 + cos(4*c + 4*d*x)/3) + (b^11*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(2*c + 2*d*x))/4 + (b^11*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(4*c + 4*d*x))/8 + (b^6*atan((4*b^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - a^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 2*a*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + a^5*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 2*a^3*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 5*a^2*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 4*a^4*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2))/(a^11*cos(c/2 + (d*x)/2)*1i - b^11*sin(c/2 + (d*x)/2)*4i - a*b^10*cos(c/2 + (d*x)/2)*2i + a^10*b*sin(c/2 + (d*x)/2)*2i + a^3*b^8*cos(c/2 + (d*x)/2)*7i - a^5*b^6*cos(c/2 + (d*x)/2)*11i + a^7*b^4*cos(c/2 + (d*x)/2)*10i - a^9*b^2*cos(c/2 + (d*x)/2)*5i + a^2*b^9*sin(c/2 + (d*x)/2)*15i - a^4*b^7*sin(c/2 + (d*x)/2)*24i + a^6*b^5*sin(c/2 + (d*x)/2)*21i - a^8*b^3*sin(c/2 + (d*x)/2)*10i))*sin(2*c + 2*d*x)*(-(a + b)^5*(a - b)^5)^(1/2)*1i)/2 + (b^6*atan((4*b^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - a^6*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 2*a*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + a^5*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 2*a^3*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 5*a^2*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 4*a^4*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2))/(a^11*cos(c/2 + (d*x)/2)*1i - b^11*sin(c/2 + (d*x)/2)*4i - a*b^10*cos(c/2 + (d*x)/2)*2i + a^10*b*sin(c/2 + (d*x)/2)*2i + a^3*b^8*cos(c/2 + (d*x)/2)*7i - a^5*b^6*cos(c/2 + (d*x)/2)*11i + a^7*b^4*cos(c/2 + (d*x)/2)*10i - a^9*b^2*cos(c/2 + (d*x)/2)*5i + a^2*b^9*sin(c/2 + (d*x)/2)*15i - a^4*b^7*sin(c/2 + (d*x)/2)*24i + a^6*b^5*sin(c/2 + (d*x)/2)*21i - a^8*b^3*sin(c/2 + (d*x)/2)*10i))*sin(4*c + 4*d*x)*(-(a + b)^5*(a - b)^5)^(1/2)*1i)/4)/(a^2*d*sin(c + d*x)*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
1358,1,5035,332,18.006624,"\text{Not used}","int(1/(cos(c + d*x)^4*sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{\frac{b^9\,\sin\left(c+d\,x\right)}{24}+\frac{41\,b^9\,\sin\left(3\,c+3\,d\,x\right)}{48}+\frac{23\,b^9\,\sin\left(5\,c+5\,d\,x\right)}{48}}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{a\,\left(\frac{19\,b^8}{48}-\frac{5\,b^8\,\cos\left(c+d\,x\right)}{12}+\frac{17\,b^8\,\cos\left(2\,c+2\,d\,x\right)}{12}+\frac{5\,b^8\,\cos\left(3\,c+3\,d\,x\right)}{24}+\frac{11\,b^8\,\cos\left(4\,c+4\,d\,x\right)}{16}+\frac{5\,b^8\,\cos\left(5\,c+5\,d\,x\right)}{24}-\frac{5\,b^8\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{16}+\frac{5\,b^8\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{32}+\frac{5\,b^8\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{32}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{a^8\,\left(\frac{b\,\sin\left(3\,c+3\,d\,x\right)}{6}-\frac{b\,\sin\left(c+d\,x\right)}{3}+\frac{b\,\sin\left(5\,c+5\,d\,x\right)}{6}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{\frac{3\,b^{10}}{16}+\frac{b^{10}\,\cos\left(2\,c+2\,d\,x\right)}{4}+\frac{b^{10}\,\cos\left(4\,c+4\,d\,x\right)}{16}+\frac{5\,b^{10}\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{16}-\frac{5\,b^{10}\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{32}-\frac{5\,b^{10}\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{32}}{a\,d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{\frac{b^{11}\,\sin\left(c+d\,x\right)}{8}+\frac{3\,b^{11}\,\sin\left(3\,c+3\,d\,x\right)}{16}+\frac{b^{11}\,\sin\left(5\,c+5\,d\,x\right)}{16}}{a^2\,d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{a^6\,\left(\frac{19\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{24}-\frac{4\,b^3\,\sin\left(c+d\,x\right)}{3}+\frac{19\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{24}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{a^4\,\left(\frac{25\,b^5\,\sin\left(3\,c+3\,d\,x\right)}{16}-\frac{15\,b^5\,\sin\left(c+d\,x\right)}{8}+\frac{23\,b^5\,\sin\left(5\,c+5\,d\,x\right)}{16}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{a^2\,\left(\frac{77\,b^7\,\sin\left(3\,c+3\,d\,x\right)}{48}-\frac{23\,b^7\,\sin\left(c+d\,x\right)}{24}+\frac{59\,b^7\,\sin\left(5\,c+5\,d\,x\right)}{48}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{a^9\,\left(\frac{5\,\cos\left(2\,c+2\,d\,x\right)}{12}-\frac{7\,\cos\left(c+d\,x\right)}{24}+\frac{7\,\cos\left(3\,c+3\,d\,x\right)}{48}+\frac{5\,\cos\left(4\,c+4\,d\,x\right)}{16}+\frac{7\,\cos\left(5\,c+5\,d\,x\right)}{48}-\frac{5\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{16}+\frac{5\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{32}+\frac{5\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{32}-\frac{11}{48}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{a^5\,\left(\frac{7\,b^4\,\cos\left(2\,c+2\,d\,x\right)}{2}-b^4-\frac{17\,b^4\,\cos\left(c+d\,x\right)}{8}+\frac{17\,b^4\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{5\,b^4\,\cos\left(4\,c+4\,d\,x\right)}{2}+\frac{17\,b^4\,\cos\left(5\,c+5\,d\,x\right)}{16}-\frac{5\,b^4\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{5\,b^4\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{5\,b^4\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{4}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{a^3\,\left(\frac{19\,b^6\,\cos\left(2\,c+2\,d\,x\right)}{6}-\frac{b^6}{6}-\frac{37\,b^6\,\cos\left(c+d\,x\right)}{24}+\frac{37\,b^6\,\cos\left(3\,c+3\,d\,x\right)}{48}+2\,b^6\,\cos\left(4\,c+4\,d\,x\right)+\frac{37\,b^6\,\cos\left(5\,c+5\,d\,x\right)}{48}-\frac{15\,b^6\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{15\,b^6\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{15\,b^6\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{16}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{a^7\,\left(\frac{23\,b^2\,\cos\left(2\,c+2\,d\,x\right)}{12}-\frac{41\,b^2}{48}-\frac{31\,b^2\,\cos\left(c+d\,x\right)}{24}+\frac{31\,b^2\,\cos\left(3\,c+3\,d\,x\right)}{48}+\frac{23\,b^2\,\cos\left(4\,c+4\,d\,x\right)}{16}+\frac{31\,b^2\,\cos\left(5\,c+5\,d\,x\right)}{48}-\frac{23\,b^2\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{16}+\frac{23\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{32}+\frac{23\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{32}\right)}{d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{b^{12}\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{16\,a^3\,d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{b^{12}\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{16\,a^3\,d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{b^{12}\,\cos\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8\,a^3\,d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{b^7\,\mathrm{atan}\left(\frac{8\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-5\,a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+4\,a\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+5\,a^7\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+a^3\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-8\,a^5\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-17\,a^4\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+18\,a^6\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}}{5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}+10{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b-23{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2-46{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+40{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+80{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-30{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-58{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+20{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-4{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-8{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,\cos\left(c+d\,x\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{4\,a^3\,d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{b^7\,\mathrm{atan}\left(\frac{8\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-5\,a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+4\,a\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+5\,a^7\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+a^3\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-8\,a^5\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-17\,a^4\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+18\,a^6\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}}{5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}+10{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b-23{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2-46{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+40{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+80{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-30{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-58{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+20{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-4{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-8{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{8\,a^3\,d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{b^7\,\mathrm{atan}\left(\frac{8\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-5\,a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+4\,a\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+5\,a^7\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+a^3\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-8\,a^5\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}-17\,a^4\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}+18\,a^6\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^{10}+5\,a^8\,b^2-10\,a^6\,b^4+10\,a^4\,b^6-5\,a^2\,b^8+b^{10}}}{5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}+10{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b-23{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2-46{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+40{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+80{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-30{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-58{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+3{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+9{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+20{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}-4{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^{12}-8{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{13}}\right)\,\cos\left(5\,c+5\,d\,x\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{8\,a^3\,d\,{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"((b^9*sin(c + d*x))/24 + (41*b^9*sin(3*c + 3*d*x))/48 + (23*b^9*sin(5*c + 5*d*x))/48)/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (a*((19*b^8)/48 - (5*b^8*cos(c + d*x))/12 + (17*b^8*cos(2*c + 2*d*x))/12 + (5*b^8*cos(3*c + 3*d*x))/24 + (11*b^8*cos(4*c + 4*d*x))/16 + (5*b^8*cos(5*c + 5*d*x))/24 - (5*b^8*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/16 + (5*b^8*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/32 + (5*b^8*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/32))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (a^8*((b*sin(3*c + 3*d*x))/6 - (b*sin(c + d*x))/3 + (b*sin(5*c + 5*d*x))/6))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + ((3*b^10)/16 + (b^10*cos(2*c + 2*d*x))/4 + (b^10*cos(4*c + 4*d*x))/16 + (5*b^10*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/16 - (5*b^10*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/32 - (5*b^10*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/32)/(a*d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - ((b^11*sin(c + d*x))/8 + (3*b^11*sin(3*c + 3*d*x))/16 + (b^11*sin(5*c + 5*d*x))/16)/(a^2*d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (a^6*((19*b^3*sin(3*c + 3*d*x))/24 - (4*b^3*sin(c + d*x))/3 + (19*b^3*sin(5*c + 5*d*x))/24))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (a^4*((25*b^5*sin(3*c + 3*d*x))/16 - (15*b^5*sin(c + d*x))/8 + (23*b^5*sin(5*c + 5*d*x))/16))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (a^2*((77*b^7*sin(3*c + 3*d*x))/48 - (23*b^7*sin(c + d*x))/24 + (59*b^7*sin(5*c + 5*d*x))/48))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (a^9*((5*cos(2*c + 2*d*x))/12 - (7*cos(c + d*x))/24 + (7*cos(3*c + 3*d*x))/48 + (5*cos(4*c + 4*d*x))/16 + (7*cos(5*c + 5*d*x))/48 - (5*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/16 + (5*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/32 + (5*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/32 - 11/48))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (a^5*((7*b^4*cos(2*c + 2*d*x))/2 - b^4 - (17*b^4*cos(c + d*x))/8 + (17*b^4*cos(3*c + 3*d*x))/16 + (5*b^4*cos(4*c + 4*d*x))/2 + (17*b^4*cos(5*c + 5*d*x))/16 - (5*b^4*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (5*b^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (5*b^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/4))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (a^3*((19*b^6*cos(2*c + 2*d*x))/6 - b^6/6 - (37*b^6*cos(c + d*x))/24 + (37*b^6*cos(3*c + 3*d*x))/48 + 2*b^6*cos(4*c + 4*d*x) + (37*b^6*cos(5*c + 5*d*x))/48 - (15*b^6*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (15*b^6*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/16 + (15*b^6*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/16))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (a^7*((23*b^2*cos(2*c + 2*d*x))/12 - (41*b^2)/48 - (31*b^2*cos(c + d*x))/24 + (31*b^2*cos(3*c + 3*d*x))/48 + (23*b^2*cos(4*c + 4*d*x))/16 + (31*b^2*cos(5*c + 5*d*x))/48 - (23*b^2*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/16 + (23*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/32 + (23*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/32))/(d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (b^12*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/(16*a^3*d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (b^12*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/(16*a^3*d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (b^12*cos(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(8*a^3*d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (b^7*atan((8*b^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 5*a^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 4*a*b^7*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 5*a^7*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + a^3*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 8*a^5*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 17*a^4*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 18*a^6*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2))/(a^13*cos(c/2 + (d*x)/2)*5i - b^13*sin(c/2 + (d*x)/2)*8i - a*b^12*cos(c/2 + (d*x)/2)*4i + a^12*b*sin(c/2 + (d*x)/2)*10i + a^3*b^10*cos(c/2 + (d*x)/2)*9i + a^5*b^8*cos(c/2 + (d*x)/2)*3i - a^7*b^6*cos(c/2 + (d*x)/2)*30i + a^9*b^4*cos(c/2 + (d*x)/2)*40i - a^11*b^2*cos(c/2 + (d*x)/2)*23i + a^2*b^11*sin(c/2 + (d*x)/2)*20i + a^4*b^9*sin(c/2 + (d*x)/2)*2i - a^6*b^7*sin(c/2 + (d*x)/2)*58i + a^8*b^5*sin(c/2 + (d*x)/2)*80i - a^10*b^3*sin(c/2 + (d*x)/2)*46i))*cos(c + d*x)*(-(a + b)^5*(a - b)^5)^(1/2)*1i)/(4*a^3*d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (b^7*atan((8*b^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 5*a^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 4*a*b^7*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 5*a^7*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + a^3*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 8*a^5*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 17*a^4*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 18*a^6*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2))/(a^13*cos(c/2 + (d*x)/2)*5i - b^13*sin(c/2 + (d*x)/2)*8i - a*b^12*cos(c/2 + (d*x)/2)*4i + a^12*b*sin(c/2 + (d*x)/2)*10i + a^3*b^10*cos(c/2 + (d*x)/2)*9i + a^5*b^8*cos(c/2 + (d*x)/2)*3i - a^7*b^6*cos(c/2 + (d*x)/2)*30i + a^9*b^4*cos(c/2 + (d*x)/2)*40i - a^11*b^2*cos(c/2 + (d*x)/2)*23i + a^2*b^11*sin(c/2 + (d*x)/2)*20i + a^4*b^9*sin(c/2 + (d*x)/2)*2i - a^6*b^7*sin(c/2 + (d*x)/2)*58i + a^8*b^5*sin(c/2 + (d*x)/2)*80i - a^10*b^3*sin(c/2 + (d*x)/2)*46i))*cos(3*c + 3*d*x)*(-(a + b)^5*(a - b)^5)^(1/2)*1i)/(8*a^3*d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (b^7*atan((8*b^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 5*a^8*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 4*a*b^7*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 5*a^7*b*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + a^3*b^5*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 8*a^5*b^3*cos(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) - 17*a^4*b^4*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2) + 18*a^6*b^2*sin(c/2 + (d*x)/2)*(b^10 - a^10 - 5*a^2*b^8 + 10*a^4*b^6 - 10*a^6*b^4 + 5*a^8*b^2)^(1/2))/(a^13*cos(c/2 + (d*x)/2)*5i - b^13*sin(c/2 + (d*x)/2)*8i - a*b^12*cos(c/2 + (d*x)/2)*4i + a^12*b*sin(c/2 + (d*x)/2)*10i + a^3*b^10*cos(c/2 + (d*x)/2)*9i + a^5*b^8*cos(c/2 + (d*x)/2)*3i - a^7*b^6*cos(c/2 + (d*x)/2)*30i + a^9*b^4*cos(c/2 + (d*x)/2)*40i - a^11*b^2*cos(c/2 + (d*x)/2)*23i + a^2*b^11*sin(c/2 + (d*x)/2)*20i + a^4*b^9*sin(c/2 + (d*x)/2)*2i - a^6*b^7*sin(c/2 + (d*x)/2)*58i + a^8*b^5*sin(c/2 + (d*x)/2)*80i - a^10*b^3*sin(c/2 + (d*x)/2)*46i))*cos(5*c + 5*d*x)*(-(a + b)^5*(a - b)^5)^(1/2)*1i)/(8*a^3*d*sin(c + d*x)^2*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^4 + b^4 - 2*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
1359,1,806,240,14.185333,"\text{Not used}","int(sin(c + d*x)^8/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}+\frac{13\,b}{8\,{\left(a-b\right)}^2}+\frac{35}{8\,\left(a-b\right)}\right)}{d}-\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-3\,a^4+a^2\,b^2+b^4\right)}{b\,{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^4-5\,a^2\,b^2+3\,b^4\right)}{b\,{\left(a^2-b^2\right)}^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(8\,a^5+7\,a^3\,b^2-11\,a\,b^4\right)}{2\,b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(8\,a^5+7\,a^3\,b^2-11\,a\,b^4\right)}{2\,b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(8\,a^5-27\,a^3\,b^2+15\,a\,b^4\right)}{4\,b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(24\,a^5-45\,a^3\,b^2+25\,a\,b^4\right)}{4\,b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(24\,a^5-45\,a^3\,b^2+25\,a\,b^4\right)}{4\,b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2-3\,b^2\right)}{b\,\left(a^2-b^2\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(2\,a^2-3\,b^2\right)}{b\,\left(a^2-b^2\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^4-5\,a^2\,b^2+3\,b^4\right)}{b\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^4-27\,a^2\,b^2+15\,b^4\right)}{4\,b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{35}{8\,\left(a+b\right)}-\frac{13\,b}{8\,{\left(a+b\right)}^2}+\frac{b^2}{4\,{\left(a+b\right)}^3}\right)}{d}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2+3\,b^2\right)}{b^3\,d}+\frac{a^8\,\ln\left(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)}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*(b^2/(4*(a - b)^3) + (13*b)/(8*(a - b)^2) + 35/(8*(a - b))))/d - ((4*tan(c/2 + (d*x)/2)^6*(b^4 - 3*a^4 + a^2*b^2))/(b*(a^2 - b^2)^2) - (2*tan(c/2 + (d*x)/2)^2*(a^4 + 3*b^4 - 5*a^2*b^2))/(b*(a^2 - b^2)^2) + (tan(c/2 + (d*x)/2)^5*(8*a^5 - 11*a*b^4 + 7*a^3*b^2))/(2*b^2*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^7*(8*a^5 - 11*a*b^4 + 7*a^3*b^2))/(2*b^2*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^11*(15*a*b^4 + 8*a^5 - 27*a^3*b^2))/(4*b^2*(a^4 + b^4 - 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^3*(25*a*b^4 + 24*a^5 - 45*a^3*b^2))/(4*b^2*(a^4 + b^4 - 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^9*(25*a*b^4 + 24*a^5 - 45*a^3*b^2))/(4*b^2*(a^4 + b^4 - 2*a^2*b^2)) + (4*tan(c/2 + (d*x)/2)^4*(2*a^2 - 3*b^2))/(b*(a^2 - b^2)) + (4*tan(c/2 + (d*x)/2)^8*(2*a^2 - 3*b^2))/(b*(a^2 - b^2)) - (2*tan(c/2 + (d*x)/2)^10*(a^4 + 3*b^4 - 5*a^2*b^2))/(b*(a^4 + b^4 - 2*a^2*b^2)) + (a*tan(c/2 + (d*x)/2)*(8*a^4 + 15*b^4 - 27*a^2*b^2))/(4*b^2*(a^4 + b^4 - 2*a^2*b^2)))/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 2*tan(c/2 + (d*x)/2)^10 - tan(c/2 + (d*x)/2)^12 - 1)) - (log(tan(c/2 + (d*x)/2) - 1)*(35/(8*(a + b)) - (13*b)/(8*(a + b)^2) + b^2/(4*(a + b)^3)))/d + (log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 + 3*b^2))/(b^3*d) + (a^8*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
1360,1,627,221,14.068448,"\text{Not used}","int(sin(c + d*x)^7/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}+\frac{11\,b}{8\,{\left(a-b\right)}^2}+\frac{3}{a-b}\right)}{d}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a\,b^2-4\,a^3\right)}{{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a\,b^2-2\,a^3\right)}{{\left(a^2-b^2\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a\,b^2-4\,a^3\right)}{{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a\,b^2-2\,a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(24\,a^4-29\,a^2\,b^2+9\,b^4\right)}{2\,b\,{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^2-5\,b^2\right)}{b\,\left(a^2-b^2\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,a^2-5\,b^2\right)}{b\,\left(a^2-b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^4-27\,a^2\,b^2+15\,b^4\right)}{4\,b\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(8\,a^4-27\,a^2\,b^2+15\,b^4\right)}{4\,b\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\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+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\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{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{3}{a+b}-\frac{11\,b}{8\,{\left(a+b\right)}^2}+\frac{b^2}{4\,{\left(a+b\right)}^3}\right)}{d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b^2\,d}-\frac{a^7\,\ln\left(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)}{d\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"- (log(tan(c/2 + (d*x)/2) + 1)*(b^2/(4*(a - b)^3) + (11*b)/(8*(a - b)^2) + 3/(a - b)))/d - ((2*tan(c/2 + (d*x)/2)^4*(3*a*b^2 - 4*a^3))/(a^2 - b^2)^2 - (2*tan(c/2 + (d*x)/2)^2*(a*b^2 - 2*a^3))/(a^2 - b^2)^2 + (2*tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 4*a^3))/(a^2 - b^2)^2 - (2*tan(c/2 + (d*x)/2)^8*(a*b^2 - 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) + (tan(c/2 + (d*x)/2)^5*(24*a^4 + 9*b^4 - 29*a^2*b^2))/(2*b*(a^2 - b^2)^2) - (2*tan(c/2 + (d*x)/2)^3*(4*a^2 - 5*b^2))/(b*(a^2 - b^2)) - (2*tan(c/2 + (d*x)/2)^7*(4*a^2 - 5*b^2))/(b*(a^2 - b^2)) + (tan(c/2 + (d*x)/2)*(8*a^4 + 15*b^4 - 27*a^2*b^2))/(4*b*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^9*(8*a^4 + 15*b^4 - 27*a^2*b^2))/(4*b*(a^4 + b^4 - 2*a^2*b^2)))/(d*(2*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (log(tan(c/2 + (d*x)/2) - 1)*(3/(a + b) - (11*b)/(8*(a + b)^2) + b^2/(4*(a + b)^3)))/d - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/(b^2*d) - (a^7*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))","B"
1361,1,549,208,13.380869,"\text{Not used}","int(sin(c + d*x)^6/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}+\frac{9\,b}{8\,{\left(a-b\right)}^2}+\frac{15}{8\,\left(a-b\right)}\right)}{d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(11\,a\,b^2-15\,a^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(3\,a\,b^2-7\,a^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(11\,a\,b^2-15\,a^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2\,b-b^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^2\,b-2\,b^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2\,b-b^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^2-3\,b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{b\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{15}{8\,\left(a+b\right)}-\frac{9\,b}{8\,{\left(a+b\right)}^2}+\frac{b^2}{4\,{\left(a+b\right)}^3}\right)}{d}-\frac{a^6\,\ln\left(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)}{d\,\left(a^6\,b-3\,a^4\,b^3+3\,a^2\,b^5-b^7\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*(b^2/(4*(a - b)^3) + (9*b)/(8*(a - b)^2) + 15/(8*(a - b))))/d - ((tan(c/2 + (d*x)/2)^3*(11*a*b^2 - 15*a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^7*(3*a*b^2 - 7*a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(11*a*b^2 - 15*a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (2*tan(c/2 + (d*x)/2)^2*(2*a^2*b - b^3))/(a^4 + b^4 - 2*a^2*b^2) + (4*tan(c/2 + (d*x)/2)^4*(3*a^2*b - 2*b^3))/(a^4 + b^4 - 2*a^2*b^2) - (2*tan(c/2 + (d*x)/2)^6*(2*a^2*b - b^3))/(a^4 + b^4 - 2*a^2*b^2) + (a*tan(c/2 + (d*x)/2)*(7*a^2 - 3*b^2))/(4*(a^4 + b^4 - 2*a^2*b^2)))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + log(tan(c/2 + (d*x)/2)^2 + 1)/(b*d) - (log(tan(c/2 + (d*x)/2) - 1)*(15/(8*(a + b)) - (9*b)/(8*(a + b)^2) + b^2/(4*(a + b)^3)))/d - (a^6*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^6*b - b^7 + 3*a^2*b^5 - 3*a^4*b^3))","B"
1362,1,498,204,12.541546,"\text{Not used}","int(sin(c + d*x)^5/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{a^5\,\ln\left(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)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{1}{a+b}-\frac{7\,b}{8\,{\left(a+b\right)}^2}+\frac{b^2}{4\,{\left(a+b\right)}^3}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}+\frac{7\,b}{8\,{\left(a-b\right)}^2}+\frac{1}{a-b}\right)}{d}-\frac{\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a\,b^2-2\,a^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(7\,a^2\,b-3\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(15\,a^2\,b-11\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(15\,a^2\,b-11\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^2-3\,b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^5*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (log(tan(c/2 + (d*x)/2) - 1)*(1/(a + b) - (7*b)/(8*(a + b)^2) + b^2/(4*(a + b)^3)))/d - (log(tan(c/2 + (d*x)/2) + 1)*(b^2/(4*(a - b)^3) + (7*b)/(8*(a - b)^2) + 1/(a - b)))/d - ((2*a^3*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^2) + (2*a^3*tan(c/2 + (d*x)/2)^6)/(a^4 + b^4 - 2*a^2*b^2) + (4*tan(c/2 + (d*x)/2)^4*(a*b^2 - 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) - (tan(c/2 + (d*x)/2)^7*(7*a^2*b - 3*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^3*(15*a^2*b - 11*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(15*a^2*b - 11*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (b*tan(c/2 + (d*x)/2)*(7*a^2 - 3*b^2))/(4*(a^4 + b^4 - 2*a^2*b^2)))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
1363,1,507,190,12.454904,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}+\frac{5\,b}{8\,{\left(a-b\right)}^2}+\frac{3}{8\,\left(a-b\right)}\right)}{d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(3\,a^3+a\,b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(7\,a\,b^2-11\,a^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(7\,a\,b^2-11\,a^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2\,b-b^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{a^4-2\,a^2\,b^2+b^4}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2+b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{3}{8\,\left(a+b\right)}-\frac{5\,b}{8\,{\left(a+b\right)}^2}+\frac{b^2}{4\,{\left(a+b\right)}^3}\right)}{d}-\frac{a^4\,b\,\ln\left(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)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*(b^2/(4*(a - b)^3) + (5*b)/(8*(a - b)^2) + 3/(8*(a - b))))/d - ((tan(c/2 + (d*x)/2)^7*(a*b^2 + 3*a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^3*(7*a*b^2 - 11*a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(7*a*b^2 - 11*a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (4*tan(c/2 + (d*x)/2)^4*(2*a^2*b - b^3))/(a^4 + b^4 - 2*a^2*b^2) - (2*a^2*b*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^2) - (2*a^2*b*tan(c/2 + (d*x)/2)^6)/(a^4 + b^4 - 2*a^2*b^2) + (a*tan(c/2 + (d*x)/2)*(3*a^2 + b^2))/(4*(a^4 + b^4 - 2*a^2*b^2)))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (log(tan(c/2 + (d*x)/2) - 1)*(3/(8*(a + b)) - (5*b)/(8*(a + b)^2) + b^2/(4*(a + b)^3)))/d - (a^4*b*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
1364,1,471,182,12.447662,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(3\,a+b\right)}{8\,d\,{\left(a+b\right)}^3}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(11\,a^2\,b-7\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^4-2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(3\,a^2\,b+b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(11\,a^2\,b-7\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{a^4-2\,a^2\,b^2+b^4}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2+b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}+\frac{3\,b}{8\,{\left(a-b\right)}^2}\right)}{d}+\frac{a^3\,b^2\,\ln\left(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)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"(b*log(tan(c/2 + (d*x)/2) - 1)*(3*a + b))/(8*d*(a + b)^3) - ((tan(c/2 + (d*x)/2)^3*(11*a^2*b - 7*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (4*a^3*tan(c/2 + (d*x)/2)^4)/(a^4 + b^4 - 2*a^2*b^2) - (tan(c/2 + (d*x)/2)^7*(3*a^2*b + b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(11*a^2*b - 7*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (2*a*b^2*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^2) + (2*a*b^2*tan(c/2 + (d*x)/2)^6)/(a^4 + b^4 - 2*a^2*b^2) - (b*tan(c/2 + (d*x)/2)*(3*a^2 + b^2))/(4*(a^4 + b^4 - 2*a^2*b^2)))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (log(tan(c/2 + (d*x)/2) + 1)*(b^2/(4*(a - b)^3) + (3*b)/(8*(a - b)^2)))/d + (a^3*b^2*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
1365,1,498,178,12.514657,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}+\frac{b}{8\,{\left(a-b\right)}^2}-\frac{1}{8\,\left(a-b\right)}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{b}{8\,{\left(a+b\right)}^2}+\frac{1}{8\,\left(a+b\right)}-\frac{b^2}{4\,{\left(a+b\right)}^3}\right)}{d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a\,b^2-7\,a^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(5\,a\,b^2-a^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a\,b^2-7\,a^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^4-2\,a^2\,b^2+b^4}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-5\,b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^2\,b^3\,\ln\left(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)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*(b^2/(4*(a - b)^3) + b/(8*(a - b)^2) - 1/(8*(a - b))))/d + (log(tan(c/2 + (d*x)/2) - 1)*(b/(8*(a + b)^2) + 1/(8*(a + b)) - b^2/(4*(a + b)^3)))/d - ((tan(c/2 + (d*x)/2)^3*(3*a*b^2 - 7*a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (2*b^3*tan(c/2 + (d*x)/2)^6)/(a^4 + b^4 - 2*a^2*b^2) - (2*b^3*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^2) + (tan(c/2 + (d*x)/2)^7*(5*a*b^2 - a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(3*a*b^2 - 7*a^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (4*a^2*b*tan(c/2 + (d*x)/2)^4)/(a^4 + b^4 - 2*a^2*b^2) - (a*tan(c/2 + (d*x)/2)*(a^2 - 5*b^2))/(4*(a^4 + b^4 - 2*a^2*b^2)))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (a^2*b^3*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
1366,1,483,177,12.402056,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{a\,b^4\,\ln\left(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)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a\,b^2-a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a\,b^2-a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a^2\,b-5\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(7\,a^2\,b-3\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(7\,a^2\,b-3\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{4\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^4-2\,a^2\,b^2+b^4}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-5\,b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{b}{8\,{\left(a+b\right)}^2}+\frac{b^2}{4\,{\left(a+b\right)}^3}\right)}{d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a-3\,b\right)}{8\,d\,{\left(a-b\right)}^3}","Not used",1,"(a*b^4*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - ((2*tan(c/2 + (d*x)/2)^2*(2*a*b^2 - a^3))/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(c/2 + (d*x)/2)^6*(2*a*b^2 - a^3))/(a^4 + b^4 - 2*a^2*b^2) + (tan(c/2 + (d*x)/2)^7*(a^2*b - 5*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^3*(7*a^2*b - 3*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(7*a^2*b - 3*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (4*a*b^2*tan(c/2 + (d*x)/2)^4)/(a^4 + b^4 - 2*a^2*b^2) + (b*tan(c/2 + (d*x)/2)*(a^2 - 5*b^2))/(4*(a^4 + b^4 - 2*a^2*b^2)))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (log(tan(c/2 + (d*x)/2) - 1)*(b/(8*(a + b)^2) + b^2/(4*(a + b)^3)))/d + (b*log(tan(c/2 + (d*x)/2) + 1)*(a - 3*b))/(8*d*(a - b)^3)","B"
1367,1,346,233,12.427801,"\text{Not used}","int(1/(cos(c + d*x)^5*sin(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)\right)}{a\,d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{5\,b}{16\,{\left(a+b\right)}^2}+\frac{1}{2\,\left(a+b\right)}+\frac{b^2}{8\,{\left(a+b\right)}^3}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{b^2}{8\,{\left(a-b\right)}^3}-\frac{5\,b}{16\,{\left(a-b\right)}^2}+\frac{1}{2\,\left(a-b\right)}\right)}{d}-\frac{\frac{5\,a\,b^2-3\,a^3}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(2\,a\,b^2-a^3\right)}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(3\,a^2\,b-7\,b^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,\sin\left(c+d\,x\right)\,\left(5\,a^2-9\,b^2\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^6\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6\right)}","Not used",1,"log(sin(c + d*x))/(a*d) - (log(sin(c + d*x) - 1)*((5*b)/(16*(a + b)^2) + 1/(2*(a + b)) + b^2/(8*(a + b)^3)))/d - (log(sin(c + d*x) + 1)*(b^2/(8*(a - b)^3) - (5*b)/(16*(a - b)^2) + 1/(2*(a - b))))/d - ((5*a*b^2 - 3*a^3)/(4*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^2*(2*a*b^2 - a^3))/(2*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^3*(3*a^2*b - 7*b^3))/(8*(a^4 + b^4 - 2*a^2*b^2)) + (b*sin(c + d*x)*(5*a^2 - 9*b^2))/(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^6*log(a + b*sin(c + d*x)))/(d*(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))","B"
1368,1,373,250,12.473101,"\text{Not used}","int(1/(cos(c + d*x)^5*sin(c + d*x)^2*(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{7\,b}{16\,{\left(a-b\right)}^2}+\frac{15}{16\,\left(a-b\right)}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{7\,b}{16\,{\left(a+b\right)}^2}+\frac{15}{16\,\left(a+b\right)}+\frac{b^2}{8\,{\left(a+b\right)}^3}\right)}{d}-\frac{\frac{1}{a}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(a^2\,b-2\,b^3\right)}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\sin\left(c+d\,x\right)\,\left(3\,a^2\,b-5\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\sin\left(c+d\,x\right)}^4\,\left(15\,a^4-27\,a^2\,b^2+8\,b^4\right)}{8\,a\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(25\,a^4-45\,a^2\,b^2+16\,b^4\right)}{8\,a\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\sin\left(c+d\,x\right)}^5-2\,{\sin\left(c+d\,x\right)}^3+\sin\left(c+d\,x\right)\right)}-\frac{b\,\ln\left(\sin\left(c+d\,x\right)\right)}{a^2\,d}-\frac{b^7\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"(log(sin(c + d*x) + 1)*(b^2/(8*(a - b)^3) - (7*b)/(16*(a - b)^2) + 15/(16*(a - b))))/d - (log(sin(c + d*x) - 1)*((7*b)/(16*(a + b)^2) + 15/(16*(a + b)) + b^2/(8*(a + b)^3)))/d - (1/a - (sin(c + d*x)^3*(a^2*b - 2*b^3))/(2*(a^4 + b^4 - 2*a^2*b^2)) + (sin(c + d*x)*(3*a^2*b - 5*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (sin(c + d*x)^4*(15*a^4 + 8*b^4 - 27*a^2*b^2))/(8*a*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^2*(25*a^4 + 16*b^4 - 45*a^2*b^2))/(8*a*(a^4 + b^4 - 2*a^2*b^2)))/(d*(sin(c + d*x) - 2*sin(c + d*x)^3 + sin(c + d*x)^5)) - (b*log(sin(c + d*x)))/(a^2*d) - (b^7*log(a + b*sin(c + d*x)))/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))","B"
1369,1,412,274,12.698762,"\text{Not used}","int(1/(cos(c + d*x)^5*sin(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)\right)\,\left(3\,a^2+b^2\right)}{a^3\,d}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{b^2}{8\,{\left(a-b\right)}^3}-\frac{9\,b}{16\,{\left(a-b\right)}^2}+\frac{3}{2\,\left(a-b\right)}\right)}{d}-\frac{\frac{1}{2\,a}-\frac{b\,\sin\left(c+d\,x\right)}{a^2}+\frac{{\sin\left(c+d\,x\right)}^4\,\left(3\,a^4-5\,a^2\,b^2+b^4\right)}{2\,a\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(9\,a^4-15\,a^2\,b^2+4\,b^4\right)}{4\,a\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^5\,\left(15\,a^4\,b-27\,a^2\,b^3+8\,b^5\right)}{8\,a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\sin\left(c+d\,x\right)}^3\,\left(25\,a^4\,b-45\,a^2\,b^3+16\,b^5\right)}{8\,a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\sin\left(c+d\,x\right)}^6-2\,{\sin\left(c+d\,x\right)}^4+{\sin\left(c+d\,x\right)}^2\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{9\,b}{16\,{\left(a+b\right)}^2}+\frac{3}{2\,\left(a+b\right)}+\frac{b^2}{8\,{\left(a+b\right)}^3}\right)}{d}+\frac{b^8\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"(log(sin(c + d*x))*(3*a^2 + b^2))/(a^3*d) - (log(sin(c + d*x) + 1)*(b^2/(8*(a - b)^3) - (9*b)/(16*(a - b)^2) + 3/(2*(a - b))))/d - (1/(2*a) - (b*sin(c + d*x))/a^2 + (sin(c + d*x)^4*(3*a^4 + b^4 - 5*a^2*b^2))/(2*a*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^2*(9*a^4 + 4*b^4 - 15*a^2*b^2))/(4*a*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^5*(15*a^4*b + 8*b^5 - 27*a^2*b^3))/(8*a^2*(a^4 + b^4 - 2*a^2*b^2)) + (sin(c + d*x)^3*(25*a^4*b + 16*b^5 - 45*a^2*b^3))/(8*a^2*(a^4 + b^4 - 2*a^2*b^2)))/(d*(sin(c + d*x)^2 - 2*sin(c + d*x)^4 + sin(c + d*x)^6)) - (log(sin(c + d*x) - 1)*((9*b)/(16*(a + b)^2) + 3/(2*(a + b)) + b^2/(8*(a + b)^3)))/d + (b^8*log(a + b*sin(c + d*x)))/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
1370,0,-1,500,0.000000,"\text{Not used}","int((sin(e + f*x)^4*(g*cos(e + f*x))^(1/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\sin\left(e+f\,x\right)}^4\,\sqrt{g\,\cos\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)^4*(g*cos(e + f*x))^(1/2))/(a + b*sin(e + f*x)), x)","F"
1371,0,-1,448,0.000000,"\text{Not used}","int((sin(e + f*x)^3*(g*cos(e + f*x))^(1/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\sin\left(e+f\,x\right)}^3\,\sqrt{g\,\cos\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)^3*(g*cos(e + f*x))^(1/2))/(a + b*sin(e + f*x)), x)","F"
1372,0,-1,369,0.000000,"\text{Not used}","int((sin(e + f*x)^2*(g*cos(e + f*x))^(1/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\sin\left(e+f\,x\right)}^2\,\sqrt{g\,\cos\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)^2*(g*cos(e + f*x))^(1/2))/(a + b*sin(e + f*x)), x)","F"
1373,0,-1,341,0.000000,"\text{Not used}","int((sin(e + f*x)*(g*cos(e + f*x))^(1/2))/(a + b*sin(e + f*x)),x)","\int \frac{\sin\left(e+f\,x\right)\,\sqrt{g\,\cos\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)*(g*cos(e + f*x))^(1/2))/(a + b*sin(e + f*x)), x)","F"
1374,0,-1,355,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1/2)/(sin(e + f*x)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}}{\sin\left(e+f\,x\right)\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(1/2)/(sin(e + f*x)*(a + b*sin(e + f*x))), x)","F"
1375,0,-1,433,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1/2)/(sin(e + f*x)^2*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}}{{\sin\left(e+f\,x\right)}^2\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(1/2)/(sin(e + f*x)^2*(a + b*sin(e + f*x))), x)","F"
1376,0,-1,544,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1/2)/(sin(e + f*x)^3*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}}{{\sin\left(e+f\,x\right)}^3\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(1/2)/(sin(e + f*x)^3*(a + b*sin(e + f*x))), x)","F"
1377,0,-1,621,0.000000,"\text{Not used}","int((sin(e + f*x)^3*(g*cos(e + f*x))^(3/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\sin\left(e+f\,x\right)}^3\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)^3*(g*cos(e + f*x))^(3/2))/(a + b*sin(e + f*x)), x)","F"
1378,0,-1,514,0.000000,"\text{Not used}","int((sin(e + f*x)^2*(g*cos(e + f*x))^(3/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\sin\left(e+f\,x\right)}^2\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)^2*(g*cos(e + f*x))^(3/2))/(a + b*sin(e + f*x)), x)","F"
1379,0,-1,426,0.000000,"\text{Not used}","int((sin(e + f*x)*(g*cos(e + f*x))^(3/2))/(a + b*sin(e + f*x)),x)","\int \frac{\sin\left(e+f\,x\right)\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)*(g*cos(e + f*x))^(3/2))/(a + b*sin(e + f*x)), x)","F"
1380,0,-1,439,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/(sin(e + f*x)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{\sin\left(e+f\,x\right)\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/(sin(e + f*x)*(a + b*sin(e + f*x))), x)","F"
1381,0,-1,469,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/(sin(e + f*x)^2*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\sin\left(e+f\,x\right)}^2\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/(sin(e + f*x)^2*(a + b*sin(e + f*x))), x)","F"
1382,0,-1,574,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/(sin(e + f*x)^3*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\sin\left(e+f\,x\right)}^3\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/(sin(e + f*x)^3*(a + b*sin(e + f*x))), x)","F"
1383,0,-1,610,0.000000,"\text{Not used}","int((sin(e + f*x)^3*(g*cos(e + f*x))^(5/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\sin\left(e+f\,x\right)}^3\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)^3*(g*cos(e + f*x))^(5/2))/(a + b*sin(e + f*x)), x)","F"
1384,0,-1,501,0.000000,"\text{Not used}","int((sin(e + f*x)^2*(g*cos(e + f*x))^(5/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\sin\left(e+f\,x\right)}^2\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)^2*(g*cos(e + f*x))^(5/2))/(a + b*sin(e + f*x)), x)","F"
1385,0,-1,413,0.000000,"\text{Not used}","int((sin(e + f*x)*(g*cos(e + f*x))^(5/2))/(a + b*sin(e + f*x)),x)","\int \frac{\sin\left(e+f\,x\right)\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((sin(e + f*x)*(g*cos(e + f*x))^(5/2))/(a + b*sin(e + f*x)), x)","F"
1386,0,-1,425,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/(sin(e + f*x)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{\sin\left(e+f\,x\right)\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/(sin(e + f*x)*(a + b*sin(e + f*x))), x)","F"
1387,0,-1,462,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/(sin(e + f*x)^2*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{{\sin\left(e+f\,x\right)}^2\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/(sin(e + f*x)^2*(a + b*sin(e + f*x))), x)","F"
1388,0,-1,557,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/(sin(e + f*x)^3*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{{\sin\left(e+f\,x\right)}^3\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/(sin(e + f*x)^3*(a + b*sin(e + f*x))), x)","F"
1389,0,-1,509,0.000000,"\text{Not used}","int(sin(e + f*x)^4/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^4}{\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^4/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1390,0,-1,457,0.000000,"\text{Not used}","int(sin(e + f*x)^3/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^3}{\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^3/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1391,0,-1,380,0.000000,"\text{Not used}","int(sin(e + f*x)^2/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^2}{\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^2/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1392,0,-1,352,0.000000,"\text{Not used}","int(sin(e + f*x)/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sin\left(e+f\,x\right)}{\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1393,0,-1,369,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)*(g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1394,0,-1,448,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1395,0,-1,557,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^3*(g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^3\,\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)^3*(g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1396,0,-1,584,0.000000,"\text{Not used}","int(sin(e + f*x)^4/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^4}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^4/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1397,0,-1,509,0.000000,"\text{Not used}","int(sin(e + f*x)^3/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^3}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^3/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1398,0,-1,453,0.000000,"\text{Not used}","int(sin(e + f*x)^2/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^2}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^2/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1399,0,-1,413,0.000000,"\text{Not used}","int(sin(e + f*x)/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sin\left(e+f\,x\right)}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1400,0,-1,507,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)*(g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1401,0,-1,627,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1402,0,-1,601,0.000000,"\text{Not used}","int(sin(e + f*x)^4/((g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^4}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^4/((g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1403,0,-1,528,0.000000,"\text{Not used}","int(sin(e + f*x)^3/((g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^3}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^3/((g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1404,0,-1,468,0.000000,"\text{Not used}","int(sin(e + f*x)^2/((g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\sin\left(e+f\,x\right)}^2}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)^2/((g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1405,0,-1,432,0.000000,"\text{Not used}","int(sin(e + f*x)/((g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sin\left(e+f\,x\right)}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(sin(e + f*x)/((g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1406,0,-1,527,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)*(g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1407,0,-1,651,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(g*cos(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1408,0,-1,926,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(5/2))/(a + b*sin(e + f*x)),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}\,{\left(d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(5/2))/(a + b*sin(e + f*x)), x)","F"
1409,0,-1,578,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(3/2))/(a + b*sin(e + f*x)),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}\,{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(3/2))/(a + b*sin(e + f*x)), x)","F"
1410,0,-1,509,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x)),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}\,\sqrt{d\,\sin\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x)), x)","F"
1411,0,-1,208,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}}{\sqrt{d\,\sin\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1412,0,-1,320,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1413,0,-1,366,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1414,0,-1,513,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(7/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{7/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(7/2)*(a + b*sin(e + f*x))), x)","F"
1415,0,-1,598,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(9/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\cos\left(e+f\,x\right)}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{9/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(1/2)/((d*sin(e + f*x))^(9/2)*(a + b*sin(e + f*x))), x)","F"
1416,0,-1,982,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(3/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(3/2))/(a + b*sin(e + f*x)), x)","F"
1417,0,-1,611,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{d\,\sin\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x)), x)","F"
1418,0,-1,577,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{d\,\sin\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1419,0,-1,321,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1420,0,-1,435,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1421,0,-1,525,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(7/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{7/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(7/2)*(a + b*sin(e + f*x))), x)","F"
1422,0,-1,688,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(9/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{9/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(9/2)*(a + b*sin(e + f*x))), x)","F"
1423,0,-1,936,0.000000,"\text{Not used}","int(((g*cos(e + f*x))^(5/2)*(d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x)),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{d\,\sin\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*cos(e + f*x))^(5/2)*(d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x)), x)","F"
1424,0,-1,572,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{d\,\sin\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1425,0,-1,616,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1426,0,-1,359,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1427,0,-1,519,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(7/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{7/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(7/2)*(a + b*sin(e + f*x))), x)","F"
1428,0,-1,612,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(9/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{9/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(9/2)*(a + b*sin(e + f*x))), x)","F"
1429,0,-1,822,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(11/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{11/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^(5/2)/((d*sin(e + f*x))^(11/2)*(a + b*sin(e + f*x))), x)","F"
1430,0,-1,616,0.000000,"\text{Not used}","int((d*sin(e + f*x))^(5/2)/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^(5/2)/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1431,0,-1,508,0.000000,"\text{Not used}","int((d*sin(e + f*x))^(3/2)/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^(3/2)/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1432,0,-1,209,0.000000,"\text{Not used}","int((d*sin(e + f*x))^(1/2)/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{d\,\sin\left(e+f\,x\right)}}{\sqrt{g\,\cos\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^(1/2)/((g*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1433,0,-1,273,0.000000,"\text{Not used}","int(1/((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{\sqrt{g\,\cos\left(e+f\,x\right)}\,\sqrt{d\,\sin\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1434,0,-1,320,0.000000,"\text{Not used}","int(1/((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{\sqrt{g\,\cos\left(e+f\,x\right)}\,{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1435,0,-1,424,0.000000,"\text{Not used}","int(1/((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{\sqrt{g\,\cos\left(e+f\,x\right)}\,{\left(d\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*cos(e + f*x))^(1/2)*(d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1436,0,-1,1064,0.000000,"\text{Not used}","int((d*sin(e + f*x))^(5/2)/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^(5/2)/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1437,0,-1,379,0.000000,"\text{Not used}","int((d*sin(e + f*x))^(3/2)/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^(3/2)/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1438,0,-1,374,0.000000,"\text{Not used}","int((d*sin(e + f*x))^(1/2)/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{d\,\sin\left(e+f\,x\right)}}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^(1/2)/((g*cos(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1439,0,-1,380,0.000000,"\text{Not used}","int(1/((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{d\,\sin\left(e+f\,x\right)}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))), x)","F"
1440,0,-1,568,0.000000,"\text{Not used}","int(1/((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(d\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(3/2)*(a + b*sin(e + f*x))), x)","F"
1441,0,-1,673,0.000000,"\text{Not used}","int(1/((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))),x)","\int \frac{1}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}\,{\left(d\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*cos(e + f*x))^(3/2)*(d*sin(e + f*x))^(5/2)*(a + b*sin(e + f*x))), x)","F"
1442,0,-1,331,0.000000,"\text{Not used}","int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{d\,\sin\left(e+f\,x\right)}\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((g*cos(e + f*x))^(3/2)/((d*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^2), x)","F"
1443,1,112,82,18.223133,"\text{Not used}","int((sin(c + d*x)^4*(a + b*sin(c + d*x)))/cos(c + d*x)^2,x)","-\frac{3\,a\,x}{2}-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{32\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{16\,b}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"- (3*a*x)/2 - ((16*b)/3 + 3*a*tan(c/2 + (d*x)/2) + 5*a*tan(c/2 + (d*x)/2)^3 + 5*a*tan(c/2 + (d*x)/2)^5 + 3*a*tan(c/2 + (d*x)/2)^7 + (32*b*tan(c/2 + (d*x)/2)^2)/3)/(d*(tan(c/2 + (d*x)/2)^2 - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
1444,1,98,65,15.966343,"\text{Not used}","int((sin(c + d*x)^3*(a + b*sin(c + d*x)))/cos(c + d*x)^2,x)","-\frac{3\,b\,x}{2}-\frac{3\,b\,{\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)}^3+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,a}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"- (3*b*x)/2 - (4*a + 3*b*tan(c/2 + (d*x)/2) + 4*a*tan(c/2 + (d*x)/2)^2 + 2*b*tan(c/2 + (d*x)/2)^3 + 3*b*tan(c/2 + (d*x)/2)^5)/(d*(tan(c/2 + (d*x)/2)^2 - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
1445,1,55,38,12.479902,"\text{Not used}","int((sin(c + d*x)^2*(a + b*sin(c + d*x)))/cos(c + d*x)^2,x)","-a\,x-\frac{2\,a\,{\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)+4\,b}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)}","Not used",1,"- a*x - (4*b + 2*a*tan(c/2 + (d*x)/2) + 2*a*tan(c/2 + (d*x)/2)^3)/(d*(tan(c/2 + (d*x)/2)^4 - 1))","B"
1446,1,41,27,11.935236,"\text{Not used}","int((sin(c + d*x)*(a + b*sin(c + d*x)))/cos(c + d*x)^2,x)","-b\,x-\frac{2\,a+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"- b*x - (2*a + 2*b*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
1447,1,52,36,11.936433,"\text{Not used}","int((a + b*sin(c + d*x))/(cos(c + d*x)^2*sin(c + d*x)),x)","\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)))/d - (2*a + 2*b*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
1448,1,92,48,11.907118,"\text{Not used}","int((a + b*sin(c + d*x))/(cos(c + d*x)^2*sin(c + d*x)^2),x)","\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a}{d\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(4*b*tan(c/2 + (d*x)/2) - a + 5*a*tan(c/2 + (d*x)/2)^2)/(d*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^3)) + (a*tan(c/2 + (d*x)/2))/(2*d) + (b*log(tan(c/2 + (d*x)/2)))/d","B"
1449,1,127,75,11.929155,"\text{Not used}","int((a + b*sin(c + d*x))/(cos(c + d*x)^2*sin(c + d*x)^3),x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{-10\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + 2*b*tan(c/2 + (d*x)/2) - (17*a*tan(c/2 + (d*x)/2)^2)/2 - 10*b*tan(c/2 + (d*x)/2)^3)/(d*(4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^4)) + (a*tan(c/2 + (d*x)/2)^2)/(8*d) + (3*a*log(tan(c/2 + (d*x)/2)))/(2*d)","B"
1450,1,149,94,18.494151,"\text{Not used}","int((sin(c + d*x)^3*(a + b*sin(c + d*x))^2)/cos(c + d*x)^2,x)","-3\,a\,b\,x-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^2+\frac{32\,b^2}{3}\right)+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^2+\frac{16\,b^2}{3}+10\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"- 3*a*b*x - (tan(c/2 + (d*x)/2)^2*(8*a^2 + (32*b^2)/3) + 4*a^2*tan(c/2 + (d*x)/2)^4 + 4*a^2 + (16*b^2)/3 + 10*a*b*tan(c/2 + (d*x)/2)^3 + 10*a*b*tan(c/2 + (d*x)/2)^5 + 6*a*b*tan(c/2 + (d*x)/2)^7 + 6*a*b*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
1451,1,145,94,17.038682,"\text{Not used}","int((sin(c + d*x)^2*(a + b*sin(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{\left(2\,a^2+3\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,a^2+2\,b^2\right)\,{\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)}^2+\left(2\,a^2+3\,b^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,a\,b}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\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)}-x\,\left(a^2+\frac{3\,b^2}{2}\right)","Not used",1,"(8*a*b + tan(c/2 + (d*x)/2)^3*(4*a^2 + 2*b^2) + tan(c/2 + (d*x)/2)^5*(2*a^2 + 3*b^2) + tan(c/2 + (d*x)/2)*(2*a^2 + 3*b^2) + 8*a*b*tan(c/2 + (d*x)/2)^2)/(d*(tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^6 + 1)) - x*(a^2 + (3*b^2)/2)","B"
1452,1,81,42,12.253323,"\text{Not used}","int((sin(c + d*x)*(a + b*sin(c + d*x))^2)/cos(c + d*x)^2,x)","-\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,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)+4\,b^2}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)}-2\,a\,b\,x","Not used",1,"- (2*a^2*tan(c/2 + (d*x)/2)^2 + 2*a^2 + 4*b^2 + 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^4 - 1)) - 2*a*b*x","B"
1453,1,62,46,11.849133,"\text{Not used}","int((a + b*sin(c + d*x))^2/(cos(c + d*x)^2*sin(c + d*x)),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a^2+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2\,b^2}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d - (2*a^2 + 2*b^2 + 4*a*b*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
1454,1,108,59,11.872159,"\text{Not used}","int((a + b*sin(c + d*x))^2/(cos(c + d*x)^2*sin(c + d*x)^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^2+4\,b^2\right)-a^2+8\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{2\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(5*a^2 + 4*b^2) - a^2 + 8*a*b*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^3)) + (a^2*tan(c/2 + (d*x)/2))/(2*d) + (2*a*b*log(tan(c/2 + (d*x)/2)))/d","B"
1455,1,148,100,11.854235,"\text{Not used}","int((a + b*sin(c + d*x))^2/(cos(c + d*x)^2*sin(c + d*x)^3),x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^2}{2}+b^2\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{17\,a^2}{2}+8\,b^2\right)-\frac{a^2}{2}+20\,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)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(8*d) + (log(tan(c/2 + (d*x)/2))*((3*a^2)/2 + b^2))/d + (tan(c/2 + (d*x)/2)^2*((17*a^2)/2 + 8*b^2) - a^2/2 + 20*a*b*tan(c/2 + (d*x)/2)^3 - 4*a*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^4)) + (a*b*tan(c/2 + (d*x)/2))/d","B"
1456,1,194,104,11.861651,"\text{Not used}","int((a + b*sin(c + d*x))^2/(cos(c + d*x)^2*sin(c + d*x)^4),x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{20\,a^2}{3}+4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(23\,a^2+20\,b^2\right)+\frac{a^2}{3}-34\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7\,a^2}{8}+\frac{b^2}{2}\right)}{d}+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{3\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (tan(c/2 + (d*x)/2)^2*((20*a^2)/3 + 4*b^2) - tan(c/2 + (d*x)/2)^4*(23*a^2 + 20*b^2) + a^2/3 - 34*a*b*tan(c/2 + (d*x)/2)^3 + 2*a*b*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 - 8*tan(c/2 + (d*x)/2)^5)) + (tan(c/2 + (d*x)/2)*((7*a^2)/8 + b^2/2))/d + (a*b*tan(c/2 + (d*x)/2)^2)/(4*d) + (3*a*b*log(tan(c/2 + (d*x)/2)))/d","B"
1457,1,323,197,16.023157,"\text{Not used}","int((sin(c + d*x)^3*(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(9\,a^2\,b+\frac{15\,b^3}{4}\right)+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a\,b^2+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a^3+32\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^3+48\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(24\,a^2\,b+10\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(9\,a^2\,b+\frac{15\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(24\,a^2\,b+10\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(30\,a^2\,b+\frac{9\,b^3}{2}\right)+4\,a^3}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\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{3\,b\,\mathrm{atan}\left(\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2+5\,b^2\right)}{36\,a^2\,b+15\,b^3}\right)\,\left(12\,a^2+5\,b^2\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(9*a^2*b + (15*b^3)/4) + 4*a^3*tan(c/2 + (d*x)/2)^6 + 16*a*b^2 + tan(c/2 + (d*x)/2)^4*(32*a*b^2 + 12*a^3) + tan(c/2 + (d*x)/2)^2*(48*a*b^2 + 12*a^3) + tan(c/2 + (d*x)/2)^3*(24*a^2*b + 10*b^3) + tan(c/2 + (d*x)/2)^9*(9*a^2*b + (15*b^3)/4) + tan(c/2 + (d*x)/2)^7*(24*a^2*b + 10*b^3) + tan(c/2 + (d*x)/2)^5*(30*a^2*b + (9*b^3)/2) + 4*a^3)/(d*(3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 - tan(c/2 + (d*x)/2)^10 + 1)) - (3*b*atan((3*b*tan(c/2 + (d*x)/2)*(12*a^2 + 5*b^2))/(36*a^2*b + 15*b^3))*(12*a^2 + 5*b^2))/(4*d)","B"
1458,1,249,146,16.657177,"\text{Not used}","int((sin(c + d*x)^2*(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+9\,a\,b^2\right)+12\,a^2\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^3+9\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^3+15\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^3+15\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(24\,a^2\,b+\frac{32\,b^3}{3}\right)+\frac{16\,b^3}{3}+12\,a^2\,b\,{\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)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+9\,b^2\right)}{2\,a^3+9\,a\,b^2}\right)\,\left(2\,a^2+9\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(9*a*b^2 + 2*a^3) + 12*a^2*b + tan(c/2 + (d*x)/2)^7*(9*a*b^2 + 2*a^3) + tan(c/2 + (d*x)/2)^3*(15*a*b^2 + 6*a^3) + tan(c/2 + (d*x)/2)^5*(15*a*b^2 + 6*a^3) + tan(c/2 + (d*x)/2)^2*(24*a^2*b + (32*b^3)/3) + (16*b^3)/3 + 12*a^2*b*tan(c/2 + (d*x)/2)^4)/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + 1)) - (a*atan((a*tan(c/2 + (d*x)/2)*(2*a^2 + 9*b^2))/(9*a*b^2 + 2*a^3))*(2*a^2 + 9*b^2))/d","B"
1459,1,219,75,16.287894,"\text{Not used}","int((sin(c + d*x)*(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(6\,a^2\,b+3\,b^3\right)+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+12\,a\,b^2+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^2\,b+3\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b+2\,b^3\right)+2\,a^3}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\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{3\,b\,\mathrm{atan}\left(\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^2\right)}{6\,a^2\,b+3\,b^3}\right)\,\left(2\,a^2+b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(6*a^2*b + 3*b^3) + 2*a^3*tan(c/2 + (d*x)/2)^4 + 12*a*b^2 + tan(c/2 + (d*x)/2)^2*(12*a*b^2 + 4*a^3) + tan(c/2 + (d*x)/2)^5*(6*a^2*b + 3*b^3) + tan(c/2 + (d*x)/2)^3*(12*a^2*b + 2*b^3) + 2*a^3)/(d*(tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^6 + 1)) - (3*b*atan((3*b*tan(c/2 + (d*x)/2)*(2*a^2 + b^2))/(6*a^2*b + 3*b^3))*(2*a^2 + b^2))/d","B"
1460,1,154,78,11.929839,"\text{Not used}","int((a + b*sin(c + d*x))^3/(cos(c + d*x)^2*sin(c + d*x)),x)","\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2\,b+2\,b^3\right)+6\,a\,b^2+2\,a^3}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{2\,b^3\,\mathrm{atan}\left(\frac{4\,b^6}{4\,a^3\,b^3+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6}-\frac{4\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^3\,b^3+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6}\right)}{d}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)))/d - (tan(c/2 + (d*x)/2)*(6*a^2*b + 2*b^3) + 6*a*b^2 + 2*a^3)/(d*(tan(c/2 + (d*x)/2)^2 - 1)) + (2*b^3*atan((4*b^6)/(4*a^3*b^3 + 4*b^6*tan(c/2 + (d*x)/2)) - (4*a^3*b^3*tan(c/2 + (d*x)/2))/(4*a^3*b^3 + 4*b^6*tan(c/2 + (d*x)/2))))/d","B"
1461,1,120,87,11.905934,"\text{Not used}","int((a + b*sin(c + d*x))^3/(cos(c + d*x)^2*sin(c + d*x)^2),x)","\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2\,b+4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^3+12\,a\,b^2\right)-a^3}{d\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{3\,a^2\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2))/(2*d) + (tan(c/2 + (d*x)/2)*(12*a^2*b + 4*b^3) + tan(c/2 + (d*x)/2)^2*(12*a*b^2 + 5*a^3) - a^3)/(d*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^3)) + (3*a^2*b*log(tan(c/2 + (d*x)/2)))/d","B"
1462,1,166,132,11.912513,"\text{Not used}","int((a + b*sin(c + d*x))^3/(cos(c + d*x)^2*sin(c + d*x)^3),x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^3}{2}+3\,a\,b^2\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{17\,a^3}{2}+24\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(30\,a^2\,b+8\,b^3\right)-\frac{a^3}{2}-6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(8*d) + (log(tan(c/2 + (d*x)/2))*(3*a*b^2 + (3*a^3)/2))/d + (tan(c/2 + (d*x)/2)^2*(24*a*b^2 + (17*a^3)/2) + tan(c/2 + (d*x)/2)^3*(30*a^2*b + 8*b^3) - a^3/2 - 6*a^2*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^4)) + (3*a^2*b*tan(c/2 + (d*x)/2))/(2*d)","B"
1463,1,218,164,11.888482,"\text{Not used}","int((a + b*sin(c + d*x))^3/(cos(c + d*x)^2*sin(c + d*x)^4),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{9\,a^2\,b}{2}+b^3\right)}{d}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{20\,a^3}{3}+12\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(23\,a^3+60\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(51\,a^2\,b+16\,b^3\right)+\frac{a^3}{3}+3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7\,a^3}{8}+\frac{3\,a\,b^2}{2}\right)}{d}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2))*((9*a^2*b)/2 + b^3))/d + (a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (tan(c/2 + (d*x)/2)^2*(12*a*b^2 + (20*a^3)/3) - tan(c/2 + (d*x)/2)^4*(60*a*b^2 + 23*a^3) - tan(c/2 + (d*x)/2)^3*(51*a^2*b + 16*b^3) + a^3/3 + 3*a^2*b*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 - 8*tan(c/2 + (d*x)/2)^5)) + (tan(c/2 + (d*x)/2)*((3*a*b^2)/2 + (7*a^3)/8))/d + (3*a^2*b*tan(c/2 + (d*x)/2)^2)/(8*d)","B"
1464,1,4797,222,19.769262,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^3+a\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^4+2\,b^4\right)}{b\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,a^2\,\left(a^2+2\,b^2\right)}{b\,{\left(a^2-b^2\right)}^2}-\frac{6\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{{\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{2\,\mathrm{atan}\left(\frac{64\,a\,b^{23}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}-\frac{704\,a^3\,b^{21}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}+\frac{3520\,a^5\,b^{19}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}-\frac{9536\,a^7\,b^{17}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}+\frac{14464\,a^9\,b^{15}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}-\frac{11072\,a^{11}\,b^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}+\frac{1024\,a^{13}\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}+\frac{5440\,a^{15}\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}-\frac{4544\,a^{17}\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}+\frac{1536\,a^{19}\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}-\frac{192\,a^{21}\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-192\,a^{21}\,b^3+1536\,a^{19}\,b^5-4544\,a^{17}\,b^7+5440\,a^{15}\,b^9+1024\,a^{13}\,b^{11}-11072\,a^{11}\,b^{13}+14464\,a^9\,b^{15}-9536\,a^7\,b^{17}+3520\,a^5\,b^{19}-704\,a^3\,b^{21}+64\,a\,b^{23}}\right)}{b^2\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+832\,a^{21}\,b^5-4608\,a^{19}\,b^7+14272\,a^{17}\,b^9-27680\,a^{15}\,b^{11}+35776\,a^{13}\,b^{13}-32096\,a^{11}\,b^{15}+20608\,a^9\,b^{17}-9632\,a^7\,b^{19}+3200\,a^5\,b^{21}-672\,a^3\,b^{23}+64\,a\,b^{25}\right)+32\,a^2\,b^{24}-320\,a^4\,b^{22}+1440\,a^6\,b^{20}-3840\,a^8\,b^{18}+6720\,a^{10}\,b^{16}-8064\,a^{12}\,b^{14}+6720\,a^{14}\,b^{12}-3840\,a^{16}\,b^{10}+1440\,a^{18}\,b^8-320\,a^{20}\,b^6+32\,a^{22}\,b^4+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{22}\,b^6+768\,a^{20}\,b^8-3840\,a^{18}\,b^{10}+10752\,a^{16}\,b^{12}-18816\,a^{14}\,b^{14}+21504\,a^{12}\,b^{16}-16128\,a^{10}\,b^{18}+7680\,a^8\,b^{20}-2112\,a^6\,b^{22}+256\,a^4\,b^{24}\right)-32\,a\,b^{27}+352\,a^3\,b^{25}-1632\,a^5\,b^{23}+4224\,a^7\,b^{21}-6720\,a^9\,b^{19}+6720\,a^{11}\,b^{17}-4032\,a^{13}\,b^{15}+1152\,a^{15}\,b^{13}+96\,a^{17}\,b^{11}-160\,a^{19}\,b^9+32\,a^{21}\,b^7+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^7+736\,a^{21}\,b^9-3840\,a^{19}\,b^{11}+12000\,a^{17}\,b^{13}-24960\,a^{15}\,b^{15}+36288\,a^{13}\,b^{17}-37632\,a^{11}\,b^{19}+27840\,a^9\,b^{21}-14400\,a^7\,b^{23}+4960\,a^5\,b^{25}-1024\,a^3\,b^{27}+96\,a\,b^{29}\right)+32\,a^2\,b^{28}-320\,a^4\,b^{26}+1440\,a^6\,b^{24}-3840\,a^8\,b^{22}+6720\,a^{10}\,b^{20}-8064\,a^{12}\,b^{18}+6720\,a^{14}\,b^{16}-3840\,a^{16}\,b^{14}+1440\,a^{18}\,b^{12}-320\,a^{20}\,b^{10}+32\,a^{22}\,b^8\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)\,1{}\mathrm{i}}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+832\,a^{21}\,b^5-4608\,a^{19}\,b^7+14272\,a^{17}\,b^9-27680\,a^{15}\,b^{11}+35776\,a^{13}\,b^{13}-32096\,a^{11}\,b^{15}+20608\,a^9\,b^{17}-9632\,a^7\,b^{19}+3200\,a^5\,b^{21}-672\,a^3\,b^{23}+64\,a\,b^{25}\right)+32\,a^2\,b^{24}-320\,a^4\,b^{22}+1440\,a^6\,b^{20}-3840\,a^8\,b^{18}+6720\,a^{10}\,b^{16}-8064\,a^{12}\,b^{14}+6720\,a^{14}\,b^{12}-3840\,a^{16}\,b^{10}+1440\,a^{18}\,b^8-320\,a^{20}\,b^6+32\,a^{22}\,b^4-\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{22}\,b^6+768\,a^{20}\,b^8-3840\,a^{18}\,b^{10}+10752\,a^{16}\,b^{12}-18816\,a^{14}\,b^{14}+21504\,a^{12}\,b^{16}-16128\,a^{10}\,b^{18}+7680\,a^8\,b^{20}-2112\,a^6\,b^{22}+256\,a^4\,b^{24}\right)-32\,a\,b^{27}+352\,a^3\,b^{25}-1632\,a^5\,b^{23}+4224\,a^7\,b^{21}-6720\,a^9\,b^{19}+6720\,a^{11}\,b^{17}-4032\,a^{13}\,b^{15}+1152\,a^{15}\,b^{13}+96\,a^{17}\,b^{11}-160\,a^{19}\,b^9+32\,a^{21}\,b^7-\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^7+736\,a^{21}\,b^9-3840\,a^{19}\,b^{11}+12000\,a^{17}\,b^{13}-24960\,a^{15}\,b^{15}+36288\,a^{13}\,b^{17}-37632\,a^{11}\,b^{19}+27840\,a^9\,b^{21}-14400\,a^7\,b^{23}+4960\,a^5\,b^{25}-1024\,a^3\,b^{27}+96\,a\,b^{29}\right)+32\,a^2\,b^{28}-320\,a^4\,b^{26}+1440\,a^6\,b^{24}-3840\,a^8\,b^{22}+6720\,a^{10}\,b^{20}-8064\,a^{12}\,b^{18}+6720\,a^{14}\,b^{16}-3840\,a^{16}\,b^{14}+1440\,a^{18}\,b^{12}-320\,a^{20}\,b^{10}+32\,a^{22}\,b^8\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)\,1{}\mathrm{i}}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{22}\,b^2+768\,a^{20}\,b^4-3840\,a^{18}\,b^6+10752\,a^{16}\,b^8-18816\,a^{14}\,b^{10}+21504\,a^{12}\,b^{12}-16128\,a^{10}\,b^{14}+7680\,a^8\,b^{16}-2112\,a^6\,b^{18}+256\,a^4\,b^{20}\right)+256\,a^5\,b^{19}-1088\,a^7\,b^{17}+1024\,a^9\,b^{15}+2368\,a^{11}\,b^{13}-7040\,a^{13}\,b^{11}+7744\,a^{15}\,b^9-4352\,a^{17}\,b^7+1216\,a^{19}\,b^5-128\,a^{21}\,b^3+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+832\,a^{21}\,b^5-4608\,a^{19}\,b^7+14272\,a^{17}\,b^9-27680\,a^{15}\,b^{11}+35776\,a^{13}\,b^{13}-32096\,a^{11}\,b^{15}+20608\,a^9\,b^{17}-9632\,a^7\,b^{19}+3200\,a^5\,b^{21}-672\,a^3\,b^{23}+64\,a\,b^{25}\right)+32\,a^2\,b^{24}-320\,a^4\,b^{22}+1440\,a^6\,b^{20}-3840\,a^8\,b^{18}+6720\,a^{10}\,b^{16}-8064\,a^{12}\,b^{14}+6720\,a^{14}\,b^{12}-3840\,a^{16}\,b^{10}+1440\,a^{18}\,b^8-320\,a^{20}\,b^6+32\,a^{22}\,b^4+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{22}\,b^6+768\,a^{20}\,b^8-3840\,a^{18}\,b^{10}+10752\,a^{16}\,b^{12}-18816\,a^{14}\,b^{14}+21504\,a^{12}\,b^{16}-16128\,a^{10}\,b^{18}+7680\,a^8\,b^{20}-2112\,a^6\,b^{22}+256\,a^4\,b^{24}\right)-32\,a\,b^{27}+352\,a^3\,b^{25}-1632\,a^5\,b^{23}+4224\,a^7\,b^{21}-6720\,a^9\,b^{19}+6720\,a^{11}\,b^{17}-4032\,a^{13}\,b^{15}+1152\,a^{15}\,b^{13}+96\,a^{17}\,b^{11}-160\,a^{19}\,b^9+32\,a^{21}\,b^7+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^7+736\,a^{21}\,b^9-3840\,a^{19}\,b^{11}+12000\,a^{17}\,b^{13}-24960\,a^{15}\,b^{15}+36288\,a^{13}\,b^{17}-37632\,a^{11}\,b^{19}+27840\,a^9\,b^{21}-14400\,a^7\,b^{23}+4960\,a^5\,b^{25}-1024\,a^3\,b^{27}+96\,a\,b^{29}\right)+32\,a^2\,b^{28}-320\,a^4\,b^{26}+1440\,a^6\,b^{24}-3840\,a^8\,b^{22}+6720\,a^{10}\,b^{20}-8064\,a^{12}\,b^{18}+6720\,a^{14}\,b^{16}-3840\,a^{16}\,b^{14}+1440\,a^{18}\,b^{12}-320\,a^{20}\,b^{10}+32\,a^{22}\,b^8\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}-\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+832\,a^{21}\,b^5-4608\,a^{19}\,b^7+14272\,a^{17}\,b^9-27680\,a^{15}\,b^{11}+35776\,a^{13}\,b^{13}-32096\,a^{11}\,b^{15}+20608\,a^9\,b^{17}-9632\,a^7\,b^{19}+3200\,a^5\,b^{21}-672\,a^3\,b^{23}+64\,a\,b^{25}\right)+32\,a^2\,b^{24}-320\,a^4\,b^{22}+1440\,a^6\,b^{20}-3840\,a^8\,b^{18}+6720\,a^{10}\,b^{16}-8064\,a^{12}\,b^{14}+6720\,a^{14}\,b^{12}-3840\,a^{16}\,b^{10}+1440\,a^{18}\,b^8-320\,a^{20}\,b^6+32\,a^{22}\,b^4-\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{22}\,b^6+768\,a^{20}\,b^8-3840\,a^{18}\,b^{10}+10752\,a^{16}\,b^{12}-18816\,a^{14}\,b^{14}+21504\,a^{12}\,b^{16}-16128\,a^{10}\,b^{18}+7680\,a^8\,b^{20}-2112\,a^6\,b^{22}+256\,a^4\,b^{24}\right)-32\,a\,b^{27}+352\,a^3\,b^{25}-1632\,a^5\,b^{23}+4224\,a^7\,b^{21}-6720\,a^9\,b^{19}+6720\,a^{11}\,b^{17}-4032\,a^{13}\,b^{15}+1152\,a^{15}\,b^{13}+96\,a^{17}\,b^{11}-160\,a^{19}\,b^9+32\,a^{21}\,b^7-\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^7+736\,a^{21}\,b^9-3840\,a^{19}\,b^{11}+12000\,a^{17}\,b^{13}-24960\,a^{15}\,b^{15}+36288\,a^{13}\,b^{17}-37632\,a^{11}\,b^{19}+27840\,a^9\,b^{21}-14400\,a^7\,b^{23}+4960\,a^5\,b^{25}-1024\,a^3\,b^{27}+96\,a\,b^{29}\right)+32\,a^2\,b^{28}-320\,a^4\,b^{26}+1440\,a^6\,b^{24}-3840\,a^8\,b^{22}+6720\,a^{10}\,b^{20}-8064\,a^{12}\,b^{18}+6720\,a^{14}\,b^{16}-3840\,a^{16}\,b^{14}+1440\,a^{18}\,b^{12}-320\,a^{20}\,b^{10}+32\,a^{22}\,b^8\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}}\right)\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{d\,\left(-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(a*b^2 + 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(c/2 + (d*x)/2)^2*(a^4 + 2*b^4))/(b*(a^4 + b^4 - 2*a^2*b^2)) - (2*a^2*(a^2 + 2*b^2))/(b*(a^2 - b^2)^2) - (6*a*b^2*tan(c/2 + (d*x)/2))/(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)) - (2*atan((64*a*b^23*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) - (704*a^3*b^21*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) + (3520*a^5*b^19*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) - (9536*a^7*b^17*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) + (14464*a^9*b^15*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) - (11072*a^11*b^13*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) + (1024*a^13*b^11*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) + (5440*a^15*b^9*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) - (4544*a^17*b^7*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) + (1536*a^19*b^5*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3) - (192*a^21*b^3*tan(c/2 + (d*x)/2))/(64*a*b^23 - 704*a^3*b^21 + 3520*a^5*b^19 - 9536*a^7*b^17 + 14464*a^9*b^15 - 11072*a^11*b^13 + 1024*a^13*b^11 + 5440*a^15*b^9 - 4544*a^17*b^7 + 1536*a^19*b^5 - 192*a^21*b^3)))/(b^2*d) + (a^3*atan(((a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(64*a*b^25 - 672*a^3*b^23 + 3200*a^5*b^21 - 9632*a^7*b^19 + 20608*a^9*b^17 - 32096*a^11*b^15 + 35776*a^13*b^13 - 27680*a^15*b^11 + 14272*a^17*b^9 - 4608*a^19*b^7 + 832*a^21*b^5 - 64*a^23*b^3) + 32*a^2*b^24 - 320*a^4*b^22 + 1440*a^6*b^20 - 3840*a^8*b^18 + 6720*a^10*b^16 - 8064*a^12*b^14 + 6720*a^14*b^12 - 3840*a^16*b^10 + 1440*a^18*b^8 - 320*a^20*b^6 + 32*a^22*b^4 + (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(256*a^4*b^24 - 2112*a^6*b^22 + 7680*a^8*b^20 - 16128*a^10*b^18 + 21504*a^12*b^16 - 18816*a^14*b^14 + 10752*a^16*b^12 - 3840*a^18*b^10 + 768*a^20*b^8 - 64*a^22*b^6) - 32*a*b^27 + 352*a^3*b^25 - 1632*a^5*b^23 + 4224*a^7*b^21 - 6720*a^9*b^19 + 6720*a^11*b^17 - 4032*a^13*b^15 + 1152*a^15*b^13 + 96*a^17*b^11 - 160*a^19*b^9 + 32*a^21*b^7 + (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(96*a*b^29 - 1024*a^3*b^27 + 4960*a^5*b^25 - 14400*a^7*b^23 + 27840*a^9*b^21 - 37632*a^11*b^19 + 36288*a^13*b^17 - 24960*a^15*b^15 + 12000*a^17*b^13 - 3840*a^19*b^11 + 736*a^21*b^9 - 64*a^23*b^7) + 32*a^2*b^28 - 320*a^4*b^26 + 1440*a^6*b^24 - 3840*a^8*b^22 + 6720*a^10*b^20 - 8064*a^12*b^18 + 6720*a^14*b^16 - 3840*a^16*b^14 + 1440*a^18*b^12 - 320*a^20*b^10 + 32*a^22*b^8))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2))*1i)/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2) + (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(64*a*b^25 - 672*a^3*b^23 + 3200*a^5*b^21 - 9632*a^7*b^19 + 20608*a^9*b^17 - 32096*a^11*b^15 + 35776*a^13*b^13 - 27680*a^15*b^11 + 14272*a^17*b^9 - 4608*a^19*b^7 + 832*a^21*b^5 - 64*a^23*b^3) + 32*a^2*b^24 - 320*a^4*b^22 + 1440*a^6*b^20 - 3840*a^8*b^18 + 6720*a^10*b^16 - 8064*a^12*b^14 + 6720*a^14*b^12 - 3840*a^16*b^10 + 1440*a^18*b^8 - 320*a^20*b^6 + 32*a^22*b^4 - (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(256*a^4*b^24 - 2112*a^6*b^22 + 7680*a^8*b^20 - 16128*a^10*b^18 + 21504*a^12*b^16 - 18816*a^14*b^14 + 10752*a^16*b^12 - 3840*a^18*b^10 + 768*a^20*b^8 - 64*a^22*b^6) - 32*a*b^27 + 352*a^3*b^25 - 1632*a^5*b^23 + 4224*a^7*b^21 - 6720*a^9*b^19 + 6720*a^11*b^17 - 4032*a^13*b^15 + 1152*a^15*b^13 + 96*a^17*b^11 - 160*a^19*b^9 + 32*a^21*b^7 - (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(96*a*b^29 - 1024*a^3*b^27 + 4960*a^5*b^25 - 14400*a^7*b^23 + 27840*a^9*b^21 - 37632*a^11*b^19 + 36288*a^13*b^17 - 24960*a^15*b^15 + 12000*a^17*b^13 - 3840*a^19*b^11 + 736*a^21*b^9 - 64*a^23*b^7) + 32*a^2*b^28 - 320*a^4*b^26 + 1440*a^6*b^24 - 3840*a^8*b^22 + 6720*a^10*b^20 - 8064*a^12*b^18 + 6720*a^14*b^16 - 3840*a^16*b^14 + 1440*a^18*b^12 - 320*a^20*b^10 + 32*a^22*b^8))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2))*1i)/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2))/(2*tan(c/2 + (d*x)/2)*(256*a^4*b^20 - 2112*a^6*b^18 + 7680*a^8*b^16 - 16128*a^10*b^14 + 21504*a^12*b^12 - 18816*a^14*b^10 + 10752*a^16*b^8 - 3840*a^18*b^6 + 768*a^20*b^4 - 64*a^22*b^2) + 256*a^5*b^19 - 1088*a^7*b^17 + 1024*a^9*b^15 + 2368*a^11*b^13 - 7040*a^13*b^11 + 7744*a^15*b^9 - 4352*a^17*b^7 + 1216*a^19*b^5 - 128*a^21*b^3 + (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(64*a*b^25 - 672*a^3*b^23 + 3200*a^5*b^21 - 9632*a^7*b^19 + 20608*a^9*b^17 - 32096*a^11*b^15 + 35776*a^13*b^13 - 27680*a^15*b^11 + 14272*a^17*b^9 - 4608*a^19*b^7 + 832*a^21*b^5 - 64*a^23*b^3) + 32*a^2*b^24 - 320*a^4*b^22 + 1440*a^6*b^20 - 3840*a^8*b^18 + 6720*a^10*b^16 - 8064*a^12*b^14 + 6720*a^14*b^12 - 3840*a^16*b^10 + 1440*a^18*b^8 - 320*a^20*b^6 + 32*a^22*b^4 + (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(256*a^4*b^24 - 2112*a^6*b^22 + 7680*a^8*b^20 - 16128*a^10*b^18 + 21504*a^12*b^16 - 18816*a^14*b^14 + 10752*a^16*b^12 - 3840*a^18*b^10 + 768*a^20*b^8 - 64*a^22*b^6) - 32*a*b^27 + 352*a^3*b^25 - 1632*a^5*b^23 + 4224*a^7*b^21 - 6720*a^9*b^19 + 6720*a^11*b^17 - 4032*a^13*b^15 + 1152*a^15*b^13 + 96*a^17*b^11 - 160*a^19*b^9 + 32*a^21*b^7 + (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(96*a*b^29 - 1024*a^3*b^27 + 4960*a^5*b^25 - 14400*a^7*b^23 + 27840*a^9*b^21 - 37632*a^11*b^19 + 36288*a^13*b^17 - 24960*a^15*b^15 + 12000*a^17*b^13 - 3840*a^19*b^11 + 736*a^21*b^9 - 64*a^23*b^7) + 32*a^2*b^28 - 320*a^4*b^26 + 1440*a^6*b^24 - 3840*a^8*b^22 + 6720*a^10*b^20 - 8064*a^12*b^18 + 6720*a^14*b^16 - 3840*a^16*b^14 + 1440*a^18*b^12 - 320*a^20*b^10 + 32*a^22*b^8))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2) - (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(64*a*b^25 - 672*a^3*b^23 + 3200*a^5*b^21 - 9632*a^7*b^19 + 20608*a^9*b^17 - 32096*a^11*b^15 + 35776*a^13*b^13 - 27680*a^15*b^11 + 14272*a^17*b^9 - 4608*a^19*b^7 + 832*a^21*b^5 - 64*a^23*b^3) + 32*a^2*b^24 - 320*a^4*b^22 + 1440*a^6*b^20 - 3840*a^8*b^18 + 6720*a^10*b^16 - 8064*a^12*b^14 + 6720*a^14*b^12 - 3840*a^16*b^10 + 1440*a^18*b^8 - 320*a^20*b^6 + 32*a^22*b^4 - (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(256*a^4*b^24 - 2112*a^6*b^22 + 7680*a^8*b^20 - 16128*a^10*b^18 + 21504*a^12*b^16 - 18816*a^14*b^14 + 10752*a^16*b^12 - 3840*a^18*b^10 + 768*a^20*b^8 - 64*a^22*b^6) - 32*a*b^27 + 352*a^3*b^25 - 1632*a^5*b^23 + 4224*a^7*b^21 - 6720*a^9*b^19 + 6720*a^11*b^17 - 4032*a^13*b^15 + 1152*a^15*b^13 + 96*a^17*b^11 - 160*a^19*b^9 + 32*a^21*b^7 - (a^3*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(96*a*b^29 - 1024*a^3*b^27 + 4960*a^5*b^25 - 14400*a^7*b^23 + 27840*a^9*b^21 - 37632*a^11*b^19 + 36288*a^13*b^17 - 24960*a^15*b^15 + 12000*a^17*b^13 - 3840*a^19*b^11 + 736*a^21*b^9 - 64*a^23*b^7) + 32*a^2*b^28 - 320*a^4*b^26 + 1440*a^6*b^24 - 3840*a^8*b^22 + 6720*a^10*b^20 - 8064*a^12*b^18 + 6720*a^14*b^16 - 3840*a^16*b^14 + 1440*a^18*b^12 - 320*a^20*b^10 + 32*a^22*b^8))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))*(a - 2*b)*(a + 2*b)*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(d*(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2))","B"
1465,1,276,212,15.275940,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","\frac{\frac{2\,a\,\left(2\,a^2+b^2\right)}{{\left(a^2-b^2\right)}^2}-\frac{6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{{\left(a^2-b^2\right)}^2}+\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^2\right)}{{\left(a^2-b^2\right)}^2}-\frac{6\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}}{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^2\,b\,\mathrm{atan}\left(\frac{\frac{a^2\,b\,\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}+\frac{a^3\,b\,\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}}}{a^2\,b}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((2*a*(2*a^2 + b^2))/(a^2 - b^2)^2 - (6*a^2*b*tan(c/2 + (d*x)/2)^3)/(a^2 - b^2)^2 + (2*b*tan(c/2 + (d*x)/2)*(a^2 + 2*b^2))/(a^2 - b^2)^2 - (6*a*b^2*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^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^2*b*atan(((a^2*b*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/(2*(a + b)^(5/2)*(a - b)^(5/2)) + (a^3*b*tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(a^2*b)))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
1466,1,313,200,15.960517,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","-\frac{\frac{6\,a^2\,b}{{\left(a^2-b^2\right)}^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a\,b^2-a^3\right)}{{\left(a^2-b^2\right)}^2}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+2\,b^2\right)}{{\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{2\,a\,\mathrm{atan}\left(\frac{\frac{a\,\left(a^2+2\,b^2\right)\,\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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^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\,a^3+4\,a\,b^2}\right)\,\left(a^2+2\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"- ((6*a^2*b)/(a^2 - b^2)^2 + (2*tan(c/2 + (d*x)/2)*(4*a*b^2 - a^3))/(a^2 - b^2)^2 - (2*b*tan(c/2 + (d*x)/2)^2*(a^2 + 2*b^2))/(a^4 + b^4 - 2*a^2*b^2) - (2*a*tan(c/2 + (d*x)/2)^3*(a^2 + 2*b^2))/(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)) - (2*a*atan(((a*(a^2 + 2*b^2)*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a^2*tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(4*a*b^2 + 2*a^3))*(a^2 + 2*b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
1467,1,310,133,16.322431,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","\frac{\frac{6\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{{\left(a^2-b^2\right)}^2}+\frac{2\,a\,\left(a^2+2\,b^2\right)}{{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,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)}^3\,\left(2\,a^2+b^2\right)}{{\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{2\,b\,\mathrm{atan}\left(\frac{\frac{b\,\left(2\,a^2+b^2\right)\,\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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^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}}}{4\,a^2\,b+2\,b^3}\right)\,\left(2\,a^2+b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((6*b^3*tan(c/2 + (d*x)/2))/(a^2 - b^2)^2 + (2*a*(a^2 + 2*b^2))/(a^2 - b^2)^2 - (2*tan(c/2 + (d*x)/2)^2*(4*a*b^2 - a^3))/(a^4 + b^4 - 2*a^2*b^2) - (2*b*tan(c/2 + (d*x)/2)^3*(2*a^2 + b^2))/(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)) + (2*b*atan(((b*(2*a^2 + b^2)*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a*b*tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(4*a^2*b + 2*b^3))*(2*a^2 + b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
1468,1,2076,229,14.861937,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)*(a + b*sin(c + d*x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{\frac{2\,\left(a^4+a^2\,b^2+b^4\right)}{a\,\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^2\,b^3+b^5\right)}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^4+3\,a^2\,b^2+b^4\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^4+b^4\right)}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{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{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{16}-16\,a^{14}\,b^2+70\,a^{12}\,b^4-168\,a^{10}\,b^6+222\,a^8\,b^8-160\,a^6\,b^{10}+58\,a^4\,b^{12}-8\,a^2\,b^{14}\right)-2\,a^{15}\,b-4\,a^3\,b^{13}+28\,a^5\,b^{11}-74\,a^7\,b^9+96\,a^9\,b^7-64\,a^{11}\,b^5+20\,a^{13}\,b^3+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(2\,a^{17}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{18}-44\,a^{16}\,b^2+138\,a^{14}\,b^4-240\,a^{12}\,b^6+250\,a^{10}\,b^8-156\,a^8\,b^{10}+54\,a^6\,b^{12}-8\,a^4\,b^{14}\right)+2\,a^5\,b^{13}-12\,a^7\,b^{11}+30\,a^9\,b^9-40\,a^{11}\,b^7+30\,a^{13}\,b^5-12\,a^{15}\,b^3\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,1{}\mathrm{i}}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}-\frac{b^3\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(2\,a^{15}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{16}-16\,a^{14}\,b^2+70\,a^{12}\,b^4-168\,a^{10}\,b^6+222\,a^8\,b^8-160\,a^6\,b^{10}+58\,a^4\,b^{12}-8\,a^2\,b^{14}\right)+4\,a^3\,b^{13}-28\,a^5\,b^{11}+74\,a^7\,b^9-96\,a^9\,b^7+64\,a^{11}\,b^5-20\,a^{13}\,b^3+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(2\,a^{17}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{18}-44\,a^{16}\,b^2+138\,a^{14}\,b^4-240\,a^{12}\,b^6+250\,a^{10}\,b^8-156\,a^8\,b^{10}+54\,a^6\,b^{12}-8\,a^4\,b^{14}\right)+2\,a^5\,b^{13}-12\,a^7\,b^{11}+30\,a^9\,b^9-40\,a^{11}\,b^7+30\,a^{13}\,b^5-12\,a^{15}\,b^3\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,1{}\mathrm{i}}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}}{4\,a\,b^{13}-32\,a^3\,b^{11}+88\,a^5\,b^9-112\,a^7\,b^7+68\,a^9\,b^5-16\,a^{11}\,b^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{10}\,b^4+4\,a^8\,b^6+48\,a^6\,b^8-44\,a^4\,b^{10}+8\,a^2\,b^{12}\right)+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{16}-16\,a^{14}\,b^2+70\,a^{12}\,b^4-168\,a^{10}\,b^6+222\,a^8\,b^8-160\,a^6\,b^{10}+58\,a^4\,b^{12}-8\,a^2\,b^{14}\right)-2\,a^{15}\,b-4\,a^3\,b^{13}+28\,a^5\,b^{11}-74\,a^7\,b^9+96\,a^9\,b^7-64\,a^{11}\,b^5+20\,a^{13}\,b^3+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(2\,a^{17}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{18}-44\,a^{16}\,b^2+138\,a^{14}\,b^4-240\,a^{12}\,b^6+250\,a^{10}\,b^8-156\,a^8\,b^{10}+54\,a^6\,b^{12}-8\,a^4\,b^{14}\right)+2\,a^5\,b^{13}-12\,a^7\,b^{11}+30\,a^9\,b^9-40\,a^{11}\,b^7+30\,a^{13}\,b^5-12\,a^{15}\,b^3\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(2\,a^{15}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{16}-16\,a^{14}\,b^2+70\,a^{12}\,b^4-168\,a^{10}\,b^6+222\,a^8\,b^8-160\,a^6\,b^{10}+58\,a^4\,b^{12}-8\,a^2\,b^{14}\right)+4\,a^3\,b^{13}-28\,a^5\,b^{11}+74\,a^7\,b^9-96\,a^9\,b^7+64\,a^{11}\,b^5-20\,a^{13}\,b^3+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(2\,a^{17}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{18}-44\,a^{16}\,b^2+138\,a^{14}\,b^4-240\,a^{12}\,b^6+250\,a^{10}\,b^8-156\,a^8\,b^{10}+54\,a^6\,b^{12}-8\,a^4\,b^{14}\right)+2\,a^5\,b^{13}-12\,a^7\,b^{11}+30\,a^9\,b^9-40\,a^{11}\,b^7+30\,a^{13}\,b^5-12\,a^{15}\,b^3\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}}\right)\,\left(2\,a+b\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,2{}\mathrm{i}}{d\,\left(a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) + ((2*(a^4 + b^4 + a^2*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (2*tan(c/2 + (d*x)/2)*(b^5 + 2*a^2*b^3))/(a^2*(a^4 + b^4 - 2*a^2*b^2)) - (2*tan(c/2 + (d*x)/2)^2*(b^4 - a^4 + 3*a^2*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)) - (2*b*tan(c/2 + (d*x)/2)^3*(2*a^4 + b^4))/(a^2*(a^4 + b^4 - 2*a^2*b^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)) - (b^3*atan(((b^3*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(tan(c/2 + (d*x)/2)*(2*a^16 - 8*a^2*b^14 + 58*a^4*b^12 - 160*a^6*b^10 + 222*a^8*b^8 - 168*a^10*b^6 + 70*a^12*b^4 - 16*a^14*b^2) - 2*a^15*b - 4*a^3*b^13 + 28*a^5*b^11 - 74*a^7*b^9 + 96*a^9*b^7 - 64*a^11*b^5 + 20*a^13*b^3 + (b^3*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(2*a^17*b - tan(c/2 + (d*x)/2)*(6*a^18 - 8*a^4*b^14 + 54*a^6*b^12 - 156*a^8*b^10 + 250*a^10*b^8 - 240*a^12*b^6 + 138*a^14*b^4 - 44*a^16*b^2) + 2*a^5*b^13 - 12*a^7*b^11 + 30*a^9*b^9 - 40*a^11*b^7 + 30*a^13*b^5 - 12*a^15*b^3))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*1i)/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2) - (b^3*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(2*a^15*b - tan(c/2 + (d*x)/2)*(2*a^16 - 8*a^2*b^14 + 58*a^4*b^12 - 160*a^6*b^10 + 222*a^8*b^8 - 168*a^10*b^6 + 70*a^12*b^4 - 16*a^14*b^2) + 4*a^3*b^13 - 28*a^5*b^11 + 74*a^7*b^9 - 96*a^9*b^7 + 64*a^11*b^5 - 20*a^13*b^3 + (b^3*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(2*a^17*b - tan(c/2 + (d*x)/2)*(6*a^18 - 8*a^4*b^14 + 54*a^6*b^12 - 156*a^8*b^10 + 250*a^10*b^8 - 240*a^12*b^6 + 138*a^14*b^4 - 44*a^16*b^2) + 2*a^5*b^13 - 12*a^7*b^11 + 30*a^9*b^9 - 40*a^11*b^7 + 30*a^13*b^5 - 12*a^15*b^3))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*1i)/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))/(4*a*b^13 - 32*a^3*b^11 + 88*a^5*b^9 - 112*a^7*b^7 + 68*a^9*b^5 - 16*a^11*b^3 + 2*tan(c/2 + (d*x)/2)*(8*a^2*b^12 - 44*a^4*b^10 + 48*a^6*b^8 + 4*a^8*b^6 - 16*a^10*b^4) + (b^3*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(tan(c/2 + (d*x)/2)*(2*a^16 - 8*a^2*b^14 + 58*a^4*b^12 - 160*a^6*b^10 + 222*a^8*b^8 - 168*a^10*b^6 + 70*a^12*b^4 - 16*a^14*b^2) - 2*a^15*b - 4*a^3*b^13 + 28*a^5*b^11 - 74*a^7*b^9 + 96*a^9*b^7 - 64*a^11*b^5 + 20*a^13*b^3 + (b^3*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(2*a^17*b - tan(c/2 + (d*x)/2)*(6*a^18 - 8*a^4*b^14 + 54*a^6*b^12 - 156*a^8*b^10 + 250*a^10*b^8 - 240*a^12*b^6 + 138*a^14*b^4 - 44*a^16*b^2) + 2*a^5*b^13 - 12*a^7*b^11 + 30*a^9*b^9 - 40*a^11*b^7 + 30*a^13*b^5 - 12*a^15*b^3))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2) + (b^3*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(2*a^15*b - tan(c/2 + (d*x)/2)*(2*a^16 - 8*a^2*b^14 + 58*a^4*b^12 - 160*a^6*b^10 + 222*a^8*b^8 - 168*a^10*b^6 + 70*a^12*b^4 - 16*a^14*b^2) + 4*a^3*b^13 - 28*a^5*b^11 + 74*a^7*b^9 - 96*a^9*b^7 + 64*a^11*b^5 - 20*a^13*b^3 + (b^3*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(2*a^17*b - tan(c/2 + (d*x)/2)*(6*a^18 - 8*a^4*b^14 + 54*a^6*b^12 - 156*a^8*b^10 + 250*a^10*b^8 - 240*a^12*b^6 + 138*a^14*b^4 - 44*a^16*b^2) + 2*a^5*b^13 - 12*a^7*b^11 + 30*a^9*b^9 - 40*a^11*b^7 + 30*a^13*b^5 - 12*a^15*b^3))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))*(2*a + b)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*2i)/(d*(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))","B"
1469,1,2151,248,13.332271,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","\frac{a+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^4\,b-2\,a^2\,b^3+3\,b^5\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^6+3\,a^4\,b^2+b^6\right)}{a\,{\left(a^2-b^2\right)}^2}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^4+2\,a^2\,b^2+3\,b^4\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(5\,a^6+2\,a^4\,b^2+a^2\,b^4+4\,b^6\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,b\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,b\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{2\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{b^4\,\mathrm{atan}\left(\frac{\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{18}\,b-32\,a^{16}\,b^3+128\,a^{14}\,b^5-288\,a^{12}\,b^7+372\,a^{10}\,b^9-272\,a^8\,b^{11}+104\,a^6\,b^{13}-16\,a^4\,b^{15}\right)-8\,a^5\,b^{14}+50\,a^7\,b^{12}-124\,a^9\,b^{10}+156\,a^{11}\,b^8-104\,a^{13}\,b^6+34\,a^{15}\,b^4-4\,a^{17}\,b^2+\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^{20}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{21}-44\,a^{19}\,b^2+138\,a^{17}\,b^4-240\,a^{15}\,b^6+250\,a^{13}\,b^8-156\,a^{11}\,b^{10}+54\,a^9\,b^{12}-8\,a^7\,b^{14}\right)+2\,a^8\,b^{13}-12\,a^{10}\,b^{11}+30\,a^{12}\,b^9-40\,a^{14}\,b^7+30\,a^{16}\,b^5-12\,a^{18}\,b^3\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)\,1{}\mathrm{i}}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}-\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(8\,a^5\,b^{14}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{18}\,b-32\,a^{16}\,b^3+128\,a^{14}\,b^5-288\,a^{12}\,b^7+372\,a^{10}\,b^9-272\,a^8\,b^{11}+104\,a^6\,b^{13}-16\,a^4\,b^{15}\right)-50\,a^7\,b^{12}+124\,a^9\,b^{10}-156\,a^{11}\,b^8+104\,a^{13}\,b^6-34\,a^{15}\,b^4+4\,a^{17}\,b^2+\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^{20}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{21}-44\,a^{19}\,b^2+138\,a^{17}\,b^4-240\,a^{15}\,b^6+250\,a^{13}\,b^8-156\,a^{11}\,b^{10}+54\,a^9\,b^{12}-8\,a^7\,b^{14}\right)+2\,a^8\,b^{13}-12\,a^{10}\,b^{11}+30\,a^{12}\,b^9-40\,a^{14}\,b^7+30\,a^{16}\,b^5-12\,a^{18}\,b^3\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)\,1{}\mathrm{i}}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}}{16\,a^2\,b^{15}-104\,a^4\,b^{13}+256\,a^6\,b^{11}-304\,a^8\,b^9+176\,a^{10}\,b^7-40\,a^{12}\,b^5-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(40\,a^{11}\,b^6-76\,a^9\,b^8+24\,a^7\,b^{10}+20\,a^5\,b^{12}-8\,a^3\,b^{14}\right)+\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{18}\,b-32\,a^{16}\,b^3+128\,a^{14}\,b^5-288\,a^{12}\,b^7+372\,a^{10}\,b^9-272\,a^8\,b^{11}+104\,a^6\,b^{13}-16\,a^4\,b^{15}\right)-8\,a^5\,b^{14}+50\,a^7\,b^{12}-124\,a^9\,b^{10}+156\,a^{11}\,b^8-104\,a^{13}\,b^6+34\,a^{15}\,b^4-4\,a^{17}\,b^2+\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^{20}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{21}-44\,a^{19}\,b^2+138\,a^{17}\,b^4-240\,a^{15}\,b^6+250\,a^{13}\,b^8-156\,a^{11}\,b^{10}+54\,a^9\,b^{12}-8\,a^7\,b^{14}\right)+2\,a^8\,b^{13}-12\,a^{10}\,b^{11}+30\,a^{12}\,b^9-40\,a^{14}\,b^7+30\,a^{16}\,b^5-12\,a^{18}\,b^3\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}+\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(8\,a^5\,b^{14}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{18}\,b-32\,a^{16}\,b^3+128\,a^{14}\,b^5-288\,a^{12}\,b^7+372\,a^{10}\,b^9-272\,a^8\,b^{11}+104\,a^6\,b^{13}-16\,a^4\,b^{15}\right)-50\,a^7\,b^{12}+124\,a^9\,b^{10}-156\,a^{11}\,b^8+104\,a^{13}\,b^6-34\,a^{15}\,b^4+4\,a^{17}\,b^2+\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^{20}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{21}-44\,a^{19}\,b^2+138\,a^{17}\,b^4-240\,a^{15}\,b^6+250\,a^{13}\,b^8-156\,a^{11}\,b^{10}+54\,a^9\,b^{12}-8\,a^7\,b^{14}\right)+2\,a^8\,b^{13}-12\,a^{10}\,b^{11}+30\,a^{12}\,b^9-40\,a^{14}\,b^7+30\,a^{16}\,b^5-12\,a^{18}\,b^3\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"(a + (2*tan(c/2 + (d*x)/2)*(5*a^4*b + 3*b^5 - 2*a^2*b^3))/(a^4 + b^4 - 2*a^2*b^2) + (4*tan(c/2 + (d*x)/2)^2*(b^6 - a^6 + 3*a^4*b^2))/(a*(a^2 - b^2)^2) - (2*b*tan(c/2 + (d*x)/2)^3*(a^4 + 3*b^4 + 2*a^2*b^2))/(a^4 + b^4 - 2*a^2*b^2) - (tan(c/2 + (d*x)/2)^4*(5*a^6 + 4*b^6 + a^2*b^4 + 2*a^4*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)))/(d*(2*a^3*tan(c/2 + (d*x)/2)^5 - 2*a^3*tan(c/2 + (d*x)/2) - 4*a^2*b*tan(c/2 + (d*x)/2)^2 + 4*a^2*b*tan(c/2 + (d*x)/2)^4)) + tan(c/2 + (d*x)/2)/(2*a^2*d) - (2*b*log(tan(c/2 + (d*x)/2)))/(a^3*d) + (b^4*atan(((b^4*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(4*a^18*b - 16*a^4*b^15 + 104*a^6*b^13 - 272*a^8*b^11 + 372*a^10*b^9 - 288*a^12*b^7 + 128*a^14*b^5 - 32*a^16*b^3) - 8*a^5*b^14 + 50*a^7*b^12 - 124*a^9*b^10 + 156*a^11*b^8 - 104*a^13*b^6 + 34*a^15*b^4 - 4*a^17*b^2 + (b^4*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^20*b - tan(c/2 + (d*x)/2)*(6*a^21 - 8*a^7*b^14 + 54*a^9*b^12 - 156*a^11*b^10 + 250*a^13*b^8 - 240*a^15*b^6 + 138*a^17*b^4 - 44*a^19*b^2) + 2*a^8*b^13 - 12*a^10*b^11 + 30*a^12*b^9 - 40*a^14*b^7 + 30*a^16*b^5 - 12*a^18*b^3))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))*1i)/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2) - (b^4*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(8*a^5*b^14 - tan(c/2 + (d*x)/2)*(4*a^18*b - 16*a^4*b^15 + 104*a^6*b^13 - 272*a^8*b^11 + 372*a^10*b^9 - 288*a^12*b^7 + 128*a^14*b^5 - 32*a^16*b^3) - 50*a^7*b^12 + 124*a^9*b^10 - 156*a^11*b^8 + 104*a^13*b^6 - 34*a^15*b^4 + 4*a^17*b^2 + (b^4*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^20*b - tan(c/2 + (d*x)/2)*(6*a^21 - 8*a^7*b^14 + 54*a^9*b^12 - 156*a^11*b^10 + 250*a^13*b^8 - 240*a^15*b^6 + 138*a^17*b^4 - 44*a^19*b^2) + 2*a^8*b^13 - 12*a^10*b^11 + 30*a^12*b^9 - 40*a^14*b^7 + 30*a^16*b^5 - 12*a^18*b^3))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))*1i)/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))/(16*a^2*b^15 - 104*a^4*b^13 + 256*a^6*b^11 - 304*a^8*b^9 + 176*a^10*b^7 - 40*a^12*b^5 - 2*tan(c/2 + (d*x)/2)*(20*a^5*b^12 - 8*a^3*b^14 + 24*a^7*b^10 - 76*a^9*b^8 + 40*a^11*b^6) + (b^4*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(4*a^18*b - 16*a^4*b^15 + 104*a^6*b^13 - 272*a^8*b^11 + 372*a^10*b^9 - 288*a^12*b^7 + 128*a^14*b^5 - 32*a^16*b^3) - 8*a^5*b^14 + 50*a^7*b^12 - 124*a^9*b^10 + 156*a^11*b^8 - 104*a^13*b^6 + 34*a^15*b^4 - 4*a^17*b^2 + (b^4*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^20*b - tan(c/2 + (d*x)/2)*(6*a^21 - 8*a^7*b^14 + 54*a^9*b^12 - 156*a^11*b^10 + 250*a^13*b^8 - 240*a^15*b^6 + 138*a^17*b^4 - 44*a^19*b^2) + 2*a^8*b^13 - 12*a^10*b^11 + 30*a^12*b^9 - 40*a^14*b^7 + 30*a^16*b^5 - 12*a^18*b^3))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2) + (b^4*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(8*a^5*b^14 - tan(c/2 + (d*x)/2)*(4*a^18*b - 16*a^4*b^15 + 104*a^6*b^13 - 272*a^8*b^11 + 372*a^10*b^9 - 288*a^12*b^7 + 128*a^14*b^5 - 32*a^16*b^3) - 50*a^7*b^12 + 124*a^9*b^10 - 156*a^11*b^8 + 104*a^13*b^6 - 34*a^15*b^4 + 4*a^17*b^2 + (b^4*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^20*b - tan(c/2 + (d*x)/2)*(6*a^21 - 8*a^7*b^14 + 54*a^9*b^12 - 156*a^11*b^10 + 250*a^13*b^8 - 240*a^15*b^6 + 138*a^17*b^4 - 44*a^19*b^2) + 2*a^8*b^13 - 12*a^10*b^11 + 30*a^12*b^9 - 40*a^14*b^7 + 30*a^16*b^5 - 12*a^18*b^3))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(5*a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
1470,1,2302,295,14.093391,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^3*(a + b*sin(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(17\,a^6-66\,a^4\,b^2+33\,a^2\,b^4-32\,b^6\right)}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{a^2}{2}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^6+2\,a^4\,b^2-2\,a^2\,b^4+2\,b^6\right)}{a^4-2\,a^2\,b^2+b^4}+3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(5\,a^6\,b-2\,a^4\,b^3+a^2\,b^5+2\,b^7\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^6\,b+14\,a^4\,b^3+a^2\,b^5+8\,b^7\right)}{a\,{\left(a^2-b^2\right)}^2}}{d\,\left(-4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-8\,b\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,b\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^2+6\,b^2\right)}{2\,a^4\,d}-\frac{b^5\,\mathrm{atan}\left(\frac{\frac{b^5\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{22}-144\,a^{20}\,b^2+264\,a^{18}\,b^4+288\,a^{16}\,b^6-1944\,a^{14}\,b^8+3312\,a^{12}\,b^{10}-2760\,a^{10}\,b^{12}+1152\,a^8\,b^{14}-192\,a^6\,b^{16}\right)-24\,a^{21}\,b-96\,a^7\,b^{15}+552\,a^9\,b^{13}-1248\,a^{11}\,b^{11}+1368\,a^{13}\,b^9-672\,a^{15}\,b^7+24\,a^{17}\,b^5+96\,a^{19}\,b^3+\frac{3\,b^5\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(16\,a^{23}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{24}-352\,a^{22}\,b^2+1104\,a^{20}\,b^4-1920\,a^{18}\,b^6+2000\,a^{16}\,b^8-1248\,a^{14}\,b^{10}+432\,a^{12}\,b^{12}-64\,a^{10}\,b^{14}\right)+16\,a^{11}\,b^{13}-96\,a^{13}\,b^{11}+240\,a^{15}\,b^9-320\,a^{17}\,b^7+240\,a^{19}\,b^5-96\,a^{21}\,b^3\right)}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}\right)\,3{}\mathrm{i}}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}-\frac{b^5\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(24\,a^{21}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{22}-144\,a^{20}\,b^2+264\,a^{18}\,b^4+288\,a^{16}\,b^6-1944\,a^{14}\,b^8+3312\,a^{12}\,b^{10}-2760\,a^{10}\,b^{12}+1152\,a^8\,b^{14}-192\,a^6\,b^{16}\right)+96\,a^7\,b^{15}-552\,a^9\,b^{13}+1248\,a^{11}\,b^{11}-1368\,a^{13}\,b^9+672\,a^{15}\,b^7-24\,a^{17}\,b^5-96\,a^{19}\,b^3+\frac{3\,b^5\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(16\,a^{23}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{24}-352\,a^{22}\,b^2+1104\,a^{20}\,b^4-1920\,a^{18}\,b^6+2000\,a^{16}\,b^8-1248\,a^{14}\,b^{10}+432\,a^{12}\,b^{12}-64\,a^{10}\,b^{14}\right)+16\,a^{11}\,b^{13}-96\,a^{13}\,b^{11}+240\,a^{15}\,b^9-320\,a^{17}\,b^7+240\,a^{19}\,b^5-96\,a^{21}\,b^3\right)}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}\right)\,3{}\mathrm{i}}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-288\,a^{14}\,b^6+720\,a^{12}\,b^8-864\,a^{10}\,b^{10}+864\,a^8\,b^{12}-576\,a^6\,b^{14}+144\,a^4\,b^{16}\right)+288\,a^3\,b^{17}-1584\,a^5\,b^{15}+3168\,a^7\,b^{13}-2592\,a^9\,b^{11}+288\,a^{11}\,b^9+720\,a^{13}\,b^7-288\,a^{15}\,b^5+\frac{3\,b^5\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{22}-144\,a^{20}\,b^2+264\,a^{18}\,b^4+288\,a^{16}\,b^6-1944\,a^{14}\,b^8+3312\,a^{12}\,b^{10}-2760\,a^{10}\,b^{12}+1152\,a^8\,b^{14}-192\,a^6\,b^{16}\right)-24\,a^{21}\,b-96\,a^7\,b^{15}+552\,a^9\,b^{13}-1248\,a^{11}\,b^{11}+1368\,a^{13}\,b^9-672\,a^{15}\,b^7+24\,a^{17}\,b^5+96\,a^{19}\,b^3+\frac{3\,b^5\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(16\,a^{23}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{24}-352\,a^{22}\,b^2+1104\,a^{20}\,b^4-1920\,a^{18}\,b^6+2000\,a^{16}\,b^8-1248\,a^{14}\,b^{10}+432\,a^{12}\,b^{12}-64\,a^{10}\,b^{14}\right)+16\,a^{11}\,b^{13}-96\,a^{13}\,b^{11}+240\,a^{15}\,b^9-320\,a^{17}\,b^7+240\,a^{19}\,b^5-96\,a^{21}\,b^3\right)}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}\right)}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}+\frac{3\,b^5\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(24\,a^{21}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{22}-144\,a^{20}\,b^2+264\,a^{18}\,b^4+288\,a^{16}\,b^6-1944\,a^{14}\,b^8+3312\,a^{12}\,b^{10}-2760\,a^{10}\,b^{12}+1152\,a^8\,b^{14}-192\,a^6\,b^{16}\right)+96\,a^7\,b^{15}-552\,a^9\,b^{13}+1248\,a^{11}\,b^{11}-1368\,a^{13}\,b^9+672\,a^{15}\,b^7-24\,a^{17}\,b^5-96\,a^{19}\,b^3+\frac{3\,b^5\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(16\,a^{23}\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{24}-352\,a^{22}\,b^2+1104\,a^{20}\,b^4-1920\,a^{18}\,b^6+2000\,a^{16}\,b^8-1248\,a^{14}\,b^{10}+432\,a^{12}\,b^{12}-64\,a^{10}\,b^{14}\right)+16\,a^{11}\,b^{13}-96\,a^{13}\,b^{11}+240\,a^{15}\,b^9-320\,a^{17}\,b^7+240\,a^{19}\,b^5-96\,a^{21}\,b^3\right)}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}\right)}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,6{}\mathrm{i}}{d\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^2*d) + ((tan(c/2 + (d*x)/2)^4*(17*a^6 - 32*b^6 + 33*a^2*b^4 - 66*a^4*b^2))/(2*(a^4 + b^4 - 2*a^2*b^2)) - a^2/2 + (8*tan(c/2 + (d*x)/2)^2*(a^6 + 2*b^6 - 2*a^2*b^4 + 2*a^4*b^2))/(a^4 + b^4 - 2*a^2*b^2) + 3*a*b*tan(c/2 + (d*x)/2) - (4*tan(c/2 + (d*x)/2)^5*(5*a^6*b + 2*b^7 + a^2*b^5 - 2*a^4*b^3))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^3*(a^6*b + 8*b^7 + a^2*b^5 + 14*a^4*b^3))/(a*(a^2 - b^2)^2))/(d*(4*a^4*tan(c/2 + (d*x)/2)^2 - 4*a^4*tan(c/2 + (d*x)/2)^6 + 8*a^3*b*tan(c/2 + (d*x)/2)^3 - 8*a^3*b*tan(c/2 + (d*x)/2)^5)) - (b*tan(c/2 + (d*x)/2))/(a^3*d) + (log(tan(c/2 + (d*x)/2))*(3*a^2 + 6*b^2))/(2*a^4*d) - (b^5*atan(((b^5*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(24*a^22 - 192*a^6*b^16 + 1152*a^8*b^14 - 2760*a^10*b^12 + 3312*a^12*b^10 - 1944*a^14*b^8 + 288*a^16*b^6 + 264*a^18*b^4 - 144*a^20*b^2) - 24*a^21*b - 96*a^7*b^15 + 552*a^9*b^13 - 1248*a^11*b^11 + 1368*a^13*b^9 - 672*a^15*b^7 + 24*a^17*b^5 + 96*a^19*b^3 + (3*b^5*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(16*a^23*b - tan(c/2 + (d*x)/2)*(48*a^24 - 64*a^10*b^14 + 432*a^12*b^12 - 1248*a^14*b^10 + 2000*a^16*b^8 - 1920*a^18*b^6 + 1104*a^20*b^4 - 352*a^22*b^2) + 16*a^11*b^13 - 96*a^13*b^11 + 240*a^15*b^9 - 320*a^17*b^7 + 240*a^19*b^5 - 96*a^21*b^3))/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))*3i)/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2) - (b^5*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(24*a^21*b - tan(c/2 + (d*x)/2)*(24*a^22 - 192*a^6*b^16 + 1152*a^8*b^14 - 2760*a^10*b^12 + 3312*a^12*b^10 - 1944*a^14*b^8 + 288*a^16*b^6 + 264*a^18*b^4 - 144*a^20*b^2) + 96*a^7*b^15 - 552*a^9*b^13 + 1248*a^11*b^11 - 1368*a^13*b^9 + 672*a^15*b^7 - 24*a^17*b^5 - 96*a^19*b^3 + (3*b^5*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(16*a^23*b - tan(c/2 + (d*x)/2)*(48*a^24 - 64*a^10*b^14 + 432*a^12*b^12 - 1248*a^14*b^10 + 2000*a^16*b^8 - 1920*a^18*b^6 + 1104*a^20*b^4 - 352*a^22*b^2) + 16*a^11*b^13 - 96*a^13*b^11 + 240*a^15*b^9 - 320*a^17*b^7 + 240*a^19*b^5 - 96*a^21*b^3))/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))*3i)/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))/(2*tan(c/2 + (d*x)/2)*(144*a^4*b^16 - 576*a^6*b^14 + 864*a^8*b^12 - 864*a^10*b^10 + 720*a^12*b^8 - 288*a^14*b^6) + 288*a^3*b^17 - 1584*a^5*b^15 + 3168*a^7*b^13 - 2592*a^9*b^11 + 288*a^11*b^9 + 720*a^13*b^7 - 288*a^15*b^5 + (3*b^5*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(24*a^22 - 192*a^6*b^16 + 1152*a^8*b^14 - 2760*a^10*b^12 + 3312*a^12*b^10 - 1944*a^14*b^8 + 288*a^16*b^6 + 264*a^18*b^4 - 144*a^20*b^2) - 24*a^21*b - 96*a^7*b^15 + 552*a^9*b^13 - 1248*a^11*b^11 + 1368*a^13*b^9 - 672*a^15*b^7 + 24*a^17*b^5 + 96*a^19*b^3 + (3*b^5*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(16*a^23*b - tan(c/2 + (d*x)/2)*(48*a^24 - 64*a^10*b^14 + 432*a^12*b^12 - 1248*a^14*b^10 + 2000*a^16*b^8 - 1920*a^18*b^6 + 1104*a^20*b^4 - 352*a^22*b^2) + 16*a^11*b^13 - 96*a^13*b^11 + 240*a^15*b^9 - 320*a^17*b^7 + 240*a^19*b^5 - 96*a^21*b^3))/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2) + (3*b^5*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(24*a^21*b - tan(c/2 + (d*x)/2)*(24*a^22 - 192*a^6*b^16 + 1152*a^8*b^14 - 2760*a^10*b^12 + 3312*a^12*b^10 - 1944*a^14*b^8 + 288*a^16*b^6 + 264*a^18*b^4 - 144*a^20*b^2) + 96*a^7*b^15 - 552*a^9*b^13 + 1248*a^11*b^11 - 1368*a^13*b^9 + 672*a^15*b^7 - 24*a^17*b^5 - 96*a^19*b^3 + (3*b^5*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(16*a^23*b - tan(c/2 + (d*x)/2)*(48*a^24 - 64*a^10*b^14 + 432*a^12*b^12 - 1248*a^14*b^10 + 2000*a^16*b^8 - 1920*a^18*b^6 + 1104*a^20*b^4 - 352*a^22*b^2) + 16*a^11*b^13 - 96*a^13*b^11 + 240*a^15*b^9 - 320*a^17*b^7 + 240*a^19*b^5 - 96*a^21*b^3))/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(2*a^2 - b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*6i)/(d*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))","B"
1471,1,585,388,18.233002,"\text{Not used}","int(sin(c + d*x)^4/(cos(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","\frac{\frac{13\,a^4\,b+2\,a^2\,b^3}{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)}^3\,\left(a^5+6\,a^3\,b^2+8\,a\,b^4\right)}{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(2\,a^4\,b+9\,a^2\,b^3+4\,b^5\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3\,a^4+40\,a^2\,b^2+8\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^2+4\,b^2\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{9\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+4\,b^2\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{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\,a^2\,\mathrm{atan}\left(\frac{\frac{3\,a^2\,\left(a^2+4\,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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,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}}}{3\,a^4+12\,a^2\,b^2}\right)\,\left(a^2+4\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((13*a^4*b + 2*a^2*b^3)/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (2*tan(c/2 + (d*x)/2)^3*(8*a*b^4 + a^5 + 6*a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (2*tan(c/2 + (d*x)/2)^2*(2*a^4*b + 4*b^5 + 9*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (a*tan(c/2 + (d*x)/2)*(8*b^4 - 3*a^4 + 40*a^2*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (3*a^3*tan(c/2 + (d*x)/2)^5*(a^2 + 4*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (9*a^2*b*tan(c/2 + (d*x)/2)^4*(a^2 + 4*b^2))/(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*a^2*atan(((3*a^2*(a^2 + 4*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^3*tan(c/2 + (d*x)/2)*(a^2 + 4*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*a^4 + 12*a^2*b^2))*(a^2 + 4*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
1472,1,583,366,17.850867,"\text{Not used}","int(sin(c + d*x)^3/(cos(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","\frac{3\,a\,b\,\mathrm{atan}\left(\frac{\frac{3\,a\,b\,\left(3\,a^2+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^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2+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}}}{9\,a^3\,b+6\,a\,b^3}\right)\,\left(3\,a^2+2\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}-\frac{\frac{4\,a^5+11\,a^3\,b^2}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^3\,b^2+2\,a\,b^4\right)}{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)}^3\,\left(3\,a^4\,b+8\,a^2\,b^3+4\,b^5\right)}{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(2\,a^5+13\,a\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^4+38\,a^2\,b^2\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^2+2\,b^2\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{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)}","Not used",1,"(3*a*b*atan(((3*a*b*(3*a^2 + 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^2*b*tan(c/2 + (d*x)/2)*(3*a^2 + 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)))/(6*a*b^3 + 9*a^3*b))*(3*a^2 + 2*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((4*a^5 + 11*a^3*b^2)/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (9*tan(c/2 + (d*x)/2)^4*(2*a*b^4 + 3*a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (2*tan(c/2 + (d*x)/2)^3*(3*a^4*b + 4*b^5 + 8*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (2*tan(c/2 + (d*x)/2)^2*(13*a*b^4 + 2*a^5))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (b*tan(c/2 + (d*x)/2)*(7*a^4 + 38*a^2*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (3*a^2*b*tan(c/2 + (d*x)/2)^5*(3*a^2 + 2*b^2))/(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)))","B"
1473,1,627,350,18.206643,"\text{Not used}","int(sin(c + d*x)^2/(cos(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","\frac{\frac{5\,\left(2\,a^4\,b+a^2\,b^3\right)}{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)}^3\,\left(2\,a^5+a^3\,b^2+12\,a\,b^4\right)}{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(2\,a^4\,b+6\,a^2\,b^3+7\,b^5\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^4\,b+11\,a^2\,b^3+2\,b^5\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^4+29\,a^2\,b^2+18\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^4+11\,a^2\,b^2+2\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{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{\mathrm{atan}\left(\frac{\frac{\left(2\,a^4+11\,a^2\,b^2+2\,b^4\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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4+11\,a^2\,b^2+2\,b^4\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\,a^4+11\,a^2\,b^2+2\,b^4}\right)\,\left(2\,a^4+11\,a^2\,b^2+2\,b^4\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((5*(2*a^4*b + a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (2*tan(c/2 + (d*x)/2)^3*(12*a*b^4 + 2*a^5 + a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (2*tan(c/2 + (d*x)/2)^2*(2*a^4*b + 7*b^5 + 6*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (3*tan(c/2 + (d*x)/2)^4*(2*a^4*b + 2*b^5 + 11*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (a*tan(c/2 + (d*x)/2)*(18*b^4 - 2*a^4 + 29*a^2*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (a*tan(c/2 + (d*x)/2)^5*(2*a^4 + 2*b^4 + 11*a^2*b^2))/(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))) - (atan((((2*a^4 + 2*b^4 + 11*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)) + (a*tan(c/2 + (d*x)/2)*(2*a^4 + 2*b^4 + 11*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)))/(2*a^4 + 2*b^4 + 11*a^2*b^2))*(2*a^4 + 2*b^4 + 11*a^2*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
1474,1,624,204,18.107034,"\text{Not used}","int(sin(c + d*x)/(cos(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","\frac{3\,a\,b\,\mathrm{atan}\left(\frac{\frac{3\,a\,b\,\left(2\,a^2+3\,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^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+3\,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}}}{6\,a^3\,b+9\,a\,b^3}\right)\,\left(2\,a^2+3\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}-\frac{\frac{2\,a^5+12\,a^3\,b^2+a\,b^4}{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)}^3\,\left(2\,a^4\,b+7\,a^2\,b^3+6\,b^5\right)}{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)}^4\,\left(-2\,a^6+24\,a^4\,b^2+21\,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{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4+39\,a^2\,b^2+4\,b^4\right)}{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(2\,a^6-2\,a^4\,b^2+14\,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{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^2+3\,b^2\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{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)}","Not used",1,"(3*a*b*atan(((3*a*b*(2*a^2 + 3*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^2*b*tan(c/2 + (d*x)/2)*(2*a^2 + 3*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/((a + b)^(7/2)*(a - b)^(7/2)))/(9*a*b^3 + 6*a^3*b))*(2*a^2 + 3*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((a*b^4 + 2*a^5 + 12*a^3*b^2)/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (2*tan(c/2 + (d*x)/2)^3*(2*a^4*b + 6*b^5 + 7*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (tan(c/2 + (d*x)/2)^4*(2*b^6 - 2*a^6 + 21*a^2*b^4 + 24*a^4*b^2))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (b*tan(c/2 + (d*x)/2)*(2*a^4 + 4*b^4 + 39*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)^2*(2*a^6 + b^6 + 14*a^2*b^4 - 2*a^4*b^2))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (3*a^2*b*tan(c/2 + (d*x)/2)^5*(2*a^2 + 3*b^2))/(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)))","B"
1475,1,2999,402,17.794339,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)*(a + b*sin(c + d*x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{\frac{2\,a^6+6\,a^4\,b^2+10\,a^2\,b^4-3\,b^6}{a\,\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\,b+22\,a^4\,b^3+29\,a^2\,b^5-8\,b^7\right)}{a^2\,\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(2\,a^6\,b+2\,a^4\,b^3+13\,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)}^5\,\left(6\,a^6\,b+2\,a^4\,b^3+11\,a^2\,b^5-4\,b^7\right)}{a^2\,\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^8-2\,a^6\,b^2+8\,a^4\,b^4+10\,a^2\,b^6-3\,b^8\right)}{a^3\,\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^8+18\,a^6\,b^2+18\,a^4\,b^4+17\,a^2\,b^6-6\,b^8\right)}{a^3\,\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{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{24}-22\,a^{22}\,b^2+148\,a^{20}\,b^4-566\,a^{18}\,b^6+1276\,a^{16}\,b^8-1790\,a^{14}\,b^{10}+1612\,a^{12}\,b^{12}-938\,a^{10}\,b^{14}+346\,a^8\,b^{16}-76\,a^6\,b^{18}+8\,a^4\,b^{20}\right)-2\,a^{23}\,b+4\,a^5\,b^{19}-37\,a^7\,b^{17}+164\,a^9\,b^{15}-433\,a^{11}\,b^{13}+722\,a^{13}\,b^{11}-769\,a^{15}\,b^9+512\,a^{17}\,b^7-199\,a^{19}\,b^5+38\,a^{21}\,b^3+\frac{b^3\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{27}-62\,a^{25}\,b^2+288\,a^{23}\,b^4-792\,a^{21}\,b^6+1428\,a^{19}\,b^8-1764\,a^{17}\,b^{10}+1512\,a^{15}\,b^{12}-888\,a^{13}\,b^{14}+342\,a^{11}\,b^{16}-78\,a^9\,b^{18}+8\,a^7\,b^{20}\right)-2\,a^{26}\,b+2\,a^8\,b^{19}-18\,a^{10}\,b^{17}+72\,a^{12}\,b^{15}-168\,a^{14}\,b^{13}+252\,a^{16}\,b^{11}-252\,a^{18}\,b^9+168\,a^{20}\,b^7-72\,a^{22}\,b^5+18\,a^{24}\,b^3\right)}{a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}}\right)\,1{}\mathrm{i}}{a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}}+\frac{b^3\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{24}-22\,a^{22}\,b^2+148\,a^{20}\,b^4-566\,a^{18}\,b^6+1276\,a^{16}\,b^8-1790\,a^{14}\,b^{10}+1612\,a^{12}\,b^{12}-938\,a^{10}\,b^{14}+346\,a^8\,b^{16}-76\,a^6\,b^{18}+8\,a^4\,b^{20}\right)-2\,a^{23}\,b+4\,a^5\,b^{19}-37\,a^7\,b^{17}+164\,a^9\,b^{15}-433\,a^{11}\,b^{13}+722\,a^{13}\,b^{11}-769\,a^{15}\,b^9+512\,a^{17}\,b^7-199\,a^{19}\,b^5+38\,a^{21}\,b^3-\frac{b^3\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{27}-62\,a^{25}\,b^2+288\,a^{23}\,b^4-792\,a^{21}\,b^6+1428\,a^{19}\,b^8-1764\,a^{17}\,b^{10}+1512\,a^{15}\,b^{12}-888\,a^{13}\,b^{14}+342\,a^{11}\,b^{16}-78\,a^9\,b^{18}+8\,a^7\,b^{20}\right)-2\,a^{26}\,b+2\,a^8\,b^{19}-18\,a^{10}\,b^{17}+72\,a^{12}\,b^{15}-168\,a^{14}\,b^{13}+252\,a^{16}\,b^{11}-252\,a^{18}\,b^9+168\,a^{20}\,b^7-72\,a^{22}\,b^5+18\,a^{24}\,b^3\right)}{a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}}\right)\,1{}\mathrm{i}}{a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(40\,a^{17}\,b^4+146\,a^{15}\,b^6-792\,a^{13}\,b^8+1135\,a^{11}\,b^{10}-715\,a^9\,b^{12}+225\,a^7\,b^{14}-41\,a^5\,b^{16}+2\,a^3\,b^{18}\right)+4\,a^2\,b^{19}-38\,a^4\,b^{17}+184\,a^6\,b^{15}-530\,a^8\,b^{13}+940\,a^{10}\,b^{11}-1034\,a^{12}\,b^9+688\,a^{14}\,b^7-254\,a^{16}\,b^5+40\,a^{18}\,b^3+\frac{b^3\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{24}-22\,a^{22}\,b^2+148\,a^{20}\,b^4-566\,a^{18}\,b^6+1276\,a^{16}\,b^8-1790\,a^{14}\,b^{10}+1612\,a^{12}\,b^{12}-938\,a^{10}\,b^{14}+346\,a^8\,b^{16}-76\,a^6\,b^{18}+8\,a^4\,b^{20}\right)-2\,a^{23}\,b+4\,a^5\,b^{19}-37\,a^7\,b^{17}+164\,a^9\,b^{15}-433\,a^{11}\,b^{13}+722\,a^{13}\,b^{11}-769\,a^{15}\,b^9+512\,a^{17}\,b^7-199\,a^{19}\,b^5+38\,a^{21}\,b^3+\frac{b^3\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{27}-62\,a^{25}\,b^2+288\,a^{23}\,b^4-792\,a^{21}\,b^6+1428\,a^{19}\,b^8-1764\,a^{17}\,b^{10}+1512\,a^{15}\,b^{12}-888\,a^{13}\,b^{14}+342\,a^{11}\,b^{16}-78\,a^9\,b^{18}+8\,a^7\,b^{20}\right)-2\,a^{26}\,b+2\,a^8\,b^{19}-18\,a^{10}\,b^{17}+72\,a^{12}\,b^{15}-168\,a^{14}\,b^{13}+252\,a^{16}\,b^{11}-252\,a^{18}\,b^9+168\,a^{20}\,b^7-72\,a^{22}\,b^5+18\,a^{24}\,b^3\right)}{a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}}\right)}{a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}}-\frac{b^3\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{24}-22\,a^{22}\,b^2+148\,a^{20}\,b^4-566\,a^{18}\,b^6+1276\,a^{16}\,b^8-1790\,a^{14}\,b^{10}+1612\,a^{12}\,b^{12}-938\,a^{10}\,b^{14}+346\,a^8\,b^{16}-76\,a^6\,b^{18}+8\,a^4\,b^{20}\right)-2\,a^{23}\,b+4\,a^5\,b^{19}-37\,a^7\,b^{17}+164\,a^9\,b^{15}-433\,a^{11}\,b^{13}+722\,a^{13}\,b^{11}-769\,a^{15}\,b^9+512\,a^{17}\,b^7-199\,a^{19}\,b^5+38\,a^{21}\,b^3-\frac{b^3\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{27}-62\,a^{25}\,b^2+288\,a^{23}\,b^4-792\,a^{21}\,b^6+1428\,a^{19}\,b^8-1764\,a^{17}\,b^{10}+1512\,a^{15}\,b^{12}-888\,a^{13}\,b^{14}+342\,a^{11}\,b^{16}-78\,a^9\,b^{18}+8\,a^7\,b^{20}\right)-2\,a^{26}\,b+2\,a^8\,b^{19}-18\,a^{10}\,b^{17}+72\,a^{12}\,b^{15}-168\,a^{14}\,b^{13}+252\,a^{16}\,b^{11}-252\,a^{18}\,b^9+168\,a^{20}\,b^7-72\,a^{22}\,b^5+18\,a^{24}\,b^3\right)}{a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}}\right)}{a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-\frac{7\,a^2\,b^2}{2}+b^4\right)\,2{}\mathrm{i}}{d\,\left(a^{17}-7\,a^{15}\,b^2+21\,a^{13}\,b^4-35\,a^{11}\,b^6+35\,a^9\,b^8-21\,a^7\,b^{10}+7\,a^5\,b^{12}-a^3\,b^{14}\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) - ((2*a^6 - 3*b^6 + 10*a^2*b^4 + 6*a^4*b^2)/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)*(2*a^6*b - 8*b^7 + 29*a^2*b^5 + 22*a^4*b^3))/(a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^3*(2*a^6*b - 2*b^7 + 13*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)^5*(6*a^6*b - 4*b^7 + 11*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)) + (2*tan(c/2 + (d*x)/2)^2*(2*a^8 - 3*b^8 + 10*a^2*b^6 + 8*a^4*b^4 - 2*a^6*b^2))/(a^3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (tan(c/2 + (d*x)/2)^4*(17*a^2*b^6 - 6*b^8 - 2*a^8 + 18*a^4*b^4 + 18*a^6*b^2))/(a^3*(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))) + (b^3*atan(((b^3*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*(tan(c/2 + (d*x)/2)*(2*a^24 + 8*a^4*b^20 - 76*a^6*b^18 + 346*a^8*b^16 - 938*a^10*b^14 + 1612*a^12*b^12 - 1790*a^14*b^10 + 1276*a^16*b^8 - 566*a^18*b^6 + 148*a^20*b^4 - 22*a^22*b^2) - 2*a^23*b + 4*a^5*b^19 - 37*a^7*b^17 + 164*a^9*b^15 - 433*a^11*b^13 + 722*a^13*b^11 - 769*a^15*b^9 + 512*a^17*b^7 - 199*a^19*b^5 + 38*a^21*b^3 + (b^3*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*(tan(c/2 + (d*x)/2)*(6*a^27 + 8*a^7*b^20 - 78*a^9*b^18 + 342*a^11*b^16 - 888*a^13*b^14 + 1512*a^15*b^12 - 1764*a^17*b^10 + 1428*a^19*b^8 - 792*a^21*b^6 + 288*a^23*b^4 - 62*a^25*b^2) - 2*a^26*b + 2*a^8*b^19 - 18*a^10*b^17 + 72*a^12*b^15 - 168*a^14*b^13 + 252*a^16*b^11 - 252*a^18*b^9 + 168*a^20*b^7 - 72*a^22*b^5 + 18*a^24*b^3))/(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2))*1i)/(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2) + (b^3*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*(tan(c/2 + (d*x)/2)*(2*a^24 + 8*a^4*b^20 - 76*a^6*b^18 + 346*a^8*b^16 - 938*a^10*b^14 + 1612*a^12*b^12 - 1790*a^14*b^10 + 1276*a^16*b^8 - 566*a^18*b^6 + 148*a^20*b^4 - 22*a^22*b^2) - 2*a^23*b + 4*a^5*b^19 - 37*a^7*b^17 + 164*a^9*b^15 - 433*a^11*b^13 + 722*a^13*b^11 - 769*a^15*b^9 + 512*a^17*b^7 - 199*a^19*b^5 + 38*a^21*b^3 - (b^3*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*(tan(c/2 + (d*x)/2)*(6*a^27 + 8*a^7*b^20 - 78*a^9*b^18 + 342*a^11*b^16 - 888*a^13*b^14 + 1512*a^15*b^12 - 1764*a^17*b^10 + 1428*a^19*b^8 - 792*a^21*b^6 + 288*a^23*b^4 - 62*a^25*b^2) - 2*a^26*b + 2*a^8*b^19 - 18*a^10*b^17 + 72*a^12*b^15 - 168*a^14*b^13 + 252*a^16*b^11 - 252*a^18*b^9 + 168*a^20*b^7 - 72*a^22*b^5 + 18*a^24*b^3))/(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2))*1i)/(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2))/(2*tan(c/2 + (d*x)/2)*(2*a^3*b^18 - 41*a^5*b^16 + 225*a^7*b^14 - 715*a^9*b^12 + 1135*a^11*b^10 - 792*a^13*b^8 + 146*a^15*b^6 + 40*a^17*b^4) + 4*a^2*b^19 - 38*a^4*b^17 + 184*a^6*b^15 - 530*a^8*b^13 + 940*a^10*b^11 - 1034*a^12*b^9 + 688*a^14*b^7 - 254*a^16*b^5 + 40*a^18*b^3 + (b^3*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*(tan(c/2 + (d*x)/2)*(2*a^24 + 8*a^4*b^20 - 76*a^6*b^18 + 346*a^8*b^16 - 938*a^10*b^14 + 1612*a^12*b^12 - 1790*a^14*b^10 + 1276*a^16*b^8 - 566*a^18*b^6 + 148*a^20*b^4 - 22*a^22*b^2) - 2*a^23*b + 4*a^5*b^19 - 37*a^7*b^17 + 164*a^9*b^15 - 433*a^11*b^13 + 722*a^13*b^11 - 769*a^15*b^9 + 512*a^17*b^7 - 199*a^19*b^5 + 38*a^21*b^3 + (b^3*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*(tan(c/2 + (d*x)/2)*(6*a^27 + 8*a^7*b^20 - 78*a^9*b^18 + 342*a^11*b^16 - 888*a^13*b^14 + 1512*a^15*b^12 - 1764*a^17*b^10 + 1428*a^19*b^8 - 792*a^21*b^6 + 288*a^23*b^4 - 62*a^25*b^2) - 2*a^26*b + 2*a^8*b^19 - 18*a^10*b^17 + 72*a^12*b^15 - 168*a^14*b^13 + 252*a^16*b^11 - 252*a^18*b^9 + 168*a^20*b^7 - 72*a^22*b^5 + 18*a^24*b^3))/(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2)))/(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2) - (b^3*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*(tan(c/2 + (d*x)/2)*(2*a^24 + 8*a^4*b^20 - 76*a^6*b^18 + 346*a^8*b^16 - 938*a^10*b^14 + 1612*a^12*b^12 - 1790*a^14*b^10 + 1276*a^16*b^8 - 566*a^18*b^6 + 148*a^20*b^4 - 22*a^22*b^2) - 2*a^23*b + 4*a^5*b^19 - 37*a^7*b^17 + 164*a^9*b^15 - 433*a^11*b^13 + 722*a^13*b^11 - 769*a^15*b^9 + 512*a^17*b^7 - 199*a^19*b^5 + 38*a^21*b^3 - (b^3*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*(tan(c/2 + (d*x)/2)*(6*a^27 + 8*a^7*b^20 - 78*a^9*b^18 + 342*a^11*b^16 - 888*a^13*b^14 + 1512*a^15*b^12 - 1764*a^17*b^10 + 1428*a^19*b^8 - 792*a^21*b^6 + 288*a^23*b^4 - 62*a^25*b^2) - 2*a^26*b + 2*a^8*b^19 - 18*a^10*b^17 + 72*a^12*b^15 - 168*a^14*b^13 + 252*a^16*b^11 - 252*a^18*b^9 + 168*a^20*b^7 - 72*a^22*b^5 + 18*a^24*b^3))/(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2)))/(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + b^4 - (7*a^2*b^2)/2)*2i)/(d*(a^17 - a^3*b^14 + 7*a^5*b^12 - 21*a^7*b^10 + 35*a^9*b^8 - 35*a^11*b^6 + 21*a^13*b^4 - 7*a^15*b^2))","B"
1476,1,3122,424,15.776958,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5\,a^8+9\,a^6\,b^2+3\,a^4\,b^4+25\,a^2\,b^6-12\,b^8\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-a^2+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(9\,a^8-7\,a^6\,b^2+23\,a^4\,b^4+55\,a^2\,b^6-20\,b^8\right)}{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)}^2\,\left(-3\,a^8+37\,a^6\,b^2+7\,a^4\,b^4+81\,a^2\,b^6-32\,b^8\right)}{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)\,\left(-8\,a^7\,b+4\,a^5\,b^3-18\,a^3\,b^5+7\,a\,b^7\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)}^3\,\left(2\,a^8\,b+2\,a^6\,b^3+4\,a^4\,b^5+12\,a^2\,b^7-5\,b^9\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(4\,a^8\,b+16\,a^6\,b^3+18\,a^4\,b^5+17\,a^2\,b^7-10\,b^9\right)}{a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left(2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^5+8\,a^3\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^5+8\,a^3\,b^2\right)-2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{b^4\,\mathrm{atan}\left(\frac{\frac{b^4\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{26}\,b-66\,a^{24}\,b^3+384\,a^{22}\,b^5-1338\,a^{20}\,b^7+2928\,a^{18}\,b^9-4170\,a^{16}\,b^{11}+3936\,a^{14}\,b^{13}-2454\,a^{12}\,b^{15}+978\,a^{10}\,b^{17}-228\,a^8\,b^{19}+24\,a^6\,b^{21}\right)+12\,a^7\,b^{20}-111\,a^9\,b^{18}+462\,a^{11}\,b^{16}-1119\,a^{13}\,b^{14}+1716\,a^{15}\,b^{12}-1707\,a^{17}\,b^{10}+1086\,a^{19}\,b^8-417\,a^{21}\,b^6+84\,a^{23}\,b^4-6\,a^{25}\,b^2-\frac{3\,b^4\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{30}-62\,a^{28}\,b^2+288\,a^{26}\,b^4-792\,a^{24}\,b^6+1428\,a^{22}\,b^8-1764\,a^{20}\,b^{10}+1512\,a^{18}\,b^{12}-888\,a^{16}\,b^{14}+342\,a^{14}\,b^{16}-78\,a^{12}\,b^{18}+8\,a^{10}\,b^{20}\right)-2\,a^{29}\,b+2\,a^{11}\,b^{19}-18\,a^{13}\,b^{17}+72\,a^{15}\,b^{15}-168\,a^{17}\,b^{13}+252\,a^{19}\,b^{11}-252\,a^{21}\,b^9+168\,a^{23}\,b^7-72\,a^{25}\,b^5+18\,a^{27}\,b^3\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{b^4\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{26}\,b-66\,a^{24}\,b^3+384\,a^{22}\,b^5-1338\,a^{20}\,b^7+2928\,a^{18}\,b^9-4170\,a^{16}\,b^{11}+3936\,a^{14}\,b^{13}-2454\,a^{12}\,b^{15}+978\,a^{10}\,b^{17}-228\,a^8\,b^{19}+24\,a^6\,b^{21}\right)+12\,a^7\,b^{20}-111\,a^9\,b^{18}+462\,a^{11}\,b^{16}-1119\,a^{13}\,b^{14}+1716\,a^{15}\,b^{12}-1707\,a^{17}\,b^{10}+1086\,a^{19}\,b^8-417\,a^{21}\,b^6+84\,a^{23}\,b^4-6\,a^{25}\,b^2+\frac{3\,b^4\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{30}-62\,a^{28}\,b^2+288\,a^{26}\,b^4-792\,a^{24}\,b^6+1428\,a^{22}\,b^8-1764\,a^{20}\,b^{10}+1512\,a^{18}\,b^{12}-888\,a^{16}\,b^{14}+342\,a^{14}\,b^{16}-78\,a^{12}\,b^{18}+8\,a^{10}\,b^{20}\right)-2\,a^{29}\,b+2\,a^{11}\,b^{19}-18\,a^{13}\,b^{17}+72\,a^{15}\,b^{15}-168\,a^{17}\,b^{13}+252\,a^{19}\,b^{11}-252\,a^{21}\,b^9+168\,a^{23}\,b^7-72\,a^{25}\,b^5+18\,a^{27}\,b^3\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(180\,a^{18}\,b^6-306\,a^{16}\,b^8-468\,a^{14}\,b^{10}+1575\,a^{12}\,b^{12}-1575\,a^{10}\,b^{14}+765\,a^8\,b^{16}-189\,a^6\,b^{18}+18\,a^4\,b^{20}\right)+36\,a^3\,b^{21}-342\,a^5\,b^{19}+1476\,a^7\,b^{17}-3690\,a^9\,b^{15}+5760\,a^{11}\,b^{13}-5706\,a^{13}\,b^{11}+3492\,a^{15}\,b^9-1206\,a^{17}\,b^7+180\,a^{19}\,b^5-\frac{3\,b^4\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{26}\,b-66\,a^{24}\,b^3+384\,a^{22}\,b^5-1338\,a^{20}\,b^7+2928\,a^{18}\,b^9-4170\,a^{16}\,b^{11}+3936\,a^{14}\,b^{13}-2454\,a^{12}\,b^{15}+978\,a^{10}\,b^{17}-228\,a^8\,b^{19}+24\,a^6\,b^{21}\right)+12\,a^7\,b^{20}-111\,a^9\,b^{18}+462\,a^{11}\,b^{16}-1119\,a^{13}\,b^{14}+1716\,a^{15}\,b^{12}-1707\,a^{17}\,b^{10}+1086\,a^{19}\,b^8-417\,a^{21}\,b^6+84\,a^{23}\,b^4-6\,a^{25}\,b^2-\frac{3\,b^4\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{30}-62\,a^{28}\,b^2+288\,a^{26}\,b^4-792\,a^{24}\,b^6+1428\,a^{22}\,b^8-1764\,a^{20}\,b^{10}+1512\,a^{18}\,b^{12}-888\,a^{16}\,b^{14}+342\,a^{14}\,b^{16}-78\,a^{12}\,b^{18}+8\,a^{10}\,b^{20}\right)-2\,a^{29}\,b+2\,a^{11}\,b^{19}-18\,a^{13}\,b^{17}+72\,a^{15}\,b^{15}-168\,a^{17}\,b^{13}+252\,a^{19}\,b^{11}-252\,a^{21}\,b^9+168\,a^{23}\,b^7-72\,a^{25}\,b^5+18\,a^{27}\,b^3\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{3\,b^4\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{26}\,b-66\,a^{24}\,b^3+384\,a^{22}\,b^5-1338\,a^{20}\,b^7+2928\,a^{18}\,b^9-4170\,a^{16}\,b^{11}+3936\,a^{14}\,b^{13}-2454\,a^{12}\,b^{15}+978\,a^{10}\,b^{17}-228\,a^8\,b^{19}+24\,a^6\,b^{21}\right)+12\,a^7\,b^{20}-111\,a^9\,b^{18}+462\,a^{11}\,b^{16}-1119\,a^{13}\,b^{14}+1716\,a^{15}\,b^{12}-1707\,a^{17}\,b^{10}+1086\,a^{19}\,b^8-417\,a^{21}\,b^6+84\,a^{23}\,b^4-6\,a^{25}\,b^2+\frac{3\,b^4\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{30}-62\,a^{28}\,b^2+288\,a^{26}\,b^4-792\,a^{24}\,b^6+1428\,a^{22}\,b^8-1764\,a^{20}\,b^{10}+1512\,a^{18}\,b^{12}-888\,a^{16}\,b^{14}+342\,a^{14}\,b^{16}-78\,a^{12}\,b^{18}+8\,a^{10}\,b^{20}\right)-2\,a^{29}\,b+2\,a^{11}\,b^{19}-18\,a^{13}\,b^{17}+72\,a^{15}\,b^{15}-168\,a^{17}\,b^{13}+252\,a^{19}\,b^{11}-252\,a^{21}\,b^9+168\,a^{23}\,b^7-72\,a^{25}\,b^5+18\,a^{27}\,b^3\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,a^4-7\,a^2\,b^2+2\,b^4\right)\,3{}\mathrm{i}}{d\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - ((tan(c/2 + (d*x)/2)^6*(5*a^8 - 12*b^8 + 25*a^2*b^6 + 3*a^4*b^4 + 9*a^6*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - a^2 + (tan(c/2 + (d*x)/2)^4*(9*a^8 - 20*b^8 + 55*a^2*b^6 + 23*a^4*b^4 - 7*a^6*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (tan(c/2 + (d*x)/2)^2*(81*a^2*b^6 - 32*b^8 - 3*a^8 + 7*a^4*b^4 + 37*a^6*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (2*tan(c/2 + (d*x)/2)*(7*a*b^7 - 8*a^7*b - 18*a^3*b^5 + 4*a^5*b^3))/(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*b - 5*b^9 + 12*a^2*b^7 + 4*a^4*b^5 + 2*a^6*b^3))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^5*(4*a^8*b - 10*b^9 + 17*a^2*b^7 + 18*a^4*b^5 + 16*a^6*b^3))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(2*a^5*tan(c/2 + (d*x)/2)^7 - tan(c/2 + (d*x)/2)^3*(2*a^5 + 8*a^3*b^2) + tan(c/2 + (d*x)/2)^5*(2*a^5 + 8*a^3*b^2) - 2*a^5*tan(c/2 + (d*x)/2) - 8*a^4*b*tan(c/2 + (d*x)/2)^2 + 8*a^4*b*tan(c/2 + (d*x)/2)^6)) - (3*b*log(tan(c/2 + (d*x)/2)))/(a^4*d) - (b^4*atan(((b^4*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*(tan(c/2 + (d*x)/2)*(6*a^26*b + 24*a^6*b^21 - 228*a^8*b^19 + 978*a^10*b^17 - 2454*a^12*b^15 + 3936*a^14*b^13 - 4170*a^16*b^11 + 2928*a^18*b^9 - 1338*a^20*b^7 + 384*a^22*b^5 - 66*a^24*b^3) + 12*a^7*b^20 - 111*a^9*b^18 + 462*a^11*b^16 - 1119*a^13*b^14 + 1716*a^15*b^12 - 1707*a^17*b^10 + 1086*a^19*b^8 - 417*a^21*b^6 + 84*a^23*b^4 - 6*a^25*b^2 - (3*b^4*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*(tan(c/2 + (d*x)/2)*(6*a^30 + 8*a^10*b^20 - 78*a^12*b^18 + 342*a^14*b^16 - 888*a^16*b^14 + 1512*a^18*b^12 - 1764*a^20*b^10 + 1428*a^22*b^8 - 792*a^24*b^6 + 288*a^26*b^4 - 62*a^28*b^2) - 2*a^29*b + 2*a^11*b^19 - 18*a^13*b^17 + 72*a^15*b^15 - 168*a^17*b^13 + 252*a^19*b^11 - 252*a^21*b^9 + 168*a^23*b^7 - 72*a^25*b^5 + 18*a^27*b^3))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*3i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (b^4*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*(tan(c/2 + (d*x)/2)*(6*a^26*b + 24*a^6*b^21 - 228*a^8*b^19 + 978*a^10*b^17 - 2454*a^12*b^15 + 3936*a^14*b^13 - 4170*a^16*b^11 + 2928*a^18*b^9 - 1338*a^20*b^7 + 384*a^22*b^5 - 66*a^24*b^3) + 12*a^7*b^20 - 111*a^9*b^18 + 462*a^11*b^16 - 1119*a^13*b^14 + 1716*a^15*b^12 - 1707*a^17*b^10 + 1086*a^19*b^8 - 417*a^21*b^6 + 84*a^23*b^4 - 6*a^25*b^2 + (3*b^4*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*(tan(c/2 + (d*x)/2)*(6*a^30 + 8*a^10*b^20 - 78*a^12*b^18 + 342*a^14*b^16 - 888*a^16*b^14 + 1512*a^18*b^12 - 1764*a^20*b^10 + 1428*a^22*b^8 - 792*a^24*b^6 + 288*a^26*b^4 - 62*a^28*b^2) - 2*a^29*b + 2*a^11*b^19 - 18*a^13*b^17 + 72*a^15*b^15 - 168*a^17*b^13 + 252*a^19*b^11 - 252*a^21*b^9 + 168*a^23*b^7 - 72*a^25*b^5 + 18*a^27*b^3))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*3i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))/(2*tan(c/2 + (d*x)/2)*(18*a^4*b^20 - 189*a^6*b^18 + 765*a^8*b^16 - 1575*a^10*b^14 + 1575*a^12*b^12 - 468*a^14*b^10 - 306*a^16*b^8 + 180*a^18*b^6) + 36*a^3*b^21 - 342*a^5*b^19 + 1476*a^7*b^17 - 3690*a^9*b^15 + 5760*a^11*b^13 - 5706*a^13*b^11 + 3492*a^15*b^9 - 1206*a^17*b^7 + 180*a^19*b^5 - (3*b^4*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*(tan(c/2 + (d*x)/2)*(6*a^26*b + 24*a^6*b^21 - 228*a^8*b^19 + 978*a^10*b^17 - 2454*a^12*b^15 + 3936*a^14*b^13 - 4170*a^16*b^11 + 2928*a^18*b^9 - 1338*a^20*b^7 + 384*a^22*b^5 - 66*a^24*b^3) + 12*a^7*b^20 - 111*a^9*b^18 + 462*a^11*b^16 - 1119*a^13*b^14 + 1716*a^15*b^12 - 1707*a^17*b^10 + 1086*a^19*b^8 - 417*a^21*b^6 + 84*a^23*b^4 - 6*a^25*b^2 - (3*b^4*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*(tan(c/2 + (d*x)/2)*(6*a^30 + 8*a^10*b^20 - 78*a^12*b^18 + 342*a^14*b^16 - 888*a^16*b^14 + 1512*a^18*b^12 - 1764*a^20*b^10 + 1428*a^22*b^8 - 792*a^24*b^6 + 288*a^26*b^4 - 62*a^28*b^2) - 2*a^29*b + 2*a^11*b^19 - 18*a^13*b^17 + 72*a^15*b^15 - 168*a^17*b^13 + 252*a^19*b^11 - 252*a^21*b^9 + 168*a^23*b^7 - 72*a^25*b^5 + 18*a^27*b^3))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (3*b^4*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*(tan(c/2 + (d*x)/2)*(6*a^26*b + 24*a^6*b^21 - 228*a^8*b^19 + 978*a^10*b^17 - 2454*a^12*b^15 + 3936*a^14*b^13 - 4170*a^16*b^11 + 2928*a^18*b^9 - 1338*a^20*b^7 + 384*a^22*b^5 - 66*a^24*b^3) + 12*a^7*b^20 - 111*a^9*b^18 + 462*a^11*b^16 - 1119*a^13*b^14 + 1716*a^15*b^12 - 1707*a^17*b^10 + 1086*a^19*b^8 - 417*a^21*b^6 + 84*a^23*b^4 - 6*a^25*b^2 + (3*b^4*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*(tan(c/2 + (d*x)/2)*(6*a^30 + 8*a^10*b^20 - 78*a^12*b^18 + 342*a^14*b^16 - 888*a^16*b^14 + 1512*a^18*b^12 - 1764*a^20*b^10 + 1428*a^22*b^8 - 792*a^24*b^6 + 288*a^26*b^4 - 62*a^28*b^2) - 2*a^29*b + 2*a^11*b^19 - 18*a^13*b^17 + 72*a^15*b^15 - 168*a^17*b^13 + 252*a^19*b^11 - 252*a^21*b^9 + 168*a^23*b^7 - 72*a^25*b^5 + 18*a^27*b^3))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(10*a^4 + 2*b^4 - 7*a^2*b^2)*3i)/(d*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))","B"
1477,1,3266,470,16.823985,"\text{Not used}","int(1/(cos(c + d*x)^2*sin(c + d*x)^3*(a + b*sin(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}+\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{a^3}{2}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^9+19\,a^7\,b^2-27\,a^5\,b^4+49\,a^3\,b^6-20\,a\,b^8\right)}{2\,\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(15\,a^8\,b-5\,a^6\,b^3+9\,a^4\,b^5+27\,a^2\,b^7-16\,b^9\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)}^5\,\left(5\,a^8\,b+7\,a^6\,b^3-7\,a^4\,b^5+43\,a^2\,b^7-18\,b^9\right)}{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)}^3\,\left(7\,a^8\,b+47\,a^6\,b^3-27\,a^4\,b^5+115\,a^2\,b^7-52\,b^9\right)}{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)}^4\,\left(33\,a^{10}-31\,a^8\,b^2+119\,a^6\,b^4+11\,a^4\,b^6+220\,a^2\,b^8-112\,b^{10}\right)}{2\,a\,\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(17\,a^{10}-195\,a^8\,b^2+83\,a^6\,b^4-257\,a^4\,b^6-120\,a^2\,b^8+112\,b^{10}\right)}{2\,a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left(4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,a^6+16\,a^4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^6+16\,a^4\,b^2\right)+16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}-\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^4\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^2+12\,b^2\right)}{2\,a^5\,d}+\frac{b^5\,\mathrm{atan}\left(\frac{\frac{b^5\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{30}-168\,a^{28}\,b^2+240\,a^{26}\,b^4+2112\,a^{24}\,b^6-12576\,a^{22}\,b^8+33168\,a^{20}\,b^{10}-52176\,a^{18}\,b^{12}+52800\,a^{16}\,b^{14}-34872\,a^{14}\,b^{16}+14616\,a^{12}\,b^{18}-3552\,a^{10}\,b^{20}+384\,a^8\,b^{22}\right)-24\,a^{29}\,b+192\,a^9\,b^{21}-1728\,a^{11}\,b^{19}+6888\,a^{13}\,b^{17}-15816\,a^{15}\,b^{15}+22800\,a^{17}\,b^{13}-21048\,a^{19}\,b^{11}+12048\,a^{21}\,b^9-3768\,a^{23}\,b^7+336\,a^{25}\,b^5+120\,a^{27}\,b^3-\frac{3\,b^5\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{33}-496\,a^{31}\,b^2+2304\,a^{29}\,b^4-6336\,a^{27}\,b^6+11424\,a^{25}\,b^8-14112\,a^{23}\,b^{10}+12096\,a^{21}\,b^{12}-7104\,a^{19}\,b^{14}+2736\,a^{17}\,b^{16}-624\,a^{15}\,b^{18}+64\,a^{13}\,b^{20}\right)-16\,a^{32}\,b+16\,a^{14}\,b^{19}-144\,a^{16}\,b^{17}+576\,a^{18}\,b^{15}-1344\,a^{20}\,b^{13}+2016\,a^{22}\,b^{11}-2016\,a^{24}\,b^9+1344\,a^{26}\,b^7-576\,a^{28}\,b^5+144\,a^{30}\,b^3\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}+\frac{b^5\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{30}-168\,a^{28}\,b^2+240\,a^{26}\,b^4+2112\,a^{24}\,b^6-12576\,a^{22}\,b^8+33168\,a^{20}\,b^{10}-52176\,a^{18}\,b^{12}+52800\,a^{16}\,b^{14}-34872\,a^{14}\,b^{16}+14616\,a^{12}\,b^{18}-3552\,a^{10}\,b^{20}+384\,a^8\,b^{22}\right)-24\,a^{29}\,b+192\,a^9\,b^{21}-1728\,a^{11}\,b^{19}+6888\,a^{13}\,b^{17}-15816\,a^{15}\,b^{15}+22800\,a^{17}\,b^{13}-21048\,a^{19}\,b^{11}+12048\,a^{21}\,b^9-3768\,a^{23}\,b^7+336\,a^{25}\,b^5+120\,a^{27}\,b^3+\frac{3\,b^5\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{33}-496\,a^{31}\,b^2+2304\,a^{29}\,b^4-6336\,a^{27}\,b^6+11424\,a^{25}\,b^8-14112\,a^{23}\,b^{10}+12096\,a^{21}\,b^{12}-7104\,a^{19}\,b^{14}+2736\,a^{17}\,b^{16}-624\,a^{15}\,b^{18}+64\,a^{13}\,b^{20}\right)-16\,a^{32}\,b+16\,a^{14}\,b^{19}-144\,a^{16}\,b^{17}+576\,a^{18}\,b^{15}-1344\,a^{20}\,b^{13}+2016\,a^{22}\,b^{11}-2016\,a^{24}\,b^9+1344\,a^{26}\,b^7-576\,a^{28}\,b^5+144\,a^{30}\,b^3\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1008\,a^{21}\,b^6-2952\,a^{19}\,b^8+7200\,a^{17}\,b^{10}-20376\,a^{15}\,b^{12}+35640\,a^{13}\,b^{14}-34128\,a^{11}\,b^{16}+18072\,a^9\,b^{18}-5040\,a^7\,b^{20}+576\,a^5\,b^{22}\right)+1152\,a^4\,b^{23}-10368\,a^6\,b^{21}+41112\,a^8\,b^{19}-92448\,a^{10}\,b^{17}+126792\,a^{12}\,b^{15}-105552\,a^{14}\,b^{13}+48168\,a^{16}\,b^{11}-6912\,a^{18}\,b^9-2952\,a^{20}\,b^7+1008\,a^{22}\,b^5-\frac{3\,b^5\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{30}-168\,a^{28}\,b^2+240\,a^{26}\,b^4+2112\,a^{24}\,b^6-12576\,a^{22}\,b^8+33168\,a^{20}\,b^{10}-52176\,a^{18}\,b^{12}+52800\,a^{16}\,b^{14}-34872\,a^{14}\,b^{16}+14616\,a^{12}\,b^{18}-3552\,a^{10}\,b^{20}+384\,a^8\,b^{22}\right)-24\,a^{29}\,b+192\,a^9\,b^{21}-1728\,a^{11}\,b^{19}+6888\,a^{13}\,b^{17}-15816\,a^{15}\,b^{15}+22800\,a^{17}\,b^{13}-21048\,a^{19}\,b^{11}+12048\,a^{21}\,b^9-3768\,a^{23}\,b^7+336\,a^{25}\,b^5+120\,a^{27}\,b^3-\frac{3\,b^5\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{33}-496\,a^{31}\,b^2+2304\,a^{29}\,b^4-6336\,a^{27}\,b^6+11424\,a^{25}\,b^8-14112\,a^{23}\,b^{10}+12096\,a^{21}\,b^{12}-7104\,a^{19}\,b^{14}+2736\,a^{17}\,b^{16}-624\,a^{15}\,b^{18}+64\,a^{13}\,b^{20}\right)-16\,a^{32}\,b+16\,a^{14}\,b^{19}-144\,a^{16}\,b^{17}+576\,a^{18}\,b^{15}-1344\,a^{20}\,b^{13}+2016\,a^{22}\,b^{11}-2016\,a^{24}\,b^9+1344\,a^{26}\,b^7-576\,a^{28}\,b^5+144\,a^{30}\,b^3\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}+\frac{3\,b^5\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{30}-168\,a^{28}\,b^2+240\,a^{26}\,b^4+2112\,a^{24}\,b^6-12576\,a^{22}\,b^8+33168\,a^{20}\,b^{10}-52176\,a^{18}\,b^{12}+52800\,a^{16}\,b^{14}-34872\,a^{14}\,b^{16}+14616\,a^{12}\,b^{18}-3552\,a^{10}\,b^{20}+384\,a^8\,b^{22}\right)-24\,a^{29}\,b+192\,a^9\,b^{21}-1728\,a^{11}\,b^{19}+6888\,a^{13}\,b^{17}-15816\,a^{15}\,b^{15}+22800\,a^{17}\,b^{13}-21048\,a^{19}\,b^{11}+12048\,a^{21}\,b^9-3768\,a^{23}\,b^7+336\,a^{25}\,b^5+120\,a^{27}\,b^3+\frac{3\,b^5\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(48\,a^{33}-496\,a^{31}\,b^2+2304\,a^{29}\,b^4-6336\,a^{27}\,b^6+11424\,a^{25}\,b^8-14112\,a^{23}\,b^{10}+12096\,a^{21}\,b^{12}-7104\,a^{19}\,b^{14}+2736\,a^{17}\,b^{16}-624\,a^{15}\,b^{18}+64\,a^{13}\,b^{20}\right)-16\,a^{32}\,b+16\,a^{14}\,b^{19}-144\,a^{16}\,b^{17}+576\,a^{18}\,b^{15}-1344\,a^{20}\,b^{13}+2016\,a^{22}\,b^{11}-2016\,a^{24}\,b^9+1344\,a^{26}\,b^7-576\,a^{28}\,b^5+144\,a^{30}\,b^3\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(14\,a^4-13\,a^2\,b^2+4\,b^4\right)\,3{}\mathrm{i}}{d\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a^3*d) + (4*a^2*b*tan(c/2 + (d*x)/2) - a^3/2 + (5*tan(c/2 + (d*x)/2)^2*(3*a^9 - 20*a*b^8 + 49*a^3*b^6 - 27*a^5*b^4 + 19*a^7*b^2))/(2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^7*(15*a^8*b - 16*b^9 + 27*a^2*b^7 + 9*a^4*b^5 - 5*a^6*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (4*tan(c/2 + (d*x)/2)^5*(5*a^8*b - 18*b^9 + 43*a^2*b^7 - 7*a^4*b^5 + 7*a^6*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (2*tan(c/2 + (d*x)/2)^3*(7*a^8*b - 52*b^9 + 115*a^2*b^7 - 27*a^4*b^5 + 47*a^6*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (tan(c/2 + (d*x)/2)^4*(33*a^10 - 112*b^10 + 220*a^2*b^8 + 11*a^4*b^6 + 119*a^6*b^4 - 31*a^8*b^2))/(2*a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^6*(17*a^10 + 112*b^10 - 120*a^2*b^8 - 257*a^4*b^6 + 83*a^6*b^4 - 195*a^8*b^2))/(2*a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(4*a^6*tan(c/2 + (d*x)/2)^2 - 4*a^6*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^4*(4*a^6 + 16*a^4*b^2) - tan(c/2 + (d*x)/2)^6*(4*a^6 + 16*a^4*b^2) + 16*a^5*b*tan(c/2 + (d*x)/2)^3 - 16*a^5*b*tan(c/2 + (d*x)/2)^7)) - (3*b*tan(c/2 + (d*x)/2))/(2*a^4*d) + (log(tan(c/2 + (d*x)/2))*(3*a^2 + 12*b^2))/(2*a^5*d) + (b^5*atan(((b^5*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*(tan(c/2 + (d*x)/2)*(24*a^30 + 384*a^8*b^22 - 3552*a^10*b^20 + 14616*a^12*b^18 - 34872*a^14*b^16 + 52800*a^16*b^14 - 52176*a^18*b^12 + 33168*a^20*b^10 - 12576*a^22*b^8 + 2112*a^24*b^6 + 240*a^26*b^4 - 168*a^28*b^2) - 24*a^29*b + 192*a^9*b^21 - 1728*a^11*b^19 + 6888*a^13*b^17 - 15816*a^15*b^15 + 22800*a^17*b^13 - 21048*a^19*b^11 + 12048*a^21*b^9 - 3768*a^23*b^7 + 336*a^25*b^5 + 120*a^27*b^3 - (3*b^5*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*(tan(c/2 + (d*x)/2)*(48*a^33 + 64*a^13*b^20 - 624*a^15*b^18 + 2736*a^17*b^16 - 7104*a^19*b^14 + 12096*a^21*b^12 - 14112*a^23*b^10 + 11424*a^25*b^8 - 6336*a^27*b^6 + 2304*a^29*b^4 - 496*a^31*b^2) - 16*a^32*b + 16*a^14*b^19 - 144*a^16*b^17 + 576*a^18*b^15 - 1344*a^20*b^13 + 2016*a^22*b^11 - 2016*a^24*b^9 + 1344*a^26*b^7 - 576*a^28*b^5 + 144*a^30*b^3))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*3i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) + (b^5*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*(tan(c/2 + (d*x)/2)*(24*a^30 + 384*a^8*b^22 - 3552*a^10*b^20 + 14616*a^12*b^18 - 34872*a^14*b^16 + 52800*a^16*b^14 - 52176*a^18*b^12 + 33168*a^20*b^10 - 12576*a^22*b^8 + 2112*a^24*b^6 + 240*a^26*b^4 - 168*a^28*b^2) - 24*a^29*b + 192*a^9*b^21 - 1728*a^11*b^19 + 6888*a^13*b^17 - 15816*a^15*b^15 + 22800*a^17*b^13 - 21048*a^19*b^11 + 12048*a^21*b^9 - 3768*a^23*b^7 + 336*a^25*b^5 + 120*a^27*b^3 + (3*b^5*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*(tan(c/2 + (d*x)/2)*(48*a^33 + 64*a^13*b^20 - 624*a^15*b^18 + 2736*a^17*b^16 - 7104*a^19*b^14 + 12096*a^21*b^12 - 14112*a^23*b^10 + 11424*a^25*b^8 - 6336*a^27*b^6 + 2304*a^29*b^4 - 496*a^31*b^2) - 16*a^32*b + 16*a^14*b^19 - 144*a^16*b^17 + 576*a^18*b^15 - 1344*a^20*b^13 + 2016*a^22*b^11 - 2016*a^24*b^9 + 1344*a^26*b^7 - 576*a^28*b^5 + 144*a^30*b^3))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*3i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))/(2*tan(c/2 + (d*x)/2)*(576*a^5*b^22 - 5040*a^7*b^20 + 18072*a^9*b^18 - 34128*a^11*b^16 + 35640*a^13*b^14 - 20376*a^15*b^12 + 7200*a^17*b^10 - 2952*a^19*b^8 + 1008*a^21*b^6) + 1152*a^4*b^23 - 10368*a^6*b^21 + 41112*a^8*b^19 - 92448*a^10*b^17 + 126792*a^12*b^15 - 105552*a^14*b^13 + 48168*a^16*b^11 - 6912*a^18*b^9 - 2952*a^20*b^7 + 1008*a^22*b^5 - (3*b^5*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*(tan(c/2 + (d*x)/2)*(24*a^30 + 384*a^8*b^22 - 3552*a^10*b^20 + 14616*a^12*b^18 - 34872*a^14*b^16 + 52800*a^16*b^14 - 52176*a^18*b^12 + 33168*a^20*b^10 - 12576*a^22*b^8 + 2112*a^24*b^6 + 240*a^26*b^4 - 168*a^28*b^2) - 24*a^29*b + 192*a^9*b^21 - 1728*a^11*b^19 + 6888*a^13*b^17 - 15816*a^15*b^15 + 22800*a^17*b^13 - 21048*a^19*b^11 + 12048*a^21*b^9 - 3768*a^23*b^7 + 336*a^25*b^5 + 120*a^27*b^3 - (3*b^5*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*(tan(c/2 + (d*x)/2)*(48*a^33 + 64*a^13*b^20 - 624*a^15*b^18 + 2736*a^17*b^16 - 7104*a^19*b^14 + 12096*a^21*b^12 - 14112*a^23*b^10 + 11424*a^25*b^8 - 6336*a^27*b^6 + 2304*a^29*b^4 - 496*a^31*b^2) - 16*a^32*b + 16*a^14*b^19 - 144*a^16*b^17 + 576*a^18*b^15 - 1344*a^20*b^13 + 2016*a^22*b^11 - 2016*a^24*b^9 + 1344*a^26*b^7 - 576*a^28*b^5 + 144*a^30*b^3))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) + (3*b^5*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*(tan(c/2 + (d*x)/2)*(24*a^30 + 384*a^8*b^22 - 3552*a^10*b^20 + 14616*a^12*b^18 - 34872*a^14*b^16 + 52800*a^16*b^14 - 52176*a^18*b^12 + 33168*a^20*b^10 - 12576*a^22*b^8 + 2112*a^24*b^6 + 240*a^26*b^4 - 168*a^28*b^2) - 24*a^29*b + 192*a^9*b^21 - 1728*a^11*b^19 + 6888*a^13*b^17 - 15816*a^15*b^15 + 22800*a^17*b^13 - 21048*a^19*b^11 + 12048*a^21*b^9 - 3768*a^23*b^7 + 336*a^25*b^5 + 120*a^27*b^3 + (3*b^5*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*(tan(c/2 + (d*x)/2)*(48*a^33 + 64*a^13*b^20 - 624*a^15*b^18 + 2736*a^17*b^16 - 7104*a^19*b^14 + 12096*a^21*b^12 - 14112*a^23*b^10 + 11424*a^25*b^8 - 6336*a^27*b^6 + 2304*a^29*b^4 - 496*a^31*b^2) - 16*a^32*b + 16*a^14*b^19 - 144*a^16*b^17 + 576*a^18*b^15 - 1344*a^20*b^13 + 2016*a^22*b^11 - 2016*a^24*b^9 + 1344*a^26*b^7 - 576*a^28*b^5 + 144*a^30*b^3))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(14*a^4 + 4*b^4 - 13*a^2*b^2)*3i)/(d*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))","B"
1478,0,-1,158,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/(cos(e + f*x)^2*(d*sin(e + f*x))^(1/2)),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{{\cos\left(e+f\,x\right)}^2\,\sqrt{d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/(cos(e + f*x)^2*(d*sin(e + f*x))^(1/2)), x)","F"
1479,0,-1,312,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(3/2)/(cos(e + f*x)^2*(d*sin(e + f*x))^(1/2)),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\cos\left(e+f\,x\right)}^2\,\sqrt{d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(3/2)/(cos(e + f*x)^2*(d*sin(e + f*x))^(1/2)), x)","F"
1480,0,-1,366,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(5/2)/(cos(e + f*x)^4*(d*sin(e + f*x))^(1/2)),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\cos\left(e+f\,x\right)}^4\,\sqrt{d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(5/2)/(cos(e + f*x)^4*(d*sin(e + f*x))^(1/2)), x)","F"
1481,1,346,155,12.270667,"\text{Not used}","int((sin(c + d*x)^7*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{3\,a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{-\frac{35\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\frac{35\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{6}+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{329\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-17\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{329\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{35\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{35\,b\,\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)}^{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{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(3\,a+\frac{35\,b}{8}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(3\,a-\frac{35\,b}{8}\right)}{d}","Not used",1,"(3*a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (6*a*tan(c/2 + (d*x)/2)^4 - 6*a*tan(c/2 + (d*x)/2)^2 - (35*b*tan(c/2 + (d*x)/2))/4 + 16*a*tan(c/2 + (d*x)/2)^6 + 16*a*tan(c/2 + (d*x)/2)^8 + 6*a*tan(c/2 + (d*x)/2)^10 - 6*a*tan(c/2 + (d*x)/2)^12 + (35*b*tan(c/2 + (d*x)/2)^3)/6 + (329*b*tan(c/2 + (d*x)/2)^5)/12 - 17*b*tan(c/2 + (d*x)/2)^7 + (329*b*tan(c/2 + (d*x)/2)^9)/12 + (35*b*tan(c/2 + (d*x)/2)^11)/6 - (35*b*tan(c/2 + (d*x)/2)^13)/4)/(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)) - (log(tan(c/2 + (d*x)/2) - 1)*(3*a + (35*b)/8))/d - (log(tan(c/2 + (d*x)/2) + 1)*(3*a - (35*b)/8))/d","B"
1482,1,304,135,12.156573,"\text{Not used}","int((sin(c + d*x)^6*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{3\,b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{15\,a}{8}+3\,b\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{15\,a}{8}-3\,b\right)}{d}-\frac{-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{4}-6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{25\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+12\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{11\,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)}^6+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}+12\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{25\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}-6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{15\,a\,\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)}^{12}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(3*b*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (log(tan(c/2 + (d*x)/2) - 1)*((15*a)/8 + 3*b))/d + (log(tan(c/2 + (d*x)/2) + 1)*((15*a)/8 - 3*b))/d - ((25*a*tan(c/2 + (d*x)/2)^3)/4 - (15*a*tan(c/2 + (d*x)/2))/4 + (11*a*tan(c/2 + (d*x)/2)^5)/2 + (11*a*tan(c/2 + (d*x)/2)^7)/2 + (25*a*tan(c/2 + (d*x)/2)^9)/4 - (15*a*tan(c/2 + (d*x)/2)^11)/4 - 6*b*tan(c/2 + (d*x)/2)^2 + 12*b*tan(c/2 + (d*x)/2)^4 + 4*b*tan(c/2 + (d*x)/2)^6 + 12*b*tan(c/2 + (d*x)/2)^8 - 6*b*tan(c/2 + (d*x)/2)^10)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 2*tan(c/2 + (d*x)/2)^10 - tan(c/2 + (d*x)/2)^12 - 1))","B"
1483,1,261,116,12.099386,"\text{Not used}","int((sin(c + d*x)^5*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a-\frac{15\,b}{8}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(a+\frac{15\,b}{8}\right)}{d}-\frac{\frac{15\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-10\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{9\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-10\,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+\frac{15\,b\,\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)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\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)}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (log(tan(c/2 + (d*x)/2) + 1)*(a - (15*b)/8))/d - (log(tan(c/2 + (d*x)/2) - 1)*(a + (15*b)/8))/d - ((15*b*tan(c/2 + (d*x)/2))/4 + 2*a*tan(c/2 + (d*x)/2)^2 - 6*a*tan(c/2 + (d*x)/2)^4 - 6*a*tan(c/2 + (d*x)/2)^6 + 2*a*tan(c/2 + (d*x)/2)^8 - 10*b*tan(c/2 + (d*x)/2)^3 + (9*b*tan(c/2 + (d*x)/2)^5)/2 - 10*b*tan(c/2 + (d*x)/2)^7 + (15*b*tan(c/2 + (d*x)/2)^9)/4)/(d*(2*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1))","B"
1484,1,221,103,12.029702,"\text{Not used}","int((sin(c + d*x)^4*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{3\,a\,\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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{3\,a}{8}+b\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{3\,a}{8}-b\right)}{d}","Not used",1,"(b*log(tan(c/2 + (d*x)/2)^2 + 1))/d - ((3*a*tan(c/2 + (d*x)/2))/4 - (11*a*tan(c/2 + (d*x)/2)^3)/4 - (11*a*tan(c/2 + (d*x)/2)^5)/4 + (3*a*tan(c/2 + (d*x)/2)^7)/4 + 2*b*tan(c/2 + (d*x)/2)^2 - 8*b*tan(c/2 + (d*x)/2)^4 + 2*b*tan(c/2 + (d*x)/2)^6)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (log(tan(c/2 + (d*x)/2) - 1)*((3*a)/8 + b))/d + (log(tan(c/2 + (d*x)/2) + 1)*((3*a)/8 - b))/d","B"
1485,1,144,74,18.079883,"\text{Not used}","int((sin(c + d*x)^3*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{11\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{11\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}-\frac{3\,b\,\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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{3\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"(4*a*tan(c/2 + (d*x)/2)^4 - (3*b*tan(c/2 + (d*x)/2))/4 + (11*b*tan(c/2 + (d*x)/2)^3)/4 + (11*b*tan(c/2 + (d*x)/2)^5)/4 - (3*b*tan(c/2 + (d*x)/2)^7)/4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (3*b*atanh(tan(c/2 + (d*x)/2)))/(4*d)","B"
1486,1,144,74,18.068718,"\text{Not used}","int((sin(c + d*x)^2*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+4\,b\,{\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}{4}+\frac{a\,\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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"((a*tan(c/2 + (d*x)/2))/4 + (7*a*tan(c/2 + (d*x)/2)^3)/4 + (7*a*tan(c/2 + (d*x)/2)^5)/4 + (a*tan(c/2 + (d*x)/2)^7)/4 + 4*b*tan(c/2 + (d*x)/2)^4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (a*atanh(tan(c/2 + (d*x)/2)))/(4*d)","B"
1487,1,158,74,18.538573,"\text{Not used}","int((sin(c + d*x)*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{b\,\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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"((b*tan(c/2 + (d*x)/2))/4 + 2*a*tan(c/2 + (d*x)/2)^2 + 2*a*tan(c/2 + (d*x)/2)^6 + (7*b*tan(c/2 + (d*x)/2)^3)/4 + (7*b*tan(c/2 + (d*x)/2)^5)/4 + (b*tan(c/2 + (d*x)/2)^7)/4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (b*atanh(tan(c/2 + (d*x)/2)))/(4*d)","B"
1488,1,116,99,11.873732,"\text{Not used}","int((a + b*sin(c + d*x))/(cos(c + d*x)^5*sin(c + d*x)),x)","\frac{-\frac{3\,b\,{\sin\left(c+d\,x\right)}^3}{8}-\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{5\,b\,\sin\left(c+d\,x\right)}{8}+\frac{3\,a}{4}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2+1\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{a}{2}-\frac{3\,b}{16}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{a}{2}+\frac{3\,b}{16}\right)}{d}+\frac{a\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}","Not used",1,"((3*a)/4 + (5*b*sin(c + d*x))/8 - (a*sin(c + d*x)^2)/2 - (3*b*sin(c + d*x)^3)/8)/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1)) - (log(sin(c + d*x) + 1)*(a/2 - (3*b)/16))/d - (log(sin(c + d*x) - 1)*(a/2 + (3*b)/16))/d + (a*log(sin(c + d*x)))/d","B"
1489,1,130,115,11.886768,"\text{Not used}","int((a + b*sin(c + d*x))/(cos(c + d*x)^5*sin(c + d*x)^2),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{15\,a}{16}-\frac{b}{2}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{15\,a}{16}+\frac{b}{2}\right)}{d}+\frac{b\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{\frac{15\,a\,{\sin\left(c+d\,x\right)}^4}{8}+\frac{b\,{\sin\left(c+d\,x\right)}^3}{2}-\frac{25\,a\,{\sin\left(c+d\,x\right)}^2}{8}-\frac{3\,b\,\sin\left(c+d\,x\right)}{4}+a}{d\,\left({\sin\left(c+d\,x\right)}^5-2\,{\sin\left(c+d\,x\right)}^3+\sin\left(c+d\,x\right)\right)}","Not used",1,"(log(sin(c + d*x) + 1)*((15*a)/16 - b/2))/d - (log(sin(c + d*x) - 1)*((15*a)/16 + b/2))/d + (b*log(sin(c + d*x)))/d - (a - (3*b*sin(c + d*x))/4 - (25*a*sin(c + d*x)^2)/8 + (15*a*sin(c + d*x)^4)/8 + (b*sin(c + d*x)^3)/2)/(d*(sin(c + d*x) - 2*sin(c + d*x)^3 + sin(c + d*x)^5))","B"
1490,1,146,135,0.110769,"\text{Not used}","int((a + b*sin(c + d*x))/(cos(c + d*x)^5*sin(c + d*x)^3),x)","\frac{3\,a\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{3\,a}{2}-\frac{15\,b}{16}\right)}{d}-\frac{\frac{15\,b\,{\sin\left(c+d\,x\right)}^5}{8}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^4}{2}-\frac{25\,b\,{\sin\left(c+d\,x\right)}^3}{8}-\frac{9\,a\,{\sin\left(c+d\,x\right)}^2}{4}+b\,\sin\left(c+d\,x\right)+\frac{a}{2}}{d\,\left({\sin\left(c+d\,x\right)}^6-2\,{\sin\left(c+d\,x\right)}^4+{\sin\left(c+d\,x\right)}^2\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{3\,a}{2}+\frac{15\,b}{16}\right)}{d}","Not used",1,"(3*a*log(sin(c + d*x)))/d - (log(sin(c + d*x) + 1)*((3*a)/2 - (15*b)/16))/d - (a/2 + b*sin(c + d*x) - (9*a*sin(c + d*x)^2)/4 + (3*a*sin(c + d*x)^4)/2 - (25*b*sin(c + d*x)^3)/8 + (15*b*sin(c + d*x)^5)/8)/(d*(sin(c + d*x)^2 - 2*sin(c + d*x)^4 + sin(c + d*x)^6)) - (log(sin(c + d*x) - 1)*((3*a)/2 + (15*b)/16))/d","B"
1491,1,157,155,11.913451,"\text{Not used}","int((a + b*sin(c + d*x))/(cos(c + d*x)^5*sin(c + d*x)^4),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{35\,a}{16}-\frac{3\,b}{2}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{35\,a}{16}+\frac{3\,b}{2}\right)}{d}+\frac{3\,b\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{\frac{35\,a\,{\sin\left(c+d\,x\right)}^6}{8}+\frac{3\,b\,{\sin\left(c+d\,x\right)}^5}{2}-\frac{175\,a\,{\sin\left(c+d\,x\right)}^4}{24}-\frac{9\,b\,{\sin\left(c+d\,x\right)}^3}{4}+\frac{7\,a\,{\sin\left(c+d\,x\right)}^2}{3}+\frac{b\,\sin\left(c+d\,x\right)}{2}+\frac{a}{3}}{d\,\left({\sin\left(c+d\,x\right)}^7-2\,{\sin\left(c+d\,x\right)}^5+{\sin\left(c+d\,x\right)}^3\right)}","Not used",1,"(log(sin(c + d*x) + 1)*((35*a)/16 - (3*b)/2))/d - (log(sin(c + d*x) - 1)*((35*a)/16 + (3*b)/2))/d + (3*b*log(sin(c + d*x)))/d - (a/3 + (b*sin(c + d*x))/2 + (7*a*sin(c + d*x)^2)/3 - (175*a*sin(c + d*x)^4)/24 + (35*a*sin(c + d*x)^6)/8 - (9*b*sin(c + d*x)^3)/4 + (3*b*sin(c + d*x)^5)/2)/(d*(sin(c + d*x)^3 - 2*sin(c + d*x)^5 + sin(c + d*x)^7))","B"
1492,1,433,189,12.333443,"\text{Not used}","int((sin(c + d*x)^6*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{15\,a^2}{8}-6\,a\,b+\frac{35\,b^2}{8}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{15\,a^2}{8}+6\,a\,b+\frac{35\,b^2}{8}\right)}{d}-\frac{\left(-\frac{15\,a^2}{4}-\frac{35\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\left(\frac{5\,a^2}{2}+\frac{35\,b^2}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(\frac{47\,a^2}{4}+\frac{329\,b^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+32\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(11\,a^2-17\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{47\,a^2}{4}+\frac{329\,b^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{5\,a^2}{2}+\frac{35\,b^2}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(-\frac{15\,a^2}{4}-\frac{35\,b^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{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{6\,a\,b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*((15*a^2)/8 - 6*a*b + (35*b^2)/8))/d - (log(tan(c/2 + (d*x)/2) - 1)*(6*a*b + (15*a^2)/8 + (35*b^2)/8))/d - (tan(c/2 + (d*x)/2)^7*(11*a^2 - 17*b^2) + tan(c/2 + (d*x)/2)^3*((5*a^2)/2 + (35*b^2)/6) + tan(c/2 + (d*x)/2)^11*((5*a^2)/2 + (35*b^2)/6) - tan(c/2 + (d*x)/2)^13*((15*a^2)/4 + (35*b^2)/4) + tan(c/2 + (d*x)/2)^5*((47*a^2)/4 + (329*b^2)/12) + tan(c/2 + (d*x)/2)^9*((47*a^2)/4 + (329*b^2)/12) - tan(c/2 + (d*x)/2)*((15*a^2)/4 + (35*b^2)/4) - 12*a*b*tan(c/2 + (d*x)/2)^2 + 12*a*b*tan(c/2 + (d*x)/2)^4 + 32*a*b*tan(c/2 + (d*x)/2)^6 + 32*a*b*tan(c/2 + (d*x)/2)^8 + 12*a*b*tan(c/2 + (d*x)/2)^10 - 12*a*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)) + (6*a*b*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
1493,1,377,162,12.224160,"\text{Not used}","int((sin(c + d*x)^5*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2+3\,b^2\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a^2-\frac{15\,a\,b}{4}+3\,b^2\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(a^2+\frac{15\,a\,b}{4}+3\,b^2\right)}{d}-\frac{-\frac{15\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{2}+\left(-2\,a^2-6\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{25\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}+\left(4\,a^2+12\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+11\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,a^2+4\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+11\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,a^2+12\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{25\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\left(-2\,a^2-6\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{15\,a\,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)}^{12}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 + 3*b^2))/d - (log(tan(c/2 + (d*x)/2) + 1)*(a^2 - (15*a*b)/4 + 3*b^2))/d - (log(tan(c/2 + (d*x)/2) - 1)*((15*a*b)/4 + a^2 + 3*b^2))/d - (tan(c/2 + (d*x)/2)^4*(4*a^2 + 12*b^2) - tan(c/2 + (d*x)/2)^10*(2*a^2 + 6*b^2) - tan(c/2 + (d*x)/2)^2*(2*a^2 + 6*b^2) + tan(c/2 + (d*x)/2)^6*(12*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^8*(4*a^2 + 12*b^2) + (25*a*b*tan(c/2 + (d*x)/2)^3)/2 + 11*a*b*tan(c/2 + (d*x)/2)^5 + 11*a*b*tan(c/2 + (d*x)/2)^7 + (25*a*b*tan(c/2 + (d*x)/2)^9)/2 - (15*a*b*tan(c/2 + (d*x)/2)^11)/2 - (15*a*b*tan(c/2 + (d*x)/2))/2)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 2*tan(c/2 + (d*x)/2)^10 - tan(c/2 + (d*x)/2)^12 - 1))","B"
1494,1,332,150,12.210676,"\text{Not used}","int((sin(c + d*x)^4*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{3\,a^2}{8}-2\,a\,b+\frac{15\,b^2}{8}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{3\,a^2}{8}+2\,a\,b+\frac{15\,b^2}{8}\right)}{d}+\frac{\left(-\frac{3\,a^2}{4}-\frac{15\,b^2}{4}\right)\,{\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)}^8+\left(2\,a^2+10\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{11\,a^2}{2}-\frac{9\,b^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(2\,a^2+10\,b^2\right)\,{\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)}^2+\left(-\frac{3\,a^2}{4}-\frac{15\,b^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\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+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\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\,a\,b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*((3*a^2)/8 - 2*a*b + (15*b^2)/8))/d - (log(tan(c/2 + (d*x)/2) - 1)*(2*a*b + (3*a^2)/8 + (15*b^2)/8))/d + (tan(c/2 + (d*x)/2)^3*(2*a^2 + 10*b^2) + tan(c/2 + (d*x)/2)^7*(2*a^2 + 10*b^2) + tan(c/2 + (d*x)/2)^5*((11*a^2)/2 - (9*b^2)/2) - tan(c/2 + (d*x)/2)^9*((3*a^2)/4 + (15*b^2)/4) - tan(c/2 + (d*x)/2)*((3*a^2)/4 + (15*b^2)/4) - 4*a*b*tan(c/2 + (d*x)/2)^2 + 12*a*b*tan(c/2 + (d*x)/2)^4 + 12*a*b*tan(c/2 + (d*x)/2)^6 - 4*a*b*tan(c/2 + (d*x)/2)^8)/(d*(2*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (2*a*b*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
1495,1,247,116,12.087104,"\text{Not used}","int((sin(c + d*x)^3*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{3\,a\,b}{4}-b^2\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(b^2+\frac{3\,a\,b}{4}\right)}{d}+\frac{b^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,a^2+8\,b^2\right)+2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{11\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{11\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}+\frac{3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+\frac{3\,a\,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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*((3*a*b)/4 - b^2))/d - (log(tan(c/2 + (d*x)/2) - 1)*((3*a*b)/4 + b^2))/d + (b^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (2*b^2*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^4*(4*a^2 + 8*b^2) + 2*b^2*tan(c/2 + (d*x)/2)^6 - (11*a*b*tan(c/2 + (d*x)/2)^3)/2 - (11*a*b*tan(c/2 + (d*x)/2)^5)/2 + (3*a*b*tan(c/2 + (d*x)/2)^7)/2 + (3*a*b*tan(c/2 + (d*x)/2))/2)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
1496,1,191,93,17.052350,"\text{Not used}","int((sin(c + d*x)^2*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\left(\frac{a^2}{4}-\frac{3\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{7\,a^2}{4}+\frac{11\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{7\,a^2}{4}+\frac{11\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{a^2}{4}-\frac{3\,b^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{a^2}{4}-\frac{3\,b^2}{4}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(a^2/4 - (3*b^2)/4) + tan(c/2 + (d*x)/2)^3*((7*a^2)/4 + (11*b^2)/4) + tan(c/2 + (d*x)/2)^5*((7*a^2)/4 + (11*b^2)/4) + tan(c/2 + (d*x)/2)*(a^2/4 - (3*b^2)/4) + 8*a*b*tan(c/2 + (d*x)/2)^4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (atanh(tan(c/2 + (d*x)/2))*(a^2/4 - (3*b^2)/4))/d","B"
1497,1,183,72,18.871290,"\text{Not used}","int((sin(c + d*x)*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+\frac{7\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}+\frac{7\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+4\,b^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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}","Not used",1,"(2*a^2*tan(c/2 + (d*x)/2)^2 + 2*a^2*tan(c/2 + (d*x)/2)^6 + 4*b^2*tan(c/2 + (d*x)/2)^4 + (7*a*b*tan(c/2 + (d*x)/2)^3)/2 + (7*a*b*tan(c/2 + (d*x)/2)^5)/2 + (a*b*tan(c/2 + (d*x)/2)^7)/2 + (a*b*tan(c/2 + (d*x)/2))/2)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (a*b*atanh(tan(c/2 + (d*x)/2)))/(2*d)","B"
1498,1,131,126,0.133569,"\text{Not used}","int((a + b*sin(c + d*x))^2/(cos(c + d*x)^5*sin(c + d*x)),x)","\frac{a^2\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}+\frac{-\frac{a^2\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{3\,a^2}{4}-\frac{3\,a\,b\,{\sin\left(c+d\,x\right)}^3}{4}+\frac{5\,a\,b\,\sin\left(c+d\,x\right)}{4}+\frac{b^2}{4}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2+1\right)}-\frac{a\,\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(4\,a+3\,b\right)}{8\,d}-\frac{a\,\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(4\,a-3\,b\right)}{8\,d}","Not used",1,"(a^2*log(sin(c + d*x)))/d + ((3*a^2)/4 + b^2/4 - (a^2*sin(c + d*x)^2)/2 + (5*a*b*sin(c + d*x))/4 - (3*a*b*sin(c + d*x)^3)/4)/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1)) - (a*log(sin(c + d*x) - 1)*(4*a + 3*b))/(8*d) - (a*log(sin(c + d*x) + 1)*(4*a - 3*b))/(8*d)","B"
1499,1,169,168,11.869417,"\text{Not used}","int((a + b*sin(c + d*x))^2/(cos(c + d*x)^5*sin(c + d*x)^2),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{15\,a^2}{16}-a\,b+\frac{3\,b^2}{16}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{15\,a^2}{16}+a\,b+\frac{3\,b^2}{16}\right)}{d}-\frac{a^2+{\sin\left(c+d\,x\right)}^4\,\left(\frac{15\,a^2}{8}+\frac{3\,b^2}{8}\right)-{\sin\left(c+d\,x\right)}^2\,\left(\frac{25\,a^2}{8}+\frac{5\,b^2}{8}\right)-\frac{3\,a\,b\,\sin\left(c+d\,x\right)}{2}+a\,b\,{\sin\left(c+d\,x\right)}^3}{d\,\left({\sin\left(c+d\,x\right)}^5-2\,{\sin\left(c+d\,x\right)}^3+\sin\left(c+d\,x\right)\right)}+\frac{2\,a\,b\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}","Not used",1,"(log(sin(c + d*x) + 1)*((15*a^2)/16 - a*b + (3*b^2)/16))/d - (log(sin(c + d*x) - 1)*(a*b + (15*a^2)/16 + (3*b^2)/16))/d - (a^2 + sin(c + d*x)^4*((15*a^2)/8 + (3*b^2)/8) - sin(c + d*x)^2*((25*a^2)/8 + (5*b^2)/8) - (3*a*b*sin(c + d*x))/2 + a*b*sin(c + d*x)^3)/(d*(sin(c + d*x) - 2*sin(c + d*x)^3 + sin(c + d*x)^5)) + (2*a*b*log(sin(c + d*x)))/d","B"
1500,1,194,185,0.135041,"\text{Not used}","int((a + b*sin(c + d*x))^2/(cos(c + d*x)^5*sin(c + d*x)^3),x)","\frac{\ln\left(\sin\left(c+d\,x\right)\right)\,\left(3\,a^2+b^2\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{3\,a^2}{2}-\frac{15\,a\,b}{8}+\frac{b^2}{2}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{3\,a^2}{2}+\frac{15\,a\,b}{8}+\frac{b^2}{2}\right)}{d}-\frac{\frac{a^2}{2}+{\sin\left(c+d\,x\right)}^4\,\left(\frac{3\,a^2}{2}+\frac{b^2}{2}\right)-{\sin\left(c+d\,x\right)}^2\,\left(\frac{9\,a^2}{4}+\frac{3\,b^2}{4}\right)+2\,a\,b\,\sin\left(c+d\,x\right)-\frac{25\,a\,b\,{\sin\left(c+d\,x\right)}^3}{4}+\frac{15\,a\,b\,{\sin\left(c+d\,x\right)}^5}{4}}{d\,\left({\sin\left(c+d\,x\right)}^6-2\,{\sin\left(c+d\,x\right)}^4+{\sin\left(c+d\,x\right)}^2\right)}","Not used",1,"(log(sin(c + d*x))*(3*a^2 + b^2))/d - (log(sin(c + d*x) + 1)*((3*a^2)/2 - (15*a*b)/8 + b^2/2))/d - (log(sin(c + d*x) - 1)*((15*a*b)/8 + (3*a^2)/2 + b^2/2))/d - (a^2/2 + sin(c + d*x)^4*((3*a^2)/2 + b^2/2) - sin(c + d*x)^2*((9*a^2)/4 + (3*b^2)/4) + 2*a*b*sin(c + d*x) - (25*a*b*sin(c + d*x)^3)/4 + (15*a*b*sin(c + d*x)^5)/4)/(d*(sin(c + d*x)^2 - 2*sin(c + d*x)^4 + sin(c + d*x)^6))","B"
1501,1,512,202,12.119441,"\text{Not used}","int((sin(c + d*x)^5*(a + b*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^3+9\,a\,b^2\right)}{d}-\frac{\left(-\frac{45\,a^2\,b}{4}-\frac{35\,b^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(-2\,a^3-18\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\left(\frac{15\,a^2\,b}{2}+\frac{35\,b^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(2\,a^3+18\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(\frac{141\,a^2\,b}{4}+\frac{329\,b^3}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(16\,a^3+48\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(33\,a^2\,b-17\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(16\,a^3+48\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{141\,a^2\,b}{4}+\frac{329\,b^3}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,a^3+18\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{15\,a^2\,b}{2}+\frac{35\,b^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3-18\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(-\frac{45\,a^2\,b}{4}-\frac{35\,b^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{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{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a-b\right)\,\left(8\,a^2-37\,a\,b+35\,b^2\right)}{8\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(a+b\right)\,\left(8\,a^2+37\,a\,b+35\,b^2\right)}{8\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1)*(9*a*b^2 + a^3))/d - (tan(c/2 + (d*x)/2)^4*(18*a*b^2 + 2*a^3) - tan(c/2 + (d*x)/2)^2*(18*a*b^2 + 2*a^3) - tan(c/2 + (d*x)/2)*((45*a^2*b)/4 + (35*b^3)/4) + tan(c/2 + (d*x)/2)^10*(18*a*b^2 + 2*a^3) - tan(c/2 + (d*x)/2)^12*(18*a*b^2 + 2*a^3) + tan(c/2 + (d*x)/2)^6*(48*a*b^2 + 16*a^3) + tan(c/2 + (d*x)/2)^8*(48*a*b^2 + 16*a^3) + tan(c/2 + (d*x)/2)^7*(33*a^2*b - 17*b^3) + tan(c/2 + (d*x)/2)^3*((15*a^2*b)/2 + (35*b^3)/6) + tan(c/2 + (d*x)/2)^11*((15*a^2*b)/2 + (35*b^3)/6) - tan(c/2 + (d*x)/2)^13*((45*a^2*b)/4 + (35*b^3)/4) + tan(c/2 + (d*x)/2)^5*((141*a^2*b)/4 + (329*b^3)/12) + tan(c/2 + (d*x)/2)^9*((141*a^2*b)/4 + (329*b^3)/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)) - (log(tan(c/2 + (d*x)/2) + 1)*(a - b)*(8*a^2 - 37*a*b + 35*b^2))/(8*d) - (log(tan(c/2 + (d*x)/2) - 1)*(a + b)*(37*a*b + 8*a^2 + 35*b^2))/(8*d)","B"
1502,1,449,177,12.108925,"\text{Not used}","int((sin(c + d*x)^4*(a + b*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(3\,a^2\,b+3\,b^3\right)}{d}-\frac{\left(-\frac{3\,a^3}{4}-\frac{45\,a\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(-6\,a^2\,b-6\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(\frac{5\,a^3}{4}+\frac{75\,a\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(12\,a^2\,b+12\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(\frac{15\,a^3}{2}+\frac{33\,a\,b^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(36\,a^2\,b+4\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{15\,a^3}{2}+\frac{33\,a\,b^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(12\,a^2\,b+12\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{5\,a^3}{4}+\frac{75\,a\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-6\,a^2\,b-6\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(-\frac{3\,a^3}{4}-\frac{45\,a\,b^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(a+b\right)\,\left(a^2+7\,a\,b+8\,b^2\right)}{8\,d}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a-b\right)\,\left(a^2-7\,a\,b+8\,b^2\right)}{8\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1)*(3*a^2*b + 3*b^3))/d - (tan(c/2 + (d*x)/2)^5*((33*a*b^2)/2 + (15*a^3)/2) - tan(c/2 + (d*x)/2)*((45*a*b^2)/4 + (3*a^3)/4) + tan(c/2 + (d*x)/2)^7*((33*a*b^2)/2 + (15*a^3)/2) - tan(c/2 + (d*x)/2)^11*((45*a*b^2)/4 + (3*a^3)/4) + tan(c/2 + (d*x)/2)^3*((75*a*b^2)/4 + (5*a^3)/4) + tan(c/2 + (d*x)/2)^9*((75*a*b^2)/4 + (5*a^3)/4) - tan(c/2 + (d*x)/2)^2*(6*a^2*b + 6*b^3) - tan(c/2 + (d*x)/2)^10*(6*a^2*b + 6*b^3) + tan(c/2 + (d*x)/2)^4*(12*a^2*b + 12*b^3) + tan(c/2 + (d*x)/2)^8*(12*a^2*b + 12*b^3) + tan(c/2 + (d*x)/2)^6*(36*a^2*b + 4*b^3))/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 2*tan(c/2 + (d*x)/2)^10 - tan(c/2 + (d*x)/2)^12 - 1)) - (3*log(tan(c/2 + (d*x)/2) - 1)*(a + b)*(7*a*b + a^2 + 8*b^2))/(8*d) + (3*log(tan(c/2 + (d*x)/2) + 1)*(a - b)*(a^2 - 7*a*b + 8*b^2))/(8*d)","B"
1503,1,356,142,12.094262,"\text{Not used}","int((sin(c + d*x)^3*(a + b*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,a^3+18\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,a^2\,b}{4}+\frac{15\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3+18\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^2\,b+10\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,a^2\,b+10\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{9\,a^2\,b}{4}+\frac{15\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{33\,a^2\,b}{2}-\frac{9\,b^3}{2}\right)-6\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,a\,b^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)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\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{3\,a\,b^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(a+b\right)\,\left(3\,a+5\,b\right)}{8\,d}+\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a-b\right)\,\left(3\,a-5\,b\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^4*(18*a*b^2 + 4*a^3) - tan(c/2 + (d*x)/2)*((9*a^2*b)/4 + (15*b^3)/4) + tan(c/2 + (d*x)/2)^6*(18*a*b^2 + 4*a^3) + tan(c/2 + (d*x)/2)^3*(6*a^2*b + 10*b^3) + tan(c/2 + (d*x)/2)^7*(6*a^2*b + 10*b^3) - tan(c/2 + (d*x)/2)^9*((9*a^2*b)/4 + (15*b^3)/4) + tan(c/2 + (d*x)/2)^5*((33*a^2*b)/2 - (9*b^3)/2) - 6*a*b^2*tan(c/2 + (d*x)/2)^2 - 6*a*b^2*tan(c/2 + (d*x)/2)^8)/(d*(2*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (3*a*b^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (3*b*log(tan(c/2 + (d*x)/2) - 1)*(a + b)*(3*a + 5*b))/(8*d) + (3*b*log(tan(c/2 + (d*x)/2) + 1)*(a - b)*(3*a - 5*b))/(8*d)","B"
1504,1,299,144,12.136485,"\text{Not used}","int((sin(c + d*x)^2*(a + b*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{b^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(-\frac{a^3}{8}+\frac{9\,a\,b^2}{8}+b^3\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{a^3}{8}-\frac{9\,a\,b^2}{8}+b^3\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,a\,b^2}{4}-\frac{a^3}{4}\right)+2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{9\,a\,b^2}{4}-\frac{a^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{7\,a^3}{4}+\frac{33\,a\,b^2}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{7\,a^3}{4}+\frac{33\,a\,b^2}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a^2\,b+8\,b^3\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(b^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (log(tan(c/2 + (d*x)/2) - 1)*((9*a*b^2)/8 - a^3/8 + b^3))/d - (log(tan(c/2 + (d*x)/2) + 1)*(a^3/8 - (9*a*b^2)/8 + b^3))/d - (tan(c/2 + (d*x)/2)*((9*a*b^2)/4 - a^3/4) + 2*b^3*tan(c/2 + (d*x)/2)^2 + 2*b^3*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^7*((9*a*b^2)/4 - a^3/4) - tan(c/2 + (d*x)/2)^3*((33*a*b^2)/4 + (7*a^3)/4) - tan(c/2 + (d*x)/2)^5*((33*a*b^2)/4 + (7*a^3)/4) - tan(c/2 + (d*x)/2)^4*(12*a^2*b + 8*b^3))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
1505,1,228,90,16.993003,"\text{Not used}","int((sin(c + d*x)*(a + b*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a^2\,b}{4}-\frac{3\,b^3}{4}\right)+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{3\,a^2\,b}{4}-\frac{3\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{21\,a^2\,b}{4}+\frac{11\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{21\,a^2\,b}{4}+\frac{11\,b^3}{4}\right)+12\,a\,b^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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{3\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-b^2\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*a^2*b)/4 - (3*b^3)/4) + 2*a^3*tan(c/2 + (d*x)/2)^2 + 2*a^3*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^7*((3*a^2*b)/4 - (3*b^3)/4) + tan(c/2 + (d*x)/2)^3*((21*a^2*b)/4 + (11*b^3)/4) + tan(c/2 + (d*x)/2)^5*((21*a^2*b)/4 + (11*b^3)/4) + 12*a*b^2*tan(c/2 + (d*x)/2)^4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (3*b*atanh(tan(c/2 + (d*x)/2))*(a^2 - b^2))/(4*d)","B"
1506,1,169,165,11.906136,"\text{Not used}","int((a + b*sin(c + d*x))^3/(cos(c + d*x)^5*sin(c + d*x)),x)","\frac{a^3\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{a^3}{2}-\frac{9\,a^2\,b}{16}+\frac{b^3}{16}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{a^3}{2}+\frac{9\,a^2\,b}{16}-\frac{b^3}{16}\right)}{d}+\frac{\frac{3\,a\,b^2}{4}-{\sin\left(c+d\,x\right)}^3\,\left(\frac{9\,a^2\,b}{8}-\frac{b^3}{8}\right)+\frac{3\,a^3}{4}+\sin\left(c+d\,x\right)\,\left(\frac{15\,a^2\,b}{8}+\frac{b^3}{8}\right)-\frac{a^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)}","Not used",1,"(a^3*log(sin(c + d*x)))/d - (log(sin(c + d*x) + 1)*(a^3/2 - (9*a^2*b)/16 + b^3/16))/d - (log(sin(c + d*x) - 1)*((9*a^2*b)/16 + a^3/2 - b^3/16))/d + ((3*a*b^2)/4 - sin(c + d*x)^3*((9*a^2*b)/8 - b^3/8) + (3*a^3)/4 + sin(c + d*x)*((15*a^2*b)/8 + b^3/8) - (a^3*sin(c + d*x)^2)/2)/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1))","B"
1507,1,182,171,0.134496,"\text{Not used}","int((a + b*sin(c + d*x))^3/(cos(c + d*x)^5*sin(c + d*x)^2),x)","\frac{3\,a^2\,b\,\ln\left(\sin\left(c+d\,x\right)\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^4\,\left(\frac{15\,a^3}{8}+\frac{9\,a\,b^2}{8}\right)-{\sin\left(c+d\,x\right)}^2\,\left(\frac{25\,a^3}{8}+\frac{15\,a\,b^2}{8}\right)+a^3-\sin\left(c+d\,x\right)\,\left(\frac{9\,a^2\,b}{4}+\frac{b^3}{4}\right)+\frac{3\,a^2\,b\,{\sin\left(c+d\,x\right)}^3}{2}}{d\,\left({\sin\left(c+d\,x\right)}^5-2\,{\sin\left(c+d\,x\right)}^3+\sin\left(c+d\,x\right)\right)}+\frac{3\,a\,\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-b\right)\,\left(5\,a-3\,b\right)}{16\,d}-\frac{3\,a\,\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(a+b\right)\,\left(5\,a+3\,b\right)}{16\,d}","Not used",1,"(3*a^2*b*log(sin(c + d*x)))/d - (sin(c + d*x)^4*((9*a*b^2)/8 + (15*a^3)/8) - sin(c + d*x)^2*((15*a*b^2)/8 + (25*a^3)/8) + a^3 - sin(c + d*x)*((9*a^2*b)/4 + b^3/4) + (3*a^2*b*sin(c + d*x)^3)/2)/(d*(sin(c + d*x) - 2*sin(c + d*x)^3 + sin(c + d*x)^5)) + (3*a*log(sin(c + d*x) + 1)*(a - b)*(5*a - 3*b))/(16*d) - (3*a*log(sin(c + d*x) - 1)*(a + b)*(5*a + 3*b))/(16*d)","B"
1508,1,221,221,11.949057,"\text{Not used}","int((a + b*sin(c + d*x))^3/(cos(c + d*x)^5*sin(c + d*x)^3),x)","\frac{3\,a\,\ln\left(\sin\left(c+d\,x\right)\right)\,\left(a^2+b^2\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^4\,\left(\frac{3\,a^3}{2}+\frac{3\,a\,b^2}{2}\right)-{\sin\left(c+d\,x\right)}^2\,\left(\frac{9\,a^3}{4}+\frac{9\,a\,b^2}{4}\right)+{\sin\left(c+d\,x\right)}^5\,\left(\frac{45\,a^2\,b}{8}+\frac{3\,b^3}{8}\right)-{\sin\left(c+d\,x\right)}^3\,\left(\frac{75\,a^2\,b}{8}+\frac{5\,b^3}{8}\right)+\frac{a^3}{2}+3\,a^2\,b\,\sin\left(c+d\,x\right)}{d\,\left({\sin\left(c+d\,x\right)}^6-2\,{\sin\left(c+d\,x\right)}^4+{\sin\left(c+d\,x\right)}^2\right)}-\frac{3\,\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-b\right)\,\left(8\,a^2-7\,a\,b+b^2\right)}{16\,d}-\frac{3\,\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(a+b\right)\,\left(8\,a^2+7\,a\,b+b^2\right)}{16\,d}","Not used",1,"(3*a*log(sin(c + d*x))*(a^2 + b^2))/d - (sin(c + d*x)^4*((3*a*b^2)/2 + (3*a^3)/2) - sin(c + d*x)^2*((9*a*b^2)/4 + (9*a^3)/4) + sin(c + d*x)^5*((45*a^2*b)/8 + (3*b^3)/8) - sin(c + d*x)^3*((75*a^2*b)/8 + (5*b^3)/8) + a^3/2 + 3*a^2*b*sin(c + d*x))/(d*(sin(c + d*x)^2 - 2*sin(c + d*x)^4 + sin(c + d*x)^6)) - (3*log(sin(c + d*x) + 1)*(a - b)*(8*a^2 - 7*a*b + b^2))/(16*d) - (3*log(sin(c + d*x) - 1)*(a + b)*(7*a*b + 8*a^2 + b^2))/(16*d)","B"
1509,0,-1,295,0.000000,"\text{Not used}","int((sin(c + d*x)^n*(a + b*sin(c + d*x))^4)/cos(c + d*x)^5,x)","\int \frac{{\sin\left(c+d\,x\right)}^n\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((sin(c + d*x)^n*(a + b*sin(c + d*x))^4)/cos(c + d*x)^5, x)","F"
1510,0,-1,186,0.000000,"\text{Not used}","int((sin(c + d*x)^n*(a + b*sin(c + d*x))^3)/cos(c + d*x)^5,x)","\int \frac{{\sin\left(c+d\,x\right)}^n\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((sin(c + d*x)^n*(a + b*sin(c + d*x))^3)/cos(c + d*x)^5, x)","F"
1511,0,-1,160,0.000000,"\text{Not used}","int((sin(c + d*x)^n*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\int \frac{{\sin\left(c+d\,x\right)}^n\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((sin(c + d*x)^n*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5, x)","F"
1512,0,-1,89,0.000000,"\text{Not used}","int((sin(c + d*x)^n*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\int \frac{{\sin\left(c+d\,x\right)}^n\,\left(a+b\,\sin\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((sin(c + d*x)^n*(a + b*sin(c + d*x)))/cos(c + d*x)^5, x)","F"
1513,0,-1,360,0.000000,"\text{Not used}","int(sin(c + d*x)^n/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\int \frac{{\sin\left(c+d\,x\right)}^n}{{\cos\left(c+d\,x\right)}^5\,\left(a+b\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(sin(c + d*x)^n/(cos(c + d*x)^5*(a + b*sin(c + d*x))), x)","F"
1514,0,-1,487,0.000000,"\text{Not used}","int((sin(c + d*x)^n*(a + b*sin(c + d*x))^p)/cos(c + d*x)^5,x)","\int \frac{{\sin\left(c+d\,x\right)}^n\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^p}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((sin(c + d*x)^n*(a + b*sin(c + d*x))^p)/cos(c + d*x)^5, x)","F"
1515,0,-1,502,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(9/2)/(cos(e + f*x)^6*(d*sin(e + f*x))^(1/2)),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\cos\left(e+f\,x\right)}^6\,\sqrt{d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(9/2)/(cos(e + f*x)^6*(d*sin(e + f*x))^(1/2)), x)","F"
1516,0,-1,458,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(4/3),x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{4/3} \,d x","Not used",1,"int(cos(e + f*x)^2*(a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(4/3), x)","F"
1517,0,-1,341,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(4/3),x)","\int {\cos\left(e+f\,x\right)}^2\,\left(a+b\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{4/3} \,d x","Not used",1,"int(cos(e + f*x)^2*(a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(4/3), x)","F"
1518,0,-1,125,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(c + d*sin(e + f*x))^(4/3),x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{4/3} \,d x","Not used",1,"int(cos(e + f*x)^2*(c + d*sin(e + f*x))^(4/3), x)","F"
1519,0,-1,38,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c + d*sin(e + f*x))^(4/3))/(a + b*sin(e + f*x)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{4/3}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",0,"int((cos(e + f*x)^2*(c + d*sin(e + f*x))^(4/3))/(a + b*sin(e + f*x)), x)","F"
1520,0,-1,38,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c + d*sin(e + f*x))^(4/3))/(a + b*sin(e + f*x))^2,x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{4/3}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",0,"int((cos(e + f*x)^2*(c + d*sin(e + f*x))^(4/3))/(a + b*sin(e + f*x))^2, x)","F"
1521,0,-1,36,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",0,"int(cos(e + f*x)^2*(a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
1522,0,-1,38,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^(4/3),x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{4/3} \,d x","Not used",0,"int(cos(e + f*x)^2*(a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^(4/3), x)","F"
1523,0,-1,552,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^2*(a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^n, x)","F"
1524,0,-1,375,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x))*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,\left(a+b\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^2*(a + b*sin(e + f*x))*(c + d*sin(e + f*x))^n, x)","F"
1525,0,-1,127,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(c + d*sin(e + f*x))^n,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(cos(e + f*x)^2*(c + d*sin(e + f*x))^n, x)","F"
1526,0,-1,36,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + b*sin(e + f*x)),x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",0,"int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + b*sin(e + f*x)), x)","F"
1527,0,-1,36,0.000000,"\text{Not used}","int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + b*sin(e + f*x))^2,x)","\int \frac{{\cos\left(e+f\,x\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",0,"int((cos(e + f*x)^2*(c + d*sin(e + f*x))^n)/(a + b*sin(e + f*x))^2, x)","F"
1528,1,156,188,0.126608,"\text{Not used}","int(cos(c + d*x)^7*(A + B*sin(c + d*x))*(a + b*sin(c + d*x)),x)","-\frac{\frac{B\,b\,{\sin\left(c+d\,x\right)}^9}{9}+\left(\frac{A\,b}{8}+\frac{B\,a}{8}\right)\,{\sin\left(c+d\,x\right)}^8+\left(\frac{A\,a}{7}-\frac{3\,B\,b}{7}\right)\,{\sin\left(c+d\,x\right)}^7+\left(-\frac{A\,b}{2}-\frac{B\,a}{2}\right)\,{\sin\left(c+d\,x\right)}^6+\left(\frac{3\,B\,b}{5}-\frac{3\,A\,a}{5}\right)\,{\sin\left(c+d\,x\right)}^5+\left(\frac{3\,A\,b}{4}+\frac{3\,B\,a}{4}\right)\,{\sin\left(c+d\,x\right)}^4+\left(A\,a-\frac{B\,b}{3}\right)\,{\sin\left(c+d\,x\right)}^3+\left(-\frac{A\,b}{2}-\frac{B\,a}{2}\right)\,{\sin\left(c+d\,x\right)}^2-A\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-(sin(c + d*x)^3*(A*a - (B*b)/3) - sin(c + d*x)^2*((A*b)/2 + (B*a)/2) - sin(c + d*x)^6*((A*b)/2 + (B*a)/2) + sin(c + d*x)^4*((3*A*b)/4 + (3*B*a)/4) - sin(c + d*x)^5*((3*A*a)/5 - (3*B*b)/5) + sin(c + d*x)^7*((A*a)/7 - (3*B*b)/7) + sin(c + d*x)^8*((A*b)/8 + (B*a)/8) - A*a*sin(c + d*x) + (B*b*sin(c + d*x)^9)/9)/d","B"
1529,1,118,143,12.057308,"\text{Not used}","int(cos(c + d*x)^5*(A + B*sin(c + d*x))*(a + b*sin(c + d*x)),x)","\frac{\frac{B\,b\,{\sin\left(c+d\,x\right)}^7}{7}+\left(\frac{A\,b}{6}+\frac{B\,a}{6}\right)\,{\sin\left(c+d\,x\right)}^6+\left(\frac{A\,a}{5}-\frac{2\,B\,b}{5}\right)\,{\sin\left(c+d\,x\right)}^5+\left(-\frac{A\,b}{2}-\frac{B\,a}{2}\right)\,{\sin\left(c+d\,x\right)}^4+\left(\frac{B\,b}{3}-\frac{2\,A\,a}{3}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{A\,b}{2}+\frac{B\,a}{2}\right)\,{\sin\left(c+d\,x\right)}^2+A\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(sin(c + d*x)^2*((A*b)/2 + (B*a)/2) - sin(c + d*x)^4*((A*b)/2 + (B*a)/2) - sin(c + d*x)^3*((2*A*a)/3 - (B*b)/3) + sin(c + d*x)^5*((A*a)/5 - (2*B*b)/5) + sin(c + d*x)^6*((A*b)/6 + (B*a)/6) + A*a*sin(c + d*x) + (B*b*sin(c + d*x)^7)/7)/d","B"
1530,1,83,97,11.991195,"\text{Not used}","int(cos(c + d*x)^3*(A + B*sin(c + d*x))*(a + b*sin(c + d*x)),x)","-\frac{\frac{B\,b\,{\sin\left(c+d\,x\right)}^5}{5}+\left(\frac{A\,b}{4}+\frac{B\,a}{4}\right)\,{\sin\left(c+d\,x\right)}^4+\left(\frac{A\,a}{3}-\frac{B\,b}{3}\right)\,{\sin\left(c+d\,x\right)}^3+\left(-\frac{A\,b}{2}-\frac{B\,a}{2}\right)\,{\sin\left(c+d\,x\right)}^2-A\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-(sin(c + d*x)^3*((A*a)/3 - (B*b)/3) - sin(c + d*x)^2*((A*b)/2 + (B*a)/2) + sin(c + d*x)^4*((A*b)/4 + (B*a)/4) - A*a*sin(c + d*x) + (B*b*sin(c + d*x)^5)/5)/d","B"
1531,1,44,52,12.036952,"\text{Not used}","int(cos(c + d*x)*(A + B*sin(c + d*x))*(a + b*sin(c + d*x)),x)","\frac{\frac{B\,b\,{\sin\left(c+d\,x\right)}^3}{3}+\left(\frac{A\,b}{2}+\frac{B\,a}{2}\right)\,{\sin\left(c+d\,x\right)}^2+A\,a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(sin(c + d*x)^2*((A*b)/2 + (B*a)/2) + A*a*sin(c + d*x) + (B*b*sin(c + d*x)^3)/3)/d","B"
1532,1,53,64,0.121316,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + b*sin(c + d*x)))/cos(c + d*x),x)","-\frac{B\,b\,\sin\left(c+d\,x\right)-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(A-B\right)\,\left(a-b\right)}{2}+\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(a+b\right)\,\left(A+B\right)}{2}}{d}","Not used",1,"-(B*b*sin(c + d*x) - (log(sin(c + d*x) + 1)*(A - B)*(a - b))/2 + (log(sin(c + d*x) - 1)*(a + b)*(A + B))/2)/d","B"
1533,1,63,59,0.109940,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + b*sin(c + d*x)))/cos(c + d*x)^3,x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(\frac{A\,a}{2}-\frac{B\,b}{2}\right)}{d}-\frac{\frac{A\,b}{2}+\frac{B\,a}{2}+\sin\left(c+d\,x\right)\,\left(\frac{A\,a}{2}+\frac{B\,b}{2}\right)}{d\,\left({\sin\left(c+d\,x\right)}^2-1\right)}","Not used",1,"(atanh(sin(c + d*x))*((A*a)/2 - (B*b)/2))/d - ((A*b)/2 + (B*a)/2 + sin(c + d*x)*((A*a)/2 + (B*b)/2))/(d*(sin(c + d*x)^2 - 1))","B"
1534,1,91,88,0.141354,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + b*sin(c + d*x)))/cos(c + d*x)^5,x)","\frac{\left(\frac{B\,b}{8}-\frac{3\,A\,a}{8}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{5\,A\,a}{8}+\frac{B\,b}{8}\right)\,\sin\left(c+d\,x\right)+\frac{A\,b}{4}+\frac{B\,a}{4}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(\frac{3\,A\,a}{8}-\frac{B\,b}{8}\right)}{d}","Not used",1,"((A*b)/4 + (B*a)/4 + sin(c + d*x)*((5*A*a)/8 + (B*b)/8) - sin(c + d*x)^3*((3*A*a)/8 - (B*b)/8))/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1)) + (atanh(sin(c + d*x))*((3*A*a)/8 - (B*b)/8))/d","B"
1535,1,120,118,12.442038,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + b*sin(c + d*x)))/cos(c + d*x)^7,x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(\frac{5\,A\,a}{16}-\frac{B\,b}{16}\right)}{d}-\frac{\left(\frac{5\,A\,a}{16}-\frac{B\,b}{16}\right)\,{\sin\left(c+d\,x\right)}^5+\left(\frac{B\,b}{6}-\frac{5\,A\,a}{6}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{11\,A\,a}{16}+\frac{B\,b}{16}\right)\,\sin\left(c+d\,x\right)+\frac{A\,b}{6}+\frac{B\,a}{6}}{d\,\left({\sin\left(c+d\,x\right)}^6-3\,{\sin\left(c+d\,x\right)}^4+3\,{\sin\left(c+d\,x\right)}^2-1\right)}","Not used",1,"(atanh(sin(c + d*x))*((5*A*a)/16 - (B*b)/16))/d - ((A*b)/6 + (B*a)/6 + sin(c + d*x)*((11*A*a)/16 + (B*b)/16) - sin(c + d*x)^3*((5*A*a)/6 - (B*b)/6) + sin(c + d*x)^5*((5*A*a)/16 - (B*b)/16))/(d*(3*sin(c + d*x)^2 - 3*sin(c + d*x)^4 + sin(c + d*x)^6 - 1))","B"
1536,1,236,349,0.180187,"\text{Not used}","int(cos(c + d*x)^7*(A + B*sin(c + d*x))*(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{B\,a^2}{2}+A\,b\,a\right)-{\sin\left(c+d\,x\right)}^9\,\left(\frac{A\,b^2}{9}+\frac{2\,B\,a\,b}{9}\right)+{\sin\left(c+d\,x\right)}^3\,\left(-A\,a^2+\frac{2\,B\,a\,b}{3}+\frac{A\,b^2}{3}\right)-{\sin\left(c+d\,x\right)}^5\,\left(-\frac{3\,A\,a^2}{5}+\frac{6\,B\,a\,b}{5}+\frac{3\,A\,b^2}{5}\right)+{\sin\left(c+d\,x\right)}^7\,\left(-\frac{A\,a^2}{7}+\frac{6\,B\,a\,b}{7}+\frac{3\,A\,b^2}{7}\right)+{\sin\left(c+d\,x\right)}^6\,\left(\frac{B\,a^2}{2}+A\,a\,b-\frac{B\,b^2}{2}\right)-{\sin\left(c+d\,x\right)}^4\,\left(\frac{3\,B\,a^2}{4}+\frac{3\,A\,a\,b}{2}-\frac{B\,b^2}{4}\right)-{\sin\left(c+d\,x\right)}^8\,\left(\frac{B\,a^2}{8}+\frac{A\,a\,b}{4}-\frac{3\,B\,b^2}{8}\right)-\frac{B\,b^2\,{\sin\left(c+d\,x\right)}^{10}}{10}+A\,a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(sin(c + d*x)^2*((B*a^2)/2 + A*a*b) - sin(c + d*x)^9*((A*b^2)/9 + (2*B*a*b)/9) + sin(c + d*x)^3*((A*b^2)/3 - A*a^2 + (2*B*a*b)/3) - sin(c + d*x)^5*((3*A*b^2)/5 - (3*A*a^2)/5 + (6*B*a*b)/5) + sin(c + d*x)^7*((3*A*b^2)/7 - (A*a^2)/7 + (6*B*a*b)/7) + sin(c + d*x)^6*((B*a^2)/2 - (B*b^2)/2 + A*a*b) - sin(c + d*x)^4*((3*B*a^2)/4 - (B*b^2)/4 + (3*A*a*b)/2) - sin(c + d*x)^8*((B*a^2)/8 - (3*B*b^2)/8 + (A*a*b)/4) - (B*b^2*sin(c + d*x)^10)/10 + A*a^2*sin(c + d*x))/d","B"
1537,1,180,231,0.106640,"\text{Not used}","int(cos(c + d*x)^5*(A + B*sin(c + d*x))*(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{B\,a^2}{2}+A\,b\,a\right)+{\sin\left(c+d\,x\right)}^7\,\left(\frac{A\,b^2}{7}+\frac{2\,B\,a\,b}{7}\right)+{\sin\left(c+d\,x\right)}^3\,\left(-\frac{2\,A\,a^2}{3}+\frac{2\,B\,a\,b}{3}+\frac{A\,b^2}{3}\right)-{\sin\left(c+d\,x\right)}^5\,\left(-\frac{A\,a^2}{5}+\frac{4\,B\,a\,b}{5}+\frac{2\,A\,b^2}{5}\right)-{\sin\left(c+d\,x\right)}^4\,\left(\frac{B\,a^2}{2}+A\,a\,b-\frac{B\,b^2}{4}\right)+{\sin\left(c+d\,x\right)}^6\,\left(\frac{B\,a^2}{6}+\frac{A\,a\,b}{3}-\frac{B\,b^2}{3}\right)+\frac{B\,b^2\,{\sin\left(c+d\,x\right)}^8}{8}+A\,a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(sin(c + d*x)^2*((B*a^2)/2 + A*a*b) + sin(c + d*x)^7*((A*b^2)/7 + (2*B*a*b)/7) + sin(c + d*x)^3*((A*b^2)/3 - (2*A*a^2)/3 + (2*B*a*b)/3) - sin(c + d*x)^5*((2*A*b^2)/5 - (A*a^2)/5 + (4*B*a*b)/5) - sin(c + d*x)^4*((B*a^2)/2 - (B*b^2)/4 + A*a*b) + sin(c + d*x)^6*((B*a^2)/6 - (B*b^2)/3 + (A*a*b)/3) + (B*b^2*sin(c + d*x)^8)/8 + A*a^2*sin(c + d*x))/d","B"
1538,1,127,132,12.297802,"\text{Not used}","int(cos(c + d*x)^3*(A + B*sin(c + d*x))*(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{B\,a^2}{2}+A\,b\,a\right)-{\sin\left(c+d\,x\right)}^5\,\left(\frac{A\,b^2}{5}+\frac{2\,B\,a\,b}{5}\right)+{\sin\left(c+d\,x\right)}^3\,\left(-\frac{A\,a^2}{3}+\frac{2\,B\,a\,b}{3}+\frac{A\,b^2}{3}\right)-{\sin\left(c+d\,x\right)}^4\,\left(\frac{B\,a^2}{4}+\frac{A\,a\,b}{2}-\frac{B\,b^2}{4}\right)-\frac{B\,b^2\,{\sin\left(c+d\,x\right)}^6}{6}+A\,a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(sin(c + d*x)^2*((B*a^2)/2 + A*a*b) - sin(c + d*x)^5*((A*b^2)/5 + (2*B*a*b)/5) + sin(c + d*x)^3*((A*b^2)/3 - (A*a^2)/3 + (2*B*a*b)/3) - sin(c + d*x)^4*((B*a^2)/4 - (B*b^2)/4 + (A*a*b)/2) - (B*b^2*sin(c + d*x)^6)/6 + A*a^2*sin(c + d*x))/d","B"
1539,1,71,54,0.065722,"\text{Not used}","int(cos(c + d*x)*(A + B*sin(c + d*x))*(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{B\,a^2}{2}+A\,b\,a\right)+{\sin\left(c+d\,x\right)}^3\,\left(\frac{A\,b^2}{3}+\frac{2\,B\,a\,b}{3}\right)+\frac{B\,b^2\,{\sin\left(c+d\,x\right)}^4}{4}+A\,a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(sin(c + d*x)^2*((B*a^2)/2 + A*a*b) + sin(c + d*x)^3*((A*b^2)/3 + (2*B*a*b)/3) + (B*b^2*sin(c + d*x)^4)/4 + A*a^2*sin(c + d*x))/d","B"
1540,1,80,94,12.370276,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + b*sin(c + d*x))^2)/cos(c + d*x),x)","-\frac{\sin\left(c+d\,x\right)\,\left(A\,b^2+2\,B\,a\,b\right)+\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^2\,\left(A+B\right)}{2}+\frac{B\,b^2\,{\sin\left(c+d\,x\right)}^2}{2}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(A-B\right)\,{\left(a-b\right)}^2}{2}}{d}","Not used",1,"-(sin(c + d*x)*(A*b^2 + 2*B*a*b) + (log(sin(c + d*x) - 1)*(a + b)^2*(A + B))/2 + (B*b^2*sin(c + d*x)^2)/2 - (log(sin(c + d*x) + 1)*(A - B)*(a - b)^2)/2)/d","B"
1541,1,118,112,12.362906,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + b*sin(c + d*x))^2)/cos(c + d*x)^3,x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-b\right)\,\left(A\,a+A\,b-2\,B\,b\right)}{4\,d}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{A\,a^2}{2}+B\,a\,b+\frac{A\,b^2}{2}\right)+\frac{B\,a^2}{2}+\frac{B\,b^2}{2}+A\,a\,b}{d\,\left({\sin\left(c+d\,x\right)}^2-1\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(a+b\right)\,\left(A\,b-A\,a+2\,B\,b\right)}{4\,d}","Not used",1,"(log(sin(c + d*x) + 1)*(a - b)*(A*a + A*b - 2*B*b))/(4*d) - (sin(c + d*x)*((A*a^2)/2 + (A*b^2)/2 + B*a*b) + (B*a^2)/2 + (B*b^2)/2 + A*a*b)/(d*(sin(c + d*x)^2 - 1)) + (log(sin(c + d*x) - 1)*(a + b)*(A*b - A*a + 2*B*b))/(4*d)","B"
1542,1,181,122,12.378378,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + b*sin(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\sin\left(c+d\,x\right)\,\left(\frac{5\,A\,a^2}{8}+\frac{B\,a\,b}{4}+\frac{A\,b^2}{8}\right)+\frac{B\,a^2}{4}-\frac{B\,b^2}{4}+{\sin\left(c+d\,x\right)}^3\,\left(-\frac{3\,A\,a^2}{8}+\frac{B\,a\,b}{4}+\frac{A\,b^2}{8}\right)+\frac{B\,b^2\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{A\,a\,b}{2}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2+1\right)}-\frac{\mathrm{atanh}\left(\frac{4\,\sin\left(c+d\,x\right)\,\left(-\frac{3\,A\,a^2}{16}+\frac{B\,a\,b}{8}+\frac{A\,b^2}{16}\right)}{-\frac{3\,A\,a^2}{4}+\frac{B\,a\,b}{2}+\frac{A\,b^2}{4}}\right)\,\left(-\frac{3\,A\,a^2}{8}+\frac{B\,a\,b}{4}+\frac{A\,b^2}{8}\right)}{d}","Not used",1,"(sin(c + d*x)*((5*A*a^2)/8 + (A*b^2)/8 + (B*a*b)/4) + (B*a^2)/4 - (B*b^2)/4 + sin(c + d*x)^3*((A*b^2)/8 - (3*A*a^2)/8 + (B*a*b)/4) + (B*b^2*sin(c + d*x)^2)/2 + (A*a*b)/2)/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1)) - (atanh((4*sin(c + d*x)*((A*b^2)/16 - (3*A*a^2)/16 + (B*a*b)/8))/((A*b^2)/4 - (3*A*a^2)/4 + (B*a*b)/2))*((A*b^2)/8 - (3*A*a^2)/8 + (B*a*b)/4))/d","B"
1543,1,220,160,12.445215,"\text{Not used}","int(((A + B*sin(c + d*x))*(a + b*sin(c + d*x))^2)/cos(c + d*x)^7,x)","-\frac{\mathrm{atanh}\left(\frac{4\,\sin\left(c+d\,x\right)\,\left(-\frac{5\,A\,a^2}{32}+\frac{B\,a\,b}{16}+\frac{A\,b^2}{32}\right)}{-\frac{5\,A\,a^2}{8}+\frac{B\,a\,b}{4}+\frac{A\,b^2}{8}}\right)\,\left(-\frac{5\,A\,a^2}{16}+\frac{B\,a\,b}{8}+\frac{A\,b^2}{16}\right)}{d}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{11\,A\,a^2}{16}+\frac{B\,a\,b}{8}+\frac{A\,b^2}{16}\right)+\frac{B\,a^2}{6}-\frac{B\,b^2}{12}+{\sin\left(c+d\,x\right)}^3\,\left(-\frac{5\,A\,a^2}{6}+\frac{B\,a\,b}{3}+\frac{A\,b^2}{6}\right)-{\sin\left(c+d\,x\right)}^5\,\left(-\frac{5\,A\,a^2}{16}+\frac{B\,a\,b}{8}+\frac{A\,b^2}{16}\right)+\frac{B\,b^2\,{\sin\left(c+d\,x\right)}^2}{4}+\frac{A\,a\,b}{3}}{d\,\left({\sin\left(c+d\,x\right)}^6-3\,{\sin\left(c+d\,x\right)}^4+3\,{\sin\left(c+d\,x\right)}^2-1\right)}","Not used",1,"- (atanh((4*sin(c + d*x)*((A*b^2)/32 - (5*A*a^2)/32 + (B*a*b)/16))/((A*b^2)/8 - (5*A*a^2)/8 + (B*a*b)/4))*((A*b^2)/16 - (5*A*a^2)/16 + (B*a*b)/8))/d - (sin(c + d*x)*((11*A*a^2)/16 + (A*b^2)/16 + (B*a*b)/8) + (B*a^2)/6 - (B*b^2)/12 + sin(c + d*x)^3*((A*b^2)/6 - (5*A*a^2)/6 + (B*a*b)/3) - sin(c + d*x)^5*((A*b^2)/16 - (5*A*a^2)/16 + (B*a*b)/8) + (B*b^2*sin(c + d*x)^2)/4 + (A*a*b)/3)/(d*(3*sin(c + d*x)^2 - 3*sin(c + d*x)^4 + sin(c + d*x)^6 - 1))","B"
1544,1,435,315,12.365893,"\text{Not used}","int((cos(c + d*x)^7*(A + B*sin(c + d*x)))/(a + b*sin(c + d*x)),x)","\frac{{\sin\left(c+d\,x\right)}^4\,\left(\frac{3\,A}{4\,b}-\frac{a\,\left(\frac{3\,B}{b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}\right)}{4\,b}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{B}{b}+\frac{a\,\left(\frac{3\,A}{b}-\frac{a\,\left(\frac{3\,B}{b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}\right)}{b}\right)}{3\,b}\right)}{d}+\frac{\sin\left(c+d\,x\right)\,\left(\frac{B}{b}+\frac{a\,\left(\frac{3\,A}{b}-\frac{a\,\left(\frac{3\,B}{b}+\frac{a\,\left(\frac{3\,A}{b}-\frac{a\,\left(\frac{3\,B}{b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}\right)}{b}\right)}{b}\right)}{b}\right)}{b}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^6\,\left(\frac{A}{6\,b}-\frac{B\,a}{6\,b^2}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,A}{2\,b}-\frac{a\,\left(\frac{3\,B}{b}+\frac{a\,\left(\frac{3\,A}{b}-\frac{a\,\left(\frac{3\,B}{b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}\right)}{b}\right)}{b}\right)}{2\,b}\right)}{d}+\frac{{\sin\left(c+d\,x\right)}^5\,\left(\frac{3\,B}{5\,b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{5\,b}\right)}{d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(B\,a^7-A\,a^6\,b-3\,B\,a^5\,b^2+3\,A\,a^4\,b^3+3\,B\,a^3\,b^4-3\,A\,a^2\,b^5-B\,a\,b^6+A\,b^7\right)}{b^8\,d}-\frac{B\,{\sin\left(c+d\,x\right)}^7}{7\,b\,d}","Not used",1,"(sin(c + d*x)^4*((3*A)/(4*b) - (a*((3*B)/b + (a*(A/b - (B*a)/b^2))/b))/(4*b)))/d - (sin(c + d*x)^3*(B/b + (a*((3*A)/b - (a*((3*B)/b + (a*(A/b - (B*a)/b^2))/b))/b))/(3*b)))/d + (sin(c + d*x)*(B/b + (a*((3*A)/b - (a*((3*B)/b + (a*((3*A)/b - (a*((3*B)/b + (a*(A/b - (B*a)/b^2))/b))/b))/b))/b))/b))/d - (sin(c + d*x)^6*(A/(6*b) - (B*a)/(6*b^2)))/d - (sin(c + d*x)^2*((3*A)/(2*b) - (a*((3*B)/b + (a*((3*A)/b - (a*((3*B)/b + (a*(A/b - (B*a)/b^2))/b))/b))/b))/(2*b)))/d + (sin(c + d*x)^5*((3*B)/(5*b) + (a*(A/b - (B*a)/b^2))/(5*b)))/d + (log(a + b*sin(c + d*x))*(A*b^7 + B*a^7 - 3*A*a^2*b^5 + 3*A*a^4*b^3 + 3*B*a^3*b^4 - 3*B*a^5*b^2 - A*a^6*b - B*a*b^6))/(b^8*d) - (B*sin(c + d*x)^7)/(7*b*d)","B"
1545,1,253,202,0.098462,"\text{Not used}","int((cos(c + d*x)^5*(A + B*sin(c + d*x)))/(a + b*sin(c + d*x)),x)","\frac{{\sin\left(c+d\,x\right)}^4\,\left(\frac{A}{4\,b}-\frac{B\,a}{4\,b^2}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{A}{b}-\frac{a\,\left(\frac{2\,B}{b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}\right)}{2\,b}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{2\,B}{3\,b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{3\,b}\right)}{d}+\frac{\sin\left(c+d\,x\right)\,\left(\frac{B}{b}+\frac{a\,\left(\frac{2\,A}{b}-\frac{a\,\left(\frac{2\,B}{b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}\right)}{b}\right)}{b}\right)}{d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(-B\,a^5+A\,a^4\,b+2\,B\,a^3\,b^2-2\,A\,a^2\,b^3-B\,a\,b^4+A\,b^5\right)}{b^6\,d}+\frac{B\,{\sin\left(c+d\,x\right)}^5}{5\,b\,d}","Not used",1,"(sin(c + d*x)^4*(A/(4*b) - (B*a)/(4*b^2)))/d - (sin(c + d*x)^2*(A/b - (a*((2*B)/b + (a*(A/b - (B*a)/b^2))/b))/(2*b)))/d - (sin(c + d*x)^3*((2*B)/(3*b) + (a*(A/b - (B*a)/b^2))/(3*b)))/d + (sin(c + d*x)*(B/b + (a*((2*A)/b - (a*((2*B)/b + (a*(A/b - (B*a)/b^2))/b))/b))/b))/d + (log(a + b*sin(c + d*x))*(A*b^5 - B*a^5 - 2*A*a^2*b^3 + 2*B*a^3*b^2 + A*a^4*b - B*a*b^4))/(b^6*d) + (B*sin(c + d*x)^5)/(5*b*d)","B"
1546,1,122,111,0.078247,"\text{Not used}","int((cos(c + d*x)^3*(A + B*sin(c + d*x)))/(a + b*sin(c + d*x)),x)","\frac{\sin\left(c+d\,x\right)\,\left(\frac{B}{b}+\frac{a\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{A}{2\,b}-\frac{B\,a}{2\,b^2}\right)}{d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(B\,a^3-A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{b^4\,d}-\frac{B\,{\sin\left(c+d\,x\right)}^3}{3\,b\,d}","Not used",1,"(sin(c + d*x)*(B/b + (a*(A/b - (B*a)/b^2))/b))/d - (sin(c + d*x)^2*(A/(2*b) - (B*a)/(2*b^2)))/d + (log(a + b*sin(c + d*x))*(A*b^3 + B*a^3 - A*a^2*b - B*a*b^2))/(b^4*d) - (B*sin(c + d*x)^3)/(3*b*d)","B"
1547,1,41,41,0.063182,"\text{Not used}","int((cos(c + d*x)*(A + B*sin(c + d*x)))/(a + b*sin(c + d*x)),x)","\frac{B\,\sin\left(c+d\,x\right)}{b\,d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(A\,b-B\,a\right)}{b^2\,d}","Not used",1,"(B*sin(c + d*x))/(b*d) + (log(a + b*sin(c + d*x))*(A*b - B*a))/(b^2*d)","B"
1548,1,89,90,0.313133,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{A}{2}-\frac{B}{2}\right)}{d\,\left(a-b\right)}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(A\,b-B\,a\right)}{d\,\left(a^2-b^2\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{A}{2}+\frac{B}{2}\right)}{d\,\left(a+b\right)}","Not used",1,"(log(sin(c + d*x) + 1)*(A/2 - B/2))/(d*(a - b)) - (log(a + b*sin(c + d*x))*(A*b - B*a))/(d*(a^2 - b^2)) - (log(sin(c + d*x) - 1)*(A/2 + B/2))/(d*(a + b))","B"
1549,1,197,159,0.523269,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(A\,b^3-B\,a\,b^2\right)}{d\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{\frac{A\,b-B\,a}{2\,\left(a^2-b^2\right)}-\frac{\sin\left(c+d\,x\right)\,\left(A\,a-B\,b\right)}{2\,\left(a^2-b^2\right)}}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(A\,a-b\,\left(2\,A-B\right)\right)}{d\,\left(4\,a^2-8\,a\,b+4\,b^2\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(A\,a+b\,\left(2\,A+B\right)\right)}{d\,\left(4\,a^2+8\,a\,b+4\,b^2\right)}","Not used",1,"(log(a + b*sin(c + d*x))*(A*b^3 - B*a*b^2))/(d*(a^4 + b^4 - 2*a^2*b^2)) - ((A*b - B*a)/(2*(a^2 - b^2)) - (sin(c + d*x)*(A*a - B*b))/(2*(a^2 - b^2)))/(d*cos(c + d*x)^2) + (log(sin(c + d*x) + 1)*(A*a - b*(2*A - B)))/(d*(4*a^2 - 8*a*b + 4*b^2)) - (log(sin(c + d*x) - 1)*(A*a + b*(2*A + B)))/(d*(8*a*b + 4*a^2 + 4*b^2))","B"
1550,1,427,263,12.954886,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{\frac{B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+3\,A\,b^3}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\sin\left(c+d\,x\right)\,\left(5\,A\,a^3-B\,a^2\,b-9\,A\,a\,b^2+5\,B\,b^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(A\,b^3-B\,a\,b^2\right)}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(3\,A\,a^3+B\,a^2\,b-7\,A\,a\,b^2+3\,B\,b^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{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(3\,A\,a^2+\left(9\,A+B\right)\,a\,b+\left(8\,A+3\,B\right)\,b^2\right)}{d\,\left(16\,a^3+48\,a^2\,b+48\,a\,b^2+16\,b^3\right)}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(A\,b^5-B\,a\,b^4\right)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(3\,A\,a^2+\left(B-9\,A\right)\,a\,b+\left(8\,A-3\,B\right)\,b^2\right)}{d\,\left(16\,a^3-48\,a^2\,b+48\,a\,b^2-16\,b^3\right)}","Not used",1,"((3*A*b^3 + B*a^3 - A*a^2*b - 3*B*a*b^2)/(4*(a^4 + b^4 - 2*a^2*b^2)) + (sin(c + d*x)*(5*A*a^3 + 5*B*b^3 - 9*A*a*b^2 - B*a^2*b))/(8*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^2*(A*b^3 - B*a*b^2))/(2*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^3*(3*A*a^3 + 3*B*b^3 - 7*A*a*b^2 + B*a^2*b))/(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)) - (log(sin(c + d*x) - 1)*(3*A*a^2 + b^2*(8*A + 3*B) + a*b*(9*A + B)))/(d*(48*a*b^2 + 48*a^2*b + 16*a^3 + 16*b^3)) - (log(a + b*sin(c + d*x))*(A*b^5 - B*a*b^4))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (log(sin(c + d*x) + 1)*(3*A*a^2 + b^2*(8*A - 3*B) - a*b*(9*A - B)))/(d*(48*a*b^2 - 48*a^2*b + 16*a^3 - 16*b^3))","B"
1551,1,729,383,13.435458,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^7*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(5\,A\,a^3+\left(B-20\,A\right)\,a^2\,b+\left(29\,A-4\,B\right)\,a\,b^2+\left(5\,B-16\,A\right)\,b^3\right)}{d\,\left(32\,a^4-128\,a^3\,b+192\,a^2\,b^2-128\,a\,b^3+32\,b^4\right)}-\frac{\frac{-2\,B\,a^5+2\,A\,a^4\,b+7\,B\,a^3\,b^2-7\,A\,a^2\,b^3-11\,B\,a\,b^4+11\,A\,b^5}{12\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\sin\left(c+d\,x\right)}^4\,\left(A\,b^5-B\,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)\,\left(11\,A\,a^5-B\,a^4\,b-32\,A\,a^3\,b^2+4\,B\,a^2\,b^3+29\,A\,a\,b^4-11\,B\,b^5\right)}{16\,\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(B\,a^3\,b^2-A\,a^2\,b^3-5\,B\,a\,b^4+5\,A\,b^5\right)}{4\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\sin\left(c+d\,x\right)}^3\,\left(5\,A\,a^5+B\,a^4\,b-16\,A\,a^3\,b^2-2\,B\,a^2\,b^3+17\,A\,a\,b^4-5\,B\,b^5\right)}{6\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{{\sin\left(c+d\,x\right)}^5\,\left(5\,A\,a^5+B\,a^4\,b-16\,A\,a^3\,b^2-4\,B\,a^2\,b^3+19\,A\,a\,b^4-5\,B\,b^5\right)}{16\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left({\cos\left(c+d\,x\right)}^2-{\sin\left(c+d\,x\right)}^6+3\,{\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(5\,A\,a^3+\left(20\,A+B\right)\,a^2\,b+\left(29\,A+4\,B\right)\,a\,b^2+\left(16\,A+5\,B\right)\,b^3\right)}{d\,\left(32\,a^4+128\,a^3\,b+192\,a^2\,b^2+128\,a\,b^3+32\,b^4\right)}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(A\,b^7-B\,a\,b^6\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)*(5*A*a^3 - b^3*(16*A - 5*B) - a^2*b*(20*A - B) + a*b^2*(29*A - 4*B)))/(d*(32*a^4 - 128*a^3*b - 128*a*b^3 + 32*b^4 + 192*a^2*b^2)) - ((11*A*b^5 - 2*B*a^5 - 7*A*a^2*b^3 + 7*B*a^3*b^2 + 2*A*a^4*b - 11*B*a*b^4)/(12*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (sin(c + d*x)^4*(A*b^5 - B*a*b^4))/(2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (sin(c + d*x)*(11*A*a^5 - 11*B*b^5 - 32*A*a^3*b^2 + 4*B*a^2*b^3 + 29*A*a*b^4 - B*a^4*b))/(16*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (sin(c + d*x)^2*(5*A*b^5 - A*a^2*b^3 + B*a^3*b^2 - 5*B*a*b^4))/(4*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (sin(c + d*x)^3*(5*A*a^5 - 5*B*b^5 - 16*A*a^3*b^2 - 2*B*a^2*b^3 + 17*A*a*b^4 + B*a^4*b))/(6*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (sin(c + d*x)^5*(5*A*a^5 - 5*B*b^5 - 16*A*a^3*b^2 - 4*B*a^2*b^3 + 19*A*a*b^4 + B*a^4*b))/(16*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(cos(c + d*x)^2 - 2*sin(c + d*x)^2 + 3*sin(c + d*x)^4 - sin(c + d*x)^6)) - (log(sin(c + d*x) - 1)*(5*A*a^3 + b^3*(16*A + 5*B) + a*b^2*(29*A + 4*B) + a^2*b*(20*A + B)))/(d*(128*a*b^3 + 128*a^3*b + 32*a^4 + 32*b^4 + 192*a^2*b^2)) + (log(a + b*sin(c + d*x))*(A*b^7 - B*a*b^6))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))","B"
1552,1,682,324,12.149041,"\text{Not used}","int((cos(c + d*x)^7*(A + B*sin(c + d*x)))/(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{A}{b^2}+\frac{a^2\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{3\,b^2}-\frac{2\,a\,\left(\frac{3\,B}{b^2}+\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{3\,b}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^5\,\left(\frac{A}{5\,b^2}-\frac{2\,B\,a}{5\,b^3}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{3\,B}{2\,b^2}+\frac{a\,\left(\frac{3\,A}{b^2}+\frac{a^2\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b^2}-\frac{2\,a\,\left(\frac{3\,B}{b^2}+\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{b}\right)}{b}+\frac{a^2\,\left(\frac{3\,B}{b^2}+\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{2\,b^2}\right)}{d}+\frac{{\sin\left(c+d\,x\right)}^4\,\left(\frac{3\,B}{4\,b^2}+\frac{a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{2\,b}+\frac{B\,a^2}{4\,b^4}\right)}{d}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{3\,A}{b^2}-\frac{2\,a\,\left(\frac{3\,B}{b^2}+\frac{2\,a\,\left(\frac{3\,A}{b^2}+\frac{a^2\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b^2}-\frac{2\,a\,\left(\frac{3\,B}{b^2}+\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{b}\right)}{b}+\frac{a^2\,\left(\frac{3\,B}{b^2}+\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{b^2}\right)}{b}+\frac{a^2\,\left(\frac{3\,A}{b^2}+\frac{a^2\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b^2}-\frac{2\,a\,\left(\frac{3\,B}{b^2}+\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{b}\right)}{b^2}\right)}{d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(-7\,B\,a^6+6\,A\,a^5\,b+15\,B\,a^4\,b^2-12\,A\,a^3\,b^3-9\,B\,a^2\,b^4+6\,A\,a\,b^5+B\,b^6\right)}{b^8\,d}-\frac{B\,a^7-A\,a^6\,b-3\,B\,a^5\,b^2+3\,A\,a^4\,b^3+3\,B\,a^3\,b^4-3\,A\,a^2\,b^5-B\,a\,b^6+A\,b^7}{b\,d\,\left(\sin\left(c+d\,x\right)\,b^8+a\,b^7\right)}-\frac{B\,{\sin\left(c+d\,x\right)}^6}{6\,b^2\,d}","Not used",1,"(sin(c + d*x)^3*(A/b^2 + (a^2*(A/b^2 - (2*B*a)/b^3))/(3*b^2) - (2*a*((3*B)/b^2 + (2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/(3*b)))/d - (sin(c + d*x)^5*(A/(5*b^2) - (2*B*a)/(5*b^3)))/d - (sin(c + d*x)^2*((3*B)/(2*b^2) + (a*((3*A)/b^2 + (a^2*(A/b^2 - (2*B*a)/b^3))/b^2 - (2*a*((3*B)/b^2 + (2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/b))/b + (a^2*((3*B)/b^2 + (2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/(2*b^2)))/d + (sin(c + d*x)^4*((3*B)/(4*b^2) + (a*(A/b^2 - (2*B*a)/b^3))/(2*b) + (B*a^2)/(4*b^4)))/d - (sin(c + d*x)*((3*A)/b^2 - (2*a*((3*B)/b^2 + (2*a*((3*A)/b^2 + (a^2*(A/b^2 - (2*B*a)/b^3))/b^2 - (2*a*((3*B)/b^2 + (2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/b))/b + (a^2*((3*B)/b^2 + (2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/b^2))/b + (a^2*((3*A)/b^2 + (a^2*(A/b^2 - (2*B*a)/b^3))/b^2 - (2*a*((3*B)/b^2 + (2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/b))/b^2))/d + (log(a + b*sin(c + d*x))*(B*b^6 - 7*B*a^6 - 12*A*a^3*b^3 - 9*B*a^2*b^4 + 15*B*a^4*b^2 + 6*A*a*b^5 + 6*A*a^5*b))/(b^8*d) - (A*b^7 + B*a^7 - 3*A*a^2*b^5 + 3*A*a^4*b^3 + 3*B*a^3*b^4 - 3*B*a^5*b^2 - A*a^6*b - B*a*b^6)/(b*d*(a*b^7 + b^8*sin(c + d*x))) - (B*sin(c + d*x)^6)/(6*b^2*d)","B"
1553,1,290,206,0.119528,"\text{Not used}","int((cos(c + d*x)^5*(A + B*sin(c + d*x)))/(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{A}{3\,b^2}-\frac{2\,B\,a}{3\,b^3}\right)}{d}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{2\,A}{b^2}+\frac{a^2\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b^2}-\frac{2\,a\,\left(\frac{2\,B}{b^2}+\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{b}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{B}{b^2}+\frac{a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{2\,b^4}\right)}{d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(5\,B\,a^4-4\,A\,a^3\,b-6\,B\,a^2\,b^2+4\,A\,a\,b^3+B\,b^4\right)}{b^6\,d}-\frac{-B\,a^5+A\,a^4\,b+2\,B\,a^3\,b^2-2\,A\,a^2\,b^3-B\,a\,b^4+A\,b^5}{b\,d\,\left(\sin\left(c+d\,x\right)\,b^6+a\,b^5\right)}+\frac{B\,{\sin\left(c+d\,x\right)}^4}{4\,b^2\,d}","Not used",1,"(sin(c + d*x)^3*(A/(3*b^2) - (2*B*a)/(3*b^3)))/d - (sin(c + d*x)*((2*A)/b^2 + (a^2*(A/b^2 - (2*B*a)/b^3))/b^2 - (2*a*((2*B)/b^2 + (2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/b))/d - (sin(c + d*x)^2*(B/b^2 + (a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/(2*b^4)))/d + (log(a + b*sin(c + d*x))*(5*B*a^4 + B*b^4 - 6*B*a^2*b^2 + 4*A*a*b^3 - 4*A*a^3*b))/(b^6*d) - (A*b^5 - B*a^5 - 2*A*a^2*b^3 + 2*B*a^3*b^2 + A*a^4*b - B*a*b^4)/(b*d*(a*b^5 + b^6*sin(c + d*x))) + (B*sin(c + d*x)^4)/(4*b^2*d)","B"
1554,1,128,113,12.098640,"\text{Not used}","int((cos(c + d*x)^3*(A + B*sin(c + d*x)))/(a + b*sin(c + d*x))^2,x)","\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(-3\,B\,a^2+2\,A\,a\,b+B\,b^2\right)}{b^4\,d}-\frac{B\,a^3-A\,a^2\,b-B\,a\,b^2+A\,b^3}{b\,d\,\left(\sin\left(c+d\,x\right)\,b^4+a\,b^3\right)}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{d}-\frac{B\,{\sin\left(c+d\,x\right)}^2}{2\,b^2\,d}","Not used",1,"(log(a + b*sin(c + d*x))*(B*b^2 - 3*B*a^2 + 2*A*a*b))/(b^4*d) - (A*b^3 + B*a^3 - A*a^2*b - B*a*b^2)/(b*d*(a*b^3 + b^4*sin(c + d*x))) - (sin(c + d*x)*(A/b^2 - (2*B*a)/b^3))/d - (B*sin(c + d*x)^2)/(2*b^2*d)","B"
1555,1,48,48,0.062617,"\text{Not used}","int((cos(c + d*x)*(A + B*sin(c + d*x)))/(a + b*sin(c + d*x))^2,x)","\frac{B\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{b^2\,d}-\frac{A\,b-B\,a}{b^2\,d\,\left(a+b\,\sin\left(c+d\,x\right)\right)}","Not used",1,"(B*log(a + b*sin(c + d*x)))/(b^2*d) - (A*b - B*a)/(b^2*d*(a + b*sin(c + d*x)))","B"
1556,1,131,135,0.417369,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)*(a + b*sin(c + d*x))^2),x)","\frac{A\,b-B\,a}{d\,\left(a^2-b^2\right)\,\left(a+b\,\sin\left(c+d\,x\right)\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{A}{2}+\frac{B}{2}\right)}{d\,{\left(a+b\right)}^2}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(B\,a^2-2\,A\,a\,b+B\,b^2\right)}{d\,{\left(a^2-b^2\right)}^2}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{A}{2}-\frac{B}{2}\right)}{d\,{\left(a-b\right)}^2}","Not used",1,"(A*b - B*a)/(d*(a^2 - b^2)*(a + b*sin(c + d*x))) - (log(sin(c + d*x) - 1)*(A/2 + B/2))/(d*(a + b)^2) + (log(a + b*sin(c + d*x))*(B*a^2 + B*b^2 - 2*A*a*b))/(d*(a^2 - b^2)^2) + (log(sin(c + d*x) + 1)*(A/2 - B/2))/(d*(a - b)^2)","B"
1557,1,327,228,12.661959,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^3*(a + b*sin(c + d*x))^2),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^2\,\left(A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{-B\,a^3+2\,A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3}{2\,{\left(a^2-b^2\right)}^2}+\frac{\sin\left(c+d\,x\right)\,\left(A\,a-B\,b\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(A\,a+b\,\left(3\,A+2\,B\right)\right)}{d\,\left(4\,a^3+12\,a^2\,b+12\,a\,b^2+4\,b^3\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(A\,a-b\,\left(3\,A-2\,B\right)\right)}{d\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(3\,B\,a^2\,b^2-4\,A\,a\,b^3+B\,b^4\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*(3*A*b^3 + A*a^2*b - 4*B*a*b^2))/(2*(a^4 + b^4 - 2*a^2*b^2)) - (2*A*b^3 - B*a^3 + 2*A*a^2*b - 3*B*a*b^2)/(2*(a^2 - b^2)^2) + (sin(c + d*x)*(A*a - B*b))/(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)*(A*a + b*(3*A + 2*B)))/(d*(12*a*b^2 + 12*a^2*b + 4*a^3 + 4*b^3)) + (log(sin(c + d*x) + 1)*(A*a - b*(3*A - 2*B)))/(d*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3)) - (log(a + b*sin(c + d*x))*(B*b^4 + 3*B*a^2*b^2 - 4*A*a*b^3))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
1558,1,615,372,13.461921,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^5*(a + b*sin(c + d*x))^2),x)","\frac{\frac{B\,a^5-2\,A\,a^4\,b-6\,B\,a^3\,b^2+10\,A\,a^2\,b^3-7\,B\,a\,b^4+4\,A\,b^5}{4\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^4\,\left(3\,A\,a^4\,b+2\,B\,a^3\,b^2-12\,A\,a^2\,b^3+22\,B\,a\,b^4-15\,A\,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(5\,A\,a^3-11\,A\,a\,b^2+6\,B\,b^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(3\,A\,a^3+2\,B\,a^2\,b-9\,A\,a\,b^2+4\,B\,b^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\,a^4\,b+10\,B\,a^3\,b^2-28\,A\,a^2\,b^3+38\,B\,a\,b^4-25\,A\,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{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(5\,B\,a^2\,b^4-6\,A\,a\,b^5+B\,b^6\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(3\,A\,a^2+\left(12\,A+2\,B\right)\,a\,b+\left(15\,A+8\,B\right)\,b^2\right)}{d\,\left(16\,a^4+64\,a^3\,b+96\,a^2\,b^2+64\,a\,b^3+16\,b^4\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(3\,A\,a^2+\left(2\,B-12\,A\right)\,a\,b+\left(15\,A-8\,B\right)\,b^2\right)}{d\,\left(16\,a^4-64\,a^3\,b+96\,a^2\,b^2-64\,a\,b^3+16\,b^4\right)}","Not used",1,"((4*A*b^5 + B*a^5 + 10*A*a^2*b^3 - 6*B*a^3*b^2 - 2*A*a^4*b - 7*B*a*b^4)/(4*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^4*(2*B*a^3*b^2 - 12*A*a^2*b^3 - 15*A*b^5 + 3*A*a^4*b + 22*B*a*b^4))/(8*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (sin(c + d*x)*(5*A*a^3 + 6*B*b^3 - 11*A*a*b^2))/(8*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^3*(3*A*a^3 + 4*B*b^3 - 9*A*a*b^2 + 2*B*a^2*b))/(8*(a^4 + b^4 - 2*a^2*b^2)) + (sin(c + d*x)^2*(10*B*a^3*b^2 - 28*A*a^2*b^3 - 25*A*b^5 + 5*A*a^4*b + 38*B*a*b^4))/(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)) + (log(a + b*sin(c + d*x))*(B*b^6 + 5*B*a^2*b^4 - 6*A*a*b^5))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (log(sin(c + d*x) - 1)*(3*A*a^2 + b^2*(15*A + 8*B) + a*b*(12*A + 2*B)))/(d*(64*a*b^3 + 64*a^3*b + 16*a^4 + 16*b^4 + 96*a^2*b^2)) + (log(sin(c + d*x) + 1)*(3*A*a^2 + b^2*(15*A - 8*B) - a*b*(12*A - 2*B)))/(d*(16*a^4 - 64*a^3*b - 64*a*b^3 + 16*b^4 + 96*a^2*b^2))","B"
1559,1,1024,550,14.384700,"\text{Not used}","int((A + B*sin(c + d*x))/(cos(c + d*x)^7*(a + b*sin(c + d*x))^2),x)","\frac{\frac{\sin\left(c+d\,x\right)\,\left(33\,A\,a^5+2\,B\,a^4\,b-106\,A\,a^3\,b^2-6\,B\,a^2\,b^3+121\,A\,a\,b^4-44\,B\,b^5\right)}{48\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\sin\left(c+d\,x\right)}^5\,\left(5\,A\,a^5+2\,B\,a^4\,b-18\,A\,a^3\,b^2-10\,B\,a^2\,b^3+29\,A\,a\,b^4-8\,B\,b^5\right)}{16\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(10\,A\,a^5+4\,B\,a^4\,b-36\,A\,a^3\,b^2-13\,B\,a^2\,b^3+50\,A\,a\,b^4-15\,B\,b^5\right)}{12\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{-2\,B\,a^7+4\,A\,a^6\,b+11\,B\,a^5\,b^2-20\,A\,a^4\,b^3-34\,B\,a^3\,b^4+52\,A\,a^2\,b^5-23\,B\,a\,b^6+12\,A\,b^7}{12\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\sin\left(c+d\,x\right)}^6\,\left(5\,A\,a^6\,b+2\,B\,a^5\,b^2-23\,A\,a^4\,b^3-12\,B\,a^3\,b^4+47\,A\,a^2\,b^5-54\,B\,a\,b^6+35\,A\,b^7\right)}{16\,\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)}^4\,\left(5\,A\,a^6\,b+2\,B\,a^5\,b^2-23\,A\,a^4\,b^3-19\,B\,a^3\,b^4+55\,A\,a^2\,b^5-55\,B\,a\,b^6+35\,A\,b^7\right)}{6\,\left(a^2-b^2\right)\,\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(11\,A\,a^6\,b+10\,B\,a^5\,b^2-57\,A\,a^4\,b^3-76\,B\,a^3\,b^4+161\,A\,a^2\,b^5-126\,B\,a\,b^6+77\,A\,b^7\right)}{16\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left(-b\,{\sin\left(c+d\,x\right)}^7-a\,{\sin\left(c+d\,x\right)}^6+3\,b\,{\sin\left(c+d\,x\right)}^5+3\,a\,{\sin\left(c+d\,x\right)}^4-3\,b\,{\sin\left(c+d\,x\right)}^3-3\,a\,{\sin\left(c+d\,x\right)}^2+b\,\sin\left(c+d\,x\right)+a\right)}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(7\,B\,a^2\,b^6-8\,A\,a\,b^7+B\,b^8\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)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(5\,A\,a^3+\left(25\,A+2\,B\right)\,a^2\,b+\left(47\,A+10\,B\right)\,a\,b^2+\left(35\,A+16\,B\right)\,b^3\right)}{d\,\left(32\,a^5+160\,a^4\,b+320\,a^3\,b^2+320\,a^2\,b^3+160\,a\,b^4+32\,b^5\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(5\,A\,a^3+\left(2\,B-25\,A\right)\,a^2\,b+\left(47\,A-10\,B\right)\,a\,b^2+\left(16\,B-35\,A\right)\,b^3\right)}{d\,\left(32\,a^5-160\,a^4\,b+320\,a^3\,b^2-320\,a^2\,b^3+160\,a\,b^4-32\,b^5\right)}","Not used",1,"((sin(c + d*x)*(33*A*a^5 - 44*B*b^5 - 106*A*a^3*b^2 - 6*B*a^2*b^3 + 121*A*a*b^4 + 2*B*a^4*b))/(48*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (sin(c + d*x)^5*(5*A*a^5 - 8*B*b^5 - 18*A*a^3*b^2 - 10*B*a^2*b^3 + 29*A*a*b^4 + 2*B*a^4*b))/(16*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (sin(c + d*x)^3*(10*A*a^5 - 15*B*b^5 - 36*A*a^3*b^2 - 13*B*a^2*b^3 + 50*A*a*b^4 + 4*B*a^4*b))/(12*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (12*A*b^7 - 2*B*a^7 + 52*A*a^2*b^5 - 20*A*a^4*b^3 - 34*B*a^3*b^4 + 11*B*a^5*b^2 + 4*A*a^6*b - 23*B*a*b^6)/(12*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (sin(c + d*x)^6*(35*A*b^7 + 47*A*a^2*b^5 - 23*A*a^4*b^3 - 12*B*a^3*b^4 + 2*B*a^5*b^2 + 5*A*a^6*b - 54*B*a*b^6))/(16*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (sin(c + d*x)^4*(35*A*b^7 + 55*A*a^2*b^5 - 23*A*a^4*b^3 - 19*B*a^3*b^4 + 2*B*a^5*b^2 + 5*A*a^6*b - 55*B*a*b^6))/(6*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (sin(c + d*x)^2*(77*A*b^7 + 161*A*a^2*b^5 - 57*A*a^4*b^3 - 76*B*a^3*b^4 + 10*B*a^5*b^2 + 11*A*a^6*b - 126*B*a*b^6))/(16*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(a + b*sin(c + d*x) - 3*a*sin(c + d*x)^2 + 3*a*sin(c + d*x)^4 - a*sin(c + d*x)^6 - 3*b*sin(c + d*x)^3 + 3*b*sin(c + d*x)^5 - b*sin(c + d*x)^7)) - (log(a + b*sin(c + d*x))*(B*b^8 + 7*B*a^2*b^6 - 8*A*a*b^7))/(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)) - (log(sin(c + d*x) - 1)*(5*A*a^3 + b^3*(35*A + 16*B) + a^2*b*(25*A + 2*B) + a*b^2*(47*A + 10*B)))/(d*(160*a*b^4 + 160*a^4*b + 32*a^5 + 32*b^5 + 320*a^2*b^3 + 320*a^3*b^2)) + (log(sin(c + d*x) + 1)*(5*A*a^3 - b^3*(35*A - 16*B) - a^2*b*(25*A - 2*B) + a*b^2*(47*A - 10*B)))/(d*(160*a*b^4 - 160*a^4*b + 32*a^5 - 32*b^5 - 320*a^2*b^3 + 320*a^3*b^2))","B"
1560,0,-1,40,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + b*sin(e + f*x))^m)/(g*cos(e + f*x))^(m + 1),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",0,"int(((A + B*sin(e + f*x))*(a + b*sin(e + f*x))^m)/(g*cos(e + f*x))^(m + 1), x)","F"
1561,0,-1,330,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p}{\left(a+b\,\sin\left(e+f\,x\right)\right)\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*cos(e + f*x))^p/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))), x)","F"
1562,0,-1,508,0.000000,"\text{Not used}","int((g*cos(e + f*x))^p/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^2),x)","\int \frac{{\left(g\,\cos\left(e+f\,x\right)\right)}^p}{\left(a+b\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((g*cos(e + f*x))^p/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^2), x)","F"
1563,0,-1,308,0.000000,"\text{Not used}","int((g/cos(e + f*x))^p/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))),x)","\int \frac{{\left(\frac{g}{\cos\left(e+f\,x\right)}\right)}^p}{\left(a+b\,\sin\left(e+f\,x\right)\right)\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g/cos(e + f*x))^p/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))), x)","F"