1,1,89,55,0.350186,"\text{Not used}","int(1/(sin(x)^5*(a + a/sin(x))),x)","\frac{7\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a}-\frac{23\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{1}{3}}{8\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+8\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24\,a}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2\,a}","Not used",1,"(7*tan(x/2))/(8*a) - (6*tan(x/2)^2 - (2*tan(x/2))/3 + 23*tan(x/2)^3 + 1/3)/(8*a*tan(x/2)^3 + 8*a*tan(x/2)^4) - tan(x/2)^2/(8*a) + tan(x/2)^3/(24*a) - (3*log(tan(x/2)))/(2*a)","B"
2,1,69,44,0.256421,"\text{Not used}","int(1/(sin(x)^4*(a + a/sin(x))),x)","\frac{10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{3\,\mathrm{tan}\left(\frac{x}{2}\right)}{2}-\frac{1}{2}}{4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2\,a}","Not used",1,"((3*tan(x/2))/2 + 10*tan(x/2)^2 - 1/2)/(4*a*tan(x/2)^2 + 4*a*tan(x/2)^3) - tan(x/2)/(2*a) + tan(x/2)^2/(8*a) + (3*log(tan(x/2)))/(2*a)","B"
3,1,49,27,0.252746,"\text{Not used}","int(1/(sin(x)^3*(a + a/sin(x))),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a}-\frac{5\,\mathrm{tan}\left(\frac{x}{2}\right)+1}{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}","Not used",1,"tan(x/2)/(2*a) - (5*tan(x/2) + 1)/(2*a*tan(x/2) + 2*a*tan(x/2)^2) - log(tan(x/2))/a","B"
4,1,23,20,0.182856,"\text{Not used}","int(1/(sin(x)^2*(a + a/sin(x))),x)","\frac{2}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}","Not used",1,"2/(a*(tan(x/2) + 1)) + log(tan(x/2))/a","B"
5,1,13,12,0.172017,"\text{Not used}","int(1/(sin(x)*(a + a/sin(x))),x)","-\frac{2}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"-2/(a*(tan(x/2) + 1))","B"
6,1,27,28,0.215738,"\text{Not used}","int(1/(a + a/sin(c + d*x)),x)","\frac{x}{a}+\frac{2}{a\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"x/a + 2/(a*d*(tan(c/2 + (d*x)/2) + 1))","B"
7,1,46,25,0.236024,"\text{Not used}","int(sin(x)/(a + a/sin(x)),x)","-\frac{x}{a}-\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{x}{2}\right)+4}{a\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"- x/a - (2*tan(x/2) + 2*tan(x/2)^2 + 4)/(a*(tan(x/2)^2 + 1)*(tan(x/2) + 1))","B"
8,1,59,40,0.273485,"\text{Not used}","int(sin(x)^2/(a + a/sin(x)),x)","\frac{3\,x}{2\,a}+\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\mathrm{tan}\left(\frac{x}{2}\right)+4}{a\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^2\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"(3*x)/(2*a) + (tan(x/2) + 5*tan(x/2)^2 + 3*tan(x/2)^3 + 3*tan(x/2)^4 + 4)/(a*(tan(x/2)^2 + 1)^2*(tan(x/2) + 1))","B"
9,1,78,53,0.346917,"\text{Not used}","int(sin(x)^3/(a + a/sin(x)),x)","-\frac{3\,x}{2\,a}-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+13\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{7\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{16}{3}}{a\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^3\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"- (3*x)/(2*a) - ((7*tan(x/2))/3 + 13*tan(x/2)^2 + 8*tan(x/2)^3 + 8*tan(x/2)^4 + 3*tan(x/2)^5 + 3*tan(x/2)^6 + 16/3)/(a*(tan(x/2)^2 + 1)^3*(tan(x/2) + 1))","B"
10,1,93,66,0.401900,"\text{Not used}","int(sin(x)^4/(a + a/sin(x)),x)","\frac{15\,x}{8\,a}+\frac{\frac{15\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8}{4}+\frac{15\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7}{4}+\frac{55\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{4}+\frac{55\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{4}+\frac{73\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{4}+\frac{91\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{12}+\frac{211\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{12}+\frac{19\,\mathrm{tan}\left(\frac{x}{2}\right)}{12}+\frac{16}{3}}{a\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^4\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"(15*x)/(8*a) + ((19*tan(x/2))/12 + (211*tan(x/2)^2)/12 + (91*tan(x/2)^3)/12 + (73*tan(x/2)^4)/4 + (55*tan(x/2)^5)/4 + (55*tan(x/2)^6)/4 + (15*tan(x/2)^7)/4 + (15*tan(x/2)^8)/4 + 16/3)/(a*(tan(x/2)^2 + 1)^4*(tan(x/2) + 1))","B"
11,1,52,57,0.405941,"\text{Not used}","int(1/(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)}^2+6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{8}{3}}{a^2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^3}","Not used",1,"x/a^2 + (6*tan(c/2 + (d*x)/2) + 2*tan(c/2 + (d*x)/2)^2 + 8/3)/(a^2*d*(tan(c/2 + (d*x)/2) + 1)^3)","B"
12,1,78,88,2.177905,"\text{Not used}","int(1/(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)}^4+10\,{\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}+\frac{38\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{44}{15}}{a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5}","Not used",1,"x/a^3 + ((38*tan(c/2 + (d*x)/2))/3 + (58*tan(c/2 + (d*x)/2)^2)/3 + 10*tan(c/2 + (d*x)/2)^3 + 2*tan(c/2 + (d*x)/2)^4 + 44/15)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^5)","B"
13,0,-1,65,0.000000,"\text{Not used}","int((a + a/sin(x))^(5/2),x)","\int {\left(a+\frac{a}{\sin\left(x\right)}\right)}^{5/2} \,d x","Not used",1,"int((a + a/sin(x))^(5/2), x)","F"
14,0,-1,44,0.000000,"\text{Not used}","int((a + a/sin(x))^(3/2),x)","\int {\left(a+\frac{a}{\sin\left(x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + a/sin(x))^(3/2), x)","F"
15,0,-1,26,0.000000,"\text{Not used}","int((a + a/sin(x))^(1/2),x)","\int \sqrt{a+\frac{a}{\sin\left(x\right)}} \,d x","Not used",1,"int((a + a/sin(x))^(1/2), x)","F"
16,0,-1,62,0.000000,"\text{Not used}","int(1/(a + a/sin(x))^(1/2),x)","\int \frac{1}{\sqrt{a+\frac{a}{\sin\left(x\right)}}} \,d x","Not used",1,"int(1/(a + a/sin(x))^(1/2), x)","F"
17,0,-1,81,0.000000,"\text{Not used}","int(1/(a + a/sin(x))^(3/2),x)","\int \frac{1}{{\left(a+\frac{a}{\sin\left(x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + a/sin(x))^(3/2), x)","F"
18,0,-1,100,0.000000,"\text{Not used}","int(1/(a + a/sin(x))^(5/2),x)","\int \frac{1}{{\left(a+\frac{a}{\sin\left(x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + a/sin(x))^(5/2), x)","F"
19,0,-1,37,0.000000,"\text{Not used}","int((a + a/sin(e + f*x))^(1/2)*(1/sin(e + f*x))^(1/2),x)","\int \sqrt{a+\frac{a}{\sin\left(e+f\,x\right)}}\,\sqrt{\frac{1}{\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a/sin(e + f*x))^(1/2)*(1/sin(e + f*x))^(1/2), x)","F"
20,0,-1,38,0.000000,"\text{Not used}","int((a - a/sin(e + f*x))^(1/2)*(-1/sin(e + f*x))^(1/2),x)","\int \sqrt{a-\frac{a}{\sin\left(e+f\,x\right)}}\,\sqrt{-\frac{1}{\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a - a/sin(e + f*x))^(1/2)*(-1/sin(e + f*x))^(1/2), x)","F"
21,0,-1,254,0.000000,"\text{Not used}","int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^(4/3),x)","\int \sqrt{a+\frac{a}{\sin\left(c+d\,x\right)}}\,{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^(4/3), x)","F"
22,0,-1,213,0.000000,"\text{Not used}","int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^(1/3),x)","\int \sqrt{a+\frac{a}{\sin\left(c+d\,x\right)}}\,{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",1,"int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^(1/3), x)","F"
23,0,-1,254,0.000000,"\text{Not used}","int((a + a/sin(c + d*x))^(1/2)/(1/sin(c + d*x))^(2/3),x)","\int \frac{\sqrt{a+\frac{a}{\sin\left(c+d\,x\right)}}}{{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((a + a/sin(c + d*x))^(1/2)/(1/sin(c + d*x))^(2/3), x)","F"
24,0,-1,514,0.000000,"\text{Not used}","int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^(5/3),x)","\int \sqrt{a+\frac{a}{\sin\left(c+d\,x\right)}}\,{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",1,"int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^(5/3), x)","F"
25,0,-1,470,0.000000,"\text{Not used}","int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^(2/3),x)","\int \sqrt{a+\frac{a}{\sin\left(c+d\,x\right)}}\,{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",1,"int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^(2/3), x)","F"
26,0,-1,508,0.000000,"\text{Not used}","int((a + a/sin(c + d*x))^(1/2)/(1/sin(c + d*x))^(1/3),x)","\int \frac{\sqrt{a+\frac{a}{\sin\left(c+d\,x\right)}}}{{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((a + a/sin(c + d*x))^(1/2)/(1/sin(c + d*x))^(1/3), x)","F"
27,0,-1,552,0.000000,"\text{Not used}","int((a + a/sin(c + d*x))^(1/2)/(1/sin(c + d*x))^(4/3),x)","\int \frac{\sqrt{a+\frac{a}{\sin\left(c+d\,x\right)}}}{{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((a + a/sin(c + d*x))^(1/2)/(1/sin(c + d*x))^(4/3), x)","F"
28,0,-1,48,0.000000,"\text{Not used}","int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^n,x)","\int \sqrt{a+\frac{a}{\sin\left(c+d\,x\right)}}\,{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^n, x)","F"
29,0,-1,69,0.000000,"\text{Not used}","int((a - a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^n,x)","\int \sqrt{a-\frac{a}{\sin\left(c+d\,x\right)}}\,{\left(\frac{1}{\sin\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/sin(c + d*x))^(1/2)*(1/sin(c + d*x))^n, x)","F"
30,0,-1,156,0.000000,"\text{Not used}","int((a + a/sin(e + f*x))^m/sin(e + f*x)^3,x)","\int \frac{{\left(a+\frac{a}{\sin\left(e+f\,x\right)}\right)}^m}{{\sin\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + a/sin(e + f*x))^m/sin(e + f*x)^3, x)","F"
31,0,-1,109,0.000000,"\text{Not used}","int((a + a/sin(e + f*x))^m/sin(e + f*x)^2,x)","\int \frac{{\left(a+\frac{a}{\sin\left(e+f\,x\right)}\right)}^m}{{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + a/sin(e + f*x))^m/sin(e + f*x)^2, x)","F"
32,0,-1,74,0.000000,"\text{Not used}","int((a + a/sin(e + f*x))^m/sin(e + f*x),x)","\int \frac{{\left(a+\frac{a}{\sin\left(e+f\,x\right)}\right)}^m}{\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a/sin(e + f*x))^m/sin(e + f*x), x)","F"
33,0,-1,84,0.000000,"\text{Not used}","int((a + a/sin(e + f*x))^m,x)","\int {\left(a+\frac{a}{\sin\left(e+f\,x\right)}\right)}^m \,d x","Not used",1,"int((a + a/sin(e + f*x))^m, x)","F"
34,0,-1,83,0.000000,"\text{Not used}","int(sin(e + f*x)*(a + a/sin(e + f*x))^m,x)","\int \sin\left(e+f\,x\right)\,{\left(a+\frac{a}{\sin\left(e+f\,x\right)}\right)}^m \,d x","Not used",1,"int(sin(e + f*x)*(a + a/sin(e + f*x))^m, x)","F"
35,0,-1,84,0.000000,"\text{Not used}","int(sin(e + f*x)^2*(a + a/sin(e + f*x))^m,x)","\int {\sin\left(e+f\,x\right)}^2\,{\left(a+\frac{a}{\sin\left(e+f\,x\right)}\right)}^m \,d x","Not used",1,"int(sin(e + f*x)^2*(a + a/sin(e + f*x))^m, x)","F"
36,1,314,107,0.622655,"\text{Not used}","int((a + b/sin(c + d*x))^4,x)","\frac{b^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{b^4\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{3\,b^4\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{3\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{2\,a^4\,\mathrm{atan}\left(\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+4\,\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}{-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+4\,\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)}{d}+\frac{2\,a\,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)}{d}+\frac{4\,a^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)}{d}-\frac{3\,a^2\,b^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}-\frac{a\,b^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d}+\frac{3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}+\frac{a\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d}","Not used",1,"(b^4*tan(c/2 + (d*x)/2)^3)/(24*d) - (b^4*cot(c/2 + (d*x)/2)^3)/(24*d) - (3*b^4*cot(c/2 + (d*x)/2))/(8*d) + (3*b^4*tan(c/2 + (d*x)/2))/(8*d) + (2*a^4*atan((a^3*cos(c/2 + (d*x)/2) + 2*b^3*sin(c/2 + (d*x)/2) + 4*a^2*b*sin(c/2 + (d*x)/2))/(2*b^3*cos(c/2 + (d*x)/2) - a^3*sin(c/2 + (d*x)/2) + 4*a^2*b*cos(c/2 + (d*x)/2))))/d + (2*a*b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*a^3*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (3*a^2*b^2*cot(c/2 + (d*x)/2))/d - (a*b^3*cot(c/2 + (d*x)/2)^2)/(2*d) + (3*a^2*b^2*tan(c/2 + (d*x)/2))/d + (a*b^3*tan(c/2 + (d*x)/2)^2)/(2*d)","B"
37,1,234,73,0.416675,"\text{Not used}","int((a + b/sin(c + d*x))^3,x)","\frac{b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{b^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,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)}{2\,d}+\frac{2\,a^3\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b+\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+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)}{d}+\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)}{d}-\frac{3\,a\,b^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{3\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(b^3*tan(c/2 + (d*x)/2)^2)/(8*d) - (b^3*cot(c/2 + (d*x)/2)^2)/(8*d) + (b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(2*d) + (2*a^3*atan((2*a^3*cos(c/2 + (d*x)/2) + b^3*sin(c/2 + (d*x)/2) + 6*a^2*b*sin(c/2 + (d*x)/2))/(b^3*cos(c/2 + (d*x)/2) - 2*a^3*sin(c/2 + (d*x)/2) + 6*a^2*b*cos(c/2 + (d*x)/2))))/d + (3*a^2*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (3*a*b^2*cot(c/2 + (d*x)/2))/(2*d) + (3*a*b^2*tan(c/2 + (d*x)/2))/(2*d)","B"
38,1,105,34,0.328838,"\text{Not used}","int((a + b/sin(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{atan}\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{b^2\,\mathrm{cot}\left(c+d\,x\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}","Not used",1,"(2*a^2*atan((a*cos(c/2 + (d*x)/2) + 2*b*sin(c/2 + (d*x)/2))/(2*b*cos(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2))))/d - (b^2*cot(c + d*x))/d + (2*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
39,1,588,112,0.789141,"\text{Not used}","int(1/(sin(x)^5*(a + b/sin(x))),x)","-\frac{b^2\,\left(\frac{3\,a\,\sin\left(2\,x\right)\,\sqrt{a^2-b^2}}{4}+\frac{3\,a\,\sin\left(3\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sqrt{a^2-b^2}}{8}-\frac{9\,a\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sin\left(x\right)\,\sqrt{a^2-b^2}}{8}\right)+b^3\,\left(\frac{\cos\left(3\,x\right)\,\sqrt{a^2-b^2}}{2}-\frac{3\,\cos\left(x\right)\,\sqrt{a^2-b^2}}{2}\right)-b\,\left(\frac{3\,a^2\,\cos\left(x\right)\,\sqrt{a^2-b^2}}{4}-\frac{3\,a^2\,\cos\left(3\,x\right)\,\sqrt{a^2-b^2}}{4}\right)-\frac{9\,a^3\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sin\left(x\right)\,\sqrt{a^2-b^2}}{4}+\frac{3\,a^3\,\sin\left(3\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sqrt{a^2-b^2}}{4}+\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,8{}\mathrm{i}-b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a\,b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a^3\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,4{}\mathrm{i}}{-8\,\sin\left(\frac{x}{2}\right)\,a^5-4\,\cos\left(\frac{x}{2}\right)\,a^4\,b+4\,\sin\left(\frac{x}{2}\right)\,a^3\,b^2+\cos\left(\frac{x}{2}\right)\,a^2\,b^3+2\,\sin\left(\frac{x}{2}\right)\,a\,b^4+\cos\left(\frac{x}{2}\right)\,b^5}\right)\,\sin\left(x\right)\,9{}\mathrm{i}}{2}-\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,8{}\mathrm{i}-b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a\,b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a^3\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,4{}\mathrm{i}}{-8\,\sin\left(\frac{x}{2}\right)\,a^5-4\,\cos\left(\frac{x}{2}\right)\,a^4\,b+4\,\sin\left(\frac{x}{2}\right)\,a^3\,b^2+\cos\left(\frac{x}{2}\right)\,a^2\,b^3+2\,\sin\left(\frac{x}{2}\right)\,a\,b^4+\cos\left(\frac{x}{2}\right)\,b^5}\right)\,\sin\left(3\,x\right)\,3{}\mathrm{i}}{2}}{\frac{3\,b^4\,\sin\left(3\,x\right)\,\sqrt{a^2-b^2}}{4}-\frac{9\,b^4\,\sin\left(x\right)\,\sqrt{a^2-b^2}}{4}}","Not used",1,"-(b^2*((3*a*sin(2*x)*(a^2 - b^2)^(1/2))/4 + (3*a*sin(3*x)*log(sin(x/2)/cos(x/2))*(a^2 - b^2)^(1/2))/8 - (9*a*log(sin(x/2)/cos(x/2))*sin(x)*(a^2 - b^2)^(1/2))/8) + b^3*((cos(3*x)*(a^2 - b^2)^(1/2))/2 - (3*cos(x)*(a^2 - b^2)^(1/2))/2) - b*((3*a^2*cos(x)*(a^2 - b^2)^(1/2))/4 - (3*a^2*cos(3*x)*(a^2 - b^2)^(1/2))/4) + (a^4*atan((a^4*sin(x/2)*(a^2 - b^2)^(1/2)*8i - b^4*sin(x/2)*(a^2 - b^2)^(1/2)*1i + a*b^3*cos(x/2)*(a^2 - b^2)^(1/2)*1i + a^3*b*cos(x/2)*(a^2 - b^2)^(1/2)*4i)/(b^5*cos(x/2) - 8*a^5*sin(x/2) + a^2*b^3*cos(x/2) + 4*a^3*b^2*sin(x/2) - 4*a^4*b*cos(x/2) + 2*a*b^4*sin(x/2)))*sin(x)*9i)/2 - (a^4*atan((a^4*sin(x/2)*(a^2 - b^2)^(1/2)*8i - b^4*sin(x/2)*(a^2 - b^2)^(1/2)*1i + a*b^3*cos(x/2)*(a^2 - b^2)^(1/2)*1i + a^3*b*cos(x/2)*(a^2 - b^2)^(1/2)*4i)/(b^5*cos(x/2) - 8*a^5*sin(x/2) + a^2*b^3*cos(x/2) + 4*a^3*b^2*sin(x/2) - 4*a^4*b*cos(x/2) + 2*a*b^4*sin(x/2)))*sin(3*x)*3i)/2 - (9*a^3*log(sin(x/2)/cos(x/2))*sin(x)*(a^2 - b^2)^(1/2))/4 + (3*a^3*sin(3*x)*log(sin(x/2)/cos(x/2))*(a^2 - b^2)^(1/2))/4)/((3*b^4*sin(3*x)*(a^2 - b^2)^(1/2))/4 - (9*b^4*sin(x)*(a^2 - b^2)^(1/2))/4)","B"
40,1,515,84,0.579908,"\text{Not used}","int(1/(sin(x)^4*(a + b/sin(x))),x)","-\frac{b^2\,\left(\frac{\cos\left(x\right)\,\sqrt{a^2-b^2}}{2}-\frac{\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sqrt{a^2-b^2}}{4}+\frac{\cos\left(2\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sqrt{a^2-b^2}}{4}\right)-\frac{a^2\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sqrt{a^2-b^2}}{2}-\frac{a\,b\,\sin\left(2\,x\right)\,\sqrt{a^2-b^2}}{2}+\frac{a^2\,\cos\left(2\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sqrt{a^2-b^2}}{2}+a^3\,\mathrm{atan}\left(\frac{a^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,8{}\mathrm{i}-b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a\,b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a^3\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,4{}\mathrm{i}}{-8\,\sin\left(\frac{x}{2}\right)\,a^5-4\,\cos\left(\frac{x}{2}\right)\,a^4\,b+4\,\sin\left(\frac{x}{2}\right)\,a^3\,b^2+\cos\left(\frac{x}{2}\right)\,a^2\,b^3+2\,\sin\left(\frac{x}{2}\right)\,a\,b^4+\cos\left(\frac{x}{2}\right)\,b^5}\right)\,1{}\mathrm{i}-a^3\,\cos\left(2\,x\right)\,\mathrm{atan}\left(\frac{a^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,8{}\mathrm{i}-b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a\,b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a^3\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,4{}\mathrm{i}}{-8\,\sin\left(\frac{x}{2}\right)\,a^5-4\,\cos\left(\frac{x}{2}\right)\,a^4\,b+4\,\sin\left(\frac{x}{2}\right)\,a^3\,b^2+\cos\left(\frac{x}{2}\right)\,a^2\,b^3+2\,\sin\left(\frac{x}{2}\right)\,a\,b^4+\cos\left(\frac{x}{2}\right)\,b^5}\right)\,1{}\mathrm{i}}{\frac{b^3\,\sqrt{a^2-b^2}}{2}-\frac{b^3\,\cos\left(2\,x\right)\,\sqrt{a^2-b^2}}{2}}","Not used",1,"-(a^3*atan((a^4*sin(x/2)*(a^2 - b^2)^(1/2)*8i - b^4*sin(x/2)*(a^2 - b^2)^(1/2)*1i + a*b^3*cos(x/2)*(a^2 - b^2)^(1/2)*1i + a^3*b*cos(x/2)*(a^2 - b^2)^(1/2)*4i)/(b^5*cos(x/2) - 8*a^5*sin(x/2) + a^2*b^3*cos(x/2) + 4*a^3*b^2*sin(x/2) - 4*a^4*b*cos(x/2) + 2*a*b^4*sin(x/2)))*1i + b^2*((cos(x)*(a^2 - b^2)^(1/2))/2 - (log(sin(x/2)/cos(x/2))*(a^2 - b^2)^(1/2))/4 + (cos(2*x)*log(sin(x/2)/cos(x/2))*(a^2 - b^2)^(1/2))/4) - (a^2*log(sin(x/2)/cos(x/2))*(a^2 - b^2)^(1/2))/2 - a^3*cos(2*x)*atan((a^4*sin(x/2)*(a^2 - b^2)^(1/2)*8i - b^4*sin(x/2)*(a^2 - b^2)^(1/2)*1i + a*b^3*cos(x/2)*(a^2 - b^2)^(1/2)*1i + a^3*b*cos(x/2)*(a^2 - b^2)^(1/2)*4i)/(b^5*cos(x/2) - 8*a^5*sin(x/2) + a^2*b^3*cos(x/2) + 4*a^3*b^2*sin(x/2) - 4*a^4*b*cos(x/2) + 2*a*b^4*sin(x/2)))*1i - (a*b*sin(2*x)*(a^2 - b^2)^(1/2))/2 + (a^2*cos(2*x)*log(sin(x/2)/cos(x/2))*(a^2 - b^2)^(1/2))/2)/((b^3*(a^2 - b^2)^(1/2))/2 - (b^3*cos(2*x)*(a^2 - b^2)^(1/2))/2)","B"
41,1,135,62,0.485143,"\text{Not used}","int(1/(sin(x)^3*(a + b/sin(x))),x)","-\frac{1}{b\,\mathrm{tan}\left(x\right)}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{b^2}-\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,4{}\mathrm{i}-b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a\,b\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3+2\,a^2\,b-3\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^2-b^3}\right)\,2{}\mathrm{i}}{b^2\,\sqrt{a^2-b^2}}","Not used",1,"- 1/(b*tan(x)) - (a*log(tan(x/2)))/b^2 - (a^2*atan((a^2*tan(x/2)*(a^2 - b^2)^(1/2)*4i - b^2*tan(x/2)*(a^2 - b^2)^(1/2)*1i + a*b*(a^2 - b^2)^(1/2)*2i)/(4*a^3*tan(x/2) + 2*a^2*b - b^3 - 3*a*b^2*tan(x/2)))*2i)/(b^2*(a^2 - b^2)^(1/2))","B"
42,1,129,53,0.429161,"\text{Not used}","int(1/(sin(x)^2*(a + b/sin(x))),x)","\frac{\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{b}-\frac{2\,a\,\mathrm{atanh}\left(\frac{\sqrt{a^2-b^2}\,\left(4{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^2+2{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a\,b-1{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,b^2\right)}{a^3\,\sin\left(\frac{x}{2}\right)\,4{}\mathrm{i}+b\,\cos\left(\frac{x}{2}\right)\,\left(a^2-b^2\right)\,1{}\mathrm{i}+a^2\,b\,\cos\left(\frac{x}{2}\right)\,1{}\mathrm{i}-a\,b^2\,\sin\left(\frac{x}{2}\right)\,3{}\mathrm{i}}\right)}{b\,\sqrt{a^2-b^2}}","Not used",1,"log(sin(x/2)/cos(x/2))/b - (2*a*atanh(((a^2 - b^2)^(1/2)*(a^2*sin(x/2)*4i - b^2*sin(x/2)*1i + a*b*cos(x/2)*2i))/(a^3*sin(x/2)*4i + b*cos(x/2)*(a^2 - b^2)*1i + a^2*b*cos(x/2)*1i - a*b^2*sin(x/2)*3i)))/(b*(a^2 - b^2)^(1/2))","B"
43,1,36,40,0.287236,"\text{Not used}","int(1/(sin(x)*(a + b/sin(x))),x)","-\frac{2\,\mathrm{atanh}\left(\frac{a+b\,\mathrm{tan}\left(\frac{x}{2}\right)}{\sqrt{a+b}\,\sqrt{a-b}}\right)}{\sqrt{a+b}\,\sqrt{a-b}}","Not used",1,"-(2*atanh((a + b*tan(x/2))/((a + b)^(1/2)*(a - b)^(1/2))))/((a + b)^(1/2)*(a - b)^(1/2))","B"
44,1,184,57,0.452484,"\text{Not used}","int(1/(a + b/sin(c + d*x)),x)","\frac{x}{a}-\frac{2\,b\,\mathrm{atanh}\left(\frac{2\,a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+a\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,a^2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{a\,\left(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\right)\,\sqrt{a^2-b^2}}\right)}{a\,d\,\sqrt{a^2-b^2}}","Not used",1,"x/a - (2*b*atanh((2*a^2*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 2*b^4*sin(c/2 + (d*x)/2) - 2*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2) + a*b^3*cos(c/2 + (d*x)/2) + 3*a^2*b^2*sin(c/2 + (d*x)/2) + a*b*cos(c/2 + (d*x)/2)*(a^2 - b^2))/(a*(2*a^2*sin(c/2 + (d*x)/2) + a*b*cos(c/2 + (d*x)/2))*(a^2 - b^2)^(1/2))))/(a*d*(a^2 - b^2)^(1/2))","B"
45,1,766,61,0.651744,"\text{Not used}","int(sin(x)/(a + b/sin(x)),x)","-\frac{2}{a\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}-\frac{b\,x}{a^2}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{a^2-b^2}\,\left(\frac{32\,b^4}{a}-\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,b^5-2\,a^3\,b^3\right)}{a^3}+\frac{b^2\,\sqrt{a^2-b^2}\,\left(32\,a^2\,b^2+64\,a\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{b^2\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^7\,b-2\,a^5\,b^3\right)}{a^3}\right)}{a^4-a^2\,b^2}\right)}{a^4-a^2\,b^2}\right)\,1{}\mathrm{i}}{a^4-a^2\,b^2}-\frac{b^2\,\sqrt{a^2-b^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,b^5-2\,a^3\,b^3\right)}{a^3}-\frac{32\,b^4}{a}+\frac{b^2\,\sqrt{a^2-b^2}\,\left(32\,a^2\,b^2+64\,a\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{b^2\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^7\,b-2\,a^5\,b^3\right)}{a^3}\right)}{a^4-a^2\,b^2}\right)}{a^4-a^2\,b^2}\right)\,1{}\mathrm{i}}{a^4-a^2\,b^2}}{\frac{128\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^3}+\frac{b^2\,\sqrt{a^2-b^2}\,\left(\frac{32\,b^4}{a}-\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,b^5-2\,a^3\,b^3\right)}{a^3}+\frac{b^2\,\sqrt{a^2-b^2}\,\left(32\,a^2\,b^2+64\,a\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{b^2\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^7\,b-2\,a^5\,b^3\right)}{a^3}\right)}{a^4-a^2\,b^2}\right)}{a^4-a^2\,b^2}\right)}{a^4-a^2\,b^2}+\frac{b^2\,\sqrt{a^2-b^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,b^5-2\,a^3\,b^3\right)}{a^3}-\frac{32\,b^4}{a}+\frac{b^2\,\sqrt{a^2-b^2}\,\left(32\,a^2\,b^2+64\,a\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{b^2\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^7\,b-2\,a^5\,b^3\right)}{a^3}\right)}{a^4-a^2\,b^2}\right)}{a^4-a^2\,b^2}\right)}{a^4-a^2\,b^2}}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{a^4-a^2\,b^2}","Not used",1,"- 2/(a*(tan(x/2)^2 + 1)) - (b*x)/a^2 - (b^2*atan(((b^2*(a^2 - b^2)^(1/2)*((32*b^4)/a - (32*tan(x/2)*(2*a*b^5 - 2*a^3*b^3))/a^3 + (b^2*(a^2 - b^2)^(1/2)*(32*a^2*b^2 + 64*a*b^3*tan(x/2) + (b^2*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (32*tan(x/2)*(3*a^7*b - 2*a^5*b^3))/a^3))/(a^4 - a^2*b^2)))/(a^4 - a^2*b^2))*1i)/(a^4 - a^2*b^2) - (b^2*(a^2 - b^2)^(1/2)*((32*tan(x/2)*(2*a*b^5 - 2*a^3*b^3))/a^3 - (32*b^4)/a + (b^2*(a^2 - b^2)^(1/2)*(32*a^2*b^2 + 64*a*b^3*tan(x/2) - (b^2*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (32*tan(x/2)*(3*a^7*b - 2*a^5*b^3))/a^3))/(a^4 - a^2*b^2)))/(a^4 - a^2*b^2))*1i)/(a^4 - a^2*b^2))/((128*b^5*tan(x/2))/a^3 + (b^2*(a^2 - b^2)^(1/2)*((32*b^4)/a - (32*tan(x/2)*(2*a*b^5 - 2*a^3*b^3))/a^3 + (b^2*(a^2 - b^2)^(1/2)*(32*a^2*b^2 + 64*a*b^3*tan(x/2) + (b^2*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (32*tan(x/2)*(3*a^7*b - 2*a^5*b^3))/a^3))/(a^4 - a^2*b^2)))/(a^4 - a^2*b^2)))/(a^4 - a^2*b^2) + (b^2*(a^2 - b^2)^(1/2)*((32*tan(x/2)*(2*a*b^5 - 2*a^3*b^3))/a^3 - (32*b^4)/a + (b^2*(a^2 - b^2)^(1/2)*(32*a^2*b^2 + 64*a*b^3*tan(x/2) - (b^2*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (32*tan(x/2)*(3*a^7*b - 2*a^5*b^3))/a^3))/(a^4 - a^2*b^2)))/(a^4 - a^2*b^2)))/(a^4 - a^2*b^2)))*(a^2 - b^2)^(1/2)*2i)/(a^4 - a^2*b^2)","B"
46,1,1147,82,0.840341,"\text{Not used}","int(sin(x)^2/(a + b/sin(x)),x)","\frac{\frac{2\,b}{a^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{a}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a}+\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{\mathrm{atan}\left(\frac{40\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a^2\,b+40\,b^3+\frac{48\,b^5}{a^2}}+\frac{48\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a^4\,b+40\,a^2\,b^3+48\,b^5}+\frac{8\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a\,b+\frac{40\,b^3}{a}+\frac{48\,b^5}{a^3}}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,2{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^3}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(a^6\,b^2+4\,a^4\,b^4+4\,a^2\,b^6\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^8\,b+7\,a^6\,b^3+4\,a^4\,b^5-8\,a^2\,b^7\right)}{a^6}+\frac{b^3\,\sqrt{a^2-b^2}\,\left(64\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8\,\left(2\,a^8\,b+2\,a^6\,b^3\right)}{a^5}+\frac{b^3\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^{10}\,b-8\,a^8\,b^3\right)}{a^6}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}+\frac{b^3\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(a^6\,b^2+4\,a^4\,b^4+4\,a^2\,b^6\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^8\,b+7\,a^6\,b^3+4\,a^4\,b^5-8\,a^2\,b^7\right)}{a^6}-\frac{b^3\,\sqrt{a^2-b^2}\,\left(64\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8\,\left(2\,a^8\,b+2\,a^6\,b^3\right)}{a^5}-\frac{b^3\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^{10}\,b-8\,a^8\,b^3\right)}{a^6}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}}{\frac{16\,\left(a^2\,b^5+2\,b^7\right)}{a^5}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^4\,b^4+8\,a^2\,b^6+8\,b^8\right)}{a^6}+\frac{b^3\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(a^6\,b^2+4\,a^4\,b^4+4\,a^2\,b^6\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^8\,b+7\,a^6\,b^3+4\,a^4\,b^5-8\,a^2\,b^7\right)}{a^6}+\frac{b^3\,\sqrt{a^2-b^2}\,\left(64\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8\,\left(2\,a^8\,b+2\,a^6\,b^3\right)}{a^5}+\frac{b^3\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^{10}\,b-8\,a^8\,b^3\right)}{a^6}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}-\frac{b^3\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(a^6\,b^2+4\,a^4\,b^4+4\,a^2\,b^6\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^8\,b+7\,a^6\,b^3+4\,a^4\,b^5-8\,a^2\,b^7\right)}{a^6}-\frac{b^3\,\sqrt{a^2-b^2}\,\left(64\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8\,\left(2\,a^8\,b+2\,a^6\,b^3\right)}{a^5}-\frac{b^3\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^{10}\,b-8\,a^8\,b^3\right)}{a^6}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{a^5-a^3\,b^2}","Not used",1,"((2*b)/a^2 - tan(x/2)/a + tan(x/2)^3/a + (2*b*tan(x/2)^2)/a^2)/(2*tan(x/2)^2 + tan(x/2)^4 + 1) - (atan((40*b^3*tan(x/2))/(8*a^2*b + 40*b^3 + (48*b^5)/a^2) + (48*b^5*tan(x/2))/(8*a^4*b + 48*b^5 + 40*a^2*b^3) + (8*a*b*tan(x/2))/(8*a*b + (40*b^3)/a + (48*b^5)/a^3))*(a^2*1i + b^2*2i)*1i)/a^3 + (b^3*atan(((b^3*(a^2 - b^2)^(1/2)*((8*(4*a^2*b^6 + 4*a^4*b^4 + a^6*b^2))/a^5 + (8*tan(x/2)*(2*a^8*b - 8*a^2*b^7 + 4*a^4*b^5 + 7*a^6*b^3))/a^6 + (b^3*(a^2 - b^2)^(1/2)*(64*b^4*tan(x/2) + (8*(2*a^8*b + 2*a^6*b^3))/a^5 + (b^3*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (8*tan(x/2)*(12*a^10*b - 8*a^8*b^3))/a^6))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2))*1i)/(a^5 - a^3*b^2) + (b^3*(a^2 - b^2)^(1/2)*((8*(4*a^2*b^6 + 4*a^4*b^4 + a^6*b^2))/a^5 + (8*tan(x/2)*(2*a^8*b - 8*a^2*b^7 + 4*a^4*b^5 + 7*a^6*b^3))/a^6 - (b^3*(a^2 - b^2)^(1/2)*(64*b^4*tan(x/2) + (8*(2*a^8*b + 2*a^6*b^3))/a^5 - (b^3*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (8*tan(x/2)*(12*a^10*b - 8*a^8*b^3))/a^6))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2))*1i)/(a^5 - a^3*b^2))/((16*(2*b^7 + a^2*b^5))/a^5 + (16*tan(x/2)*(8*b^8 + 8*a^2*b^6 + 2*a^4*b^4))/a^6 + (b^3*(a^2 - b^2)^(1/2)*((8*(4*a^2*b^6 + 4*a^4*b^4 + a^6*b^2))/a^5 + (8*tan(x/2)*(2*a^8*b - 8*a^2*b^7 + 4*a^4*b^5 + 7*a^6*b^3))/a^6 + (b^3*(a^2 - b^2)^(1/2)*(64*b^4*tan(x/2) + (8*(2*a^8*b + 2*a^6*b^3))/a^5 + (b^3*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (8*tan(x/2)*(12*a^10*b - 8*a^8*b^3))/a^6))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2) - (b^3*(a^2 - b^2)^(1/2)*((8*(4*a^2*b^6 + 4*a^4*b^4 + a^6*b^2))/a^5 + (8*tan(x/2)*(2*a^8*b - 8*a^2*b^7 + 4*a^4*b^5 + 7*a^6*b^3))/a^6 - (b^3*(a^2 - b^2)^(1/2)*(64*b^4*tan(x/2) + (8*(2*a^8*b + 2*a^6*b^3))/a^5 - (b^3*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (8*tan(x/2)*(12*a^10*b - 8*a^8*b^3))/a^6))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2)))*(a^2 - b^2)^(1/2)*2i)/(a^5 - a^3*b^2)","B"
47,1,1218,110,0.945466,"\text{Not used}","int(sin(x)^3/(a + b/sin(x)),x)","-\frac{\frac{2\,\left(2\,a^2+3\,b^2\right)}{3\,a^3}+\frac{b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{a^2}+\frac{2\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^3}+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^2+b^2\right)}{a^3}-\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{b\,\mathrm{atan}\left(\frac{8\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,b^4+\frac{40\,b^6}{a^2}+\frac{48\,b^8}{a^4}}+\frac{40\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{40\,b^6+8\,a^2\,b^4+\frac{48\,b^8}{a^2}}+\frac{48\,b^8\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a^4\,b^4+40\,a^2\,b^6+48\,b^8}\right)\,\left(a^2+2\,b^2\right)}{a^4}-\frac{b^4\,\mathrm{atan}\left(\frac{\frac{b^4\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(a^7\,b^4+4\,a^5\,b^6+4\,a^3\,b^8\right)}{a^8}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^9\,b^3+7\,a^7\,b^5+4\,a^5\,b^7-8\,a^3\,b^9\right)}{a^9}+\frac{b^4\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(2\,a^{10}\,b^2+2\,a^8\,b^4\right)}{a^8}+\frac{64\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}+\frac{b^4\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^{13}\,b-8\,a^{11}\,b^3\right)}{a^9}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b^4\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(a^7\,b^4+4\,a^5\,b^6+4\,a^3\,b^8\right)}{a^8}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^9\,b^3+7\,a^7\,b^5+4\,a^5\,b^7-8\,a^3\,b^9\right)}{a^9}-\frac{b^4\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(2\,a^{10}\,b^2+2\,a^8\,b^4\right)}{a^8}+\frac{64\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}-\frac{b^4\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^{13}\,b-8\,a^{11}\,b^3\right)}{a^9}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(a^2\,b^8+2\,b^{10}\right)}{a^8}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^4\,b^7+8\,a^2\,b^9+8\,b^{11}\right)}{a^9}+\frac{b^4\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(a^7\,b^4+4\,a^5\,b^6+4\,a^3\,b^8\right)}{a^8}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^9\,b^3+7\,a^7\,b^5+4\,a^5\,b^7-8\,a^3\,b^9\right)}{a^9}+\frac{b^4\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(2\,a^{10}\,b^2+2\,a^8\,b^4\right)}{a^8}+\frac{64\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}+\frac{b^4\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^{13}\,b-8\,a^{11}\,b^3\right)}{a^9}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}-\frac{b^4\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(a^7\,b^4+4\,a^5\,b^6+4\,a^3\,b^8\right)}{a^8}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^9\,b^3+7\,a^7\,b^5+4\,a^5\,b^7-8\,a^3\,b^9\right)}{a^9}-\frac{b^4\,\sqrt{a^2-b^2}\,\left(\frac{8\,\left(2\,a^{10}\,b^2+2\,a^8\,b^4\right)}{a^8}+\frac{64\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}-\frac{b^4\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^{13}\,b-8\,a^{11}\,b^3\right)}{a^9}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{a^6-a^4\,b^2}","Not used",1,"- ((2*(2*a^2 + 3*b^2))/(3*a^3) + (b*tan(x/2)^5)/a^2 + (2*b^2*tan(x/2)^4)/a^3 + (4*tan(x/2)^2*(a^2 + b^2))/a^3 - (b*tan(x/2))/a^2)/(3*tan(x/2)^2 + 3*tan(x/2)^4 + tan(x/2)^6 + 1) - (b^4*atan(((b^4*(a^2 - b^2)^(1/2)*((8*(4*a^3*b^8 + 4*a^5*b^6 + a^7*b^4))/a^8 + (8*tan(x/2)*(4*a^5*b^7 - 8*a^3*b^9 + 7*a^7*b^5 + 2*a^9*b^3))/a^9 + (b^4*(a^2 - b^2)^(1/2)*((8*(2*a^8*b^4 + 2*a^10*b^2))/a^8 + (64*b^5*tan(x/2))/a + (b^4*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (8*tan(x/2)*(12*a^13*b - 8*a^11*b^3))/a^9))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) + (b^4*(a^2 - b^2)^(1/2)*((8*(4*a^3*b^8 + 4*a^5*b^6 + a^7*b^4))/a^8 + (8*tan(x/2)*(4*a^5*b^7 - 8*a^3*b^9 + 7*a^7*b^5 + 2*a^9*b^3))/a^9 - (b^4*(a^2 - b^2)^(1/2)*((8*(2*a^8*b^4 + 2*a^10*b^2))/a^8 + (64*b^5*tan(x/2))/a - (b^4*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (8*tan(x/2)*(12*a^13*b - 8*a^11*b^3))/a^9))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2))/((16*(2*b^10 + a^2*b^8))/a^8 + (16*tan(x/2)*(8*b^11 + 8*a^2*b^9 + 2*a^4*b^7))/a^9 + (b^4*(a^2 - b^2)^(1/2)*((8*(4*a^3*b^8 + 4*a^5*b^6 + a^7*b^4))/a^8 + (8*tan(x/2)*(4*a^5*b^7 - 8*a^3*b^9 + 7*a^7*b^5 + 2*a^9*b^3))/a^9 + (b^4*(a^2 - b^2)^(1/2)*((8*(2*a^8*b^4 + 2*a^10*b^2))/a^8 + (64*b^5*tan(x/2))/a + (b^4*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (8*tan(x/2)*(12*a^13*b - 8*a^11*b^3))/a^9))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) - (b^4*(a^2 - b^2)^(1/2)*((8*(4*a^3*b^8 + 4*a^5*b^6 + a^7*b^4))/a^8 + (8*tan(x/2)*(4*a^5*b^7 - 8*a^3*b^9 + 7*a^7*b^5 + 2*a^9*b^3))/a^9 - (b^4*(a^2 - b^2)^(1/2)*((8*(2*a^8*b^4 + 2*a^10*b^2))/a^8 + (64*b^5*tan(x/2))/a - (b^4*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (8*tan(x/2)*(12*a^13*b - 8*a^11*b^3))/a^9))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*(a^2 - b^2)^(1/2)*2i)/(a^6 - a^4*b^2) - (b*atan((8*b^4*tan(x/2))/(8*b^4 + (40*b^6)/a^2 + (48*b^8)/a^4) + (40*b^6*tan(x/2))/(40*b^6 + 8*a^2*b^4 + (48*b^8)/a^2) + (48*b^8*tan(x/2))/(48*b^8 + 40*a^2*b^6 + 8*a^4*b^4))*(a^2 + 2*b^2))/a^4","B"
48,1,1639,144,1.258079,"\text{Not used}","int(sin(x)^4/(a + b/sin(x)),x)","\frac{\frac{2\,\left(2\,a^2\,b+3\,b^3\right)}{3\,a^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^2+4\,b^2\right)}{4\,a^3}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(3\,a^2+4\,b^2\right)}{4\,a^3}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(11\,a^2+4\,b^2\right)}{4\,a^3}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(11\,a^2+4\,b^2\right)}{4\,a^3}+\frac{2\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{a^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(2\,a^2\,b+3\,b^3\right)}{a^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(8\,a^2\,b+9\,b^3\right)}{3\,a^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{\mathrm{atan}\left(\frac{81\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,\left(\frac{27\,a^2\,b}{8}+\frac{81\,b^3}{8}+\frac{63\,b^5}{2\,a^2}+\frac{35\,b^7}{a^4}+\frac{40\,b^9}{a^6}\right)}+\frac{63\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,\left(\frac{27\,a^4\,b}{8}+\frac{63\,b^5}{2}+\frac{81\,a^2\,b^3}{8}+\frac{35\,b^7}{a^2}+\frac{40\,b^9}{a^4}\right)}+\frac{35\,b^7\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{27\,a^6\,b}{8}+35\,b^7+\frac{63\,a^2\,b^5}{2}+\frac{81\,a^4\,b^3}{8}+\frac{40\,b^9}{a^2}}+\frac{40\,b^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{27\,a^8\,b}{8}+\frac{81\,a^6\,b^3}{8}+\frac{63\,a^4\,b^5}{2}+35\,a^2\,b^7+40\,b^9}+\frac{27\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,\left(\frac{27\,a\,b}{8}+\frac{81\,b^3}{8\,a}+\frac{63\,b^5}{2\,a^3}+\frac{35\,b^7}{a^5}+\frac{40\,b^9}{a^7}\right)}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{4\,a^5}+\frac{b^5\,\mathrm{atan}\left(\frac{\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{\frac{9\,a^{12}\,b^2}{2}+12\,a^{10}\,b^4+32\,a^8\,b^6+32\,a^6\,b^8+32\,a^4\,b^{10}}{a^{11}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{14}\,b+39\,a^{12}\,b^3+104\,a^{10}\,b^5+64\,a^8\,b^7+64\,a^6\,b^9-128\,a^4\,b^{11}\right)}{2\,a^{12}}+\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{12\,a^{14}\,b+4\,a^{12}\,b^3+16\,a^{10}\,b^5}{a^{11}}+\frac{64\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}+\frac{b^5\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(192\,a^{16}\,b-128\,a^{14}\,b^3\right)}{2\,a^{12}}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}+\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{\frac{9\,a^{12}\,b^2}{2}+12\,a^{10}\,b^4+32\,a^8\,b^6+32\,a^6\,b^8+32\,a^4\,b^{10}}{a^{11}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{14}\,b+39\,a^{12}\,b^3+104\,a^{10}\,b^5+64\,a^8\,b^7+64\,a^6\,b^9-128\,a^4\,b^{11}\right)}{2\,a^{12}}-\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{12\,a^{14}\,b+4\,a^{12}\,b^3+16\,a^{10}\,b^5}{a^{11}}+\frac{64\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}-\frac{b^5\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(192\,a^{16}\,b-128\,a^{14}\,b^3\right)}{2\,a^{12}}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}}{\frac{9\,a^6\,b^7+24\,a^4\,b^9+40\,a^2\,b^{11}+32\,b^{13}}{a^{11}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^8\,b^6+48\,a^6\,b^8+128\,a^4\,b^{10}+128\,a^2\,b^{12}+128\,b^{14}\right)}{a^{12}}+\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{\frac{9\,a^{12}\,b^2}{2}+12\,a^{10}\,b^4+32\,a^8\,b^6+32\,a^6\,b^8+32\,a^4\,b^{10}}{a^{11}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{14}\,b+39\,a^{12}\,b^3+104\,a^{10}\,b^5+64\,a^8\,b^7+64\,a^6\,b^9-128\,a^4\,b^{11}\right)}{2\,a^{12}}+\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{12\,a^{14}\,b+4\,a^{12}\,b^3+16\,a^{10}\,b^5}{a^{11}}+\frac{64\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}+\frac{b^5\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(192\,a^{16}\,b-128\,a^{14}\,b^3\right)}{2\,a^{12}}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}-\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{\frac{9\,a^{12}\,b^2}{2}+12\,a^{10}\,b^4+32\,a^8\,b^6+32\,a^6\,b^8+32\,a^4\,b^{10}}{a^{11}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{14}\,b+39\,a^{12}\,b^3+104\,a^{10}\,b^5+64\,a^8\,b^7+64\,a^6\,b^9-128\,a^4\,b^{11}\right)}{2\,a^{12}}-\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{12\,a^{14}\,b+4\,a^{12}\,b^3+16\,a^{10}\,b^5}{a^{11}}+\frac{64\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}-\frac{b^5\,\sqrt{a^2-b^2}\,\left(32\,a^3\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(192\,a^{16}\,b-128\,a^{14}\,b^3\right)}{2\,a^{12}}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{a^7-a^5\,b^2}","Not used",1,"((2*(2*a^2*b + 3*b^3))/(3*a^4) - (tan(x/2)*(3*a^2 + 4*b^2))/(4*a^3) + (tan(x/2)^7*(3*a^2 + 4*b^2))/(4*a^3) - (tan(x/2)^3*(11*a^2 + 4*b^2))/(4*a^3) + (tan(x/2)^5*(11*a^2 + 4*b^2))/(4*a^3) + (2*b^3*tan(x/2)^6)/a^4 + (2*tan(x/2)^4*(2*a^2*b + 3*b^3))/a^4 + (2*tan(x/2)^2*(8*a^2*b + 9*b^3))/(3*a^4))/(4*tan(x/2)^2 + 6*tan(x/2)^4 + 4*tan(x/2)^6 + tan(x/2)^8 + 1) - (atan((81*b^3*tan(x/2))/(8*((27*a^2*b)/8 + (81*b^3)/8 + (63*b^5)/(2*a^2) + (35*b^7)/a^4 + (40*b^9)/a^6)) + (63*b^5*tan(x/2))/(2*((27*a^4*b)/8 + (63*b^5)/2 + (81*a^2*b^3)/8 + (35*b^7)/a^2 + (40*b^9)/a^4)) + (35*b^7*tan(x/2))/((27*a^6*b)/8 + 35*b^7 + (63*a^2*b^5)/2 + (81*a^4*b^3)/8 + (40*b^9)/a^2) + (40*b^9*tan(x/2))/((27*a^8*b)/8 + 40*b^9 + 35*a^2*b^7 + (63*a^4*b^5)/2 + (81*a^6*b^3)/8) + (27*a*b*tan(x/2))/(8*((27*a*b)/8 + (81*b^3)/(8*a) + (63*b^5)/(2*a^3) + (35*b^7)/a^5 + (40*b^9)/a^7)))*(a^4*3i + b^4*8i + a^2*b^2*4i)*1i)/(4*a^5) + (b^5*atan(((b^5*(a^2 - b^2)^(1/2)*((32*a^4*b^10 + 32*a^6*b^8 + 32*a^8*b^6 + 12*a^10*b^4 + (9*a^12*b^2)/2)/a^11 + (tan(x/2)*(18*a^14*b - 128*a^4*b^11 + 64*a^6*b^9 + 64*a^8*b^7 + 104*a^10*b^5 + 39*a^12*b^3))/(2*a^12) + (b^5*(a^2 - b^2)^(1/2)*((12*a^14*b + 16*a^10*b^5 + 4*a^12*b^3)/a^11 + (64*b^6*tan(x/2))/a^2 + (b^5*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (tan(x/2)*(192*a^16*b - 128*a^14*b^3))/(2*a^12)))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2) + (b^5*(a^2 - b^2)^(1/2)*((32*a^4*b^10 + 32*a^6*b^8 + 32*a^8*b^6 + 12*a^10*b^4 + (9*a^12*b^2)/2)/a^11 + (tan(x/2)*(18*a^14*b - 128*a^4*b^11 + 64*a^6*b^9 + 64*a^8*b^7 + 104*a^10*b^5 + 39*a^12*b^3))/(2*a^12) - (b^5*(a^2 - b^2)^(1/2)*((12*a^14*b + 16*a^10*b^5 + 4*a^12*b^3)/a^11 + (64*b^6*tan(x/2))/a^2 - (b^5*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (tan(x/2)*(192*a^16*b - 128*a^14*b^3))/(2*a^12)))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2))/((32*b^13 + 40*a^2*b^11 + 24*a^4*b^9 + 9*a^6*b^7)/a^11 + (tan(x/2)*(128*b^14 + 128*a^2*b^12 + 128*a^4*b^10 + 48*a^6*b^8 + 18*a^8*b^6))/a^12 + (b^5*(a^2 - b^2)^(1/2)*((32*a^4*b^10 + 32*a^6*b^8 + 32*a^8*b^6 + 12*a^10*b^4 + (9*a^12*b^2)/2)/a^11 + (tan(x/2)*(18*a^14*b - 128*a^4*b^11 + 64*a^6*b^9 + 64*a^8*b^7 + 104*a^10*b^5 + 39*a^12*b^3))/(2*a^12) + (b^5*(a^2 - b^2)^(1/2)*((12*a^14*b + 16*a^10*b^5 + 4*a^12*b^3)/a^11 + (64*b^6*tan(x/2))/a^2 + (b^5*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (tan(x/2)*(192*a^16*b - 128*a^14*b^3))/(2*a^12)))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2) - (b^5*(a^2 - b^2)^(1/2)*((32*a^4*b^10 + 32*a^6*b^8 + 32*a^8*b^6 + 12*a^10*b^4 + (9*a^12*b^2)/2)/a^11 + (tan(x/2)*(18*a^14*b - 128*a^4*b^11 + 64*a^6*b^9 + 64*a^8*b^7 + 104*a^10*b^5 + 39*a^12*b^3))/(2*a^12) - (b^5*(a^2 - b^2)^(1/2)*((12*a^14*b + 16*a^10*b^5 + 4*a^12*b^3)/a^11 + (64*b^6*tan(x/2))/a^2 - (b^5*(a^2 - b^2)^(1/2)*(32*a^3*b^2 + (tan(x/2)*(192*a^16*b - 128*a^14*b^3))/(2*a^12)))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2)))*(a^2 - b^2)^(1/2)*2i)/(a^7 - a^5*b^2)","B"
49,1,2677,108,4.178973,"\text{Not used}","int(1/(a + b/sin(c + d*x))^2,x)","-\frac{2\,\mathrm{atan}\left(\frac{64\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{64\,a^3\,b^9}{a^6-2\,a^4\,b^2+a^2\,b^4}-\frac{192\,a^5\,b^7}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{128\,a^7\,b^5}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{64\,a^9\,b^3}{a^6-2\,a^4\,b^2+a^2\,b^4}-\frac{64\,a^{11}\,b}{a^6-2\,a^4\,b^2+a^2\,b^4}}-\frac{64\,a\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{64\,a^3\,b^9}{a^6-2\,a^4\,b^2+a^2\,b^4}-\frac{192\,a^5\,b^7}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{128\,a^7\,b^5}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{64\,a^9\,b^3}{a^6-2\,a^4\,b^2+a^2\,b^4}-\frac{64\,a^{11}\,b}{a^6-2\,a^4\,b^2+a^2\,b^4}}+\frac{64\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{64\,a^3\,b^9}{a^6-2\,a^4\,b^2+a^2\,b^4}-\frac{192\,a^5\,b^7}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{128\,a^7\,b^5}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{64\,a^9\,b^3}{a^6-2\,a^4\,b^2+a^2\,b^4}-\frac{64\,a^{11}\,b}{a^6-2\,a^4\,b^2+a^2\,b^4}}\right)}{a^2\,d}-\frac{\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2-b^2}+\frac{2\,b^2}{a\,\left(a^2-b^2\right)}}{d\,\left(b\,{\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)+b\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^5\,b^2-2\,a^3\,b^4+a\,b^6\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^7\,b+9\,a^5\,b^3-8\,a^3\,b^5+2\,a\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^8\,b-a^6\,b^3\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8\,b^2-6\,a^6\,b^4+2\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^9\,b^2-2\,a^7\,b^4+a^5\,b^6\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{11}\,b-8\,a^9\,b^3+7\,a^7\,b^5-2\,a^5\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}-\frac{b\,\left(2\,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(-2\,a^7\,b+9\,a^5\,b^3-8\,a^3\,b^5+2\,a\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{32\,\left(a^5\,b^2-2\,a^3\,b^4+a\,b^6\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^8\,b-a^6\,b^3\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8\,b^2-6\,a^6\,b^4+2\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^9\,b^2-2\,a^7\,b^4+a^5\,b^6\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{11}\,b-8\,a^9\,b^3+7\,a^7\,b^5-2\,a^5\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(b^5-2\,a^2\,b^3\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{64\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^4\,b^2-6\,a^2\,b^4+2\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^5\,b^2-2\,a^3\,b^4+a\,b^6\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^7\,b+9\,a^5\,b^3-8\,a^3\,b^5+2\,a\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^8\,b-a^6\,b^3\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8\,b^2-6\,a^6\,b^4+2\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^9\,b^2-2\,a^7\,b^4+a^5\,b^6\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{11}\,b-8\,a^9\,b^3+7\,a^7\,b^5-2\,a^5\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{b\,\left(2\,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(-2\,a^7\,b+9\,a^5\,b^3-8\,a^3\,b^5+2\,a\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{32\,\left(a^5\,b^2-2\,a^3\,b^4+a\,b^6\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^8\,b-a^6\,b^3\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8\,b^2-6\,a^6\,b^4+2\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^9\,b^2-2\,a^7\,b^4+a^5\,b^6\right)}{a^6-2\,a^4\,b^2+a^2\,b^4}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{11}\,b-8\,a^9\,b^3+7\,a^7\,b^5-2\,a^5\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"(b*atan(((b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^6 - 2*a^3*b^4 + a^5*b^2))/(a^6 + a^2*b^4 - 2*a^4*b^2) - (32*tan(c/2 + (d*x)/2)*(2*a*b^7 - 2*a^7*b - 8*a^3*b^5 + 9*a^5*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a^8*b - a^6*b^3))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(2*a^4*b^6 - 6*a^6*b^4 + 4*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a^5*b^6 - 2*a^7*b^4 + a^9*b^2))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(3*a^11*b - 2*a^5*b^7 + 7*a^7*b^5 - 8*a^9*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) - (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*a*b^7 - 2*a^7*b - 8*a^3*b^5 + 9*a^5*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (32*(a*b^6 - 2*a^3*b^4 + a^5*b^2))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a^8*b - a^6*b^3))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(2*a^4*b^6 - 6*a^6*b^4 + 4*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a^5*b^6 - 2*a^7*b^4 + a^9*b^2))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(3*a^11*b - 2*a^5*b^7 + 7*a^7*b^5 - 8*a^9*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(b^5 - 2*a^2*b^3))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (64*tan(c/2 + (d*x)/2)*(2*b^6 - 6*a^2*b^4 + 4*a^4*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^6 - 2*a^3*b^4 + a^5*b^2))/(a^6 + a^2*b^4 - 2*a^4*b^2) - (32*tan(c/2 + (d*x)/2)*(2*a*b^7 - 2*a^7*b - 8*a^3*b^5 + 9*a^5*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a^8*b - a^6*b^3))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(2*a^4*b^6 - 6*a^6*b^4 + 4*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a^5*b^6 - 2*a^7*b^4 + a^9*b^2))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(3*a^11*b - 2*a^5*b^7 + 7*a^7*b^5 - 8*a^9*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*a*b^7 - 2*a^7*b - 8*a^3*b^5 + 9*a^5*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (32*(a*b^6 - 2*a^3*b^4 + a^5*b^2))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a^8*b - a^6*b^3))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(2*a^4*b^6 - 6*a^6*b^4 + 4*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (b*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*((32*(a^5*b^6 - 2*a^7*b^4 + a^9*b^2))/(a^6 + a^2*b^4 - 2*a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(3*a^11*b - 2*a^5*b^7 + 7*a^7*b^5 - 8*a^9*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(2*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)) - ((2*b*tan(c/2 + (d*x)/2))/(a^2 - b^2) + (2*b^2)/(a*(a^2 - b^2)))/(d*(b + 2*a*tan(c/2 + (d*x)/2) + b*tan(c/2 + (d*x)/2)^2)) - (2*atan((64*a^5*b*tan(c/2 + (d*x)/2))/((64*a^3*b^9)/(a^6 + a^2*b^4 - 2*a^4*b^2) - (192*a^5*b^7)/(a^6 + a^2*b^4 - 2*a^4*b^2) + (128*a^7*b^5)/(a^6 + a^2*b^4 - 2*a^4*b^2) + (64*a^9*b^3)/(a^6 + a^2*b^4 - 2*a^4*b^2) - (64*a^11*b)/(a^6 + a^2*b^4 - 2*a^4*b^2)) - (64*a*b^5*tan(c/2 + (d*x)/2))/((64*a^3*b^9)/(a^6 + a^2*b^4 - 2*a^4*b^2) - (192*a^5*b^7)/(a^6 + a^2*b^4 - 2*a^4*b^2) + (128*a^7*b^5)/(a^6 + a^2*b^4 - 2*a^4*b^2) + (64*a^9*b^3)/(a^6 + a^2*b^4 - 2*a^4*b^2) - (64*a^11*b)/(a^6 + a^2*b^4 - 2*a^4*b^2)) + (64*a^3*b^3*tan(c/2 + (d*x)/2))/((64*a^3*b^9)/(a^6 + a^2*b^4 - 2*a^4*b^2) - (192*a^5*b^7)/(a^6 + a^2*b^4 - 2*a^4*b^2) + (128*a^7*b^5)/(a^6 + a^2*b^4 - 2*a^4*b^2) + (64*a^9*b^3)/(a^6 + a^2*b^4 - 2*a^4*b^2) - (64*a^11*b)/(a^6 + a^2*b^4 - 2*a^4*b^2))))/(a^2*d)","B"
50,1,5917,170,8.803477,"\text{Not used}","int(1/(a + b/sin(c + d*x))^3,x)","\frac{\frac{2\,b^5-5\,a^2\,b^3}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,b^4-16\,a^2\,b^2\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(b^4-4\,a^2\,b^2\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)}^2\,\left(5\,a^2\,b-2\,b^3\right)\,\left(2\,a^2+b^2\right)}{a^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)}^2\,\left(4\,a^2+2\,b^2\right)+b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+b^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{\frac{\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{12}\,b-72\,a^{10}\,b^3+124\,a^8\,b^5-105\,a^6\,b^7+44\,a^4\,b^9-8\,a^2\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{\left(\frac{8\,\left(4\,a^{14}\,b-8\,a^{12}\,b^3+6\,a^{10}\,b^5-4\,a^8\,b^7+2\,a^6\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}\,b^2-68\,a^{12}\,b^4+72\,a^{10}\,b^6-36\,a^8\,b^8+8\,a^6\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{\left(\frac{8\,\left(4\,a^{16}\,b^2-16\,a^{14}\,b^4+24\,a^{12}\,b^6-16\,a^{10}\,b^8+4\,a^8\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{18}\,b-56\,a^{16}\,b^3+104\,a^{14}\,b^5-96\,a^{12}\,b^7+44\,a^{10}\,b^9-8\,a^8\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}}{a^3}+\frac{\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{12}\,b-72\,a^{10}\,b^3+124\,a^8\,b^5-105\,a^6\,b^7+44\,a^4\,b^9-8\,a^2\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}+\frac{\left(\frac{8\,\left(4\,a^{14}\,b-8\,a^{12}\,b^3+6\,a^{10}\,b^5-4\,a^8\,b^7+2\,a^6\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}\,b^2-68\,a^{12}\,b^4+72\,a^{10}\,b^6-36\,a^8\,b^8+8\,a^6\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}+\frac{\left(\frac{8\,\left(4\,a^{16}\,b^2-16\,a^{14}\,b^4+24\,a^{12}\,b^6-16\,a^{10}\,b^8+4\,a^8\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{18}\,b-56\,a^{16}\,b^3+104\,a^{14}\,b^5-96\,a^{12}\,b^7+44\,a^{10}\,b^9-8\,a^8\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}}{a^3}}{\frac{16\,\left(-24\,a^6\,b^3+26\,a^4\,b^5-13\,a^2\,b^7+2\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^8\,b^2-68\,a^6\,b^4+72\,a^4\,b^6-36\,a^2\,b^8+8\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{12}\,b-72\,a^{10}\,b^3+124\,a^8\,b^5-105\,a^6\,b^7+44\,a^4\,b^9-8\,a^2\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{\left(\frac{8\,\left(4\,a^{14}\,b-8\,a^{12}\,b^3+6\,a^{10}\,b^5-4\,a^8\,b^7+2\,a^6\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}\,b^2-68\,a^{12}\,b^4+72\,a^{10}\,b^6-36\,a^8\,b^8+8\,a^6\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{\left(\frac{8\,\left(4\,a^{16}\,b^2-16\,a^{14}\,b^4+24\,a^{12}\,b^6-16\,a^{10}\,b^8+4\,a^8\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{18}\,b-56\,a^{16}\,b^3+104\,a^{14}\,b^5-96\,a^{12}\,b^7+44\,a^{10}\,b^9-8\,a^8\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{12}\,b-72\,a^{10}\,b^3+124\,a^8\,b^5-105\,a^6\,b^7+44\,a^4\,b^9-8\,a^2\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}+\frac{\left(\frac{8\,\left(4\,a^{14}\,b-8\,a^{12}\,b^3+6\,a^{10}\,b^5-4\,a^8\,b^7+2\,a^6\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}\,b^2-68\,a^{12}\,b^4+72\,a^{10}\,b^6-36\,a^8\,b^8+8\,a^6\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}+\frac{\left(\frac{8\,\left(4\,a^{16}\,b^2-16\,a^{14}\,b^4+24\,a^{12}\,b^6-16\,a^{10}\,b^8+4\,a^8\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{18}\,b-56\,a^{16}\,b^3+104\,a^{14}\,b^5-96\,a^{12}\,b^7+44\,a^{10}\,b^9-8\,a^8\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}}\right)}{a^3\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{12}\,b-72\,a^{10}\,b^3+124\,a^8\,b^5-105\,a^6\,b^7+44\,a^4\,b^9-8\,a^2\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{14}\,b-8\,a^{12}\,b^3+6\,a^{10}\,b^5-4\,a^8\,b^7+2\,a^6\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}\,b^2-68\,a^{12}\,b^4+72\,a^{10}\,b^6-36\,a^8\,b^8+8\,a^6\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{b\,\left(\frac{8\,\left(4\,a^{16}\,b^2-16\,a^{14}\,b^4+24\,a^{12}\,b^6-16\,a^{10}\,b^8+4\,a^8\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{18}\,b-56\,a^{16}\,b^3+104\,a^{14}\,b^5-96\,a^{12}\,b^7+44\,a^{10}\,b^9-8\,a^8\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\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)}\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\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)}\right)\,1{}\mathrm{i}}{2\,\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)}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{12}\,b-72\,a^{10}\,b^3+124\,a^8\,b^5-105\,a^6\,b^7+44\,a^4\,b^9-8\,a^2\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{14}\,b-8\,a^{12}\,b^3+6\,a^{10}\,b^5-4\,a^8\,b^7+2\,a^6\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}\,b^2-68\,a^{12}\,b^4+72\,a^{10}\,b^6-36\,a^8\,b^8+8\,a^6\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}+\frac{b\,\left(\frac{8\,\left(4\,a^{16}\,b^2-16\,a^{14}\,b^4+24\,a^{12}\,b^6-16\,a^{10}\,b^8+4\,a^8\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{18}\,b-56\,a^{16}\,b^3+104\,a^{14}\,b^5-96\,a^{12}\,b^7+44\,a^{10}\,b^9-8\,a^8\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\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)}\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\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)}\right)\,1{}\mathrm{i}}{2\,\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)}}{\frac{16\,\left(-24\,a^6\,b^3+26\,a^4\,b^5-13\,a^2\,b^7+2\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^8\,b^2-68\,a^6\,b^4+72\,a^4\,b^6-36\,a^2\,b^8+8\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{12}\,b-72\,a^{10}\,b^3+124\,a^8\,b^5-105\,a^6\,b^7+44\,a^4\,b^9-8\,a^2\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{14}\,b-8\,a^{12}\,b^3+6\,a^{10}\,b^5-4\,a^8\,b^7+2\,a^6\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}\,b^2-68\,a^{12}\,b^4+72\,a^{10}\,b^6-36\,a^8\,b^8+8\,a^6\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}-\frac{b\,\left(\frac{8\,\left(4\,a^{16}\,b^2-16\,a^{14}\,b^4+24\,a^{12}\,b^6-16\,a^{10}\,b^8+4\,a^8\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{18}\,b-56\,a^{16}\,b^3+104\,a^{14}\,b^5-96\,a^{12}\,b^7+44\,a^{10}\,b^9-8\,a^8\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\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)}\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\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)}\right)}{2\,\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)}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{12}\,b-72\,a^{10}\,b^3+124\,a^8\,b^5-105\,a^6\,b^7+44\,a^4\,b^9-8\,a^2\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{14}\,b-8\,a^{12}\,b^3+6\,a^{10}\,b^5-4\,a^8\,b^7+2\,a^6\,b^9\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{14}\,b^2-68\,a^{12}\,b^4+72\,a^{10}\,b^6-36\,a^8\,b^8+8\,a^6\,b^{10}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}+\frac{b\,\left(\frac{8\,\left(4\,a^{16}\,b^2-16\,a^{14}\,b^4+24\,a^{12}\,b^6-16\,a^{10}\,b^8+4\,a^8\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{18}\,b-56\,a^{16}\,b^3+104\,a^{14}\,b^5-96\,a^{12}\,b^7+44\,a^{10}\,b^9-8\,a^8\,b^{11}\right)}{a^{14}-4\,a^{12}\,b^2+6\,a^{10}\,b^4-4\,a^8\,b^6+a^6\,b^8}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\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)}\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\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)}\right)}{2\,\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)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,1{}\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,"((2*b^5 - 5*a^2*b^3)/(a^2*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)*(7*b^4 - 16*a^2*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^3*(b^4 - 4*a^2*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^2*(5*a^2*b - 2*b^3)*(2*a^2 + b^2))/(a^2*(a^4 + b^4 - 2*a^2*b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a^2 + 2*b^2) + b^2*tan(c/2 + (d*x)/2)^4 + b^2 + 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))) + (2*atan((((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) - (((8*(4*a^14*b + 2*a^6*b^9 - 4*a^8*b^7 + 6*a^10*b^5 - 8*a^12*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) - (((8*(4*a^8*b^10 - 16*a^10*b^8 + 24*a^12*b^6 - 16*a^14*b^4 + 4*a^16*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^18*b - 8*a^8*b^11 + 44*a^10*b^9 - 96*a^12*b^7 + 104*a^14*b^5 - 56*a^16*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(8*a^6*b^10 - 36*a^8*b^8 + 72*a^10*b^6 - 68*a^12*b^4 + 24*a^14*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(8*a^12*b - 8*a^2*b^11 + 44*a^4*b^9 - 105*a^6*b^7 + 124*a^8*b^5 - 72*a^10*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))/a^3 + ((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (((((8*(4*a^8*b^10 - 16*a^10*b^8 + 24*a^12*b^6 - 16*a^14*b^4 + 4*a^16*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^18*b - 8*a^8*b^11 + 44*a^10*b^9 - 96*a^12*b^7 + 104*a^14*b^5 - 56*a^16*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (8*(4*a^14*b + 2*a^6*b^9 - 4*a^8*b^7 + 6*a^10*b^5 - 8*a^12*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^6*b^10 - 36*a^8*b^8 + 72*a^10*b^6 - 68*a^12*b^4 + 24*a^14*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(8*a^12*b - 8*a^2*b^11 + 44*a^4*b^9 - 105*a^6*b^7 + 124*a^8*b^5 - 72*a^10*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))/a^3)/((16*(2*b^9 - 13*a^2*b^7 + 26*a^4*b^5 - 24*a^6*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) - (((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) - (((8*(4*a^14*b + 2*a^6*b^9 - 4*a^8*b^7 + 6*a^10*b^5 - 8*a^12*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) - (((8*(4*a^8*b^10 - 16*a^10*b^8 + 24*a^12*b^6 - 16*a^14*b^4 + 4*a^16*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^18*b - 8*a^8*b^11 + 44*a^10*b^9 - 96*a^12*b^7 + 104*a^14*b^5 - 56*a^16*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(8*a^6*b^10 - 36*a^8*b^8 + 72*a^10*b^6 - 68*a^12*b^4 + 24*a^14*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(8*a^12*b - 8*a^2*b^11 + 44*a^4*b^9 - 105*a^6*b^7 + 124*a^8*b^5 - 72*a^10*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (((((8*(4*a^8*b^10 - 16*a^10*b^8 + 24*a^12*b^6 - 16*a^14*b^4 + 4*a^16*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^18*b - 8*a^8*b^11 + 44*a^10*b^9 - 96*a^12*b^7 + 104*a^14*b^5 - 56*a^16*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (8*(4*a^14*b + 2*a^6*b^9 - 4*a^8*b^7 + 6*a^10*b^5 - 8*a^12*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^6*b^10 - 36*a^8*b^8 + 72*a^10*b^6 - 68*a^12*b^4 + 24*a^14*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(8*a^12*b - 8*a^2*b^11 + 44*a^4*b^9 - 105*a^6*b^7 + 124*a^8*b^5 - 72*a^10*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*1i)/a^3 + (16*tan(c/2 + (d*x)/2)*(8*b^10 - 36*a^2*b^8 + 72*a^4*b^6 - 68*a^6*b^4 + 24*a^8*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))))/(a^3*d) + (b*atan(((b*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^12*b - 8*a^2*b^11 + 44*a^4*b^9 - 105*a^6*b^7 + 124*a^8*b^5 - 72*a^10*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) - (b*((a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^14*b + 2*a^6*b^9 - 4*a^8*b^7 + 6*a^10*b^5 - 8*a^12*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^6*b^10 - 36*a^8*b^8 + 72*a^10*b^6 - 68*a^12*b^4 + 24*a^14*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) - (b*((8*(4*a^8*b^10 - 16*a^10*b^8 + 24*a^12*b^6 - 16*a^14*b^4 + 4*a^16*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^18*b - 8*a^8*b^11 + 44*a^10*b^9 - 96*a^12*b^7 + 104*a^14*b^5 - 56*a^16*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(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)))*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(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)))*1i)/(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*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^12*b - 8*a^2*b^11 + 44*a^4*b^9 - 105*a^6*b^7 + 124*a^8*b^5 - 72*a^10*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) + (b*((a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^14*b + 2*a^6*b^9 - 4*a^8*b^7 + 6*a^10*b^5 - 8*a^12*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^6*b^10 - 36*a^8*b^8 + 72*a^10*b^6 - 68*a^12*b^4 + 24*a^14*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) + (b*((8*(4*a^8*b^10 - 16*a^10*b^8 + 24*a^12*b^6 - 16*a^14*b^4 + 4*a^16*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^18*b - 8*a^8*b^11 + 44*a^10*b^9 - 96*a^12*b^7 + 104*a^14*b^5 - 56*a^16*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(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)))*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(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)))*1i)/(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)))/((16*(2*b^9 - 13*a^2*b^7 + 26*a^4*b^5 - 24*a^6*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (16*tan(c/2 + (d*x)/2)*(8*b^10 - 36*a^2*b^8 + 72*a^4*b^6 - 68*a^6*b^4 + 24*a^8*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) - (b*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^12*b - 8*a^2*b^11 + 44*a^4*b^9 - 105*a^6*b^7 + 124*a^8*b^5 - 72*a^10*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) - (b*((a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^14*b + 2*a^6*b^9 - 4*a^8*b^7 + 6*a^10*b^5 - 8*a^12*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^6*b^10 - 36*a^8*b^8 + 72*a^10*b^6 - 68*a^12*b^4 + 24*a^14*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) - (b*((8*(4*a^8*b^10 - 16*a^10*b^8 + 24*a^12*b^6 - 16*a^14*b^4 + 4*a^16*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^18*b - 8*a^8*b^11 + 44*a^10*b^9 - 96*a^12*b^7 + 104*a^14*b^5 - 56*a^16*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(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)))*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(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))))/(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*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^12*b - 8*a^2*b^11 + 44*a^4*b^9 - 105*a^6*b^7 + 124*a^8*b^5 - 72*a^10*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) + (b*((a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^14*b + 2*a^6*b^9 - 4*a^8*b^7 + 6*a^10*b^5 - 8*a^12*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^6*b^10 - 36*a^8*b^8 + 72*a^10*b^6 - 68*a^12*b^4 + 24*a^14*b^2))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2) + (b*((8*(4*a^8*b^10 - 16*a^10*b^8 + 24*a^12*b^6 - 16*a^14*b^4 + 4*a^16*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^18*b - 8*a^8*b^11 + 44*a^10*b^9 - 96*a^12*b^7 + 104*a^14*b^5 - 56*a^16*b^3))/(a^14 + a^6*b^8 - 4*a^8*b^6 + 6*a^10*b^4 - 4*a^12*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(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)))*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(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))))/(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))))*((a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*1i)/(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"
51,1,8167,239,12.383925,"\text{Not used}","int(1/(a + b/sin(c + d*x))^4,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{8\,\left(4\,a^{15}\,b^2-24\,a^{13}\,b^4+60\,a^{11}\,b^6-80\,a^9\,b^8+60\,a^7\,b^{10}-24\,a^5\,b^{12}+4\,a^3\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-116\,a^{15}\,b^3+272\,a^{13}\,b^5-396\,a^{11}\,b^7+344\,a^9\,b^9-189\,a^7\,b^{11}+60\,a^5\,b^{13}-8\,a^3\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{\left(\frac{8\,\left(4\,a^{20}\,b-12\,a^{18}\,b^3+20\,a^{16}\,b^5-30\,a^{14}\,b^7+30\,a^{12}\,b^9-14\,a^{10}\,b^{11}+2\,a^8\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{20}\,b^2-128\,a^{18}\,b^4+220\,a^{16}\,b^6-220\,a^{14}\,b^8+140\,a^{12}\,b^{10}-52\,a^{10}\,b^{12}+8\,a^8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{\left(\frac{8\,\left(4\,a^{23}\,b^2-24\,a^{21}\,b^4+60\,a^{19}\,b^6-80\,a^{17}\,b^8+60\,a^{15}\,b^{10}-24\,a^{13}\,b^{12}+4\,a^{11}\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{25}\,b-80\,a^{23}\,b^3+228\,a^{21}\,b^5-360\,a^{19}\,b^7+340\,a^{17}\,b^9-192\,a^{15}\,b^{11}+60\,a^{13}\,b^{13}-8\,a^{11}\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}}{a^4}+\frac{\frac{8\,\left(4\,a^{15}\,b^2-24\,a^{13}\,b^4+60\,a^{11}\,b^6-80\,a^9\,b^8+60\,a^7\,b^{10}-24\,a^5\,b^{12}+4\,a^3\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-116\,a^{15}\,b^3+272\,a^{13}\,b^5-396\,a^{11}\,b^7+344\,a^9\,b^9-189\,a^7\,b^{11}+60\,a^5\,b^{13}-8\,a^3\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}+\frac{\left(\frac{8\,\left(4\,a^{20}\,b-12\,a^{18}\,b^3+20\,a^{16}\,b^5-30\,a^{14}\,b^7+30\,a^{12}\,b^9-14\,a^{10}\,b^{11}+2\,a^8\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{20}\,b^2-128\,a^{18}\,b^4+220\,a^{16}\,b^6-220\,a^{14}\,b^8+140\,a^{12}\,b^{10}-52\,a^{10}\,b^{12}+8\,a^8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}+\frac{\left(\frac{8\,\left(4\,a^{23}\,b^2-24\,a^{21}\,b^4+60\,a^{19}\,b^6-80\,a^{17}\,b^8+60\,a^{15}\,b^{10}-24\,a^{13}\,b^{12}+4\,a^{11}\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{25}\,b-80\,a^{23}\,b^3+228\,a^{21}\,b^5-360\,a^{19}\,b^7+340\,a^{17}\,b^9-192\,a^{15}\,b^{11}+60\,a^{13}\,b^{13}-8\,a^{11}\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}}{a^4}}{\frac{16\,\left(-48\,a^{10}\,b^3+64\,a^8\,b^5-66\,a^6\,b^7+34\,a^4\,b^9-11\,a^2\,b^{11}+2\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^2-128\,a^{10}\,b^4+220\,a^8\,b^6-220\,a^6\,b^8+140\,a^4\,b^{10}-52\,a^2\,b^{12}+8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{\left(\frac{8\,\left(4\,a^{15}\,b^2-24\,a^{13}\,b^4+60\,a^{11}\,b^6-80\,a^9\,b^8+60\,a^7\,b^{10}-24\,a^5\,b^{12}+4\,a^3\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-116\,a^{15}\,b^3+272\,a^{13}\,b^5-396\,a^{11}\,b^7+344\,a^9\,b^9-189\,a^7\,b^{11}+60\,a^5\,b^{13}-8\,a^3\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{\left(\frac{8\,\left(4\,a^{20}\,b-12\,a^{18}\,b^3+20\,a^{16}\,b^5-30\,a^{14}\,b^7+30\,a^{12}\,b^9-14\,a^{10}\,b^{11}+2\,a^8\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{20}\,b^2-128\,a^{18}\,b^4+220\,a^{16}\,b^6-220\,a^{14}\,b^8+140\,a^{12}\,b^{10}-52\,a^{10}\,b^{12}+8\,a^8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{\left(\frac{8\,\left(4\,a^{23}\,b^2-24\,a^{21}\,b^4+60\,a^{19}\,b^6-80\,a^{17}\,b^8+60\,a^{15}\,b^{10}-24\,a^{13}\,b^{12}+4\,a^{11}\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{25}\,b-80\,a^{23}\,b^3+228\,a^{21}\,b^5-360\,a^{19}\,b^7+340\,a^{17}\,b^9-192\,a^{15}\,b^{11}+60\,a^{13}\,b^{13}-8\,a^{11}\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{\left(\frac{8\,\left(4\,a^{15}\,b^2-24\,a^{13}\,b^4+60\,a^{11}\,b^6-80\,a^9\,b^8+60\,a^7\,b^{10}-24\,a^5\,b^{12}+4\,a^3\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-116\,a^{15}\,b^3+272\,a^{13}\,b^5-396\,a^{11}\,b^7+344\,a^9\,b^9-189\,a^7\,b^{11}+60\,a^5\,b^{13}-8\,a^3\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}+\frac{\left(\frac{8\,\left(4\,a^{20}\,b-12\,a^{18}\,b^3+20\,a^{16}\,b^5-30\,a^{14}\,b^7+30\,a^{12}\,b^9-14\,a^{10}\,b^{11}+2\,a^8\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{20}\,b^2-128\,a^{18}\,b^4+220\,a^{16}\,b^6-220\,a^{14}\,b^8+140\,a^{12}\,b^{10}-52\,a^{10}\,b^{12}+8\,a^8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}+\frac{\left(\frac{8\,\left(4\,a^{23}\,b^2-24\,a^{21}\,b^4+60\,a^{19}\,b^6-80\,a^{17}\,b^8+60\,a^{15}\,b^{10}-24\,a^{13}\,b^{12}+4\,a^{11}\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{25}\,b-80\,a^{23}\,b^3+228\,a^{21}\,b^5-360\,a^{19}\,b^7+340\,a^{17}\,b^9-192\,a^{15}\,b^{11}+60\,a^{13}\,b^{13}-8\,a^{11}\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}}\right)}{a^4\,d}-\frac{\frac{26\,a^4\,b^4-17\,a^2\,b^6+6\,b^8}{3\,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)\,\left(46\,a^4\,b^3-32\,a^2\,b^5+11\,b^7\right)}{a^2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(28\,a^6\,b^2-4\,a^4\,b^4-a^2\,b^6+2\,b^8\right)}{a^3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(38\,a^6\,b^2-19\,a^4\,b^4+4\,a^2\,b^6+2\,b^8\right)}{a^3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^2+3\,b^2\right)\,\left(26\,a^4\,b-17\,a^2\,b^3+6\,b^5\right)}{3\,a^2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^4-2\,a^2\,b^2+b^4\right)}{a^2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left(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)}^3\,\left(8\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^2\,b+3\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a^2\,b+3\,b^3\right)+b^3+6\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,a^{15}\,b^2-24\,a^{13}\,b^4+60\,a^{11}\,b^6-80\,a^9\,b^8+60\,a^7\,b^{10}-24\,a^5\,b^{12}+4\,a^3\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-116\,a^{15}\,b^3+272\,a^{13}\,b^5-396\,a^{11}\,b^7+344\,a^9\,b^9-189\,a^7\,b^{11}+60\,a^5\,b^{13}-8\,a^3\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,a^{20}\,b-12\,a^{18}\,b^3+20\,a^{16}\,b^5-30\,a^{14}\,b^7+30\,a^{12}\,b^9-14\,a^{10}\,b^{11}+2\,a^8\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{20}\,b^2-128\,a^{18}\,b^4+220\,a^{16}\,b^6-220\,a^{14}\,b^8+140\,a^{12}\,b^{10}-52\,a^{10}\,b^{12}+8\,a^8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{b\,\left(\frac{8\,\left(4\,a^{23}\,b^2-24\,a^{21}\,b^4+60\,a^{19}\,b^6-80\,a^{17}\,b^8+60\,a^{15}\,b^{10}-24\,a^{13}\,b^{12}+4\,a^{11}\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{25}\,b-80\,a^{23}\,b^3+228\,a^{21}\,b^5-360\,a^{19}\,b^7+340\,a^{17}\,b^9-192\,a^{15}\,b^{11}+60\,a^{13}\,b^{13}-8\,a^{11}\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)\,1{}\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\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,a^{15}\,b^2-24\,a^{13}\,b^4+60\,a^{11}\,b^6-80\,a^9\,b^8+60\,a^7\,b^{10}-24\,a^5\,b^{12}+4\,a^3\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-116\,a^{15}\,b^3+272\,a^{13}\,b^5-396\,a^{11}\,b^7+344\,a^9\,b^9-189\,a^7\,b^{11}+60\,a^5\,b^{13}-8\,a^3\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}+\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,a^{20}\,b-12\,a^{18}\,b^3+20\,a^{16}\,b^5-30\,a^{14}\,b^7+30\,a^{12}\,b^9-14\,a^{10}\,b^{11}+2\,a^8\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{20}\,b^2-128\,a^{18}\,b^4+220\,a^{16}\,b^6-220\,a^{14}\,b^8+140\,a^{12}\,b^{10}-52\,a^{10}\,b^{12}+8\,a^8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}+\frac{b\,\left(\frac{8\,\left(4\,a^{23}\,b^2-24\,a^{21}\,b^4+60\,a^{19}\,b^6-80\,a^{17}\,b^8+60\,a^{15}\,b^{10}-24\,a^{13}\,b^{12}+4\,a^{11}\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{25}\,b-80\,a^{23}\,b^3+228\,a^{21}\,b^5-360\,a^{19}\,b^7+340\,a^{17}\,b^9-192\,a^{15}\,b^{11}+60\,a^{13}\,b^{13}-8\,a^{11}\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)\,1{}\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{16\,\left(-48\,a^{10}\,b^3+64\,a^8\,b^5-66\,a^6\,b^7+34\,a^4\,b^9-11\,a^2\,b^{11}+2\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}\,b^2-128\,a^{10}\,b^4+220\,a^8\,b^6-220\,a^6\,b^8+140\,a^4\,b^{10}-52\,a^2\,b^{12}+8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,a^{15}\,b^2-24\,a^{13}\,b^4+60\,a^{11}\,b^6-80\,a^9\,b^8+60\,a^7\,b^{10}-24\,a^5\,b^{12}+4\,a^3\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-116\,a^{15}\,b^3+272\,a^{13}\,b^5-396\,a^{11}\,b^7+344\,a^9\,b^9-189\,a^7\,b^{11}+60\,a^5\,b^{13}-8\,a^3\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,a^{20}\,b-12\,a^{18}\,b^3+20\,a^{16}\,b^5-30\,a^{14}\,b^7+30\,a^{12}\,b^9-14\,a^{10}\,b^{11}+2\,a^8\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{20}\,b^2-128\,a^{18}\,b^4+220\,a^{16}\,b^6-220\,a^{14}\,b^8+140\,a^{12}\,b^{10}-52\,a^{10}\,b^{12}+8\,a^8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}-\frac{b\,\left(\frac{8\,\left(4\,a^{23}\,b^2-24\,a^{21}\,b^4+60\,a^{19}\,b^6-80\,a^{17}\,b^8+60\,a^{15}\,b^{10}-24\,a^{13}\,b^{12}+4\,a^{11}\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{25}\,b-80\,a^{23}\,b^3+228\,a^{21}\,b^5-360\,a^{19}\,b^7+340\,a^{17}\,b^9-192\,a^{15}\,b^{11}+60\,a^{13}\,b^{13}-8\,a^{11}\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,a^{15}\,b^2-24\,a^{13}\,b^4+60\,a^{11}\,b^6-80\,a^9\,b^8+60\,a^7\,b^{10}-24\,a^5\,b^{12}+4\,a^3\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-116\,a^{15}\,b^3+272\,a^{13}\,b^5-396\,a^{11}\,b^7+344\,a^9\,b^9-189\,a^7\,b^{11}+60\,a^5\,b^{13}-8\,a^3\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}+\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,a^{20}\,b-12\,a^{18}\,b^3+20\,a^{16}\,b^5-30\,a^{14}\,b^7+30\,a^{12}\,b^9-14\,a^{10}\,b^{11}+2\,a^8\,b^{13}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{20}\,b^2-128\,a^{18}\,b^4+220\,a^{16}\,b^6-220\,a^{14}\,b^8+140\,a^{12}\,b^{10}-52\,a^{10}\,b^{12}+8\,a^8\,b^{14}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}+\frac{b\,\left(\frac{8\,\left(4\,a^{23}\,b^2-24\,a^{21}\,b^4+60\,a^{19}\,b^6-80\,a^{17}\,b^8+60\,a^{15}\,b^{10}-24\,a^{13}\,b^{12}+4\,a^{11}\,b^{14}\right)}{a^{20}-6\,a^{18}\,b^2+15\,a^{16}\,b^4-20\,a^{14}\,b^6+15\,a^{12}\,b^8-6\,a^{10}\,b^{10}+a^8\,b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{25}\,b-80\,a^{23}\,b^3+228\,a^{21}\,b^5-360\,a^{19}\,b^7+340\,a^{17}\,b^9-192\,a^{15}\,b^{11}+60\,a^{13}\,b^{13}-8\,a^{11}\,b^{15}\right)}{a^{21}-6\,a^{19}\,b^2+15\,a^{17}\,b^4-20\,a^{15}\,b^6+15\,a^{13}\,b^8-6\,a^{11}\,b^{10}+a^9\,b^{12}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)\,1{}\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,"(2*atan((((8*(4*a^3*b^14 - 24*a^5*b^12 + 60*a^7*b^10 - 80*a^9*b^8 + 60*a^11*b^6 - 24*a^13*b^4 + 4*a^15*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) - (((8*(4*a^20*b + 2*a^8*b^13 - 14*a^10*b^11 + 30*a^12*b^9 - 30*a^14*b^7 + 20*a^16*b^5 - 12*a^18*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) - (((8*(4*a^11*b^14 - 24*a^13*b^12 + 60*a^15*b^10 - 80*a^17*b^8 + 60*a^19*b^6 - 24*a^21*b^4 + 4*a^23*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^25*b - 8*a^11*b^15 + 60*a^13*b^13 - 192*a^15*b^11 + 340*a^17*b^9 - 360*a^19*b^7 + 228*a^21*b^5 - 80*a^23*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (8*tan(c/2 + (d*x)/2)*(8*a^8*b^14 - 52*a^10*b^12 + 140*a^12*b^10 - 220*a^14*b^8 + 220*a^16*b^6 - 128*a^18*b^4 + 32*a^20*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (8*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^3*b^15 + 60*a^5*b^13 - 189*a^7*b^11 + 344*a^9*b^9 - 396*a^11*b^7 + 272*a^13*b^5 - 116*a^15*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))/a^4 + ((((((8*(4*a^11*b^14 - 24*a^13*b^12 + 60*a^15*b^10 - 80*a^17*b^8 + 60*a^19*b^6 - 24*a^21*b^4 + 4*a^23*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^25*b - 8*a^11*b^15 + 60*a^13*b^13 - 192*a^15*b^11 + 340*a^17*b^9 - 360*a^19*b^7 + 228*a^21*b^5 - 80*a^23*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (8*(4*a^20*b + 2*a^8*b^13 - 14*a^10*b^11 + 30*a^12*b^9 - 30*a^14*b^7 + 20*a^16*b^5 - 12*a^18*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^8*b^14 - 52*a^10*b^12 + 140*a^12*b^10 - 220*a^14*b^8 + 220*a^16*b^6 - 128*a^18*b^4 + 32*a^20*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (8*(4*a^3*b^14 - 24*a^5*b^12 + 60*a^7*b^10 - 80*a^9*b^8 + 60*a^11*b^6 - 24*a^13*b^4 + 4*a^15*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^3*b^15 + 60*a^5*b^13 - 189*a^7*b^11 + 344*a^9*b^9 - 396*a^11*b^7 + 272*a^13*b^5 - 116*a^15*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))/a^4)/((16*(2*b^13 - 11*a^2*b^11 + 34*a^4*b^9 - 66*a^6*b^7 + 64*a^8*b^5 - 48*a^10*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) - (((8*(4*a^3*b^14 - 24*a^5*b^12 + 60*a^7*b^10 - 80*a^9*b^8 + 60*a^11*b^6 - 24*a^13*b^4 + 4*a^15*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) - (((8*(4*a^20*b + 2*a^8*b^13 - 14*a^10*b^11 + 30*a^12*b^9 - 30*a^14*b^7 + 20*a^16*b^5 - 12*a^18*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) - (((8*(4*a^11*b^14 - 24*a^13*b^12 + 60*a^15*b^10 - 80*a^17*b^8 + 60*a^19*b^6 - 24*a^21*b^4 + 4*a^23*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^25*b - 8*a^11*b^15 + 60*a^13*b^13 - 192*a^15*b^11 + 340*a^17*b^9 - 360*a^19*b^7 + 228*a^21*b^5 - 80*a^23*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (8*tan(c/2 + (d*x)/2)*(8*a^8*b^14 - 52*a^10*b^12 + 140*a^12*b^10 - 220*a^14*b^8 + 220*a^16*b^6 - 128*a^18*b^4 + 32*a^20*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (8*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^3*b^15 + 60*a^5*b^13 - 189*a^7*b^11 + 344*a^9*b^9 - 396*a^11*b^7 + 272*a^13*b^5 - 116*a^15*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (((((((8*(4*a^11*b^14 - 24*a^13*b^12 + 60*a^15*b^10 - 80*a^17*b^8 + 60*a^19*b^6 - 24*a^21*b^4 + 4*a^23*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^25*b - 8*a^11*b^15 + 60*a^13*b^13 - 192*a^15*b^11 + 340*a^17*b^9 - 360*a^19*b^7 + 228*a^21*b^5 - 80*a^23*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (8*(4*a^20*b + 2*a^8*b^13 - 14*a^10*b^11 + 30*a^12*b^9 - 30*a^14*b^7 + 20*a^16*b^5 - 12*a^18*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^8*b^14 - 52*a^10*b^12 + 140*a^12*b^10 - 220*a^14*b^8 + 220*a^16*b^6 - 128*a^18*b^4 + 32*a^20*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (8*(4*a^3*b^14 - 24*a^5*b^12 + 60*a^7*b^10 - 80*a^9*b^8 + 60*a^11*b^6 - 24*a^13*b^4 + 4*a^15*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^3*b^15 + 60*a^5*b^13 - 189*a^7*b^11 + 344*a^9*b^9 - 396*a^11*b^7 + 272*a^13*b^5 - 116*a^15*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*1i)/a^4 + (16*tan(c/2 + (d*x)/2)*(8*b^14 - 52*a^2*b^12 + 140*a^4*b^10 - 220*a^6*b^8 + 220*a^8*b^6 - 128*a^10*b^4 + 32*a^12*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))))/(a^4*d) - ((6*b^8 - 17*a^2*b^6 + 26*a^4*b^4)/(3*a^3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)*(11*b^7 - 32*a^2*b^5 + 46*a^4*b^3))/(a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^4*(2*b^8 - a^2*b^6 - 4*a^4*b^4 + 28*a^6*b^2))/(a^3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^2*(2*b^8 + 4*a^2*b^6 - 19*a^4*b^4 + 38*a^6*b^2))/(a^3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^3*(2*a^2 + 3*b^2)*(26*a^4*b + 6*b^5 - 17*a^2*b^3))/(3*a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (b^3*tan(c/2 + (d*x)/2)^5*(6*a^4 + b^4 - 2*a^2*b^2))/(a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(b^3*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^3*(12*a*b^2 + 8*a^3) + tan(c/2 + (d*x)/2)^2*(12*a^2*b + 3*b^3) + tan(c/2 + (d*x)/2)^4*(12*a^2*b + 3*b^3) + b^3 + 6*a*b^2*tan(c/2 + (d*x)/2) + 6*a*b^2*tan(c/2 + (d*x)/2)^5)) + (b*atan(((b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*a^3*b^14 - 24*a^5*b^12 + 60*a^7*b^10 - 80*a^9*b^8 + 60*a^11*b^6 - 24*a^13*b^4 + 4*a^15*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^3*b^15 + 60*a^5*b^13 - 189*a^7*b^11 + 344*a^9*b^9 - 396*a^11*b^7 + 272*a^13*b^5 - 116*a^15*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) - (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*a^20*b + 2*a^8*b^13 - 14*a^10*b^11 + 30*a^12*b^9 - 30*a^14*b^7 + 20*a^16*b^5 - 12*a^18*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^8*b^14 - 52*a^10*b^12 + 140*a^12*b^10 - 220*a^14*b^8 + 220*a^16*b^6 - 128*a^18*b^4 + 32*a^20*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) - (b*((8*(4*a^11*b^14 - 24*a^13*b^12 + 60*a^15*b^10 - 80*a^17*b^8 + 60*a^19*b^6 - 24*a^21*b^4 + 4*a^23*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^25*b - 8*a^11*b^15 + 60*a^13*b^13 - 192*a^15*b^11 + 340*a^17*b^9 - 360*a^19*b^7 + 228*a^21*b^5 - 80*a^23*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*((a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*1i)/(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*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*a^3*b^14 - 24*a^5*b^12 + 60*a^7*b^10 - 80*a^9*b^8 + 60*a^11*b^6 - 24*a^13*b^4 + 4*a^15*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^3*b^15 + 60*a^5*b^13 - 189*a^7*b^11 + 344*a^9*b^9 - 396*a^11*b^7 + 272*a^13*b^5 - 116*a^15*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) + (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*a^20*b + 2*a^8*b^13 - 14*a^10*b^11 + 30*a^12*b^9 - 30*a^14*b^7 + 20*a^16*b^5 - 12*a^18*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^8*b^14 - 52*a^10*b^12 + 140*a^12*b^10 - 220*a^14*b^8 + 220*a^16*b^6 - 128*a^18*b^4 + 32*a^20*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) + (b*((8*(4*a^11*b^14 - 24*a^13*b^12 + 60*a^15*b^10 - 80*a^17*b^8 + 60*a^19*b^6 - 24*a^21*b^4 + 4*a^23*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^25*b - 8*a^11*b^15 + 60*a^13*b^13 - 192*a^15*b^11 + 340*a^17*b^9 - 360*a^19*b^7 + 228*a^21*b^5 - 80*a^23*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*((a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*1i)/(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)))/((16*(2*b^13 - 11*a^2*b^11 + 34*a^4*b^9 - 66*a^6*b^7 + 64*a^8*b^5 - 48*a^10*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (16*tan(c/2 + (d*x)/2)*(8*b^14 - 52*a^2*b^12 + 140*a^4*b^10 - 220*a^6*b^8 + 220*a^8*b^6 - 128*a^10*b^4 + 32*a^12*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) - (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*a^3*b^14 - 24*a^5*b^12 + 60*a^7*b^10 - 80*a^9*b^8 + 60*a^11*b^6 - 24*a^13*b^4 + 4*a^15*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^3*b^15 + 60*a^5*b^13 - 189*a^7*b^11 + 344*a^9*b^9 - 396*a^11*b^7 + 272*a^13*b^5 - 116*a^15*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) - (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*a^20*b + 2*a^8*b^13 - 14*a^10*b^11 + 30*a^12*b^9 - 30*a^14*b^7 + 20*a^16*b^5 - 12*a^18*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^8*b^14 - 52*a^10*b^12 + 140*a^12*b^10 - 220*a^14*b^8 + 220*a^16*b^6 - 128*a^18*b^4 + 32*a^20*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) - (b*((8*(4*a^11*b^14 - 24*a^13*b^12 + 60*a^15*b^10 - 80*a^17*b^8 + 60*a^19*b^6 - 24*a^21*b^4 + 4*a^23*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^25*b - 8*a^11*b^15 + 60*a^13*b^13 - 192*a^15*b^11 + 340*a^17*b^9 - 360*a^19*b^7 + 228*a^21*b^5 - 80*a^23*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*((a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)) + (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*a^3*b^14 - 24*a^5*b^12 + 60*a^7*b^10 - 80*a^9*b^8 + 60*a^11*b^6 - 24*a^13*b^4 + 4*a^15*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^3*b^15 + 60*a^5*b^13 - 189*a^7*b^11 + 344*a^9*b^9 - 396*a^11*b^7 + 272*a^13*b^5 - 116*a^15*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) + (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*a^20*b + 2*a^8*b^13 - 14*a^10*b^11 + 30*a^12*b^9 - 30*a^14*b^7 + 20*a^16*b^5 - 12*a^18*b^3))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^8*b^14 - 52*a^10*b^12 + 140*a^12*b^10 - 220*a^14*b^8 + 220*a^16*b^6 - 128*a^18*b^4 + 32*a^20*b^2))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2) + (b*((8*(4*a^11*b^14 - 24*a^13*b^12 + 60*a^15*b^10 - 80*a^17*b^8 + 60*a^19*b^6 - 24*a^21*b^4 + 4*a^23*b^2))/(a^20 + a^8*b^12 - 6*a^10*b^10 + 15*a^12*b^8 - 20*a^14*b^6 + 15*a^16*b^4 - 6*a^18*b^2) + (8*tan(c/2 + (d*x)/2)*(12*a^25*b - 8*a^11*b^15 + 60*a^13*b^13 - 192*a^15*b^11 + 340*a^17*b^9 - 360*a^19*b^7 + 228*a^21*b^5 - 80*a^23*b^3))/(a^21 + a^9*b^12 - 6*a^11*b^10 + 15*a^13*b^8 - 20*a^15*b^6 + 15*a^17*b^4 - 6*a^19*b^2))*((a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*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)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*1i)/(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"
52,1,39,31,0.245006,"\text{Not used}","int(1/(5/sin(c + d*x) + 3),x)","\frac{x}{3}-\frac{5\,\mathrm{atan}\left(\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-15}{24\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+20}\right)}{6\,d}","Not used",1,"x/3 - (5*atan((7*tan(c/2 + (d*x)/2) - 15)/(24*tan(c/2 + (d*x)/2) + 20)))/(6*d)","B"
53,1,27,68,0.290695,"\text{Not used}","int(1/(3/sin(c + d*x) + 5),x)","\frac{x}{5}-\frac{3\,\mathrm{atanh}\left(\frac{1}{2\,\left(\frac{200\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{27}+\frac{20}{9}\right)}+\frac{41}{40}\right)}{10\,d}","Not used",1,"x/5 - (3*atanh(1/(2*((200*tan(c/2 + (d*x)/2))/27 + 20/9)) + 41/40))/(10*d)","B"
54,0,-1,274,0.000000,"\text{Not used}","int((a + b/sin(e + f*x))^m/sin(e + f*x)^3,x)","\int \frac{{\left(a+\frac{b}{\sin\left(e+f\,x\right)}\right)}^m}{{\sin\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b/sin(e + f*x))^m/sin(e + f*x)^3, x)","F"
55,0,-1,220,0.000000,"\text{Not used}","int((a + b/sin(e + f*x))^m/sin(e + f*x)^2,x)","\int \frac{{\left(a+\frac{b}{\sin\left(e+f\,x\right)}\right)}^m}{{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b/sin(e + f*x))^m/sin(e + f*x)^2, x)","F"
56,0,-1,104,0.000000,"\text{Not used}","int((a + b/sin(e + f*x))^m/sin(e + f*x),x)","\int \frac{{\left(a+\frac{b}{\sin\left(e+f\,x\right)}\right)}^m}{\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b/sin(e + f*x))^m/sin(e + f*x), x)","F"
57,0,-1,15,0.000000,"\text{Not used}","int((a + b/sin(e + f*x))^m,x)","\int {\left(a+\frac{b}{\sin\left(e+f\,x\right)}\right)}^m \,d x","Not used",0,"int((a + b/sin(e + f*x))^m, x)","F"
58,0,-1,22,0.000000,"\text{Not used}","int(sin(e + f*x)*(a + b/sin(e + f*x))^m,x)","\int \sin\left(e+f\,x\right)\,{\left(a+\frac{b}{\sin\left(e+f\,x\right)}\right)}^m \,d x","Not used",0,"int(sin(e + f*x)*(a + b/sin(e + f*x))^m, x)","F"
59,0,-1,24,0.000000,"\text{Not used}","int(sin(e + f*x)^2*(a + b/sin(e + f*x))^m,x)","\int {\sin\left(e+f\,x\right)}^2\,{\left(a+\frac{b}{\sin\left(e+f\,x\right)}\right)}^m \,d x","Not used",0,"int(sin(e + f*x)^2*(a + b/sin(e + f*x))^m, x)","F"