1,0,-1,53,0.000000,"\text{Not used}","int((a*sin(x)^2)^(5/2),x)","\int {\left(a\,{\sin\left(x\right)}^2\right)}^{5/2} \,d x","Not used",1,"int((a*sin(x)^2)^(5/2), x)","F"
2,0,-1,34,0.000000,"\text{Not used}","int((a*sin(x)^2)^(3/2),x)","\int {\left(a\,{\sin\left(x\right)}^2\right)}^{3/2} \,d x","Not used",1,"int((a*sin(x)^2)^(3/2), x)","F"
3,1,40,14,13.637784,"\text{Not used}","int((a*sin(x)^2)^(1/2),x)","-\frac{\sqrt{2}\,\sqrt{a}\,\sqrt{2\,{\sin\left(x\right)}^2}\,\left(-{\sin\left(x\right)}^2+\frac{\sin\left(2\,x\right)\,1{}\mathrm{i}}{2}+1\right)}{{\sin\left(x\right)}^2\,2{}\mathrm{i}+\sin\left(2\,x\right)}","Not used",1,"-(2^(1/2)*a^(1/2)*(2*sin(x)^2)^(1/2)*((sin(2*x)*1i)/2 - sin(x)^2 + 1))/(sin(2*x) + sin(x)^2*2i)","B"
4,0,-1,17,0.000000,"\text{Not used}","int(1/(a*sin(x)^2)^(1/2),x)","\int \frac{1}{\sqrt{a\,{\sin\left(x\right)}^2}} \,d x","Not used",1,"int(1/(a*sin(x)^2)^(1/2), x)","F"
5,0,-1,42,0.000000,"\text{Not used}","int(1/(a*sin(x)^2)^(3/2),x)","\int \frac{1}{{\left(a\,{\sin\left(x\right)}^2\right)}^{3/2}} \,d x","Not used",1,"int(1/(a*sin(x)^2)^(3/2), x)","F"
6,0,-1,61,0.000000,"\text{Not used}","int(1/(a*sin(x)^2)^(5/2),x)","\int \frac{1}{{\left(a\,{\sin\left(x\right)}^2\right)}^{5/2}} \,d x","Not used",1,"int(1/(a*sin(x)^2)^(5/2), x)","F"
7,0,-1,123,0.000000,"\text{Not used}","int((a*sin(x)^3)^(5/2),x)","\int {\left(a\,{\sin\left(x\right)}^3\right)}^{5/2} \,d x","Not used",1,"int((a*sin(x)^3)^(5/2), x)","F"
8,0,-1,73,0.000000,"\text{Not used}","int((a*sin(x)^3)^(3/2),x)","\int {\left(a\,{\sin\left(x\right)}^3\right)}^{3/2} \,d x","Not used",1,"int((a*sin(x)^3)^(3/2), x)","F"
9,0,-1,50,0.000000,"\text{Not used}","int((a*sin(x)^3)^(1/2),x)","\int \sqrt{a\,{\sin\left(x\right)}^3} \,d x","Not used",1,"int((a*sin(x)^3)^(1/2), x)","F"
10,0,-1,48,0.000000,"\text{Not used}","int(1/(a*sin(x)^3)^(1/2),x)","\int \frac{1}{\sqrt{a\,{\sin\left(x\right)}^3}} \,d x","Not used",1,"int(1/(a*sin(x)^3)^(1/2), x)","F"
11,0,-1,77,0.000000,"\text{Not used}","int(1/(a*sin(x)^3)^(3/2),x)","\int \frac{1}{{\left(a\,{\sin\left(x\right)}^3\right)}^{3/2}} \,d x","Not used",1,"int(1/(a*sin(x)^3)^(3/2), x)","F"
12,0,-1,123,0.000000,"\text{Not used}","int(1/(a*sin(x)^3)^(5/2),x)","\int \frac{1}{{\left(a\,{\sin\left(x\right)}^3\right)}^{5/2}} \,d x","Not used",1,"int(1/(a*sin(x)^3)^(5/2), x)","F"
13,0,-1,132,0.000000,"\text{Not used}","int((a*sin(x)^4)^(5/2),x)","\int {\left(a\,{\sin\left(x\right)}^4\right)}^{5/2} \,d x","Not used",1,"int((a*sin(x)^4)^(5/2), x)","F"
14,0,-1,78,0.000000,"\text{Not used}","int((a*sin(x)^4)^(3/2),x)","\int {\left(a\,{\sin\left(x\right)}^4\right)}^{3/2} \,d x","Not used",1,"int((a*sin(x)^4)^(3/2), x)","F"
15,0,-1,36,0.000000,"\text{Not used}","int((a*sin(x)^4)^(1/2),x)","\int \sqrt{a\,{\sin\left(x\right)}^4} \,d x","Not used",1,"int((a*sin(x)^4)^(1/2), x)","F"
16,1,7,16,13.712005,"\text{Not used}","int(1/(a*sin(x)^4)^(1/2),x)","-\frac{\mathrm{cot}\left(x\right)}{\sqrt{a}}","Not used",1,"-cot(x)/a^(1/2)","B"
17,1,44,68,14.279367,"\text{Not used}","int(1/(a*sin(x)^4)^(3/2),x)","\frac{\frac{8{}\mathrm{i}}{15\,a^{3/2}}-\frac{4\,\left(2\,{\sin\left(2\,x\right)}^3-9\,\sin\left(2\,x\right)+3\,\sin\left(4\,x\right)+2{}\mathrm{i}\right)}{15\,a^{3/2}}}{{\left(\cos\left(2\,x\right)-1\right)}^3}","Not used",1,"(8i/(15*a^(3/2)) - (4*(3*sin(4*x) - 9*sin(2*x) + 2*sin(2*x)^3 + 2i))/(15*a^(3/2)))/(cos(2*x) - 1)^3","B"
18,1,117,118,16.558332,"\text{Not used}","int(1/(a*sin(x)^4)^(5/2),x)","\frac{256\,\left({\mathrm{e}}^{x\,46{}\mathrm{i}}\,1{}\mathrm{i}-{\mathrm{e}}^{x\,48{}\mathrm{i}}\,9{}\mathrm{i}+{\mathrm{e}}^{x\,50{}\mathrm{i}}\,36{}\mathrm{i}-{\mathrm{e}}^{x\,52{}\mathrm{i}}\,84{}\mathrm{i}+{\mathrm{e}}^{x\,54{}\mathrm{i}}\,126{}\mathrm{i}\right)}{315\,a^{5/2}\,\left({\mathrm{e}}^{x\,46{}\mathrm{i}}-9\,{\mathrm{e}}^{x\,48{}\mathrm{i}}+36\,{\mathrm{e}}^{x\,50{}\mathrm{i}}-84\,{\mathrm{e}}^{x\,52{}\mathrm{i}}+126\,{\mathrm{e}}^{x\,54{}\mathrm{i}}-126\,{\mathrm{e}}^{x\,56{}\mathrm{i}}+84\,{\mathrm{e}}^{x\,58{}\mathrm{i}}-36\,{\mathrm{e}}^{x\,60{}\mathrm{i}}+9\,{\mathrm{e}}^{x\,62{}\mathrm{i}}-{\mathrm{e}}^{x\,64{}\mathrm{i}}\right)}","Not used",1,"(256*(exp(x*46i)*1i - exp(x*48i)*9i + exp(x*50i)*36i - exp(x*52i)*84i + exp(x*54i)*126i))/(315*a^(5/2)*(exp(x*46i) - 9*exp(x*48i) + 36*exp(x*50i) - 84*exp(x*52i) + 126*exp(x*54i) - 126*exp(x*56i) + 84*exp(x*58i) - 36*exp(x*60i) + 9*exp(x*62i) - exp(x*64i)))","B"
19,0,-1,89,0.000000,"\text{Not used}","int((c*sin(a + b*x)^m)^(5/2),x)","\int {\left(c\,{\sin\left(a+b\,x\right)}^m\right)}^{5/2} \,d x","Not used",1,"int((c*sin(a + b*x)^m)^(5/2), x)","F"
20,0,-1,83,0.000000,"\text{Not used}","int((c*sin(a + b*x)^m)^(3/2),x)","\int {\left(c\,{\sin\left(a+b\,x\right)}^m\right)}^{3/2} \,d x","Not used",1,"int((c*sin(a + b*x)^m)^(3/2), x)","F"
21,0,-1,74,0.000000,"\text{Not used}","int((c*sin(a + b*x)^m)^(1/2),x)","\int \sqrt{c\,{\sin\left(a+b\,x\right)}^m} \,d x","Not used",1,"int((c*sin(a + b*x)^m)^(1/2), x)","F"
22,0,-1,80,0.000000,"\text{Not used}","int(1/(c*sin(a + b*x)^m)^(1/2),x)","\int \frac{1}{\sqrt{c\,{\sin\left(a+b\,x\right)}^m}} \,d x","Not used",1,"int(1/(c*sin(a + b*x)^m)^(1/2), x)","F"
23,0,-1,89,0.000000,"\text{Not used}","int(1/(c*sin(a + b*x)^m)^(3/2),x)","\int \frac{1}{{\left(c\,{\sin\left(a+b\,x\right)}^m\right)}^{3/2}} \,d x","Not used",1,"int(1/(c*sin(a + b*x)^m)^(3/2), x)","F"
24,0,-1,89,0.000000,"\text{Not used}","int(1/(c*sin(a + b*x)^m)^(5/2),x)","\int \frac{1}{{\left(c\,{\sin\left(a+b\,x\right)}^m\right)}^{5/2}} \,d x","Not used",1,"int(1/(c*sin(a + b*x)^m)^(5/2), x)","F"
25,0,-1,77,0.000000,"\text{Not used}","int((b*sin(c + d*x)^n)^p,x)","\int {\left(b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",1,"int((b*sin(c + d*x)^n)^p, x)","F"
26,0,-1,77,0.000000,"\text{Not used}","int((c*sin(a + b*x)^2)^p,x)","\int {\left(c\,{\sin\left(a+b\,x\right)}^2\right)}^p \,d x","Not used",1,"int((c*sin(a + b*x)^2)^p, x)","F"
27,0,-1,75,0.000000,"\text{Not used}","int((c*sin(a + b*x)^3)^p,x)","\int {\left(c\,{\sin\left(a+b\,x\right)}^3\right)}^p \,d x","Not used",1,"int((c*sin(a + b*x)^3)^p, x)","F"
28,0,-1,77,0.000000,"\text{Not used}","int((c*sin(a + b*x)^4)^p,x)","\int {\left(c\,{\sin\left(a+b\,x\right)}^4\right)}^p \,d x","Not used",1,"int((c*sin(a + b*x)^4)^p, x)","F"
29,1,36,25,13.747890,"\text{Not used}","int((c*sin(a + b*x)^n)^(1/n),x)","-\frac{\sin\left(2\,a+2\,b\,x\right)\,{\left(c\,{\sin\left(a+b\,x\right)}^n\right)}^{1/n}}{2\,b\,{\sin\left(a+b\,x\right)}^2}","Not used",1,"-(sin(2*a + 2*b*x)*(c*sin(a + b*x)^n)^(1/n))/(2*b*sin(a + b*x)^2)","B"
30,0,-1,79,0.000000,"\text{Not used}","int((a*(b*sin(c + d*x))^p)^n,x)","\int {\left(a\,{\left(b\,\sin\left(c+d\,x\right)\right)}^p\right)}^n \,d x","Not used",1,"int((a*(b*sin(c + d*x))^p)^n, x)","F"
31,1,11,16,13.575442,"\text{Not used}","int(a - a*sin(x)^2,x)","\frac{a\,\left(2\,x+\sin\left(2\,x\right)\right)}{4}","Not used",1,"(a*(2*x + sin(2*x)))/4","B"
32,1,33,33,13.762424,"\text{Not used}","int((a - a*sin(x)^2)^2,x)","\frac{\frac{3\,a^2\,{\mathrm{tan}\left(x\right)}^3}{8}+\frac{5\,a^2\,\mathrm{tan}\left(x\right)}{8}}{{\left({\mathrm{tan}\left(x\right)}^2+1\right)}^2}+\frac{3\,a^2\,x}{8}","Not used",1,"((5*a^2*tan(x))/8 + (3*a^2*tan(x)^3)/8)/(tan(x)^2 + 1)^2 + (3*a^2*x)/8","B"
33,1,42,46,13.684705,"\text{Not used}","int((a - a*sin(x)^2)^3,x)","\frac{11\,a^3\,{\cos\left(x\right)}^5\,\sin\left(x\right)}{16}+\frac{5\,a^3\,{\cos\left(x\right)}^3\,{\sin\left(x\right)}^3}{6}+\frac{5\,a^3\,\cos\left(x\right)\,{\sin\left(x\right)}^5}{16}+\frac{5\,x\,a^3}{16}","Not used",1,"(5*a^3*x)/16 + (5*a^3*cos(x)*sin(x)^5)/16 + (11*a^3*cos(x)^5*sin(x))/16 + (5*a^3*cos(x)^3*sin(x)^3)/6","B"
34,1,51,59,13.693812,"\text{Not used}","int((a - a*sin(x)^2)^4,x)","\frac{\frac{35\,a^4\,{\mathrm{tan}\left(x\right)}^7}{128}+\frac{385\,a^4\,{\mathrm{tan}\left(x\right)}^5}{384}+\frac{511\,a^4\,{\mathrm{tan}\left(x\right)}^3}{384}+\frac{93\,a^4\,\mathrm{tan}\left(x\right)}{128}}{{\left({\mathrm{tan}\left(x\right)}^2+1\right)}^4}+\frac{35\,a^4\,x}{128}","Not used",1,"((93*a^4*tan(x))/128 + (511*a^4*tan(x)^3)/384 + (385*a^4*tan(x)^5)/384 + (35*a^4*tan(x)^7)/128)/(tan(x)^2 + 1)^4 + (35*a^4*x)/128","B"
35,1,54,62,13.648347,"\text{Not used}","int(sin(c + d*x)^7/(a - a*sin(c + d*x)^2),x)","\frac{\frac{3\,\cos\left(c+d\,x\right)}{a}+\frac{1}{a\,\cos\left(c+d\,x\right)}-\frac{{\cos\left(c+d\,x\right)}^3}{a}+\frac{{\cos\left(c+d\,x\right)}^5}{5\,a}}{d}","Not used",1,"((3*cos(c + d*x))/a + 1/(a*cos(c + d*x)) - cos(c + d*x)^3/a + cos(c + d*x)^5/(5*a))/d","B"
36,1,38,46,0.056830,"\text{Not used}","int(sin(c + d*x)^5/(a - a*sin(c + d*x)^2),x)","\frac{-{\cos\left(c+d\,x\right)}^4+6\,{\cos\left(c+d\,x\right)}^2+3}{3\,a\,d\,\cos\left(c+d\,x\right)}","Not used",1,"(6*cos(c + d*x)^2 - cos(c + d*x)^4 + 3)/(3*a*d*cos(c + d*x))","B"
37,1,25,27,0.044649,"\text{Not used}","int(sin(c + d*x)^3/(a - a*sin(c + d*x)^2),x)","\frac{{\cos\left(c+d\,x\right)}^2+1}{a\,d\,\cos\left(c+d\,x\right)}","Not used",1,"(cos(c + d*x)^2 + 1)/(a*d*cos(c + d*x))","B"
38,1,15,13,13.601326,"\text{Not used}","int(sin(c + d*x)/(a - a*sin(c + d*x)^2),x)","\frac{1}{a\,d\,\cos\left(c+d\,x\right)}","Not used",1,"1/(a*d*cos(c + d*x))","B"
39,1,31,29,0.084422,"\text{Not used}","int(1/(sin(c + d*x)*(a - a*sin(c + d*x)^2)),x)","\frac{1}{a\,d\,\cos\left(c+d\,x\right)}-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{a\,d}","Not used",1,"1/(a*d*cos(c + d*x)) - atanh(cos(c + d*x))/(a*d)","B"
40,1,55,58,0.087619,"\text{Not used}","int(1/(sin(c + d*x)^3*(a - a*sin(c + d*x)^2)),x)","-\frac{\frac{3\,{\cos\left(c+d\,x\right)}^2}{2}-1}{d\,\left(a\,\cos\left(c+d\,x\right)-a\,{\cos\left(c+d\,x\right)}^3\right)}-\frac{3\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{2\,a\,d}","Not used",1,"- ((3*cos(c + d*x)^2)/2 - 1)/(d*(a*cos(c + d*x) - a*cos(c + d*x)^3)) - (3*atanh(cos(c + d*x)))/(2*a*d)","B"
41,1,74,82,0.096096,"\text{Not used}","int(1/(sin(c + d*x)^5*(a - a*sin(c + d*x)^2)),x)","\frac{\frac{15\,{\cos\left(c+d\,x\right)}^4}{8}-\frac{25\,{\cos\left(c+d\,x\right)}^2}{8}+1}{d\,\left(a\,{\cos\left(c+d\,x\right)}^5-2\,a\,{\cos\left(c+d\,x\right)}^3+a\,\cos\left(c+d\,x\right)\right)}-\frac{15\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{8\,a\,d}","Not used",1,"((15*cos(c + d*x)^4)/8 - (25*cos(c + d*x)^2)/8 + 1)/(d*(a*cos(c + d*x) - 2*a*cos(c + d*x)^3 + a*cos(c + d*x)^5)) - (15*atanh(cos(c + d*x)))/(8*a*d)","B"
42,1,68,73,13.717736,"\text{Not used}","int(sin(c + d*x)^6/(a - a*sin(c + d*x)^2),x)","\frac{\mathrm{tan}\left(c+d\,x\right)}{a\,d}-\frac{15\,x}{8\,a}+\frac{\frac{9\,{\mathrm{tan}\left(c+d\,x\right)}^3}{8}+\frac{7\,\mathrm{tan}\left(c+d\,x\right)}{8}}{d\,\left(a\,{\mathrm{tan}\left(c+d\,x\right)}^4+2\,a\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}","Not used",1,"tan(c + d*x)/(a*d) - (15*x)/(8*a) + ((7*tan(c + d*x))/8 + (9*tan(c + d*x)^3)/8)/(d*(a + 2*a*tan(c + d*x)^2 + a*tan(c + d*x)^4))","B"
43,1,45,49,13.532115,"\text{Not used}","int(sin(c + d*x)^4/(a - a*sin(c + d*x)^2),x)","\frac{\mathrm{tan}\left(c+d\,x\right)}{2\,d\,\left(a\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}-\frac{3\,x}{2\,a}+\frac{\mathrm{tan}\left(c+d\,x\right)}{a\,d}","Not used",1,"tan(c + d*x)/(2*d*(a + a*tan(c + d*x)^2)) - (3*x)/(2*a) + tan(c + d*x)/(a*d)","B"
44,1,20,20,13.736966,"\text{Not used}","int(sin(c + d*x)^2/(a - a*sin(c + d*x)^2),x)","\frac{\mathrm{tan}\left(c+d\,x\right)}{a\,d}-\frac{x}{a}","Not used",1,"tan(c + d*x)/(a*d) - x/a","B"
45,1,13,13,13.594681,"\text{Not used}","int(1/(a - a*sin(c + d*x)^2),x)","\frac{\mathrm{tan}\left(c+d\,x\right)}{a\,d}","Not used",1,"tan(c + d*x)/(a*d)","B"
46,1,17,28,13.504475,"\text{Not used}","int(1/(sin(c + d*x)^2*(a - a*sin(c + d*x)^2)),x)","-\frac{2\,\mathrm{cot}\left(2\,c+2\,d\,x\right)}{a\,d}","Not used",1,"-(2*cot(2*c + 2*d*x))/(a*d)","B"
47,1,38,46,13.726760,"\text{Not used}","int(1/(sin(c + d*x)^4*(a - a*sin(c + d*x)^2)),x)","-\frac{-{\mathrm{tan}\left(c+d\,x\right)}^4+2\,{\mathrm{tan}\left(c+d\,x\right)}^2+\frac{1}{3}}{a\,d\,{\mathrm{tan}\left(c+d\,x\right)}^3}","Not used",1,"-(2*tan(c + d*x)^2 - tan(c + d*x)^4 + 1/3)/(a*d*tan(c + d*x)^3)","B"
48,1,50,62,13.955468,"\text{Not used}","int(1/(sin(c + d*x)^6*(a - a*sin(c + d*x)^2)),x)","\frac{\mathrm{tan}\left(c+d\,x\right)}{a\,d}-\frac{3\,{\mathrm{tan}\left(c+d\,x\right)}^4+{\mathrm{tan}\left(c+d\,x\right)}^2+\frac{1}{5}}{a\,d\,{\mathrm{tan}\left(c+d\,x\right)}^5}","Not used",1,"tan(c + d*x)/(a*d) - (tan(c + d*x)^2 + 3*tan(c + d*x)^4 + 1/5)/(a*d*tan(c + d*x)^5)","B"
49,1,48,65,13.642697,"\text{Not used}","int(sin(c + d*x)^7/(a - a*sin(c + d*x)^2)^2,x)","-\frac{-{\cos\left(c+d\,x\right)}^6+9\,{\cos\left(c+d\,x\right)}^4+9\,{\cos\left(c+d\,x\right)}^2-1}{3\,a^2\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"-(9*cos(c + d*x)^2 + 9*cos(c + d*x)^4 - cos(c + d*x)^6 - 1)/(3*a^2*d*cos(c + d*x)^3)","B"
50,1,36,47,0.054229,"\text{Not used}","int(sin(c + d*x)^5/(a - a*sin(c + d*x)^2)^2,x)","-\frac{{\cos\left(c+d\,x\right)}^4+2\,{\cos\left(c+d\,x\right)}^2-\frac{1}{3}}{a^2\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"-(2*cos(c + d*x)^2 + cos(c + d*x)^4 - 1/3)/(a^2*d*cos(c + d*x)^3)","B"
51,1,26,33,13.556681,"\text{Not used}","int(sin(c + d*x)^3/(a - a*sin(c + d*x)^2)^2,x)","-\frac{{\cos\left(c+d\,x\right)}^2-\frac{1}{3}}{a^2\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"-(cos(c + d*x)^2 - 1/3)/(a^2*d*cos(c + d*x)^3)","B"
52,1,16,18,13.588035,"\text{Not used}","int(sin(c + d*x)/(a - a*sin(c + d*x)^2)^2,x)","\frac{1}{3\,a^2\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"1/(3*a^2*d*cos(c + d*x)^3)","B"
53,1,41,47,0.088243,"\text{Not used}","int(1/(sin(c + d*x)*(a - a*sin(c + d*x)^2)^2),x)","\frac{{\cos\left(c+d\,x\right)}^2+\frac{1}{3}}{a^2\,d\,{\cos\left(c+d\,x\right)}^3}-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{a^2\,d}","Not used",1,"(cos(c + d*x)^2 + 1/3)/(a^2*d*cos(c + d*x)^3) - atanh(cos(c + d*x))/(a^2*d)","B"
54,1,70,78,13.760553,"\text{Not used}","int(1/(sin(c + d*x)^3*(a - a*sin(c + d*x)^2)^2),x)","\frac{-\frac{5\,{\cos\left(c+d\,x\right)}^4}{2}+\frac{5\,{\cos\left(c+d\,x\right)}^2}{3}+\frac{1}{3}}{d\,\left(a^2\,{\cos\left(c+d\,x\right)}^3-a^2\,{\cos\left(c+d\,x\right)}^5\right)}-\frac{5\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{2\,a^2\,d}","Not used",1,"((5*cos(c + d*x)^2)/3 - (5*cos(c + d*x)^4)/2 + 1/3)/(d*(a^2*cos(c + d*x)^3 - a^2*cos(c + d*x)^5)) - (5*atanh(cos(c + d*x)))/(2*a^2*d)","B"
55,1,66,69,13.808360,"\text{Not used}","int(sin(c + d*x)^6/(a - a*sin(c + d*x)^2)^2,x)","\frac{5\,x}{2\,a^2}-\frac{\mathrm{tan}\left(c+d\,x\right)}{2\,d\,\left(a^2\,{\mathrm{tan}\left(c+d\,x\right)}^2+a^2\right)}-\frac{2\,\mathrm{tan}\left(c+d\,x\right)}{a^2\,d}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{3\,a^2\,d}","Not used",1,"(5*x)/(2*a^2) - tan(c + d*x)/(2*d*(a^2 + a^2*tan(c + d*x)^2)) - (2*tan(c + d*x))/(a^2*d) + tan(c + d*x)^3/(3*a^2*d)","B"
56,1,31,38,13.479150,"\text{Not used}","int(sin(c + d*x)^4/(a - a*sin(c + d*x)^2)^2,x)","\frac{x}{a^2}-\frac{\mathrm{tan}\left(c+d\,x\right)-\frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{3}}{a^2\,d}","Not used",1,"x/a^2 - (tan(c + d*x) - tan(c + d*x)^3/3)/(a^2*d)","B"
57,1,16,18,13.376298,"\text{Not used}","int(sin(c + d*x)^2/(a - a*sin(c + d*x)^2)^2,x)","\frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{3\,a^2\,d}","Not used",1,"tan(c + d*x)^3/(3*a^2*d)","B"
58,1,24,32,13.454633,"\text{Not used}","int(1/(a - a*sin(c + d*x)^2)^2,x)","\frac{\mathrm{tan}\left(c+d\,x\right)\,\left({\mathrm{tan}\left(c+d\,x\right)}^2+3\right)}{3\,a^2\,d}","Not used",1,"(tan(c + d*x)*(tan(c + d*x)^2 + 3))/(3*a^2*d)","B"
59,1,36,47,13.575034,"\text{Not used}","int(1/(sin(c + d*x)^2*(a - a*sin(c + d*x)^2)^2),x)","\frac{{\mathrm{tan}\left(c+d\,x\right)}^4+6\,{\mathrm{tan}\left(c+d\,x\right)}^2-3}{3\,a^2\,d\,\mathrm{tan}\left(c+d\,x\right)}","Not used",1,"(6*tan(c + d*x)^2 + tan(c + d*x)^4 - 3)/(3*a^2*d*tan(c + d*x))","B"
60,1,48,65,13.681780,"\text{Not used}","int(1/(sin(c + d*x)^4*(a - a*sin(c + d*x)^2)^2),x)","-\frac{-{\mathrm{tan}\left(c+d\,x\right)}^6-9\,{\mathrm{tan}\left(c+d\,x\right)}^4+9\,{\mathrm{tan}\left(c+d\,x\right)}^2+1}{3\,a^2\,d\,{\mathrm{tan}\left(c+d\,x\right)}^3}","Not used",1,"-(9*tan(c + d*x)^2 - 9*tan(c + d*x)^4 - tan(c + d*x)^6 + 1)/(3*a^2*d*tan(c + d*x)^3)","B"
61,1,21,29,13.410402,"\text{Not used}","int(1/(a - a*sin(x)^2)^3,x)","\frac{\mathrm{tan}\left(x\right)\,\left(3\,{\mathrm{tan}\left(x\right)}^4+10\,{\mathrm{tan}\left(x\right)}^2+15\right)}{15\,a^3}","Not used",1,"(tan(x)*(10*tan(x)^2 + 3*tan(x)^4 + 15))/(15*a^3)","B"
62,1,33,37,13.407617,"\text{Not used}","int(1/(a - a*sin(x)^2)^4,x)","\frac{\mathrm{tan}\left(x\right)}{a^4}+\frac{{\mathrm{tan}\left(x\right)}^3}{a^4}+\frac{3\,{\mathrm{tan}\left(x\right)}^5}{5\,a^4}+\frac{{\mathrm{tan}\left(x\right)}^7}{7\,a^4}","Not used",1,"tan(x)/a^4 + tan(x)^3/a^4 + (3*tan(x)^5)/(5*a^4) + tan(x)^7/(7*a^4)","B"
63,1,43,51,13.344734,"\text{Not used}","int(1/(a - a*sin(x)^2)^5,x)","\frac{\mathrm{tan}\left(x\right)}{a^5}+\frac{4\,{\mathrm{tan}\left(x\right)}^3}{3\,a^5}+\frac{6\,{\mathrm{tan}\left(x\right)}^5}{5\,a^5}+\frac{4\,{\mathrm{tan}\left(x\right)}^7}{7\,a^5}+\frac{{\mathrm{tan}\left(x\right)}^9}{9\,a^5}","Not used",1,"tan(x)/a^5 + (4*tan(x)^3)/(3*a^5) + (6*tan(x)^5)/(5*a^5) + (4*tan(x)^7)/(7*a^5) + tan(x)^9/(9*a^5)","B"
64,1,44,51,13.365942,"\text{Not used}","int(sin(c + d*x)^3*(a + b*sin(c + d*x)^2),x)","-\frac{\frac{b\,{\cos\left(c+d\,x\right)}^5}{5}+\left(-\frac{a}{3}-\frac{2\,b}{3}\right)\,{\cos\left(c+d\,x\right)}^3+\left(a+b\right)\,\cos\left(c+d\,x\right)}{d}","Not used",1,"-((b*cos(c + d*x)^5)/5 - cos(c + d*x)^3*(a/3 + (2*b)/3) + cos(c + d*x)*(a + b))/d","B"
65,1,27,31,13.313328,"\text{Not used}","int(sin(c + d*x)*(a + b*sin(c + d*x)^2),x)","\frac{\frac{b\,{\cos\left(c+d\,x\right)}^3}{3}-\cos\left(c+d\,x\right)\,\left(a+b\right)}{d}","Not used",1,"((b*cos(c + d*x)^3)/3 - cos(c + d*x)*(a + b))/d","B"
66,1,23,26,13.365529,"\text{Not used}","int((a + b*sin(c + d*x)^2)/sin(c + d*x),x)","-\frac{b\,\cos\left(c+d\,x\right)+a\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(b*cos(c + d*x) + a*atanh(cos(c + d*x)))/d","B"
67,1,42,40,13.388444,"\text{Not used}","int((a + b*sin(c + d*x)^2)/sin(c + d*x)^3,x)","\frac{a\,\cos\left(c+d\,x\right)}{2\,d\,\left({\cos\left(c+d\,x\right)}^2-1\right)}-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)\,\left(\frac{a}{2}+b\right)}{d}","Not used",1,"(a*cos(c + d*x))/(2*d*(cos(c + d*x)^2 - 1)) - (atanh(cos(c + d*x))*(a/2 + b))/d","B"
68,1,92,89,13.944385,"\text{Not used}","int(sin(c + d*x)^4*(a + b*sin(c + d*x)^2),x)","x\,\left(\frac{3\,a}{8}+\frac{5\,b}{16}\right)-\frac{\left(\frac{5\,a}{8}+\frac{11\,b}{16}\right)\,{\mathrm{tan}\left(c+d\,x\right)}^5+\left(a+\frac{5\,b}{6}\right)\,{\mathrm{tan}\left(c+d\,x\right)}^3+\left(\frac{3\,a}{8}+\frac{5\,b}{16}\right)\,\mathrm{tan}\left(c+d\,x\right)}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^6+3\,{\mathrm{tan}\left(c+d\,x\right)}^4+3\,{\mathrm{tan}\left(c+d\,x\right)}^2+1\right)}","Not used",1,"x*((3*a)/8 + (5*b)/16) - (tan(c + d*x)^5*((5*a)/8 + (11*b)/16) + tan(c + d*x)*((3*a)/8 + (5*b)/16) + tan(c + d*x)^3*(a + (5*b)/6))/(d*(3*tan(c + d*x)^2 + 3*tan(c + d*x)^4 + tan(c + d*x)^6 + 1))","B"
69,1,68,61,13.545469,"\text{Not used}","int(sin(c + d*x)^2*(a + b*sin(c + d*x)^2),x)","x\,\left(\frac{a}{2}+\frac{3\,b}{8}\right)-\frac{\left(\frac{a}{2}+\frac{5\,b}{8}\right)\,{\mathrm{tan}\left(c+d\,x\right)}^3+\left(\frac{a}{2}+\frac{3\,b}{8}\right)\,\mathrm{tan}\left(c+d\,x\right)}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4+2\,{\mathrm{tan}\left(c+d\,x\right)}^2+1\right)}","Not used",1,"x*(a/2 + (3*b)/8) - (tan(c + d*x)^3*(a/2 + (5*b)/8) + tan(c + d*x)*(a/2 + (3*b)/8))/(d*(2*tan(c + d*x)^2 + tan(c + d*x)^4 + 1))","B"
70,1,27,30,13.400746,"\text{Not used}","int(a + b*sin(c + d*x)^2,x)","-\frac{\frac{b\,\sin\left(2\,c+2\,d\,x\right)}{4}-d\,x\,\left(a+\frac{b}{2}\right)}{d}","Not used",1,"-((b*sin(2*c + 2*d*x))/4 - d*x*(a + b/2))/d","B"
71,1,16,16,13.356959,"\text{Not used}","int((a + b*sin(c + d*x)^2)/sin(c + d*x)^2,x)","b\,x-\frac{a\,\mathrm{cot}\left(c+d\,x\right)}{d}","Not used",1,"b*x - (a*cot(c + d*x))/d","B"
72,1,29,43,13.368083,"\text{Not used}","int((a + b*sin(c + d*x)^2)/sin(c + d*x)^4,x)","-\frac{a\,{\mathrm{cot}\left(c+d\,x\right)}^3}{3\,d}-\frac{\mathrm{cot}\left(c+d\,x\right)\,\left(a+b\right)}{d}","Not used",1,"- (a*cot(c + d*x)^3)/(3*d) - (cot(c + d*x)*(a + b))/d","B"
73,1,49,65,13.383413,"\text{Not used}","int((a + b*sin(c + d*x)^2)/sin(c + d*x)^6,x)","-\frac{a\,{\mathrm{cot}\left(c+d\,x\right)}^5}{5\,d}-\frac{\mathrm{cot}\left(c+d\,x\right)\,\left(a+b\right)}{d}-\frac{{\mathrm{cot}\left(c+d\,x\right)}^3\,\left(\frac{2\,a}{3}+\frac{b}{3}\right)}{d}","Not used",1,"- (a*cot(c + d*x)^5)/(5*d) - (cot(c + d*x)*(a + b))/d - (cot(c + d*x)^3*((2*a)/3 + b/3))/d","B"
74,1,15,19,13.310358,"\text{Not used}","int(a + b*sin(x)^2,x)","x\,\left(a+\frac{b}{2}\right)-\frac{b\,\sin\left(2\,x\right)}{4}","Not used",1,"x*(a + b/2) - (b*sin(2*x))/4","B"
75,1,44,50,13.520689,"\text{Not used}","int((a + b*sin(x)^2)^2,x)","x\,a^2-\sin\left(x\right)\,a\,b\,\cos\left(x\right)+x\,a\,b+\frac{\sin\left(x\right)\,b^2\,{\cos\left(x\right)}^3}{4}-\frac{5\,\sin\left(x\right)\,b^2\,\cos\left(x\right)}{8}+\frac{3\,x\,b^2}{8}","Not used",1,"a^2*x + (3*b^2*x)/8 + (b^2*cos(x)^3*sin(x))/4 + a*b*x - (5*b^2*cos(x)*sin(x))/8 - a*b*cos(x)*sin(x)","B"
76,1,118,87,14.129344,"\text{Not used}","int((a + b*sin(x)^2)^3,x)","a^3\,x+\frac{5\,b^3\,x}{16}-\frac{\left(72\,a^2\,b+90\,a\,b^2+33\,b^3\right)\,{\mathrm{tan}\left(x\right)}^5+\left(144\,a^2\,b+144\,a\,b^2+40\,b^3\right)\,{\mathrm{tan}\left(x\right)}^3+\left(72\,a^2\,b+54\,a\,b^2+15\,b^3\right)\,\mathrm{tan}\left(x\right)}{48\,{\mathrm{tan}\left(x\right)}^6+144\,{\mathrm{tan}\left(x\right)}^4+144\,{\mathrm{tan}\left(x\right)}^2+48}+\frac{9\,a\,b^2\,x}{8}+\frac{3\,a^2\,b\,x}{2}","Not used",1,"a^3*x + (5*b^3*x)/16 - (tan(x)^5*(90*a*b^2 + 72*a^2*b + 33*b^3) + tan(x)^3*(144*a*b^2 + 144*a^2*b + 40*b^3) + tan(x)*(54*a*b^2 + 72*a^2*b + 15*b^3))/(144*tan(x)^2 + 144*tan(x)^4 + 48*tan(x)^6 + 48) + (9*a*b^2*x)/8 + (3*a^2*b*x)/2","B"
77,1,147,140,13.631790,"\text{Not used}","int((a + b*sin(x)^2)^4,x)","x\,a^4-2\,\sin\left(x\right)\,a^3\,b\,\cos\left(x\right)+2\,x\,a^3\,b+\frac{3\,\sin\left(x\right)\,a^2\,b^2\,{\cos\left(x\right)}^3}{2}-\frac{15\,\sin\left(x\right)\,a^2\,b^2\,\cos\left(x\right)}{4}+\frac{9\,x\,a^2\,b^2}{4}-\frac{2\,\sin\left(x\right)\,a\,b^3\,{\cos\left(x\right)}^5}{3}+\frac{13\,\sin\left(x\right)\,a\,b^3\,{\cos\left(x\right)}^3}{6}-\frac{11\,\sin\left(x\right)\,a\,b^3\,\cos\left(x\right)}{4}+\frac{5\,x\,a\,b^3}{4}+\frac{\sin\left(x\right)\,b^4\,{\cos\left(x\right)}^7}{8}-\frac{25\,\sin\left(x\right)\,b^4\,{\cos\left(x\right)}^5}{48}+\frac{163\,\sin\left(x\right)\,b^4\,{\cos\left(x\right)}^3}{192}-\frac{93\,\sin\left(x\right)\,b^4\,\cos\left(x\right)}{128}+\frac{35\,x\,b^4}{128}","Not used",1,"a^4*x + (35*b^4*x)/128 + (163*b^4*cos(x)^3*sin(x))/192 - (25*b^4*cos(x)^5*sin(x))/48 + (b^4*cos(x)^7*sin(x))/8 + (9*a^2*b^2*x)/4 - (93*b^4*cos(x)*sin(x))/128 + (5*a*b^3*x)/4 + 2*a^3*b*x + (3*a^2*b^2*cos(x)^3*sin(x))/2 - (11*a*b^3*cos(x)*sin(x))/4 - 2*a^3*b*cos(x)*sin(x) - (15*a^2*b^2*cos(x)*sin(x))/4 + (13*a*b^3*cos(x)^3*sin(x))/6 - (2*a*b^3*cos(x)^5*sin(x))/3","B"
78,1,112,106,0.162580,"\text{Not used}","int(sin(c + d*x)^7/(a + b*sin(c + d*x)^2),x)","\frac{a^3\,\mathrm{atanh}\left(\frac{\sqrt{b}\,\cos\left(c+d\,x\right)}{\sqrt{a+b}}\right)}{b^{7/2}\,d\,\sqrt{a+b}}-\frac{{\cos\left(c+d\,x\right)}^5}{5\,b\,d}-\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{a+b}{3\,b^2}-\frac{1}{b}\right)}{d}-\frac{\cos\left(c+d\,x\right)\,\left(\frac{3}{b}+\frac{\left(a+b\right)\,\left(\frac{a+b}{b^2}-\frac{3}{b}\right)}{b}\right)}{d}","Not used",1,"(a^3*atanh((b^(1/2)*cos(c + d*x))/(a + b)^(1/2)))/(b^(7/2)*d*(a + b)^(1/2)) - cos(c + d*x)^5/(5*b*d) - (cos(c + d*x)^3*((a + b)/(3*b^2) - 1/b))/d - (cos(c + d*x)*(3/b + ((a + b)*((a + b)/b^2 - 3/b))/b))/d","B"
79,1,72,77,0.110070,"\text{Not used}","int(sin(c + d*x)^5/(a + b*sin(c + d*x)^2),x)","\frac{\cos\left(c+d\,x\right)\,\left(\frac{a+b}{b^2}-\frac{2}{b}\right)}{d}+\frac{{\cos\left(c+d\,x\right)}^3}{3\,b\,d}-\frac{a^2\,\mathrm{atanh}\left(\frac{\sqrt{b}\,\cos\left(c+d\,x\right)}{\sqrt{a+b}}\right)}{b^{5/2}\,d\,\sqrt{a+b}}","Not used",1,"(cos(c + d*x)*((a + b)/b^2 - 2/b))/d + cos(c + d*x)^3/(3*b*d) - (a^2*atanh((b^(1/2)*cos(c + d*x))/(a + b)^(1/2)))/(b^(5/2)*d*(a + b)^(1/2))","B"
80,1,44,52,0.096981,"\text{Not used}","int(sin(c + d*x)^3/(a + b*sin(c + d*x)^2),x)","\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{b}\,\cos\left(c+d\,x\right)}{\sqrt{a+b}}\right)}{b^{3/2}\,d\,\sqrt{a+b}}-\frac{\cos\left(c+d\,x\right)}{b\,d}","Not used",1,"(a*atanh((b^(1/2)*cos(c + d*x))/(a + b)^(1/2)))/(b^(3/2)*d*(a + b)^(1/2)) - cos(c + d*x)/(b*d)","B"
81,1,29,37,0.087089,"\text{Not used}","int(sin(c + d*x)/(a + b*sin(c + d*x)^2),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{b}\,\cos\left(c+d\,x\right)}{\sqrt{a+b}}\right)}{\sqrt{b}\,d\,\sqrt{a+b}}","Not used",1,"-atanh((b^(1/2)*cos(c + d*x))/(a + b)^(1/2))/(b^(1/2)*d*(a + b)^(1/2))","B"
82,1,457,55,13.726663,"\text{Not used}","int(1/(sin(c + d*x)*(a + b*sin(c + d*x)^2)),x)","-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{a\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,b^3\,\cos\left(c+d\,x\right)+\frac{\left(2\,a^2\,b^2-\frac{\cos\left(c+d\,x\right)\,\left(8\,a^3\,b^2+16\,a^2\,b^3\right)\,\sqrt{b\,\left(a+b\right)}}{4\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}\,1{}\mathrm{i}}{a^2+b\,a}+\frac{\left(2\,b^3\,\cos\left(c+d\,x\right)-\frac{\left(2\,a^2\,b^2+\frac{\cos\left(c+d\,x\right)\,\left(8\,a^3\,b^2+16\,a^2\,b^3\right)\,\sqrt{b\,\left(a+b\right)}}{4\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}\,1{}\mathrm{i}}{a^2+b\,a}}{\frac{\left(2\,b^3\,\cos\left(c+d\,x\right)+\frac{\left(2\,a^2\,b^2-\frac{\cos\left(c+d\,x\right)\,\left(8\,a^3\,b^2+16\,a^2\,b^3\right)\,\sqrt{b\,\left(a+b\right)}}{4\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{a^2+b\,a}-\frac{\left(2\,b^3\,\cos\left(c+d\,x\right)-\frac{\left(2\,a^2\,b^2+\frac{\cos\left(c+d\,x\right)\,\left(8\,a^3\,b^2+16\,a^2\,b^3\right)\,\sqrt{b\,\left(a+b\right)}}{4\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{a^2+b\,a}}\right)\,\sqrt{b\,\left(a+b\right)}\,1{}\mathrm{i}}{d\,\left(a^2+b\,a\right)}","Not used",1,"- atanh(cos(c + d*x))/(a*d) - (atan((((2*b^3*cos(c + d*x) + ((2*a^2*b^2 - (cos(c + d*x)*(16*a^2*b^3 + 8*a^3*b^2)*(b*(a + b))^(1/2))/(4*(a*b + a^2)))*(b*(a + b))^(1/2))/(2*(a*b + a^2)))*(b*(a + b))^(1/2)*1i)/(a*b + a^2) + ((2*b^3*cos(c + d*x) - ((2*a^2*b^2 + (cos(c + d*x)*(16*a^2*b^3 + 8*a^3*b^2)*(b*(a + b))^(1/2))/(4*(a*b + a^2)))*(b*(a + b))^(1/2))/(2*(a*b + a^2)))*(b*(a + b))^(1/2)*1i)/(a*b + a^2))/(((2*b^3*cos(c + d*x) + ((2*a^2*b^2 - (cos(c + d*x)*(16*a^2*b^3 + 8*a^3*b^2)*(b*(a + b))^(1/2))/(4*(a*b + a^2)))*(b*(a + b))^(1/2))/(2*(a*b + a^2)))*(b*(a + b))^(1/2))/(a*b + a^2) - ((2*b^3*cos(c + d*x) - ((2*a^2*b^2 + (cos(c + d*x)*(16*a^2*b^3 + 8*a^3*b^2)*(b*(a + b))^(1/2))/(4*(a*b + a^2)))*(b*(a + b))^(1/2))/(2*(a*b + a^2)))*(b*(a + b))^(1/2))/(a*b + a^2)))*(b*(a + b))^(1/2)*1i)/(d*(a*b + a^2))","B"
83,1,592,85,13.913825,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + b*sin(c + d*x)^2)),x)","-\frac{a\,\left(b\,\cos\left(c+d\,x\right)-b\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)+b\,{\cos\left(c+d\,x\right)}^2\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)\right)+a^2\,\left(\cos\left(c+d\,x\right)+\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)-{\cos\left(c+d\,x\right)}^2\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)\right)-2\,b^2\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)+\mathrm{atan}\left(\frac{-a\,\cos\left(c+d\,x\right)\,{\left(b^4+a\,b^3\right)}^{3/2}\,4{}\mathrm{i}-b\,\cos\left(c+d\,x\right)\,{\left(b^4+a\,b^3\right)}^{3/2}\,8{}\mathrm{i}+b^5\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,8{}\mathrm{i}+a^2\,b^3\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,1{}\mathrm{i}-a^3\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,2{}\mathrm{i}+a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,12{}\mathrm{i}+a^4\,b\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,1{}\mathrm{i}}{-a^5\,b^2+a^4\,b^3+5\,a^3\,b^4+3\,a^2\,b^5}\right)\,\sqrt{b^4+a\,b^3}\,2{}\mathrm{i}+2\,b^2\,{\cos\left(c+d\,x\right)}^2\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)-{\cos\left(c+d\,x\right)}^2\,\mathrm{atan}\left(\frac{-a\,\cos\left(c+d\,x\right)\,{\left(b^4+a\,b^3\right)}^{3/2}\,4{}\mathrm{i}-b\,\cos\left(c+d\,x\right)\,{\left(b^4+a\,b^3\right)}^{3/2}\,8{}\mathrm{i}+b^5\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,8{}\mathrm{i}+a^2\,b^3\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,1{}\mathrm{i}-a^3\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,2{}\mathrm{i}+a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,12{}\mathrm{i}+a^4\,b\,\cos\left(c+d\,x\right)\,\sqrt{b^4+a\,b^3}\,1{}\mathrm{i}}{-a^5\,b^2+a^4\,b^3+5\,a^3\,b^4+3\,a^2\,b^5}\right)\,\sqrt{b^4+a\,b^3}\,2{}\mathrm{i}}{d\,\left(-2\,a^3\,{\cos\left(c+d\,x\right)}^2+2\,a^3-2\,b\,a^2\,{\cos\left(c+d\,x\right)}^2+2\,b\,a^2\right)}","Not used",1,"-(a*(b*cos(c + d*x) - b*atanh(cos(c + d*x)) + b*cos(c + d*x)^2*atanh(cos(c + d*x))) + a^2*(cos(c + d*x) + atanh(cos(c + d*x)) - cos(c + d*x)^2*atanh(cos(c + d*x))) - 2*b^2*atanh(cos(c + d*x)) + atan((b^5*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*8i - b*cos(c + d*x)*(a*b^3 + b^4)^(3/2)*8i - a*cos(c + d*x)*(a*b^3 + b^4)^(3/2)*4i + a^2*b^3*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*1i - a^3*b^2*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*2i + a*b^4*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*12i + a^4*b*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*1i)/(3*a^2*b^5 + 5*a^3*b^4 + a^4*b^3 - a^5*b^2))*(a*b^3 + b^4)^(1/2)*2i + 2*b^2*cos(c + d*x)^2*atanh(cos(c + d*x)) - cos(c + d*x)^2*atan((b^5*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*8i - b*cos(c + d*x)*(a*b^3 + b^4)^(3/2)*8i - a*cos(c + d*x)*(a*b^3 + b^4)^(3/2)*4i + a^2*b^3*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*1i - a^3*b^2*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*2i + a*b^4*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*12i + a^4*b*cos(c + d*x)*(a*b^3 + b^4)^(1/2)*1i)/(3*a^2*b^5 + 5*a^3*b^4 + a^4*b^3 - a^5*b^2))*(a*b^3 + b^4)^(1/2)*2i)/(d*(2*a^2*b + 2*a^3 - 2*a^3*cos(c + d*x)^2 - 2*a^2*b*cos(c + d*x)^2))","B"
84,1,1105,125,13.927860,"\text{Not used}","int(1/(sin(c + d*x)^5*(a + b*sin(c + d*x)^2)),x)","-\frac{\frac{\cos\left(c+d\,x\right)\,\left(5\,a-4\,b\right)}{8\,a^2}-\frac{{\cos\left(c+d\,x\right)}^3\,\left(3\,a-4\,b\right)}{8\,a^2}}{d\,\left({\cos\left(c+d\,x\right)}^4-{\cos\left(c+d\,x\right)}^2+{\sin\left(c+d\,x\right)}^2\right)}-\frac{\mathrm{atanh}\left(\frac{63\,b^4\,\cos\left(c+d\,x\right)}{64\,\left(\frac{63\,b^4}{64}-\frac{81\,a\,b^3}{256}+\frac{27\,a^2\,b^2}{256}-\frac{35\,b^5}{32\,a}+\frac{5\,b^6}{4\,a^2}\right)}-\frac{81\,b^3\,\cos\left(c+d\,x\right)}{256\,\left(\frac{27\,a\,b^2}{256}-\frac{81\,b^3}{256}+\frac{63\,b^4}{64\,a}-\frac{35\,b^5}{32\,a^2}+\frac{5\,b^6}{4\,a^3}\right)}-\frac{35\,b^5\,\cos\left(c+d\,x\right)}{32\,\left(\frac{63\,a\,b^4}{64}-\frac{35\,b^5}{32}-\frac{81\,a^2\,b^3}{256}+\frac{27\,a^3\,b^2}{256}+\frac{5\,b^6}{4\,a}\right)}+\frac{5\,b^6\,\cos\left(c+d\,x\right)}{4\,\left(\frac{27\,a^4\,b^2}{256}-\frac{81\,a^3\,b^3}{256}+\frac{63\,a^2\,b^4}{64}-\frac{35\,a\,b^5}{32}+\frac{5\,b^6}{4}\right)}+\frac{27\,b^2\,\cos\left(c+d\,x\right)}{256\,\left(\frac{27\,b^2}{256}-\frac{81\,b^3}{256\,a}+\frac{63\,b^4}{64\,a^2}-\frac{35\,b^5}{32\,a^3}+\frac{5\,b^6}{4\,a^4}\right)}\right)\,\left(3\,a^2-4\,a\,b+8\,b^2\right)}{8\,a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b^5\,\left(a+b\right)}\,\left(\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b^3-24\,a^3\,b^4+64\,a^2\,b^5-64\,a\,b^6+128\,b^7\right)}{64\,a^4}+\frac{\sqrt{b^5\,\left(a+b\right)}\,\left(\frac{\frac{3\,a^8\,b^2}{2}-\frac{a^7\,b^3}{2}+2\,a^6\,b^4}{2\,a^6}-\frac{\cos\left(c+d\,x\right)\,\left(256\,a^7\,b^2+512\,a^6\,b^3\right)\,\sqrt{b^5\,\left(a+b\right)}}{128\,a^4\,\left(a^4+b\,a^3\right)}\right)}{2\,\left(a^4+b\,a^3\right)}\right)\,1{}\mathrm{i}}{a^4+b\,a^3}+\frac{\sqrt{b^5\,\left(a+b\right)}\,\left(\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b^3-24\,a^3\,b^4+64\,a^2\,b^5-64\,a\,b^6+128\,b^7\right)}{64\,a^4}-\frac{\sqrt{b^5\,\left(a+b\right)}\,\left(\frac{\frac{3\,a^8\,b^2}{2}-\frac{a^7\,b^3}{2}+2\,a^6\,b^4}{2\,a^6}+\frac{\cos\left(c+d\,x\right)\,\left(256\,a^7\,b^2+512\,a^6\,b^3\right)\,\sqrt{b^5\,\left(a+b\right)}}{128\,a^4\,\left(a^4+b\,a^3\right)}\right)}{2\,\left(a^4+b\,a^3\right)}\right)\,1{}\mathrm{i}}{a^4+b\,a^3}}{\frac{\frac{9\,a^3\,b^5}{32}-\frac{3\,a^2\,b^6}{4}+\frac{5\,a\,b^7}{4}-b^8}{a^6}+\frac{\sqrt{b^5\,\left(a+b\right)}\,\left(\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b^3-24\,a^3\,b^4+64\,a^2\,b^5-64\,a\,b^6+128\,b^7\right)}{64\,a^4}+\frac{\sqrt{b^5\,\left(a+b\right)}\,\left(\frac{\frac{3\,a^8\,b^2}{2}-\frac{a^7\,b^3}{2}+2\,a^6\,b^4}{2\,a^6}-\frac{\cos\left(c+d\,x\right)\,\left(256\,a^7\,b^2+512\,a^6\,b^3\right)\,\sqrt{b^5\,\left(a+b\right)}}{128\,a^4\,\left(a^4+b\,a^3\right)}\right)}{2\,\left(a^4+b\,a^3\right)}\right)}{a^4+b\,a^3}-\frac{\sqrt{b^5\,\left(a+b\right)}\,\left(\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b^3-24\,a^3\,b^4+64\,a^2\,b^5-64\,a\,b^6+128\,b^7\right)}{64\,a^4}-\frac{\sqrt{b^5\,\left(a+b\right)}\,\left(\frac{\frac{3\,a^8\,b^2}{2}-\frac{a^7\,b^3}{2}+2\,a^6\,b^4}{2\,a^6}+\frac{\cos\left(c+d\,x\right)\,\left(256\,a^7\,b^2+512\,a^6\,b^3\right)\,\sqrt{b^5\,\left(a+b\right)}}{128\,a^4\,\left(a^4+b\,a^3\right)}\right)}{2\,\left(a^4+b\,a^3\right)}\right)}{a^4+b\,a^3}}\right)\,\sqrt{b^5\,\left(a+b\right)}\,1{}\mathrm{i}}{d\,\left(a^4+b\,a^3\right)}","Not used",1,"- ((cos(c + d*x)*(5*a - 4*b))/(8*a^2) - (cos(c + d*x)^3*(3*a - 4*b))/(8*a^2))/(d*(cos(c + d*x)^4 - cos(c + d*x)^2 + sin(c + d*x)^2)) - (atanh((63*b^4*cos(c + d*x))/(64*((63*b^4)/64 - (81*a*b^3)/256 + (27*a^2*b^2)/256 - (35*b^5)/(32*a) + (5*b^6)/(4*a^2))) - (81*b^3*cos(c + d*x))/(256*((27*a*b^2)/256 - (81*b^3)/256 + (63*b^4)/(64*a) - (35*b^5)/(32*a^2) + (5*b^6)/(4*a^3))) - (35*b^5*cos(c + d*x))/(32*((63*a*b^4)/64 - (35*b^5)/32 - (81*a^2*b^3)/256 + (27*a^3*b^2)/256 + (5*b^6)/(4*a))) + (5*b^6*cos(c + d*x))/(4*((5*b^6)/4 - (35*a*b^5)/32 + (63*a^2*b^4)/64 - (81*a^3*b^3)/256 + (27*a^4*b^2)/256)) + (27*b^2*cos(c + d*x))/(256*((27*b^2)/256 - (81*b^3)/(256*a) + (63*b^4)/(64*a^2) - (35*b^5)/(32*a^3) + (5*b^6)/(4*a^4))))*(3*a^2 - 4*a*b + 8*b^2))/(8*a^3*d) - (atan((((b^5*(a + b))^(1/2)*((cos(c + d*x)*(128*b^7 - 64*a*b^6 + 64*a^2*b^5 - 24*a^3*b^4 + 9*a^4*b^3))/(64*a^4) + ((b^5*(a + b))^(1/2)*((2*a^6*b^4 - (a^7*b^3)/2 + (3*a^8*b^2)/2)/(2*a^6) - (cos(c + d*x)*(512*a^6*b^3 + 256*a^7*b^2)*(b^5*(a + b))^(1/2))/(128*a^4*(a^3*b + a^4))))/(2*(a^3*b + a^4)))*1i)/(a^3*b + a^4) + ((b^5*(a + b))^(1/2)*((cos(c + d*x)*(128*b^7 - 64*a*b^6 + 64*a^2*b^5 - 24*a^3*b^4 + 9*a^4*b^3))/(64*a^4) - ((b^5*(a + b))^(1/2)*((2*a^6*b^4 - (a^7*b^3)/2 + (3*a^8*b^2)/2)/(2*a^6) + (cos(c + d*x)*(512*a^6*b^3 + 256*a^7*b^2)*(b^5*(a + b))^(1/2))/(128*a^4*(a^3*b + a^4))))/(2*(a^3*b + a^4)))*1i)/(a^3*b + a^4))/(((5*a*b^7)/4 - b^8 - (3*a^2*b^6)/4 + (9*a^3*b^5)/32)/a^6 + ((b^5*(a + b))^(1/2)*((cos(c + d*x)*(128*b^7 - 64*a*b^6 + 64*a^2*b^5 - 24*a^3*b^4 + 9*a^4*b^3))/(64*a^4) + ((b^5*(a + b))^(1/2)*((2*a^6*b^4 - (a^7*b^3)/2 + (3*a^8*b^2)/2)/(2*a^6) - (cos(c + d*x)*(512*a^6*b^3 + 256*a^7*b^2)*(b^5*(a + b))^(1/2))/(128*a^4*(a^3*b + a^4))))/(2*(a^3*b + a^4))))/(a^3*b + a^4) - ((b^5*(a + b))^(1/2)*((cos(c + d*x)*(128*b^7 - 64*a*b^6 + 64*a^2*b^5 - 24*a^3*b^4 + 9*a^4*b^3))/(64*a^4) - ((b^5*(a + b))^(1/2)*((2*a^6*b^4 - (a^7*b^3)/2 + (3*a^8*b^2)/2)/(2*a^6) + (cos(c + d*x)*(512*a^6*b^3 + 256*a^7*b^2)*(b^5*(a + b))^(1/2))/(128*a^4*(a^3*b + a^4))))/(2*(a^3*b + a^4))))/(a^3*b + a^4)))*(b^5*(a + b))^(1/2)*1i)/(d*(a^3*b + a^4))","B"
85,1,2244,163,15.318632,"\text{Not used}","int(sin(c + d*x)^8/(a + b*sin(c + d*x)^2),x)","-\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^2-6\,a\,b+5\,b^2\right)}{16\,b^3}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(6\,a^2-6\,a\,b+5\,b^2\right)}{6\,b^3}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(8\,a^2-10\,a\,b+11\,b^2\right)}{16\,b^3}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^6+3\,{\mathrm{tan}\left(c+d\,x\right)}^4+3\,{\mathrm{tan}\left(c+d\,x\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^9+768\,a^8\,b+256\,a^7\,b^2-140\,a^5\,b^4-224\,a^4\,b^5-63\,a^3\,b^6+11\,a^2\,b^7+15\,a\,b^8+25\,b^9\right)}{128\,b^6}-\frac{\left(\frac{2\,a^5\,b^8+\frac{5\,a^4\,b^9}{2}+\frac{a^3\,b^{10}}{4}+a^2\,b^{11}+\frac{5\,a\,b^{12}}{4}}{b^9}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)\,\left(2048\,a^3\,b^8+5120\,a^2\,b^9+4096\,a\,b^{10}+1024\,b^{11}\right)}{4096\,b^{10}}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)}{32\,b^4}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{32\,b^4}+\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^9+768\,a^8\,b+256\,a^7\,b^2-140\,a^5\,b^4-224\,a^4\,b^5-63\,a^3\,b^6+11\,a^2\,b^7+15\,a\,b^8+25\,b^9\right)}{128\,b^6}+\frac{\left(\frac{2\,a^5\,b^8+\frac{5\,a^4\,b^9}{2}+\frac{a^3\,b^{10}}{4}+a^2\,b^{11}+\frac{5\,a\,b^{12}}{4}}{b^9}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)\,\left(2048\,a^3\,b^8+5120\,a^2\,b^9+4096\,a\,b^{10}+1024\,b^{11}\right)}{4096\,b^{10}}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)}{32\,b^4}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{32\,b^4}}{\frac{a^{11}+\frac{a^{10}\,b}{4}-\frac{a^9\,b^2}{8}-\frac{15\,a^8\,b^3}{32}-\frac{21\,a^7\,b^4}{32}+\frac{21\,a^6\,b^5}{128}-\frac{5\,a^5\,b^6}{64}+\frac{25\,a^4\,b^7}{128}}{b^9}-\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^9+768\,a^8\,b+256\,a^7\,b^2-140\,a^5\,b^4-224\,a^4\,b^5-63\,a^3\,b^6+11\,a^2\,b^7+15\,a\,b^8+25\,b^9\right)}{128\,b^6}-\frac{\left(\frac{2\,a^5\,b^8+\frac{5\,a^4\,b^9}{2}+\frac{a^3\,b^{10}}{4}+a^2\,b^{11}+\frac{5\,a\,b^{12}}{4}}{b^9}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)\,\left(2048\,a^3\,b^8+5120\,a^2\,b^9+4096\,a\,b^{10}+1024\,b^{11}\right)}{4096\,b^{10}}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)}{32\,b^4}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)}{32\,b^4}+\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^9+768\,a^8\,b+256\,a^7\,b^2-140\,a^5\,b^4-224\,a^4\,b^5-63\,a^3\,b^6+11\,a^2\,b^7+15\,a\,b^8+25\,b^9\right)}{128\,b^6}+\frac{\left(\frac{2\,a^5\,b^8+\frac{5\,a^4\,b^9}{2}+\frac{a^3\,b^{10}}{4}+a^2\,b^{11}+\frac{5\,a\,b^{12}}{4}}{b^9}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)\,\left(2048\,a^3\,b^8+5120\,a^2\,b^9+4096\,a\,b^{10}+1024\,b^{11}\right)}{4096\,b^{10}}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)}{32\,b^4}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)}{32\,b^4}}\right)\,\left(a^3\,16{}\mathrm{i}-a^2\,b\,8{}\mathrm{i}+a\,b^2\,6{}\mathrm{i}-b^3\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a^7\,\left(a+b\right)}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^9+768\,a^8\,b+256\,a^7\,b^2-140\,a^5\,b^4-224\,a^4\,b^5-63\,a^3\,b^6+11\,a^2\,b^7+15\,a\,b^8+25\,b^9\right)}{128\,b^6}-\frac{\sqrt{-a^7\,\left(a+b\right)}\,\left(\frac{512\,a^5\,b^8+640\,a^4\,b^9+64\,a^3\,b^{10}+256\,a^2\,b^{11}+320\,a\,b^{12}}{256\,b^9}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a^7\,\left(a+b\right)}\,\left(2048\,a^3\,b^8+5120\,a^2\,b^9+4096\,a\,b^{10}+1024\,b^{11}\right)}{256\,b^6\,\left(b^5+a\,b^4\right)}\right)}{2\,\left(b^5+a\,b^4\right)}\right)\,1{}\mathrm{i}}{2\,\left(b^5+a\,b^4\right)}+\frac{\sqrt{-a^7\,\left(a+b\right)}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^9+768\,a^8\,b+256\,a^7\,b^2-140\,a^5\,b^4-224\,a^4\,b^5-63\,a^3\,b^6+11\,a^2\,b^7+15\,a\,b^8+25\,b^9\right)}{128\,b^6}+\frac{\sqrt{-a^7\,\left(a+b\right)}\,\left(\frac{512\,a^5\,b^8+640\,a^4\,b^9+64\,a^3\,b^{10}+256\,a^2\,b^{11}+320\,a\,b^{12}}{256\,b^9}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a^7\,\left(a+b\right)}\,\left(2048\,a^3\,b^8+5120\,a^2\,b^9+4096\,a\,b^{10}+1024\,b^{11}\right)}{256\,b^6\,\left(b^5+a\,b^4\right)}\right)}{2\,\left(b^5+a\,b^4\right)}\right)\,1{}\mathrm{i}}{2\,\left(b^5+a\,b^4\right)}}{\frac{128\,a^{11}+32\,a^{10}\,b-16\,a^9\,b^2-60\,a^8\,b^3-84\,a^7\,b^4+21\,a^6\,b^5-10\,a^5\,b^6+25\,a^4\,b^7}{128\,b^9}-\frac{\sqrt{-a^7\,\left(a+b\right)}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^9+768\,a^8\,b+256\,a^7\,b^2-140\,a^5\,b^4-224\,a^4\,b^5-63\,a^3\,b^6+11\,a^2\,b^7+15\,a\,b^8+25\,b^9\right)}{128\,b^6}-\frac{\sqrt{-a^7\,\left(a+b\right)}\,\left(\frac{512\,a^5\,b^8+640\,a^4\,b^9+64\,a^3\,b^{10}+256\,a^2\,b^{11}+320\,a\,b^{12}}{256\,b^9}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a^7\,\left(a+b\right)}\,\left(2048\,a^3\,b^8+5120\,a^2\,b^9+4096\,a\,b^{10}+1024\,b^{11}\right)}{256\,b^6\,\left(b^5+a\,b^4\right)}\right)}{2\,\left(b^5+a\,b^4\right)}\right)}{2\,\left(b^5+a\,b^4\right)}+\frac{\sqrt{-a^7\,\left(a+b\right)}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^9+768\,a^8\,b+256\,a^7\,b^2-140\,a^5\,b^4-224\,a^4\,b^5-63\,a^3\,b^6+11\,a^2\,b^7+15\,a\,b^8+25\,b^9\right)}{128\,b^6}+\frac{\sqrt{-a^7\,\left(a+b\right)}\,\left(\frac{512\,a^5\,b^8+640\,a^4\,b^9+64\,a^3\,b^{10}+256\,a^2\,b^{11}+320\,a\,b^{12}}{256\,b^9}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a^7\,\left(a+b\right)}\,\left(2048\,a^3\,b^8+5120\,a^2\,b^9+4096\,a\,b^{10}+1024\,b^{11}\right)}{256\,b^6\,\left(b^5+a\,b^4\right)}\right)}{2\,\left(b^5+a\,b^4\right)}\right)}{2\,\left(b^5+a\,b^4\right)}}\right)\,\sqrt{-a^7\,\left(a+b\right)}\,1{}\mathrm{i}}{d\,\left(b^5+a\,b^4\right)}","Not used",1,"(atan(((((tan(c + d*x)*(15*a*b^8 + 768*a^8*b + 512*a^9 + 25*b^9 + 11*a^2*b^7 - 63*a^3*b^6 - 224*a^4*b^5 - 140*a^5*b^4 + 256*a^7*b^2))/(128*b^6) - ((((5*a*b^12)/4 + a^2*b^11 + (a^3*b^10)/4 + (5*a^4*b^9)/2 + 2*a^5*b^8)/b^9 - (tan(c + d*x)*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i)*(4096*a*b^10 + 1024*b^11 + 5120*a^2*b^9 + 2048*a^3*b^8))/(4096*b^10))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i))/(32*b^4))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i)*1i)/(32*b^4) + (((tan(c + d*x)*(15*a*b^8 + 768*a^8*b + 512*a^9 + 25*b^9 + 11*a^2*b^7 - 63*a^3*b^6 - 224*a^4*b^5 - 140*a^5*b^4 + 256*a^7*b^2))/(128*b^6) + ((((5*a*b^12)/4 + a^2*b^11 + (a^3*b^10)/4 + (5*a^4*b^9)/2 + 2*a^5*b^8)/b^9 + (tan(c + d*x)*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i)*(4096*a*b^10 + 1024*b^11 + 5120*a^2*b^9 + 2048*a^3*b^8))/(4096*b^10))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i))/(32*b^4))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i)*1i)/(32*b^4))/(((a^10*b)/4 + a^11 + (25*a^4*b^7)/128 - (5*a^5*b^6)/64 + (21*a^6*b^5)/128 - (21*a^7*b^4)/32 - (15*a^8*b^3)/32 - (a^9*b^2)/8)/b^9 - (((tan(c + d*x)*(15*a*b^8 + 768*a^8*b + 512*a^9 + 25*b^9 + 11*a^2*b^7 - 63*a^3*b^6 - 224*a^4*b^5 - 140*a^5*b^4 + 256*a^7*b^2))/(128*b^6) - ((((5*a*b^12)/4 + a^2*b^11 + (a^3*b^10)/4 + (5*a^4*b^9)/2 + 2*a^5*b^8)/b^9 - (tan(c + d*x)*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i)*(4096*a*b^10 + 1024*b^11 + 5120*a^2*b^9 + 2048*a^3*b^8))/(4096*b^10))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i))/(32*b^4))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i))/(32*b^4) + (((tan(c + d*x)*(15*a*b^8 + 768*a^8*b + 512*a^9 + 25*b^9 + 11*a^2*b^7 - 63*a^3*b^6 - 224*a^4*b^5 - 140*a^5*b^4 + 256*a^7*b^2))/(128*b^6) + ((((5*a*b^12)/4 + a^2*b^11 + (a^3*b^10)/4 + (5*a^4*b^9)/2 + 2*a^5*b^8)/b^9 + (tan(c + d*x)*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i)*(4096*a*b^10 + 1024*b^11 + 5120*a^2*b^9 + 2048*a^3*b^8))/(4096*b^10))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i))/(32*b^4))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i))/(32*b^4)))*(a*b^2*6i - a^2*b*8i + a^3*16i - b^3*5i)*1i)/(16*b^4*d) - ((tan(c + d*x)*(8*a^2 - 6*a*b + 5*b^2))/(16*b^3) + (tan(c + d*x)^3*(6*a^2 - 6*a*b + 5*b^2))/(6*b^3) + (tan(c + d*x)^5*(8*a^2 - 10*a*b + 11*b^2))/(16*b^3))/(d*(3*tan(c + d*x)^2 + 3*tan(c + d*x)^4 + tan(c + d*x)^6 + 1)) + (atan((((-a^7*(a + b))^(1/2)*((tan(c + d*x)*(15*a*b^8 + 768*a^8*b + 512*a^9 + 25*b^9 + 11*a^2*b^7 - 63*a^3*b^6 - 224*a^4*b^5 - 140*a^5*b^4 + 256*a^7*b^2))/(128*b^6) - ((-a^7*(a + b))^(1/2)*((320*a*b^12 + 256*a^2*b^11 + 64*a^3*b^10 + 640*a^4*b^9 + 512*a^5*b^8)/(256*b^9) - (tan(c + d*x)*(-a^7*(a + b))^(1/2)*(4096*a*b^10 + 1024*b^11 + 5120*a^2*b^9 + 2048*a^3*b^8))/(256*b^6*(a*b^4 + b^5))))/(2*(a*b^4 + b^5)))*1i)/(2*(a*b^4 + b^5)) + ((-a^7*(a + b))^(1/2)*((tan(c + d*x)*(15*a*b^8 + 768*a^8*b + 512*a^9 + 25*b^9 + 11*a^2*b^7 - 63*a^3*b^6 - 224*a^4*b^5 - 140*a^5*b^4 + 256*a^7*b^2))/(128*b^6) + ((-a^7*(a + b))^(1/2)*((320*a*b^12 + 256*a^2*b^11 + 64*a^3*b^10 + 640*a^4*b^9 + 512*a^5*b^8)/(256*b^9) + (tan(c + d*x)*(-a^7*(a + b))^(1/2)*(4096*a*b^10 + 1024*b^11 + 5120*a^2*b^9 + 2048*a^3*b^8))/(256*b^6*(a*b^4 + b^5))))/(2*(a*b^4 + b^5)))*1i)/(2*(a*b^4 + b^5)))/((32*a^10*b + 128*a^11 + 25*a^4*b^7 - 10*a^5*b^6 + 21*a^6*b^5 - 84*a^7*b^4 - 60*a^8*b^3 - 16*a^9*b^2)/(128*b^9) - ((-a^7*(a + b))^(1/2)*((tan(c + d*x)*(15*a*b^8 + 768*a^8*b + 512*a^9 + 25*b^9 + 11*a^2*b^7 - 63*a^3*b^6 - 224*a^4*b^5 - 140*a^5*b^4 + 256*a^7*b^2))/(128*b^6) - ((-a^7*(a + b))^(1/2)*((320*a*b^12 + 256*a^2*b^11 + 64*a^3*b^10 + 640*a^4*b^9 + 512*a^5*b^8)/(256*b^9) - (tan(c + d*x)*(-a^7*(a + b))^(1/2)*(4096*a*b^10 + 1024*b^11 + 5120*a^2*b^9 + 2048*a^3*b^8))/(256*b^6*(a*b^4 + b^5))))/(2*(a*b^4 + b^5))))/(2*(a*b^4 + b^5)) + ((-a^7*(a + b))^(1/2)*((tan(c + d*x)*(15*a*b^8 + 768*a^8*b + 512*a^9 + 25*b^9 + 11*a^2*b^7 - 63*a^3*b^6 - 224*a^4*b^5 - 140*a^5*b^4 + 256*a^7*b^2))/(128*b^6) + ((-a^7*(a + b))^(1/2)*((320*a*b^12 + 256*a^2*b^11 + 64*a^3*b^10 + 640*a^4*b^9 + 512*a^5*b^8)/(256*b^9) + (tan(c + d*x)*(-a^7*(a + b))^(1/2)*(4096*a*b^10 + 1024*b^11 + 5120*a^2*b^9 + 2048*a^3*b^8))/(256*b^6*(a*b^4 + b^5))))/(2*(a*b^4 + b^5))))/(2*(a*b^4 + b^5))))*(-a^7*(a + b))^(1/2)*1i)/(d*(a*b^4 + b^5))","B"
86,1,1892,117,14.819814,"\text{Not used}","int(sin(c + d*x)^6/(a + b*sin(c + d*x)^2),x)","\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a-3\,b\right)}{8\,b^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(4\,a-5\,b\right)}{8\,b^2}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4+2\,{\mathrm{tan}\left(c+d\,x\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{-2\,a^4\,b^6-\frac{5\,a^3\,b^7}{2}+a^2\,b^8+\frac{3\,a\,b^9}{2}}{2\,b^6}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a^5\,\left(a+b\right)}\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{128\,b^4\,\left(b^4+a\,b^3\right)}\right)\,\sqrt{-a^5\,\left(a+b\right)}}{2\,\left(b^4+a\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^7+192\,a^6\,b+64\,a^5\,b^2+40\,a^4\,b^3+65\,a^3\,b^4+19\,a^2\,b^5+3\,a\,b^6+9\,b^7\right)}{64\,b^4}\right)\,\sqrt{-a^5\,\left(a+b\right)}\,1{}\mathrm{i}}{b^4+a\,b^3}-\frac{\left(\frac{\left(\frac{-2\,a^4\,b^6-\frac{5\,a^3\,b^7}{2}+a^2\,b^8+\frac{3\,a\,b^9}{2}}{2\,b^6}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a^5\,\left(a+b\right)}\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{128\,b^4\,\left(b^4+a\,b^3\right)}\right)\,\sqrt{-a^5\,\left(a+b\right)}}{2\,\left(b^4+a\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^7+192\,a^6\,b+64\,a^5\,b^2+40\,a^4\,b^3+65\,a^3\,b^4+19\,a^2\,b^5+3\,a\,b^6+9\,b^7\right)}{64\,b^4}\right)\,\sqrt{-a^5\,\left(a+b\right)}\,1{}\mathrm{i}}{b^4+a\,b^3}}{\frac{\left(\frac{\left(\frac{-2\,a^4\,b^6-\frac{5\,a^3\,b^7}{2}+a^2\,b^8+\frac{3\,a\,b^9}{2}}{2\,b^6}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a^5\,\left(a+b\right)}\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{128\,b^4\,\left(b^4+a\,b^3\right)}\right)\,\sqrt{-a^5\,\left(a+b\right)}}{2\,\left(b^4+a\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^7+192\,a^6\,b+64\,a^5\,b^2+40\,a^4\,b^3+65\,a^3\,b^4+19\,a^2\,b^5+3\,a\,b^6+9\,b^7\right)}{64\,b^4}\right)\,\sqrt{-a^5\,\left(a+b\right)}}{b^4+a\,b^3}-\frac{a^8+\frac{a^7\,b}{4}+\frac{a^6\,b^2}{2}+\frac{25\,a^5\,b^3}{32}-\frac{3\,a^4\,b^4}{16}+\frac{9\,a^3\,b^5}{32}}{b^6}+\frac{\left(\frac{\left(\frac{-2\,a^4\,b^6-\frac{5\,a^3\,b^7}{2}+a^2\,b^8+\frac{3\,a\,b^9}{2}}{2\,b^6}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a^5\,\left(a+b\right)}\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{128\,b^4\,\left(b^4+a\,b^3\right)}\right)\,\sqrt{-a^5\,\left(a+b\right)}}{2\,\left(b^4+a\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^7+192\,a^6\,b+64\,a^5\,b^2+40\,a^4\,b^3+65\,a^3\,b^4+19\,a^2\,b^5+3\,a\,b^6+9\,b^7\right)}{64\,b^4}\right)\,\sqrt{-a^5\,\left(a+b\right)}}{b^4+a\,b^3}}\right)\,\sqrt{-a^5\,\left(a+b\right)}\,1{}\mathrm{i}}{d\,\left(b^4+a\,b^3\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{-2\,a^4\,b^6-\frac{5\,a^3\,b^7}{2}+a^2\,b^8+\frac{3\,a\,b^9}{2}}{b^6}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{512\,b^7}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)}{16\,b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^7+192\,a^6\,b+64\,a^5\,b^2+40\,a^4\,b^3+65\,a^3\,b^4+19\,a^2\,b^5+3\,a\,b^6+9\,b^7\right)}{32\,b^4}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^3}-\frac{\left(\frac{\left(\frac{-2\,a^4\,b^6-\frac{5\,a^3\,b^7}{2}+a^2\,b^8+\frac{3\,a\,b^9}{2}}{b^6}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{512\,b^7}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)}{16\,b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^7+192\,a^6\,b+64\,a^5\,b^2+40\,a^4\,b^3+65\,a^3\,b^4+19\,a^2\,b^5+3\,a\,b^6+9\,b^7\right)}{32\,b^4}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^3}}{-\frac{a^8+\frac{a^7\,b}{4}+\frac{a^6\,b^2}{2}+\frac{25\,a^5\,b^3}{32}-\frac{3\,a^4\,b^4}{16}+\frac{9\,a^3\,b^5}{32}}{b^6}+\frac{\left(\frac{\left(\frac{-2\,a^4\,b^6-\frac{5\,a^3\,b^7}{2}+a^2\,b^8+\frac{3\,a\,b^9}{2}}{b^6}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{512\,b^7}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)}{16\,b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^7+192\,a^6\,b+64\,a^5\,b^2+40\,a^4\,b^3+65\,a^3\,b^4+19\,a^2\,b^5+3\,a\,b^6+9\,b^7\right)}{32\,b^4}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)}{16\,b^3}+\frac{\left(\frac{\left(\frac{-2\,a^4\,b^6-\frac{5\,a^3\,b^7}{2}+a^2\,b^8+\frac{3\,a\,b^9}{2}}{b^6}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{512\,b^7}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)}{16\,b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^7+192\,a^6\,b+64\,a^5\,b^2+40\,a^4\,b^3+65\,a^3\,b^4+19\,a^2\,b^5+3\,a\,b^6+9\,b^7\right)}{32\,b^4}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)}{16\,b^3}}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^3\,d}","Not used",1,"((tan(c + d*x)*(4*a - 3*b))/(8*b^2) + (tan(c + d*x)^3*(4*a - 5*b))/(8*b^2))/(d*(2*tan(c + d*x)^2 + tan(c + d*x)^4 + 1)) - (atan((((((((3*a*b^9)/2 + a^2*b^8 - (5*a^3*b^7)/2 - 2*a^4*b^6)/(2*b^6) - (tan(c + d*x)*(-a^5*(a + b))^(1/2)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(128*b^4*(a*b^3 + b^4)))*(-a^5*(a + b))^(1/2))/(2*(a*b^3 + b^4)) - (tan(c + d*x)*(3*a*b^6 + 192*a^6*b + 128*a^7 + 9*b^7 + 19*a^2*b^5 + 65*a^3*b^4 + 40*a^4*b^3 + 64*a^5*b^2))/(64*b^4))*(-a^5*(a + b))^(1/2)*1i)/(a*b^3 + b^4) - ((((((3*a*b^9)/2 + a^2*b^8 - (5*a^3*b^7)/2 - 2*a^4*b^6)/(2*b^6) + (tan(c + d*x)*(-a^5*(a + b))^(1/2)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(128*b^4*(a*b^3 + b^4)))*(-a^5*(a + b))^(1/2))/(2*(a*b^3 + b^4)) + (tan(c + d*x)*(3*a*b^6 + 192*a^6*b + 128*a^7 + 9*b^7 + 19*a^2*b^5 + 65*a^3*b^4 + 40*a^4*b^3 + 64*a^5*b^2))/(64*b^4))*(-a^5*(a + b))^(1/2)*1i)/(a*b^3 + b^4))/(((((((3*a*b^9)/2 + a^2*b^8 - (5*a^3*b^7)/2 - 2*a^4*b^6)/(2*b^6) - (tan(c + d*x)*(-a^5*(a + b))^(1/2)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(128*b^4*(a*b^3 + b^4)))*(-a^5*(a + b))^(1/2))/(2*(a*b^3 + b^4)) - (tan(c + d*x)*(3*a*b^6 + 192*a^6*b + 128*a^7 + 9*b^7 + 19*a^2*b^5 + 65*a^3*b^4 + 40*a^4*b^3 + 64*a^5*b^2))/(64*b^4))*(-a^5*(a + b))^(1/2))/(a*b^3 + b^4) - ((a^7*b)/4 + a^8 + (9*a^3*b^5)/32 - (3*a^4*b^4)/16 + (25*a^5*b^3)/32 + (a^6*b^2)/2)/b^6 + ((((((3*a*b^9)/2 + a^2*b^8 - (5*a^3*b^7)/2 - 2*a^4*b^6)/(2*b^6) + (tan(c + d*x)*(-a^5*(a + b))^(1/2)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(128*b^4*(a*b^3 + b^4)))*(-a^5*(a + b))^(1/2))/(2*(a*b^3 + b^4)) + (tan(c + d*x)*(3*a*b^6 + 192*a^6*b + 128*a^7 + 9*b^7 + 19*a^2*b^5 + 65*a^3*b^4 + 40*a^4*b^3 + 64*a^5*b^2))/(64*b^4))*(-a^5*(a + b))^(1/2))/(a*b^3 + b^4)))*(-a^5*(a + b))^(1/2)*1i)/(d*(a*b^3 + b^4)) - (atan((((((((3*a*b^9)/2 + a^2*b^8 - (5*a^3*b^7)/2 - 2*a^4*b^6)/b^6 - (tan(c + d*x)*(a^2*8i - a*b*4i + b^2*3i)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(512*b^7))*(a^2*8i - a*b*4i + b^2*3i))/(16*b^3) - (tan(c + d*x)*(3*a*b^6 + 192*a^6*b + 128*a^7 + 9*b^7 + 19*a^2*b^5 + 65*a^3*b^4 + 40*a^4*b^3 + 64*a^5*b^2))/(32*b^4))*(a^2*8i - a*b*4i + b^2*3i)*1i)/(16*b^3) - ((((((3*a*b^9)/2 + a^2*b^8 - (5*a^3*b^7)/2 - 2*a^4*b^6)/b^6 + (tan(c + d*x)*(a^2*8i - a*b*4i + b^2*3i)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(512*b^7))*(a^2*8i - a*b*4i + b^2*3i))/(16*b^3) + (tan(c + d*x)*(3*a*b^6 + 192*a^6*b + 128*a^7 + 9*b^7 + 19*a^2*b^5 + 65*a^3*b^4 + 40*a^4*b^3 + 64*a^5*b^2))/(32*b^4))*(a^2*8i - a*b*4i + b^2*3i)*1i)/(16*b^3))/(((((((3*a*b^9)/2 + a^2*b^8 - (5*a^3*b^7)/2 - 2*a^4*b^6)/b^6 - (tan(c + d*x)*(a^2*8i - a*b*4i + b^2*3i)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(512*b^7))*(a^2*8i - a*b*4i + b^2*3i))/(16*b^3) - (tan(c + d*x)*(3*a*b^6 + 192*a^6*b + 128*a^7 + 9*b^7 + 19*a^2*b^5 + 65*a^3*b^4 + 40*a^4*b^3 + 64*a^5*b^2))/(32*b^4))*(a^2*8i - a*b*4i + b^2*3i))/(16*b^3) - ((a^7*b)/4 + a^8 + (9*a^3*b^5)/32 - (3*a^4*b^4)/16 + (25*a^5*b^3)/32 + (a^6*b^2)/2)/b^6 + ((((((3*a*b^9)/2 + a^2*b^8 - (5*a^3*b^7)/2 - 2*a^4*b^6)/b^6 + (tan(c + d*x)*(a^2*8i - a*b*4i + b^2*3i)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(512*b^7))*(a^2*8i - a*b*4i + b^2*3i))/(16*b^3) + (tan(c + d*x)*(3*a*b^6 + 192*a^6*b + 128*a^7 + 9*b^7 + 19*a^2*b^5 + 65*a^3*b^4 + 40*a^4*b^3 + 64*a^5*b^2))/(32*b^4))*(a^2*8i - a*b*4i + b^2*3i))/(16*b^3)))*(a^2*8i - a*b*4i + b^2*3i)*1i)/(8*b^3*d)","B"
87,1,481,77,13.974235,"\text{Not used}","int(sin(c + d*x)^4/(a + b*sin(c + d*x)^2),x)","\frac{b^2\,\mathrm{atan}\left(\frac{\sin\left(c+d\,x\right)}{\cos\left(c+d\,x\right)}\right)}{d\,\left(2\,b^3+2\,a\,b^2\right)}-\frac{2\,a^2\,\mathrm{atan}\left(\frac{\sin\left(c+d\,x\right)}{\cos\left(c+d\,x\right)}\right)}{d\,\left(2\,b^3+2\,a\,b^2\right)}-\frac{b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\left(2\,b^3+2\,a\,b^2\right)}-\frac{a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\left(2\,b^3+2\,a\,b^2\right)}-\frac{a\,b\,\mathrm{atan}\left(\frac{\sin\left(c+d\,x\right)}{\cos\left(c+d\,x\right)}\right)}{d\,\left(2\,b^3+2\,a\,b^2\right)}-\frac{\mathrm{atan}\left(\frac{a\,\sin\left(c+d\,x\right)\,{\left(-a^4-b\,a^3\right)}^{3/2}\,8{}\mathrm{i}+b\,\sin\left(c+d\,x\right)\,{\left(-a^4-b\,a^3\right)}^{3/2}\,4{}\mathrm{i}+a^5\,\sin\left(c+d\,x\right)\,\sqrt{-a^4-b\,a^3}\,8{}\mathrm{i}+b^5\,\sin\left(c+d\,x\right)\,\sqrt{-a^4-b\,a^3}\,1{}\mathrm{i}-a\,b^4\,\sin\left(c+d\,x\right)\,\sqrt{-a^4-b\,a^3}\,1{}\mathrm{i}+a^4\,b\,\sin\left(c+d\,x\right)\,\sqrt{-a^4-b\,a^3}\,12{}\mathrm{i}-a^2\,b^3\,\sin\left(c+d\,x\right)\,\sqrt{-a^4-b\,a^3}\,5{}\mathrm{i}+a^3\,b^2\,\sin\left(c+d\,x\right)\,\sqrt{-a^4-b\,a^3}\,1{}\mathrm{i}}{3\,\cos\left(c+d\,x\right)\,a^5\,b^2+5\,\cos\left(c+d\,x\right)\,a^4\,b^3+\cos\left(c+d\,x\right)\,a^3\,b^4-\cos\left(c+d\,x\right)\,a^2\,b^5}\right)\,\sqrt{-a^4-b\,a^3}\,2{}\mathrm{i}}{d\,\left(2\,b^3+2\,a\,b^2\right)}","Not used",1,"(b^2*atan(sin(c + d*x)/cos(c + d*x)))/(d*(2*a*b^2 + 2*b^3)) - (2*a^2*atan(sin(c + d*x)/cos(c + d*x)))/(d*(2*a*b^2 + 2*b^3)) - (b^2*sin(2*c + 2*d*x))/(2*d*(2*a*b^2 + 2*b^3)) - (atan((a*sin(c + d*x)*(- a^3*b - a^4)^(3/2)*8i + b*sin(c + d*x)*(- a^3*b - a^4)^(3/2)*4i + a^5*sin(c + d*x)*(- a^3*b - a^4)^(1/2)*8i + b^5*sin(c + d*x)*(- a^3*b - a^4)^(1/2)*1i - a*b^4*sin(c + d*x)*(- a^3*b - a^4)^(1/2)*1i + a^4*b*sin(c + d*x)*(- a^3*b - a^4)^(1/2)*12i - a^2*b^3*sin(c + d*x)*(- a^3*b - a^4)^(1/2)*5i + a^3*b^2*sin(c + d*x)*(- a^3*b - a^4)^(1/2)*1i)/(a^3*b^4*cos(c + d*x) - a^2*b^5*cos(c + d*x) + 5*a^4*b^3*cos(c + d*x) + 3*a^5*b^2*cos(c + d*x)))*(- a^3*b - a^4)^(1/2)*2i)/(d*(2*a*b^2 + 2*b^3)) - (a*b*sin(2*c + 2*d*x))/(2*d*(2*a*b^2 + 2*b^3)) - (a*b*atan(sin(c + d*x)/cos(c + d*x)))/(d*(2*a*b^2 + 2*b^3))","B"
88,1,104,46,13.481130,"\text{Not used}","int(sin(c + d*x)^2/(a + b*sin(c + d*x)^2),x)","\frac{\mathrm{atan}\left(\frac{2\,a\,b^2\,\mathrm{tan}\left(c+d\,x\right)}{2\,a^2\,b+2\,a\,b^2}+\frac{2\,a^2\,b\,\mathrm{tan}\left(c+d\,x\right)}{2\,a^2\,b+2\,a\,b^2}\right)}{b\,d}+\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,\left(a+b\right)}}{a}\right)\,\sqrt{-a\,\left(a+b\right)}}{d\,\left(b^2+a\,b\right)}","Not used",1,"atan((2*a*b^2*tan(c + d*x))/(2*a*b^2 + 2*a^2*b) + (2*a^2*b*tan(c + d*x))/(2*a*b^2 + 2*a^2*b))/(b*d) + (atanh((tan(c + d*x)*(-a*(a + b))^(1/2))/a)*(-a*(a + b))^(1/2))/(d*(a*b + b^2))","B"
89,1,33,36,13.526988,"\text{Not used}","int(1/(a + b*sin(c + d*x)^2),x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a+b\right)}{\sqrt{a^2+b\,a}}\right)}{d\,\sqrt{a^2+b\,a}}","Not used",1,"atan((tan(c + d*x)*(a + b))/(a*b + a^2)^(1/2))/(d*(a*b + a^2)^(1/2))","B"
90,1,45,53,13.475099,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + b*sin(c + d*x)^2)),x)","-\frac{\mathrm{cot}\left(c+d\,x\right)}{a\,d}-\frac{b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{a+b}}{\sqrt{a}}\right)}{a^{3/2}\,d\,\sqrt{a+b}}","Not used",1,"- cot(c + d*x)/(a*d) - (b*atan((tan(c + d*x)*(a + b)^(1/2))/a^(1/2)))/(a^(3/2)*d*(a + b)^(1/2))","B"
91,1,68,77,13.431147,"\text{Not used}","int(1/(sin(c + d*x)^4*(a + b*sin(c + d*x)^2)),x)","\frac{b^2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{a+b}}{\sqrt{a}}\right)}{a^{5/2}\,d\,\sqrt{a+b}}-\frac{\frac{1}{3\,a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(a-b\right)}{a^2}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^3}","Not used",1,"(b^2*atan((tan(c + d*x)*(a + b)^(1/2))/a^(1/2)))/(a^(5/2)*d*(a + b)^(1/2)) - (1/(3*a) + (tan(c + d*x)^2*(a - b))/a^2)/(d*tan(c + d*x)^3)","B"
92,1,95,109,13.798436,"\text{Not used}","int(1/(sin(c + d*x)^6*(a + b*sin(c + d*x)^2)),x)","-\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(a^2-a\,b+b^2\right)+\frac{a^2}{5}-{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(\frac{a\,b}{3}-\frac{2\,a^2}{3}\right)}{a^3\,d\,{\mathrm{tan}\left(c+d\,x\right)}^5}-\frac{b^3\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{a+b}}{\sqrt{a}}\right)}{a^{7/2}\,d\,\sqrt{a+b}}","Not used",1,"- (tan(c + d*x)^4*(a^2 - a*b + b^2) + a^2/5 - tan(c + d*x)^2*((a*b)/3 - (2*a^2)/3))/(a^3*d*tan(c + d*x)^5) - (b^3*atan((tan(c + d*x)*(a + b)^(1/2))/a^(1/2)))/(a^(7/2)*d*(a + b)^(1/2))","B"
93,1,130,140,15.073984,"\text{Not used}","int(1/(sin(c + d*x)^8*(a + b*sin(c + d*x)^2)),x)","\frac{b^4\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{a+b}}{\sqrt{a}}\right)}{a^{9/2}\,d\,\sqrt{a+b}}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(a^3-\frac{2\,a^2\,b}{3}+\frac{a\,b^2}{3}\right)-{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(\frac{a^2\,b}{5}-\frac{3\,a^3}{5}\right)+{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(a^3-a^2\,b+a\,b^2-b^3\right)+\frac{a^3}{7}}{a^4\,d\,{\mathrm{tan}\left(c+d\,x\right)}^7}","Not used",1,"(b^4*atan((tan(c + d*x)*(a + b)^(1/2))/a^(1/2)))/(a^(9/2)*d*(a + b)^(1/2)) - (tan(c + d*x)^4*((a*b^2)/3 - (2*a^2*b)/3 + a^3) - tan(c + d*x)^2*((a^2*b)/5 - (3*a^3)/5) + tan(c + d*x)^6*(a*b^2 - a^2*b + a^3 - b^3) + a^3/7)/(a^4*d*tan(c + d*x)^7)","B"
94,1,123,128,0.217075,"\text{Not used}","int(sin(c + d*x)^7/(a + b*sin(c + d*x)^2)^2,x)","\frac{\cos\left(c+d\,x\right)\,\left(\frac{2\,\left(a+b\right)}{b^3}-\frac{3}{b^2}\right)}{d}+\frac{{\cos\left(c+d\,x\right)}^3}{3\,b^2\,d}+\frac{a^3\,\cos\left(c+d\,x\right)}{2\,d\,\left(a+b\right)\,\left(-b^4\,{\cos\left(c+d\,x\right)}^2+b^4+a\,b^3\right)}-\frac{a^2\,\mathrm{atanh}\left(\frac{\sqrt{b}\,\cos\left(c+d\,x\right)}{\sqrt{a+b}}\right)\,\left(5\,a+6\,b\right)}{2\,b^{7/2}\,d\,{\left(a+b\right)}^{3/2}}","Not used",1,"(cos(c + d*x)*((2*(a + b))/b^3 - 3/b^2))/d + cos(c + d*x)^3/(3*b^2*d) + (a^3*cos(c + d*x))/(2*d*(a + b)*(a*b^3 + b^4 - b^4*cos(c + d*x)^2)) - (a^2*atanh((b^(1/2)*cos(c + d*x))/(a + b)^(1/2))*(5*a + 6*b))/(2*b^(7/2)*d*(a + b)^(3/2))","B"
95,1,95,102,0.163758,"\text{Not used}","int(sin(c + d*x)^5/(a + b*sin(c + d*x)^2)^2,x)","\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{b}\,\cos\left(c+d\,x\right)}{\sqrt{a+b}}\right)\,\left(3\,a+4\,b\right)}{2\,b^{5/2}\,d\,{\left(a+b\right)}^{3/2}}-\frac{a^2\,\cos\left(c+d\,x\right)}{2\,d\,\left(a+b\right)\,\left(-b^3\,{\cos\left(c+d\,x\right)}^2+b^3+a\,b^2\right)}-\frac{\cos\left(c+d\,x\right)}{b^2\,d}","Not used",1,"(a*atanh((b^(1/2)*cos(c + d*x))/(a + b)^(1/2))*(3*a + 4*b))/(2*b^(5/2)*d*(a + b)^(3/2)) - (a^2*cos(c + d*x))/(2*d*(a + b)*(a*b^2 + b^3 - b^3*cos(c + d*x)^2)) - cos(c + d*x)/(b^2*d)","B"
96,1,71,83,13.490289,"\text{Not used}","int(sin(c + d*x)^3/(a + b*sin(c + d*x)^2)^2,x)","\frac{a\,\cos\left(c+d\,x\right)}{2\,b\,d\,\left(a+b\right)\,\left(-b\,{\cos\left(c+d\,x\right)}^2+a+b\right)}-\frac{\mathrm{atanh}\left(\frac{\sqrt{b}\,\cos\left(c+d\,x\right)}{\sqrt{a+b}}\right)\,\left(a+2\,b\right)}{2\,b^{3/2}\,d\,{\left(a+b\right)}^{3/2}}","Not used",1,"(a*cos(c + d*x))/(2*b*d*(a + b)*(a + b - b*cos(c + d*x)^2)) - (atanh((b^(1/2)*cos(c + d*x))/(a + b)^(1/2))*(a + 2*b))/(2*b^(3/2)*d*(a + b)^(3/2))","B"
97,1,62,74,0.105037,"\text{Not used}","int(sin(c + d*x)/(a + b*sin(c + d*x)^2)^2,x)","-\frac{\cos\left(c+d\,x\right)}{2\,d\,\left(a+b\right)\,\left(-b\,{\cos\left(c+d\,x\right)}^2+a+b\right)}-\frac{\mathrm{atanh}\left(\frac{\sqrt{b}\,\cos\left(c+d\,x\right)}{\sqrt{a+b}}\right)}{2\,\sqrt{b}\,d\,{\left(a+b\right)}^{3/2}}","Not used",1,"- cos(c + d*x)/(2*d*(a + b)*(a + b - b*cos(c + d*x)^2)) - atanh((b^(1/2)*cos(c + d*x))/(a + b)^(1/2))/(2*b^(1/2)*d*(a + b)^(3/2))","B"
98,1,2039,103,14.631471,"\text{Not used}","int(1/(sin(c + d*x)*(a + b*sin(c + d*x)^2)^2),x)","\frac{b\,\cos\left(c+d\,x\right)}{2\,a\,d\,\left(a+b\right)\,\left(-b\,{\cos\left(c+d\,x\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{\left(\frac{4\,a^6\,b^2+6\,a^5\,b^3+2\,a^4\,b^4}{2\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(16\,a^7\,b^2+64\,a^6\,b^3+80\,a^5\,b^4+32\,a^4\,b^5\right)}{8\,a^2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}\right)\,1{}\mathrm{i}}{2\,a^2}+\frac{\cos\left(c+d\,x\right)\,\left(13\,a^2\,b^3+20\,a\,b^4+8\,b^5\right)\,1{}\mathrm{i}}{4\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{a^2}-\frac{\frac{\left(\frac{4\,a^6\,b^2+6\,a^5\,b^3+2\,a^4\,b^4}{2\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(16\,a^7\,b^2+64\,a^6\,b^3+80\,a^5\,b^4+32\,a^4\,b^5\right)}{8\,a^2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}\right)\,1{}\mathrm{i}}{2\,a^2}-\frac{\cos\left(c+d\,x\right)\,\left(13\,a^2\,b^3+20\,a\,b^4+8\,b^5\right)\,1{}\mathrm{i}}{4\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{a^2}}{\frac{\frac{\frac{4\,a^6\,b^2+6\,a^5\,b^3+2\,a^4\,b^4}{2\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(16\,a^7\,b^2+64\,a^6\,b^3+80\,a^5\,b^4+32\,a^4\,b^5\right)}{8\,a^2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{2\,a^2}+\frac{\cos\left(c+d\,x\right)\,\left(13\,a^2\,b^3+20\,a\,b^4+8\,b^5\right)}{4\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{a^2}+\frac{\frac{\frac{4\,a^6\,b^2+6\,a^5\,b^3+2\,a^4\,b^4}{2\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(16\,a^7\,b^2+64\,a^6\,b^3+80\,a^5\,b^4+32\,a^4\,b^5\right)}{8\,a^2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{2\,a^2}-\frac{\cos\left(c+d\,x\right)\,\left(13\,a^2\,b^3+20\,a\,b^4+8\,b^5\right)}{4\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{a^2}-\frac{b^4+\frac{3\,a\,b^3}{2}}{a^5+2\,a^4\,b+a^3\,b^2}}\right)\,1{}\mathrm{i}}{a^2\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\cos\left(c+d\,x\right)\,\left(13\,a^2\,b^3+20\,a\,b^4+8\,b^5\right)}{2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}+\frac{\sqrt{b\,{\left(a+b\right)}^3}\,\left(\frac{4\,a^6\,b^2+6\,a^5\,b^3+2\,a^4\,b^4}{a^5+2\,a^4\,b+a^3\,b^2}-\frac{\cos\left(c+d\,x\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,\left(16\,a^7\,b^2+64\,a^6\,b^3+80\,a^5\,b^4+32\,a^4\,b^5\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,1{}\mathrm{i}}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}+\frac{\left(\frac{\cos\left(c+d\,x\right)\,\left(13\,a^2\,b^3+20\,a\,b^4+8\,b^5\right)}{2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}-\frac{\sqrt{b\,{\left(a+b\right)}^3}\,\left(\frac{4\,a^6\,b^2+6\,a^5\,b^3+2\,a^4\,b^4}{a^5+2\,a^4\,b+a^3\,b^2}+\frac{\cos\left(c+d\,x\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,\left(16\,a^7\,b^2+64\,a^6\,b^3+80\,a^5\,b^4+32\,a^4\,b^5\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,1{}\mathrm{i}}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}}{\frac{b^4+\frac{3\,a\,b^3}{2}}{a^5+2\,a^4\,b+a^3\,b^2}-\frac{\left(\frac{\cos\left(c+d\,x\right)\,\left(13\,a^2\,b^3+20\,a\,b^4+8\,b^5\right)}{2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}+\frac{\sqrt{b\,{\left(a+b\right)}^3}\,\left(\frac{4\,a^6\,b^2+6\,a^5\,b^3+2\,a^4\,b^4}{a^5+2\,a^4\,b+a^3\,b^2}-\frac{\cos\left(c+d\,x\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,\left(16\,a^7\,b^2+64\,a^6\,b^3+80\,a^5\,b^4+32\,a^4\,b^5\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}+\frac{\left(\frac{\cos\left(c+d\,x\right)\,\left(13\,a^2\,b^3+20\,a\,b^4+8\,b^5\right)}{2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}-\frac{\sqrt{b\,{\left(a+b\right)}^3}\,\left(\frac{4\,a^6\,b^2+6\,a^5\,b^3+2\,a^4\,b^4}{a^5+2\,a^4\,b+a^3\,b^2}+\frac{\cos\left(c+d\,x\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,\left(16\,a^7\,b^2+64\,a^6\,b^3+80\,a^5\,b^4+32\,a^4\,b^5\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}}\right)\,\sqrt{b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,1{}\mathrm{i}}{2\,d\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}","Not used",1,"(atan(((((cos(c + d*x)*(20*a*b^4 + 8*b^5 + 13*a^2*b^3))/(2*(2*a^3*b + a^4 + a^2*b^2)) + ((b*(a + b)^3)^(1/2)*((2*a^4*b^4 + 6*a^5*b^3 + 4*a^6*b^2)/(2*a^4*b + a^5 + a^3*b^2) - (cos(c + d*x)*(b*(a + b)^3)^(1/2)*(3*a + 2*b)*(32*a^4*b^5 + 80*a^5*b^4 + 64*a^6*b^3 + 16*a^7*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(b*(a + b)^3)^(1/2)*(3*a + 2*b)*1i)/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) + (((cos(c + d*x)*(20*a*b^4 + 8*b^5 + 13*a^2*b^3))/(2*(2*a^3*b + a^4 + a^2*b^2)) - ((b*(a + b)^3)^(1/2)*((2*a^4*b^4 + 6*a^5*b^3 + 4*a^6*b^2)/(2*a^4*b + a^5 + a^3*b^2) + (cos(c + d*x)*(b*(a + b)^3)^(1/2)*(3*a + 2*b)*(32*a^4*b^5 + 80*a^5*b^4 + 64*a^6*b^3 + 16*a^7*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(b*(a + b)^3)^(1/2)*(3*a + 2*b)*1i)/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))/(((3*a*b^3)/2 + b^4)/(2*a^4*b + a^5 + a^3*b^2) - (((cos(c + d*x)*(20*a*b^4 + 8*b^5 + 13*a^2*b^3))/(2*(2*a^3*b + a^4 + a^2*b^2)) + ((b*(a + b)^3)^(1/2)*((2*a^4*b^4 + 6*a^5*b^3 + 4*a^6*b^2)/(2*a^4*b + a^5 + a^3*b^2) - (cos(c + d*x)*(b*(a + b)^3)^(1/2)*(3*a + 2*b)*(32*a^4*b^5 + 80*a^5*b^4 + 64*a^6*b^3 + 16*a^7*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(b*(a + b)^3)^(1/2)*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) + (((cos(c + d*x)*(20*a*b^4 + 8*b^5 + 13*a^2*b^3))/(2*(2*a^3*b + a^4 + a^2*b^2)) - ((b*(a + b)^3)^(1/2)*((2*a^4*b^4 + 6*a^5*b^3 + 4*a^6*b^2)/(2*a^4*b + a^5 + a^3*b^2) + (cos(c + d*x)*(b*(a + b)^3)^(1/2)*(3*a + 2*b)*(32*a^4*b^5 + 80*a^5*b^4 + 64*a^6*b^3 + 16*a^7*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(b*(a + b)^3)^(1/2)*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2))))*(b*(a + b)^3)^(1/2)*(3*a + 2*b)*1i)/(2*d*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) - (atan((((((2*a^4*b^4 + 6*a^5*b^3 + 4*a^6*b^2)/(2*(2*a^4*b + a^5 + a^3*b^2)) - (cos(c + d*x)*(32*a^4*b^5 + 80*a^5*b^4 + 64*a^6*b^3 + 16*a^7*b^2))/(8*a^2*(2*a^3*b + a^4 + a^2*b^2)))*1i)/(2*a^2) + (cos(c + d*x)*(20*a*b^4 + 8*b^5 + 13*a^2*b^3)*1i)/(4*(2*a^3*b + a^4 + a^2*b^2)))/a^2 - ((((2*a^4*b^4 + 6*a^5*b^3 + 4*a^6*b^2)/(2*(2*a^4*b + a^5 + a^3*b^2)) + (cos(c + d*x)*(32*a^4*b^5 + 80*a^5*b^4 + 64*a^6*b^3 + 16*a^7*b^2))/(8*a^2*(2*a^3*b + a^4 + a^2*b^2)))*1i)/(2*a^2) - (cos(c + d*x)*(20*a*b^4 + 8*b^5 + 13*a^2*b^3)*1i)/(4*(2*a^3*b + a^4 + a^2*b^2)))/a^2)/((((2*a^4*b^4 + 6*a^5*b^3 + 4*a^6*b^2)/(2*(2*a^4*b + a^5 + a^3*b^2)) - (cos(c + d*x)*(32*a^4*b^5 + 80*a^5*b^4 + 64*a^6*b^3 + 16*a^7*b^2))/(8*a^2*(2*a^3*b + a^4 + a^2*b^2)))/(2*a^2) + (cos(c + d*x)*(20*a*b^4 + 8*b^5 + 13*a^2*b^3))/(4*(2*a^3*b + a^4 + a^2*b^2)))/a^2 + (((2*a^4*b^4 + 6*a^5*b^3 + 4*a^6*b^2)/(2*(2*a^4*b + a^5 + a^3*b^2)) + (cos(c + d*x)*(32*a^4*b^5 + 80*a^5*b^4 + 64*a^6*b^3 + 16*a^7*b^2))/(8*a^2*(2*a^3*b + a^4 + a^2*b^2)))/(2*a^2) - (cos(c + d*x)*(20*a*b^4 + 8*b^5 + 13*a^2*b^3))/(4*(2*a^3*b + a^4 + a^2*b^2)))/a^2 - ((3*a*b^3)/2 + b^4)/(2*a^4*b + a^5 + a^3*b^2)))*1i)/(a^2*d) + (b*cos(c + d*x))/(2*a*d*(a + b)*(a + b - b*cos(c + d*x)^2))","B"
99,1,2338,153,14.946324,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + b*sin(c + d*x)^2)^2),x)","-\frac{\frac{\cos\left(c+d\,x\right)\,\left(a^2+2\,a\,b+2\,b^2\right)}{2\,a^2\,\left(a+b\right)}-\frac{b\,{\cos\left(c+d\,x\right)}^3\,\left(a+2\,b\right)}{2\,a^2\,\left(a+b\right)}}{d\,\left(b\,{\cos\left(c+d\,x\right)}^4+\left(-a-2\,b\right)\,{\cos\left(c+d\,x\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a-4\,b\right)\,\left(\frac{\cos\left(c+d\,x\right)\,\left(a^4\,b^3-6\,a^3\,b^4+26\,a^2\,b^5+64\,a\,b^6+32\,b^7\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}+\frac{\left(\frac{-2\,a^9\,b^2+2\,a^8\,b^3+8\,a^7\,b^4+4\,a^6\,b^5}{a^8+2\,a^7\,b+a^6\,b^2}-\frac{\cos\left(c+d\,x\right)\,\left(a-4\,b\right)\,\left(16\,a^9\,b^2+64\,a^8\,b^3+80\,a^7\,b^4+32\,a^6\,b^5\right)}{8\,a^3\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}\right)\,\left(a-4\,b\right)}{4\,a^3}\right)\,1{}\mathrm{i}}{4\,a^3}+\frac{\left(a-4\,b\right)\,\left(\frac{\cos\left(c+d\,x\right)\,\left(a^4\,b^3-6\,a^3\,b^4+26\,a^2\,b^5+64\,a\,b^6+32\,b^7\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}-\frac{\left(\frac{-2\,a^9\,b^2+2\,a^8\,b^3+8\,a^7\,b^4+4\,a^6\,b^5}{a^8+2\,a^7\,b+a^6\,b^2}+\frac{\cos\left(c+d\,x\right)\,\left(a-4\,b\right)\,\left(16\,a^9\,b^2+64\,a^8\,b^3+80\,a^7\,b^4+32\,a^6\,b^5\right)}{8\,a^3\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}\right)\,\left(a-4\,b\right)}{4\,a^3}\right)\,1{}\mathrm{i}}{4\,a^3}}{\frac{-\frac{5\,a^3\,b^4}{4}+\frac{3\,a^2\,b^5}{2}+12\,a\,b^6+8\,b^7}{a^8+2\,a^7\,b+a^6\,b^2}-\frac{\left(a-4\,b\right)\,\left(\frac{\cos\left(c+d\,x\right)\,\left(a^4\,b^3-6\,a^3\,b^4+26\,a^2\,b^5+64\,a\,b^6+32\,b^7\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}+\frac{\left(\frac{-2\,a^9\,b^2+2\,a^8\,b^3+8\,a^7\,b^4+4\,a^6\,b^5}{a^8+2\,a^7\,b+a^6\,b^2}-\frac{\cos\left(c+d\,x\right)\,\left(a-4\,b\right)\,\left(16\,a^9\,b^2+64\,a^8\,b^3+80\,a^7\,b^4+32\,a^6\,b^5\right)}{8\,a^3\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}\right)\,\left(a-4\,b\right)}{4\,a^3}\right)}{4\,a^3}+\frac{\left(a-4\,b\right)\,\left(\frac{\cos\left(c+d\,x\right)\,\left(a^4\,b^3-6\,a^3\,b^4+26\,a^2\,b^5+64\,a\,b^6+32\,b^7\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}-\frac{\left(\frac{-2\,a^9\,b^2+2\,a^8\,b^3+8\,a^7\,b^4+4\,a^6\,b^5}{a^8+2\,a^7\,b+a^6\,b^2}+\frac{\cos\left(c+d\,x\right)\,\left(a-4\,b\right)\,\left(16\,a^9\,b^2+64\,a^8\,b^3+80\,a^7\,b^4+32\,a^6\,b^5\right)}{8\,a^3\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}\right)\,\left(a-4\,b\right)}{4\,a^3}\right)}{4\,a^3}}\right)\,\left(a-4\,b\right)\,1{}\mathrm{i}}{2\,a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,\left(\frac{\cos\left(c+d\,x\right)\,\left(a^4\,b^3-6\,a^3\,b^4+26\,a^2\,b^5+64\,a\,b^6+32\,b^7\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}+\frac{\left(\frac{-2\,a^9\,b^2+2\,a^8\,b^3+8\,a^7\,b^4+4\,a^6\,b^5}{a^8+2\,a^7\,b+a^6\,b^2}-\frac{\cos\left(c+d\,x\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,\left(16\,a^9\,b^2+64\,a^8\,b^3+80\,a^7\,b^4+32\,a^6\,b^5\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}}{a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3}\right)\,1{}\mathrm{i}}{a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3}+\frac{\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,\left(\frac{\cos\left(c+d\,x\right)\,\left(a^4\,b^3-6\,a^3\,b^4+26\,a^2\,b^5+64\,a\,b^6+32\,b^7\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}-\frac{\left(\frac{-2\,a^9\,b^2+2\,a^8\,b^3+8\,a^7\,b^4+4\,a^6\,b^5}{a^8+2\,a^7\,b+a^6\,b^2}+\frac{\cos\left(c+d\,x\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,\left(16\,a^9\,b^2+64\,a^8\,b^3+80\,a^7\,b^4+32\,a^6\,b^5\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}}{a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3}\right)\,1{}\mathrm{i}}{a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3}}{\frac{-\frac{5\,a^3\,b^4}{4}+\frac{3\,a^2\,b^5}{2}+12\,a\,b^6+8\,b^7}{a^8+2\,a^7\,b+a^6\,b^2}-\frac{\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,\left(\frac{\cos\left(c+d\,x\right)\,\left(a^4\,b^3-6\,a^3\,b^4+26\,a^2\,b^5+64\,a\,b^6+32\,b^7\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}+\frac{\left(\frac{-2\,a^9\,b^2+2\,a^8\,b^3+8\,a^7\,b^4+4\,a^6\,b^5}{a^8+2\,a^7\,b+a^6\,b^2}-\frac{\cos\left(c+d\,x\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,\left(16\,a^9\,b^2+64\,a^8\,b^3+80\,a^7\,b^4+32\,a^6\,b^5\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}}{a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3}\right)}{a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3}+\frac{\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,\left(\frac{\cos\left(c+d\,x\right)\,\left(a^4\,b^3-6\,a^3\,b^4+26\,a^2\,b^5+64\,a\,b^6+32\,b^7\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)}-\frac{\left(\frac{-2\,a^9\,b^2+2\,a^8\,b^3+8\,a^7\,b^4+4\,a^6\,b^5}{a^8+2\,a^7\,b+a^6\,b^2}+\frac{\cos\left(c+d\,x\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,\left(16\,a^9\,b^2+64\,a^8\,b^3+80\,a^7\,b^4+32\,a^6\,b^5\right)}{2\,\left(a^6+2\,a^5\,b+a^4\,b^2\right)\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}}{a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3}\right)}{a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3}}\right)\,\left(\frac{5\,a}{4}+b\right)\,\sqrt{b^3\,{\left(a+b\right)}^3}\,2{}\mathrm{i}}{d\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}","Not used",1,"- ((cos(c + d*x)*(2*a*b + a^2 + 2*b^2))/(2*a^2*(a + b)) - (b*cos(c + d*x)^3*(a + 2*b))/(2*a^2*(a + b)))/(d*(a + b + b*cos(c + d*x)^4 - cos(c + d*x)^2*(a + 2*b))) - (atan((((a - 4*b)*((cos(c + d*x)*(64*a*b^6 + 32*b^7 + 26*a^2*b^5 - 6*a^3*b^4 + a^4*b^3))/(2*(2*a^5*b + a^6 + a^4*b^2)) + (((4*a^6*b^5 + 8*a^7*b^4 + 2*a^8*b^3 - 2*a^9*b^2)/(2*a^7*b + a^8 + a^6*b^2) - (cos(c + d*x)*(a - 4*b)*(32*a^6*b^5 + 80*a^7*b^4 + 64*a^8*b^3 + 16*a^9*b^2))/(8*a^3*(2*a^5*b + a^6 + a^4*b^2)))*(a - 4*b))/(4*a^3))*1i)/(4*a^3) + ((a - 4*b)*((cos(c + d*x)*(64*a*b^6 + 32*b^7 + 26*a^2*b^5 - 6*a^3*b^4 + a^4*b^3))/(2*(2*a^5*b + a^6 + a^4*b^2)) - (((4*a^6*b^5 + 8*a^7*b^4 + 2*a^8*b^3 - 2*a^9*b^2)/(2*a^7*b + a^8 + a^6*b^2) + (cos(c + d*x)*(a - 4*b)*(32*a^6*b^5 + 80*a^7*b^4 + 64*a^8*b^3 + 16*a^9*b^2))/(8*a^3*(2*a^5*b + a^6 + a^4*b^2)))*(a - 4*b))/(4*a^3))*1i)/(4*a^3))/((12*a*b^6 + 8*b^7 + (3*a^2*b^5)/2 - (5*a^3*b^4)/4)/(2*a^7*b + a^8 + a^6*b^2) - ((a - 4*b)*((cos(c + d*x)*(64*a*b^6 + 32*b^7 + 26*a^2*b^5 - 6*a^3*b^4 + a^4*b^3))/(2*(2*a^5*b + a^6 + a^4*b^2)) + (((4*a^6*b^5 + 8*a^7*b^4 + 2*a^8*b^3 - 2*a^9*b^2)/(2*a^7*b + a^8 + a^6*b^2) - (cos(c + d*x)*(a - 4*b)*(32*a^6*b^5 + 80*a^7*b^4 + 64*a^8*b^3 + 16*a^9*b^2))/(8*a^3*(2*a^5*b + a^6 + a^4*b^2)))*(a - 4*b))/(4*a^3)))/(4*a^3) + ((a - 4*b)*((cos(c + d*x)*(64*a*b^6 + 32*b^7 + 26*a^2*b^5 - 6*a^3*b^4 + a^4*b^3))/(2*(2*a^5*b + a^6 + a^4*b^2)) - (((4*a^6*b^5 + 8*a^7*b^4 + 2*a^8*b^3 - 2*a^9*b^2)/(2*a^7*b + a^8 + a^6*b^2) + (cos(c + d*x)*(a - 4*b)*(32*a^6*b^5 + 80*a^7*b^4 + 64*a^8*b^3 + 16*a^9*b^2))/(8*a^3*(2*a^5*b + a^6 + a^4*b^2)))*(a - 4*b))/(4*a^3)))/(4*a^3)))*(a - 4*b)*1i)/(2*a^3*d) - (atan(((((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*((cos(c + d*x)*(64*a*b^6 + 32*b^7 + 26*a^2*b^5 - 6*a^3*b^4 + a^4*b^3))/(2*(2*a^5*b + a^6 + a^4*b^2)) + (((4*a^6*b^5 + 8*a^7*b^4 + 2*a^8*b^3 - 2*a^9*b^2)/(2*a^7*b + a^8 + a^6*b^2) - (cos(c + d*x)*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*(32*a^6*b^5 + 80*a^7*b^4 + 64*a^8*b^3 + 16*a^9*b^2))/(2*(2*a^5*b + a^6 + a^4*b^2)*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2))/(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2))*1i)/(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2) + (((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*((cos(c + d*x)*(64*a*b^6 + 32*b^7 + 26*a^2*b^5 - 6*a^3*b^4 + a^4*b^3))/(2*(2*a^5*b + a^6 + a^4*b^2)) - (((4*a^6*b^5 + 8*a^7*b^4 + 2*a^8*b^3 - 2*a^9*b^2)/(2*a^7*b + a^8 + a^6*b^2) + (cos(c + d*x)*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*(32*a^6*b^5 + 80*a^7*b^4 + 64*a^8*b^3 + 16*a^9*b^2))/(2*(2*a^5*b + a^6 + a^4*b^2)*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2))/(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2))*1i)/(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2))/((12*a*b^6 + 8*b^7 + (3*a^2*b^5)/2 - (5*a^3*b^4)/4)/(2*a^7*b + a^8 + a^6*b^2) - (((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*((cos(c + d*x)*(64*a*b^6 + 32*b^7 + 26*a^2*b^5 - 6*a^3*b^4 + a^4*b^3))/(2*(2*a^5*b + a^6 + a^4*b^2)) + (((4*a^6*b^5 + 8*a^7*b^4 + 2*a^8*b^3 - 2*a^9*b^2)/(2*a^7*b + a^8 + a^6*b^2) - (cos(c + d*x)*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*(32*a^6*b^5 + 80*a^7*b^4 + 64*a^8*b^3 + 16*a^9*b^2))/(2*(2*a^5*b + a^6 + a^4*b^2)*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2))/(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))/(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2) + (((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*((cos(c + d*x)*(64*a*b^6 + 32*b^7 + 26*a^2*b^5 - 6*a^3*b^4 + a^4*b^3))/(2*(2*a^5*b + a^6 + a^4*b^2)) - (((4*a^6*b^5 + 8*a^7*b^4 + 2*a^8*b^3 - 2*a^9*b^2)/(2*a^7*b + a^8 + a^6*b^2) + (cos(c + d*x)*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*(32*a^6*b^5 + 80*a^7*b^4 + 64*a^8*b^3 + 16*a^9*b^2))/(2*(2*a^5*b + a^6 + a^4*b^2)*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2))/(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))/(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*((5*a)/4 + b)*(b^3*(a + b)^3)^(1/2)*2i)/(d*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2))","B"
100,1,2295,148,16.064177,"\text{Not used}","int(sin(c + d*x)^6/(a + b*sin(c + d*x)^2)^2,x)","-\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(2\,a^2+2\,a\,b+b^2\right)}{2\,b^2\,\left(a+b\right)}+\frac{a\,\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+b\right)}{2\,b^2\,\left(a+b\right)}}{d\,\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^4+\left(2\,a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{4\,a^4\,b^6+10\,a^3\,b^7+8\,a^2\,b^8+2\,a\,b^9}{b^7+a\,b^6}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)\,\left(32\,a^4\,b^6+112\,a^3\,b^7+144\,a^2\,b^8+80\,a\,b^9+16\,b^{10}\right)}{2\,b^3\,\left(b^5+a\,b^4\right)}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)}{b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^6+96\,a^5\,b+90\,a^4\,b^2+20\,a^3\,b^3-10\,a^2\,b^4-4\,a\,b^5+b^6\right)}{2\,\left(b^5+a\,b^4\right)}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)\,1{}\mathrm{i}}{b^3}-\frac{\left(\frac{\left(\frac{4\,a^4\,b^6+10\,a^3\,b^7+8\,a^2\,b^8+2\,a\,b^9}{b^7+a\,b^6}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)\,\left(32\,a^4\,b^6+112\,a^3\,b^7+144\,a^2\,b^8+80\,a\,b^9+16\,b^{10}\right)}{2\,b^3\,\left(b^5+a\,b^4\right)}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)}{b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^6+96\,a^5\,b+90\,a^4\,b^2+20\,a^3\,b^3-10\,a^2\,b^4-4\,a\,b^5+b^6\right)}{2\,\left(b^5+a\,b^4\right)}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)\,1{}\mathrm{i}}{b^3}}{\frac{8\,a^6+16\,a^5\,b+\frac{3\,a^4\,b^2}{2}-\frac{13\,a^3\,b^3}{2}+\frac{5\,a^2\,b^4}{4}}{b^7+a\,b^6}+\frac{\left(\frac{\left(\frac{4\,a^4\,b^6+10\,a^3\,b^7+8\,a^2\,b^8+2\,a\,b^9}{b^7+a\,b^6}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)\,\left(32\,a^4\,b^6+112\,a^3\,b^7+144\,a^2\,b^8+80\,a\,b^9+16\,b^{10}\right)}{2\,b^3\,\left(b^5+a\,b^4\right)}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)}{b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^6+96\,a^5\,b+90\,a^4\,b^2+20\,a^3\,b^3-10\,a^2\,b^4-4\,a\,b^5+b^6\right)}{2\,\left(b^5+a\,b^4\right)}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)}{b^3}+\frac{\left(\frac{\left(\frac{4\,a^4\,b^6+10\,a^3\,b^7+8\,a^2\,b^8+2\,a\,b^9}{b^7+a\,b^6}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)\,\left(32\,a^4\,b^6+112\,a^3\,b^7+144\,a^2\,b^8+80\,a\,b^9+16\,b^{10}\right)}{2\,b^3\,\left(b^5+a\,b^4\right)}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)}{b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^6+96\,a^5\,b+90\,a^4\,b^2+20\,a^3\,b^3-10\,a^2\,b^4-4\,a\,b^5+b^6\right)}{2\,\left(b^5+a\,b^4\right)}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)}{b^3}}\right)\,\left(a\,1{}\mathrm{i}-\frac{b\,1{}\mathrm{i}}{4}\right)\,2{}\mathrm{i}}{b^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^6+96\,a^5\,b+90\,a^4\,b^2+20\,a^3\,b^3-10\,a^2\,b^4-4\,a\,b^5+b^6\right)}{2\,\left(b^5+a\,b^4\right)}+\frac{\left(\frac{4\,a^4\,b^6+10\,a^3\,b^7+8\,a^2\,b^8+2\,a\,b^9}{b^7+a\,b^6}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(32\,a^4\,b^6+112\,a^3\,b^7+144\,a^2\,b^8+80\,a\,b^9+16\,b^{10}\right)}{2\,\left(b^5+a\,b^4\right)\,\left(a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6\right)}\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}}{a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6}\right)\,1{}\mathrm{i}}{a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6}+\frac{\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^6+96\,a^5\,b+90\,a^4\,b^2+20\,a^3\,b^3-10\,a^2\,b^4-4\,a\,b^5+b^6\right)}{2\,\left(b^5+a\,b^4\right)}-\frac{\left(\frac{4\,a^4\,b^6+10\,a^3\,b^7+8\,a^2\,b^8+2\,a\,b^9}{b^7+a\,b^6}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(32\,a^4\,b^6+112\,a^3\,b^7+144\,a^2\,b^8+80\,a\,b^9+16\,b^{10}\right)}{2\,\left(b^5+a\,b^4\right)\,\left(a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6\right)}\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}}{a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6}\right)\,1{}\mathrm{i}}{a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6}}{\frac{8\,a^6+16\,a^5\,b+\frac{3\,a^4\,b^2}{2}-\frac{13\,a^3\,b^3}{2}+\frac{5\,a^2\,b^4}{4}}{b^7+a\,b^6}+\frac{\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^6+96\,a^5\,b+90\,a^4\,b^2+20\,a^3\,b^3-10\,a^2\,b^4-4\,a\,b^5+b^6\right)}{2\,\left(b^5+a\,b^4\right)}+\frac{\left(\frac{4\,a^4\,b^6+10\,a^3\,b^7+8\,a^2\,b^8+2\,a\,b^9}{b^7+a\,b^6}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(32\,a^4\,b^6+112\,a^3\,b^7+144\,a^2\,b^8+80\,a\,b^9+16\,b^{10}\right)}{2\,\left(b^5+a\,b^4\right)\,\left(a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6\right)}\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}}{a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6}\right)}{a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6}-\frac{\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^6+96\,a^5\,b+90\,a^4\,b^2+20\,a^3\,b^3-10\,a^2\,b^4-4\,a\,b^5+b^6\right)}{2\,\left(b^5+a\,b^4\right)}-\frac{\left(\frac{4\,a^4\,b^6+10\,a^3\,b^7+8\,a^2\,b^8+2\,a\,b^9}{b^7+a\,b^6}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(32\,a^4\,b^6+112\,a^3\,b^7+144\,a^2\,b^8+80\,a\,b^9+16\,b^{10}\right)}{2\,\left(b^5+a\,b^4\right)\,\left(a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6\right)}\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}}{a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6}\right)}{a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6}}\right)\,\left(a+\frac{5\,b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,2{}\mathrm{i}}{d\,\left(a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5+b^6\right)}","Not used",1,"(atan((((a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*((tan(c + d*x)*(96*a^5*b - 4*a*b^5 + 32*a^6 + b^6 - 10*a^2*b^4 + 20*a^3*b^3 + 90*a^4*b^2))/(2*(a*b^4 + b^5)) + (((2*a*b^9 + 8*a^2*b^8 + 10*a^3*b^7 + 4*a^4*b^6)/(a*b^6 + b^7) + (tan(c + d*x)*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*(80*a*b^9 + 16*b^10 + 144*a^2*b^8 + 112*a^3*b^7 + 32*a^4*b^6))/(2*(a*b^4 + b^5)*(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3)))*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2))/(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3))*1i)/(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3) + ((a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*((tan(c + d*x)*(96*a^5*b - 4*a*b^5 + 32*a^6 + b^6 - 10*a^2*b^4 + 20*a^3*b^3 + 90*a^4*b^2))/(2*(a*b^4 + b^5)) - (((2*a*b^9 + 8*a^2*b^8 + 10*a^3*b^7 + 4*a^4*b^6)/(a*b^6 + b^7) - (tan(c + d*x)*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*(80*a*b^9 + 16*b^10 + 144*a^2*b^8 + 112*a^3*b^7 + 32*a^4*b^6))/(2*(a*b^4 + b^5)*(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3)))*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2))/(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3))*1i)/(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3))/((16*a^5*b + 8*a^6 + (5*a^2*b^4)/4 - (13*a^3*b^3)/2 + (3*a^4*b^2)/2)/(a*b^6 + b^7) + ((a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*((tan(c + d*x)*(96*a^5*b - 4*a*b^5 + 32*a^6 + b^6 - 10*a^2*b^4 + 20*a^3*b^3 + 90*a^4*b^2))/(2*(a*b^4 + b^5)) + (((2*a*b^9 + 8*a^2*b^8 + 10*a^3*b^7 + 4*a^4*b^6)/(a*b^6 + b^7) + (tan(c + d*x)*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*(80*a*b^9 + 16*b^10 + 144*a^2*b^8 + 112*a^3*b^7 + 32*a^4*b^6))/(2*(a*b^4 + b^5)*(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3)))*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2))/(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3)))/(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3) - ((a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*((tan(c + d*x)*(96*a^5*b - 4*a*b^5 + 32*a^6 + b^6 - 10*a^2*b^4 + 20*a^3*b^3 + 90*a^4*b^2))/(2*(a*b^4 + b^5)) - (((2*a*b^9 + 8*a^2*b^8 + 10*a^3*b^7 + 4*a^4*b^6)/(a*b^6 + b^7) - (tan(c + d*x)*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*(80*a*b^9 + 16*b^10 + 144*a^2*b^8 + 112*a^3*b^7 + 32*a^4*b^6))/(2*(a*b^4 + b^5)*(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3)))*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2))/(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3)))/(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3)))*(a + (5*b)/4)*(-a^3*(a + b)^3)^(1/2)*2i)/(d*(3*a*b^5 + b^6 + 3*a^2*b^4 + a^3*b^3)) - (atan(((((((2*a*b^9 + 8*a^2*b^8 + 10*a^3*b^7 + 4*a^4*b^6)/(a*b^6 + b^7) - (tan(c + d*x)*(a*1i - (b*1i)/4)*(80*a*b^9 + 16*b^10 + 144*a^2*b^8 + 112*a^3*b^7 + 32*a^4*b^6))/(2*b^3*(a*b^4 + b^5)))*(a*1i - (b*1i)/4))/b^3 - (tan(c + d*x)*(96*a^5*b - 4*a*b^5 + 32*a^6 + b^6 - 10*a^2*b^4 + 20*a^3*b^3 + 90*a^4*b^2))/(2*(a*b^4 + b^5)))*(a*1i - (b*1i)/4)*1i)/b^3 - (((((2*a*b^9 + 8*a^2*b^8 + 10*a^3*b^7 + 4*a^4*b^6)/(a*b^6 + b^7) + (tan(c + d*x)*(a*1i - (b*1i)/4)*(80*a*b^9 + 16*b^10 + 144*a^2*b^8 + 112*a^3*b^7 + 32*a^4*b^6))/(2*b^3*(a*b^4 + b^5)))*(a*1i - (b*1i)/4))/b^3 + (tan(c + d*x)*(96*a^5*b - 4*a*b^5 + 32*a^6 + b^6 - 10*a^2*b^4 + 20*a^3*b^3 + 90*a^4*b^2))/(2*(a*b^4 + b^5)))*(a*1i - (b*1i)/4)*1i)/b^3)/((16*a^5*b + 8*a^6 + (5*a^2*b^4)/4 - (13*a^3*b^3)/2 + (3*a^4*b^2)/2)/(a*b^6 + b^7) + (((((2*a*b^9 + 8*a^2*b^8 + 10*a^3*b^7 + 4*a^4*b^6)/(a*b^6 + b^7) - (tan(c + d*x)*(a*1i - (b*1i)/4)*(80*a*b^9 + 16*b^10 + 144*a^2*b^8 + 112*a^3*b^7 + 32*a^4*b^6))/(2*b^3*(a*b^4 + b^5)))*(a*1i - (b*1i)/4))/b^3 - (tan(c + d*x)*(96*a^5*b - 4*a*b^5 + 32*a^6 + b^6 - 10*a^2*b^4 + 20*a^3*b^3 + 90*a^4*b^2))/(2*(a*b^4 + b^5)))*(a*1i - (b*1i)/4))/b^3 + (((((2*a*b^9 + 8*a^2*b^8 + 10*a^3*b^7 + 4*a^4*b^6)/(a*b^6 + b^7) + (tan(c + d*x)*(a*1i - (b*1i)/4)*(80*a*b^9 + 16*b^10 + 144*a^2*b^8 + 112*a^3*b^7 + 32*a^4*b^6))/(2*b^3*(a*b^4 + b^5)))*(a*1i - (b*1i)/4))/b^3 + (tan(c + d*x)*(96*a^5*b - 4*a*b^5 + 32*a^6 + b^6 - 10*a^2*b^4 + 20*a^3*b^3 + 90*a^4*b^2))/(2*(a*b^4 + b^5)))*(a*1i - (b*1i)/4))/b^3))*(a*1i - (b*1i)/4)*2i)/(b^3*d) - ((tan(c + d*x)^3*(2*a*b + 2*a^2 + b^2))/(2*b^2*(a + b)) + (a*tan(c + d*x)*(2*a + b))/(2*b^2*(a + b)))/(d*(a + tan(c + d*x)^4*(a + b) + tan(c + d*x)^2*(2*a + b)))","B"
101,1,1959,93,15.227395,"\text{Not used}","int(sin(c + d*x)^4/(a + b*sin(c + d*x)^2)^2,x)","\frac{a\,\mathrm{tan}\left(c+d\,x\right)}{2\,d\,\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)\,\left(b^2+a\,b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^4\,b^4+112\,a^3\,b^5+144\,a^2\,b^6+80\,a\,b^7+16\,b^8\right)}{8\,b^2\,\left(b^3+a\,b^2\right)}+\frac{\left(2\,a^3\,b^4+4\,a^2\,b^5+2\,a\,b^6\right)\,1{}\mathrm{i}}{2\,\left(b^4+a\,b^3\right)}}{2\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^4+28\,a^3\,b+33\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)}{4\,\left(b^3+a\,b^2\right)}}{b^2}-\frac{\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^4\,b^4+112\,a^3\,b^5+144\,a^2\,b^6+80\,a\,b^7+16\,b^8\right)}{8\,b^2\,\left(b^3+a\,b^2\right)}+\frac{\left(2\,a^3\,b^4+4\,a^2\,b^5+2\,a\,b^6\right)\,1{}\mathrm{i}}{2\,\left(b^4+a\,b^3\right)}}{2\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^4+28\,a^3\,b+33\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)}{4\,\left(b^3+a\,b^2\right)}}{b^2}}{\frac{a^3+\frac{7\,a^2\,b}{2}+3\,a\,b^2}{b^4+a\,b^3}+\frac{\frac{\left(-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^4\,b^4+112\,a^3\,b^5+144\,a^2\,b^6+80\,a\,b^7+16\,b^8\right)}{8\,b^2\,\left(b^3+a\,b^2\right)}+\frac{\left(2\,a^3\,b^4+4\,a^2\,b^5+2\,a\,b^6\right)\,1{}\mathrm{i}}{2\,\left(b^4+a\,b^3\right)}\right)\,1{}\mathrm{i}}{2\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^4+28\,a^3\,b+33\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)\,1{}\mathrm{i}}{4\,\left(b^3+a\,b^2\right)}}{b^2}+\frac{\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(32\,a^4\,b^4+112\,a^3\,b^5+144\,a^2\,b^6+80\,a\,b^7+16\,b^8\right)}{8\,b^2\,\left(b^3+a\,b^2\right)}+\frac{\left(2\,a^3\,b^4+4\,a^2\,b^5+2\,a\,b^6\right)\,1{}\mathrm{i}}{2\,\left(b^4+a\,b^3\right)}\right)\,1{}\mathrm{i}}{2\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^4+28\,a^3\,b+33\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)\,1{}\mathrm{i}}{4\,\left(b^3+a\,b^2\right)}}{b^2}}\right)}{b^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^4+28\,a^3\,b+33\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)}{2\,\left(b^3+a\,b^2\right)}-\frac{\left(\frac{2\,a^3\,b^4+4\,a^2\,b^5+2\,a\,b^6}{b^4+a\,b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)\,\left(32\,a^4\,b^4+112\,a^3\,b^5+144\,a^2\,b^6+80\,a\,b^7+16\,b^8\right)}{8\,\left(b^3+a\,b^2\right)\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)}{4\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}\right)\,\left(2\,a+3\,b\right)\,1{}\mathrm{i}}{4\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}+\frac{\sqrt{-a\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^4+28\,a^3\,b+33\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)}{2\,\left(b^3+a\,b^2\right)}+\frac{\left(\frac{2\,a^3\,b^4+4\,a^2\,b^5+2\,a\,b^6}{b^4+a\,b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)\,\left(32\,a^4\,b^4+112\,a^3\,b^5+144\,a^2\,b^6+80\,a\,b^7+16\,b^8\right)}{8\,\left(b^3+a\,b^2\right)\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)}{4\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}\right)\,\left(2\,a+3\,b\right)\,1{}\mathrm{i}}{4\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}}{\frac{a^3+\frac{7\,a^2\,b}{2}+3\,a\,b^2}{b^4+a\,b^3}-\frac{\sqrt{-a\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^4+28\,a^3\,b+33\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)}{2\,\left(b^3+a\,b^2\right)}-\frac{\left(\frac{2\,a^3\,b^4+4\,a^2\,b^5+2\,a\,b^6}{b^4+a\,b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)\,\left(32\,a^4\,b^4+112\,a^3\,b^5+144\,a^2\,b^6+80\,a\,b^7+16\,b^8\right)}{8\,\left(b^3+a\,b^2\right)\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)}{4\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}\right)\,\left(2\,a+3\,b\right)}{4\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}+\frac{\sqrt{-a\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^4+28\,a^3\,b+33\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)}{2\,\left(b^3+a\,b^2\right)}+\frac{\left(\frac{2\,a^3\,b^4+4\,a^2\,b^5+2\,a\,b^6}{b^4+a\,b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)\,\left(32\,a^4\,b^4+112\,a^3\,b^5+144\,a^2\,b^6+80\,a\,b^7+16\,b^8\right)}{8\,\left(b^3+a\,b^2\right)\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)}{4\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}\right)\,\left(2\,a+3\,b\right)}{4\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}}\right)\,\sqrt{-a\,{\left(a+b\right)}^3}\,\left(2\,a+3\,b\right)\,1{}\mathrm{i}}{2\,d\,\left(a^3\,b^2+3\,a^2\,b^3+3\,a\,b^4+b^5\right)}","Not used",1,"(a*tan(c + d*x))/(2*d*(a + tan(c + d*x)^2*(a + b))*(a*b + b^2)) - atan((((((2*a*b^6 + 4*a^2*b^5 + 2*a^3*b^4)*1i)/(2*(a*b^3 + b^4)) - (tan(c + d*x)*(80*a*b^7 + 16*b^8 + 144*a^2*b^6 + 112*a^3*b^5 + 32*a^4*b^4))/(8*b^2*(a*b^2 + b^3)))/(2*b^2) + (tan(c + d*x)*(16*a*b^3 + 28*a^3*b + 8*a^4 + 4*b^4 + 33*a^2*b^2))/(4*(a*b^2 + b^3)))/b^2 - ((((2*a*b^6 + 4*a^2*b^5 + 2*a^3*b^4)*1i)/(2*(a*b^3 + b^4)) + (tan(c + d*x)*(80*a*b^7 + 16*b^8 + 144*a^2*b^6 + 112*a^3*b^5 + 32*a^4*b^4))/(8*b^2*(a*b^2 + b^3)))/(2*b^2) - (tan(c + d*x)*(16*a*b^3 + 28*a^3*b + 8*a^4 + 4*b^4 + 33*a^2*b^2))/(4*(a*b^2 + b^3)))/b^2)/((3*a*b^2 + (7*a^2*b)/2 + a^3)/(a*b^3 + b^4) + (((((2*a*b^6 + 4*a^2*b^5 + 2*a^3*b^4)*1i)/(2*(a*b^3 + b^4)) - (tan(c + d*x)*(80*a*b^7 + 16*b^8 + 144*a^2*b^6 + 112*a^3*b^5 + 32*a^4*b^4))/(8*b^2*(a*b^2 + b^3)))*1i)/(2*b^2) + (tan(c + d*x)*(16*a*b^3 + 28*a^3*b + 8*a^4 + 4*b^4 + 33*a^2*b^2)*1i)/(4*(a*b^2 + b^3)))/b^2 + (((((2*a*b^6 + 4*a^2*b^5 + 2*a^3*b^4)*1i)/(2*(a*b^3 + b^4)) + (tan(c + d*x)*(80*a*b^7 + 16*b^8 + 144*a^2*b^6 + 112*a^3*b^5 + 32*a^4*b^4))/(8*b^2*(a*b^2 + b^3)))*1i)/(2*b^2) - (tan(c + d*x)*(16*a*b^3 + 28*a^3*b + 8*a^4 + 4*b^4 + 33*a^2*b^2)*1i)/(4*(a*b^2 + b^3)))/b^2))/(b^2*d) - (atan((((-a*(a + b)^3)^(1/2)*((tan(c + d*x)*(16*a*b^3 + 28*a^3*b + 8*a^4 + 4*b^4 + 33*a^2*b^2))/(2*(a*b^2 + b^3)) - (((2*a*b^6 + 4*a^2*b^5 + 2*a^3*b^4)/(a*b^3 + b^4) - (tan(c + d*x)*(-a*(a + b)^3)^(1/2)*(2*a + 3*b)*(80*a*b^7 + 16*b^8 + 144*a^2*b^6 + 112*a^3*b^5 + 32*a^4*b^4))/(8*(a*b^2 + b^3)*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))*(-a*(a + b)^3)^(1/2)*(2*a + 3*b))/(4*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))*(2*a + 3*b)*1i)/(4*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)) + ((-a*(a + b)^3)^(1/2)*((tan(c + d*x)*(16*a*b^3 + 28*a^3*b + 8*a^4 + 4*b^4 + 33*a^2*b^2))/(2*(a*b^2 + b^3)) + (((2*a*b^6 + 4*a^2*b^5 + 2*a^3*b^4)/(a*b^3 + b^4) + (tan(c + d*x)*(-a*(a + b)^3)^(1/2)*(2*a + 3*b)*(80*a*b^7 + 16*b^8 + 144*a^2*b^6 + 112*a^3*b^5 + 32*a^4*b^4))/(8*(a*b^2 + b^3)*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))*(-a*(a + b)^3)^(1/2)*(2*a + 3*b))/(4*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))*(2*a + 3*b)*1i)/(4*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))/((3*a*b^2 + (7*a^2*b)/2 + a^3)/(a*b^3 + b^4) - ((-a*(a + b)^3)^(1/2)*((tan(c + d*x)*(16*a*b^3 + 28*a^3*b + 8*a^4 + 4*b^4 + 33*a^2*b^2))/(2*(a*b^2 + b^3)) - (((2*a*b^6 + 4*a^2*b^5 + 2*a^3*b^4)/(a*b^3 + b^4) - (tan(c + d*x)*(-a*(a + b)^3)^(1/2)*(2*a + 3*b)*(80*a*b^7 + 16*b^8 + 144*a^2*b^6 + 112*a^3*b^5 + 32*a^4*b^4))/(8*(a*b^2 + b^3)*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))*(-a*(a + b)^3)^(1/2)*(2*a + 3*b))/(4*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))*(2*a + 3*b))/(4*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)) + ((-a*(a + b)^3)^(1/2)*((tan(c + d*x)*(16*a*b^3 + 28*a^3*b + 8*a^4 + 4*b^4 + 33*a^2*b^2))/(2*(a*b^2 + b^3)) + (((2*a*b^6 + 4*a^2*b^5 + 2*a^3*b^4)/(a*b^3 + b^4) + (tan(c + d*x)*(-a*(a + b)^3)^(1/2)*(2*a + 3*b)*(80*a*b^7 + 16*b^8 + 144*a^2*b^6 + 112*a^3*b^5 + 32*a^4*b^4))/(8*(a*b^2 + b^3)*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))*(-a*(a + b)^3)^(1/2)*(2*a + 3*b))/(4*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2)))*(2*a + 3*b))/(4*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2))))*(-a*(a + b)^3)^(1/2)*(2*a + 3*b)*1i)/(2*d*(3*a*b^4 + b^5 + 3*a^2*b^3 + a^3*b^2))","B"
102,1,72,78,13.433318,"\text{Not used}","int(sin(c + d*x)^2/(a + b*sin(c + d*x)^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,{\left(2\,a+2\,b\right)}^2}{4\,\sqrt{a}\,{\left(a+b\right)}^{3/2}}\right)}{2\,\sqrt{a}\,d\,{\left(a+b\right)}^{3/2}}-\frac{\mathrm{tan}\left(c+d\,x\right)}{2\,d\,\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)\,\left(a+b\right)}","Not used",1,"atan((tan(c + d*x)*(2*a + 2*b)^2)/(4*a^(1/2)*(a + b)^(3/2)))/(2*a^(1/2)*d*(a + b)^(3/2)) - tan(c + d*x)/(2*d*(a + tan(c + d*x)^2*(a + b))*(a + b))","B"
103,1,79,87,13.425822,"\text{Not used}","int(1/(a + b*sin(c + d*x)^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)}{2\,\sqrt{a}\,\sqrt{a+b}}\right)\,\left(2\,a+b\right)}{2\,a^{3/2}\,d\,{\left(a+b\right)}^{3/2}}+\frac{b\,\mathrm{tan}\left(c+d\,x\right)}{2\,a\,d\,\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)\,\left(a+b\right)}","Not used",1,"(atan((tan(c + d*x)*(2*a + 2*b))/(2*a^(1/2)*(a + b)^(1/2)))*(2*a + b))/(2*a^(3/2)*d*(a + b)^(3/2)) + (b*tan(c + d*x))/(2*a*d*(a + tan(c + d*x)^2*(a + b))*(a + b))","B"
104,1,132,127,13.599323,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + b*sin(c + d*x)^2)^2),x)","-\frac{\frac{1}{a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(2\,a^2+4\,a\,b+3\,b^2\right)}{2\,a^2\,\left(a+b\right)}}{d\,\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^3+a\,\mathrm{tan}\left(c+d\,x\right)\right)}-\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3+b\,a^2\right)\,\left(4\,a+3\,b\right)}{a^{5/2}\,\sqrt{a+b}\,\left(3\,b^2+4\,a\,b\right)}\right)\,\left(4\,a+3\,b\right)}{2\,a^{5/2}\,d\,{\left(a+b\right)}^{3/2}}","Not used",1,"- (1/a + (tan(c + d*x)^2*(4*a*b + 2*a^2 + 3*b^2))/(2*a^2*(a + b)))/(d*(a*tan(c + d*x) + tan(c + d*x)^3*(a + b))) - (b*atan((b*tan(c + d*x)*(a^2*b + a^3)*(4*a + 3*b))/(a^(5/2)*(a + b)^(1/2)*(4*a*b + 3*b^2)))*(4*a + 3*b))/(2*a^(5/2)*d*(a + b)^(3/2))","B"
105,1,164,162,14.398140,"\text{Not used}","int(1/(sin(c + d*x)^4*(a + b*sin(c + d*x)^2)^2),x)","\frac{b^2\,\mathrm{atan}\left(\frac{b^2\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4+b\,a^3\right)\,\left(6\,a+5\,b\right)}{a^{7/2}\,\left(5\,b^3+6\,a\,b^2\right)\,\sqrt{a+b}}\right)\,\left(6\,a+5\,b\right)}{2\,a^{7/2}\,d\,{\left(a+b\right)}^{3/2}}-\frac{\frac{1}{3\,a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(4\,a-5\,b\right)}{3\,a^2}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(-2\,a^3+6\,a\,b^2+5\,b^3\right)}{2\,a^3\,\left(a+b\right)}}{d\,\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^5+a\,{\mathrm{tan}\left(c+d\,x\right)}^3\right)}","Not used",1,"(b^2*atan((b^2*tan(c + d*x)*(a^3*b + a^4)*(6*a + 5*b))/(a^(7/2)*(6*a*b^2 + 5*b^3)*(a + b)^(1/2)))*(6*a + 5*b))/(2*a^(7/2)*d*(a + b)^(3/2)) - (1/(3*a) + (tan(c + d*x)^2*(4*a - 5*b))/(3*a^2) - (tan(c + d*x)^4*(6*a*b^2 - 2*a^3 + 5*b^3))/(2*a^3*(a + b)))/(d*(tan(c + d*x)^5*(a + b) + a*tan(c + d*x)^3))","B"
106,1,3189,148,17.956557,"\text{Not used}","int(sin(c + d*x)^6/(a + b*sin(c + d*x)^2)^3,x)","\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(4\,a^2+9\,b\,a\right)}{8\,\left(b^3+a\,b^2\right)}+\frac{a\,\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^2+7\,b\,a\right)}{8\,\left(a^2\,b^2+2\,a\,b^3+b^4\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4\,\left(a^2+2\,a\,b+b^2\right)+a^2+{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(2\,a^2+2\,b\,a\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^6\,b^6+2816\,a^5\,b^7+6400\,a^4\,b^8+7680\,a^3\,b^9+5120\,a^2\,b^{10}+1792\,a\,b^{11}+256\,b^{12}\right)}{128\,b^3\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}+\frac{\left(2\,a^5\,b^6+\frac{19\,a^4\,b^7}{2}+\frac{33\,a^3\,b^8}{2}+\frac{25\,a^2\,b^9}{2}+\frac{7\,a\,b^{10}}{2}\right)\,1{}\mathrm{i}}{2\,\left(a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9\right)}}{2\,b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^6+704\,a^5\,b+1600\,a^4\,b^2+1880\,a^3\,b^3+1185\,a^2\,b^4+384\,a\,b^5+64\,b^6\right)}{64\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}}{b^3}-\frac{\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^6\,b^6+2816\,a^5\,b^7+6400\,a^4\,b^8+7680\,a^3\,b^9+5120\,a^2\,b^{10}+1792\,a\,b^{11}+256\,b^{12}\right)}{128\,b^3\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}+\frac{\left(2\,a^5\,b^6+\frac{19\,a^4\,b^7}{2}+\frac{33\,a^3\,b^8}{2}+\frac{25\,a^2\,b^9}{2}+\frac{7\,a\,b^{10}}{2}\right)\,1{}\mathrm{i}}{2\,\left(a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9\right)}}{2\,b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^6+704\,a^5\,b+1600\,a^4\,b^2+1880\,a^3\,b^3+1185\,a^2\,b^4+384\,a\,b^5+64\,b^6\right)}{64\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}}{b^3}}{\frac{a^5+\frac{19\,a^4\,b}{4}+\frac{19\,a^3\,b^2}{2}+\frac{295\,a^2\,b^3}{32}+\frac{15\,a\,b^4}{4}}{a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9}+\frac{\frac{\left(-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^6\,b^6+2816\,a^5\,b^7+6400\,a^4\,b^8+7680\,a^3\,b^9+5120\,a^2\,b^{10}+1792\,a\,b^{11}+256\,b^{12}\right)}{128\,b^3\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}+\frac{\left(2\,a^5\,b^6+\frac{19\,a^4\,b^7}{2}+\frac{33\,a^3\,b^8}{2}+\frac{25\,a^2\,b^9}{2}+\frac{7\,a\,b^{10}}{2}\right)\,1{}\mathrm{i}}{2\,\left(a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9\right)}\right)\,1{}\mathrm{i}}{2\,b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^6+704\,a^5\,b+1600\,a^4\,b^2+1880\,a^3\,b^3+1185\,a^2\,b^4+384\,a\,b^5+64\,b^6\right)\,1{}\mathrm{i}}{64\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}}{b^3}+\frac{\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(512\,a^6\,b^6+2816\,a^5\,b^7+6400\,a^4\,b^8+7680\,a^3\,b^9+5120\,a^2\,b^{10}+1792\,a\,b^{11}+256\,b^{12}\right)}{128\,b^3\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}+\frac{\left(2\,a^5\,b^6+\frac{19\,a^4\,b^7}{2}+\frac{33\,a^3\,b^8}{2}+\frac{25\,a^2\,b^9}{2}+\frac{7\,a\,b^{10}}{2}\right)\,1{}\mathrm{i}}{2\,\left(a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9\right)}\right)\,1{}\mathrm{i}}{2\,b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^6+704\,a^5\,b+1600\,a^4\,b^2+1880\,a^3\,b^3+1185\,a^2\,b^4+384\,a\,b^5+64\,b^6\right)\,1{}\mathrm{i}}{64\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}}{b^3}}\right)}{b^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^6+704\,a^5\,b+1600\,a^4\,b^2+1880\,a^3\,b^3+1185\,a^2\,b^4+384\,a\,b^5+64\,b^6\right)}{32\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}-\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{2\,a^5\,b^6+\frac{19\,a^4\,b^7}{2}+\frac{33\,a^3\,b^8}{2}+\frac{25\,a^2\,b^9}{2}+\frac{7\,a\,b^{10}}{2}}{a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(8\,a^2+20\,a\,b+15\,b^2\right)\,\left(512\,a^6\,b^6+2816\,a^5\,b^7+6400\,a^4\,b^8+7680\,a^3\,b^9+5120\,a^2\,b^{10}+1792\,a\,b^{11}+256\,b^{12}\right)}{512\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}\right)\,\left(8\,a^2+20\,a\,b+15\,b^2\right)}{16\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}\right)\,\left(8\,a^2+20\,a\,b+15\,b^2\right)\,1{}\mathrm{i}}{16\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}+\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^6+704\,a^5\,b+1600\,a^4\,b^2+1880\,a^3\,b^3+1185\,a^2\,b^4+384\,a\,b^5+64\,b^6\right)}{32\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}+\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{2\,a^5\,b^6+\frac{19\,a^4\,b^7}{2}+\frac{33\,a^3\,b^8}{2}+\frac{25\,a^2\,b^9}{2}+\frac{7\,a\,b^{10}}{2}}{a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(8\,a^2+20\,a\,b+15\,b^2\right)\,\left(512\,a^6\,b^6+2816\,a^5\,b^7+6400\,a^4\,b^8+7680\,a^3\,b^9+5120\,a^2\,b^{10}+1792\,a\,b^{11}+256\,b^{12}\right)}{512\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}\right)\,\left(8\,a^2+20\,a\,b+15\,b^2\right)}{16\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}\right)\,\left(8\,a^2+20\,a\,b+15\,b^2\right)\,1{}\mathrm{i}}{16\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}}{\frac{a^5+\frac{19\,a^4\,b}{4}+\frac{19\,a^3\,b^2}{2}+\frac{295\,a^2\,b^3}{32}+\frac{15\,a\,b^4}{4}}{a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9}-\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^6+704\,a^5\,b+1600\,a^4\,b^2+1880\,a^3\,b^3+1185\,a^2\,b^4+384\,a\,b^5+64\,b^6\right)}{32\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}-\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{2\,a^5\,b^6+\frac{19\,a^4\,b^7}{2}+\frac{33\,a^3\,b^8}{2}+\frac{25\,a^2\,b^9}{2}+\frac{7\,a\,b^{10}}{2}}{a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(8\,a^2+20\,a\,b+15\,b^2\right)\,\left(512\,a^6\,b^6+2816\,a^5\,b^7+6400\,a^4\,b^8+7680\,a^3\,b^9+5120\,a^2\,b^{10}+1792\,a\,b^{11}+256\,b^{12}\right)}{512\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}\right)\,\left(8\,a^2+20\,a\,b+15\,b^2\right)}{16\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}\right)\,\left(8\,a^2+20\,a\,b+15\,b^2\right)}{16\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}+\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(128\,a^6+704\,a^5\,b+1600\,a^4\,b^2+1880\,a^3\,b^3+1185\,a^2\,b^4+384\,a\,b^5+64\,b^6\right)}{32\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)}+\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{2\,a^5\,b^6+\frac{19\,a^4\,b^7}{2}+\frac{33\,a^3\,b^8}{2}+\frac{25\,a^2\,b^9}{2}+\frac{7\,a\,b^{10}}{2}}{a^3\,b^6+3\,a^2\,b^7+3\,a\,b^8+b^9}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(8\,a^2+20\,a\,b+15\,b^2\right)\,\left(512\,a^6\,b^6+2816\,a^5\,b^7+6400\,a^4\,b^8+7680\,a^3\,b^9+5120\,a^2\,b^{10}+1792\,a\,b^{11}+256\,b^{12}\right)}{512\,\left(a^3\,b^4+3\,a^2\,b^5+3\,a\,b^6+b^7\right)\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}\right)\,\left(8\,a^2+20\,a\,b+15\,b^2\right)}{16\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}\right)\,\left(8\,a^2+20\,a\,b+15\,b^2\right)}{16\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}}\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(8\,a^2+20\,a\,b+15\,b^2\right)\,1{}\mathrm{i}}{8\,d\,\left(a^5\,b^3+5\,a^4\,b^4+10\,a^3\,b^5+10\,a^2\,b^6+5\,a\,b^7+b^8\right)}","Not used",1,"((tan(c + d*x)^3*(9*a*b + 4*a^2))/(8*(a*b^2 + b^3)) + (a*tan(c + d*x)*(7*a*b + 4*a^2))/(8*(2*a*b^3 + b^4 + a^2*b^2)))/(d*(tan(c + d*x)^4*(2*a*b + a^2 + b^2) + a^2 + tan(c + d*x)^2*(2*a*b + 2*a^2))) - atan(((((((7*a*b^10)/2 + (25*a^2*b^9)/2 + (33*a^3*b^8)/2 + (19*a^4*b^7)/2 + 2*a^5*b^6)*1i)/(2*(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6)) - (tan(c + d*x)*(1792*a*b^11 + 256*b^12 + 5120*a^2*b^10 + 7680*a^3*b^9 + 6400*a^4*b^8 + 2816*a^5*b^7 + 512*a^6*b^6))/(128*b^3*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)))/(2*b^3) + (tan(c + d*x)*(384*a*b^5 + 704*a^5*b + 128*a^6 + 64*b^6 + 1185*a^2*b^4 + 1880*a^3*b^3 + 1600*a^4*b^2))/(64*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)))/b^3 - (((((7*a*b^10)/2 + (25*a^2*b^9)/2 + (33*a^3*b^8)/2 + (19*a^4*b^7)/2 + 2*a^5*b^6)*1i)/(2*(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6)) + (tan(c + d*x)*(1792*a*b^11 + 256*b^12 + 5120*a^2*b^10 + 7680*a^3*b^9 + 6400*a^4*b^8 + 2816*a^5*b^7 + 512*a^6*b^6))/(128*b^3*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)))/(2*b^3) - (tan(c + d*x)*(384*a*b^5 + 704*a^5*b + 128*a^6 + 64*b^6 + 1185*a^2*b^4 + 1880*a^3*b^3 + 1600*a^4*b^2))/(64*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)))/b^3)/(((15*a*b^4)/4 + (19*a^4*b)/4 + a^5 + (295*a^2*b^3)/32 + (19*a^3*b^2)/2)/(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6) + ((((((7*a*b^10)/2 + (25*a^2*b^9)/2 + (33*a^3*b^8)/2 + (19*a^4*b^7)/2 + 2*a^5*b^6)*1i)/(2*(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6)) - (tan(c + d*x)*(1792*a*b^11 + 256*b^12 + 5120*a^2*b^10 + 7680*a^3*b^9 + 6400*a^4*b^8 + 2816*a^5*b^7 + 512*a^6*b^6))/(128*b^3*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)))*1i)/(2*b^3) + (tan(c + d*x)*(384*a*b^5 + 704*a^5*b + 128*a^6 + 64*b^6 + 1185*a^2*b^4 + 1880*a^3*b^3 + 1600*a^4*b^2)*1i)/(64*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)))/b^3 + ((((((7*a*b^10)/2 + (25*a^2*b^9)/2 + (33*a^3*b^8)/2 + (19*a^4*b^7)/2 + 2*a^5*b^6)*1i)/(2*(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6)) + (tan(c + d*x)*(1792*a*b^11 + 256*b^12 + 5120*a^2*b^10 + 7680*a^3*b^9 + 6400*a^4*b^8 + 2816*a^5*b^7 + 512*a^6*b^6))/(128*b^3*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)))*1i)/(2*b^3) - (tan(c + d*x)*(384*a*b^5 + 704*a^5*b + 128*a^6 + 64*b^6 + 1185*a^2*b^4 + 1880*a^3*b^3 + 1600*a^4*b^2)*1i)/(64*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)))/b^3))/(b^3*d) - (atan((((-a*(a + b)^5)^(1/2)*((tan(c + d*x)*(384*a*b^5 + 704*a^5*b + 128*a^6 + 64*b^6 + 1185*a^2*b^4 + 1880*a^3*b^3 + 1600*a^4*b^2))/(32*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)) - ((-a*(a + b)^5)^(1/2)*(((7*a*b^10)/2 + (25*a^2*b^9)/2 + (33*a^3*b^8)/2 + (19*a^4*b^7)/2 + 2*a^5*b^6)/(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6) - (tan(c + d*x)*(-a*(a + b)^5)^(1/2)*(20*a*b + 8*a^2 + 15*b^2)*(1792*a*b^11 + 256*b^12 + 5120*a^2*b^10 + 7680*a^3*b^9 + 6400*a^4*b^8 + 2816*a^5*b^7 + 512*a^6*b^6))/(512*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))*(20*a*b + 8*a^2 + 15*b^2))/(16*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))*(20*a*b + 8*a^2 + 15*b^2)*1i)/(16*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)) + ((-a*(a + b)^5)^(1/2)*((tan(c + d*x)*(384*a*b^5 + 704*a^5*b + 128*a^6 + 64*b^6 + 1185*a^2*b^4 + 1880*a^3*b^3 + 1600*a^4*b^2))/(32*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)) + ((-a*(a + b)^5)^(1/2)*(((7*a*b^10)/2 + (25*a^2*b^9)/2 + (33*a^3*b^8)/2 + (19*a^4*b^7)/2 + 2*a^5*b^6)/(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6) + (tan(c + d*x)*(-a*(a + b)^5)^(1/2)*(20*a*b + 8*a^2 + 15*b^2)*(1792*a*b^11 + 256*b^12 + 5120*a^2*b^10 + 7680*a^3*b^9 + 6400*a^4*b^8 + 2816*a^5*b^7 + 512*a^6*b^6))/(512*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))*(20*a*b + 8*a^2 + 15*b^2))/(16*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))*(20*a*b + 8*a^2 + 15*b^2)*1i)/(16*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))/(((15*a*b^4)/4 + (19*a^4*b)/4 + a^5 + (295*a^2*b^3)/32 + (19*a^3*b^2)/2)/(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6) - ((-a*(a + b)^5)^(1/2)*((tan(c + d*x)*(384*a*b^5 + 704*a^5*b + 128*a^6 + 64*b^6 + 1185*a^2*b^4 + 1880*a^3*b^3 + 1600*a^4*b^2))/(32*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)) - ((-a*(a + b)^5)^(1/2)*(((7*a*b^10)/2 + (25*a^2*b^9)/2 + (33*a^3*b^8)/2 + (19*a^4*b^7)/2 + 2*a^5*b^6)/(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6) - (tan(c + d*x)*(-a*(a + b)^5)^(1/2)*(20*a*b + 8*a^2 + 15*b^2)*(1792*a*b^11 + 256*b^12 + 5120*a^2*b^10 + 7680*a^3*b^9 + 6400*a^4*b^8 + 2816*a^5*b^7 + 512*a^6*b^6))/(512*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))*(20*a*b + 8*a^2 + 15*b^2))/(16*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))*(20*a*b + 8*a^2 + 15*b^2))/(16*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)) + ((-a*(a + b)^5)^(1/2)*((tan(c + d*x)*(384*a*b^5 + 704*a^5*b + 128*a^6 + 64*b^6 + 1185*a^2*b^4 + 1880*a^3*b^3 + 1600*a^4*b^2))/(32*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)) + ((-a*(a + b)^5)^(1/2)*(((7*a*b^10)/2 + (25*a^2*b^9)/2 + (33*a^3*b^8)/2 + (19*a^4*b^7)/2 + 2*a^5*b^6)/(3*a*b^8 + b^9 + 3*a^2*b^7 + a^3*b^6) + (tan(c + d*x)*(-a*(a + b)^5)^(1/2)*(20*a*b + 8*a^2 + 15*b^2)*(1792*a*b^11 + 256*b^12 + 5120*a^2*b^10 + 7680*a^3*b^9 + 6400*a^4*b^8 + 2816*a^5*b^7 + 512*a^6*b^6))/(512*(3*a*b^6 + b^7 + 3*a^2*b^5 + a^3*b^4)*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))*(20*a*b + 8*a^2 + 15*b^2))/(16*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3)))*(20*a*b + 8*a^2 + 15*b^2))/(16*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3))))*(-a*(a + b)^5)^(1/2)*(20*a*b + 8*a^2 + 15*b^2)*1i)/(8*d*(5*a*b^7 + b^8 + 10*a^2*b^6 + 10*a^3*b^5 + 5*a^4*b^4 + a^5*b^3))","B"
107,1,149,110,13.689109,"\text{Not used}","int(sin(c + d*x)^4/(a + b*sin(c + d*x)^2)^3,x)","\frac{3\,\mathrm{atan}\left(\frac{3\,\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)\,\left(\frac{8\,a^2}{3}+\frac{16\,a\,b}{3}+\frac{8\,b^2}{3}\right)}{16\,\sqrt{a}\,{\left(a+b\right)}^{5/2}}\right)}{8\,\sqrt{a}\,d\,{\left(a+b\right)}^{5/2}}-\frac{\frac{5\,{\mathrm{tan}\left(c+d\,x\right)}^3}{8\,\left(a+b\right)}+\frac{3\,a\,\mathrm{tan}\left(c+d\,x\right)}{8\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4\,\left(a^2+2\,a\,b+b^2\right)+a^2+{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(2\,a^2+2\,b\,a\right)\right)}","Not used",1,"(3*atan((3*tan(c + d*x)*(2*a + 2*b)*((16*a*b)/3 + (8*a^2)/3 + (8*b^2)/3))/(16*a^(1/2)*(a + b)^(5/2))))/(8*a^(1/2)*d*(a + b)^(5/2)) - ((5*tan(c + d*x)^3)/(8*(a + b)) + (3*a*tan(c + d*x))/(8*(2*a*b + a^2 + b^2)))/(d*(tan(c + d*x)^4*(2*a*b + a^2 + b^2) + a^2 + tan(c + d*x)^2*(2*a*b + 2*a^2)))","B"
108,1,159,131,13.854338,"\text{Not used}","int(sin(c + d*x)^2/(a + b*sin(c + d*x)^2)^3,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)\,\left(a^2+2\,a\,b+b^2\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{5/2}}\right)\,\left(4\,a+b\right)}{8\,a^{3/2}\,d\,{\left(a+b\right)}^{5/2}}-\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a+b\right)}{8\,\left(a^2+2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(4\,a-b\right)}{8\,a\,\left(a+b\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4\,\left(a^2+2\,a\,b+b^2\right)+a^2+{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(2\,a^2+2\,b\,a\right)\right)}","Not used",1,"(atan((tan(c + d*x)*(2*a + 2*b)*(2*a*b + a^2 + b^2))/(2*a^(1/2)*(a + b)^(5/2)))*(4*a + b))/(8*a^(3/2)*d*(a + b)^(5/2)) - ((tan(c + d*x)*(4*a + b))/(8*(2*a*b + a^2 + b^2)) + (tan(c + d*x)^3*(4*a - b))/(8*a*(a + b)))/(d*(tan(c + d*x)^4*(2*a*b + a^2 + b^2) + a^2 + tan(c + d*x)^2*(2*a*b + 2*a^2)))","B"
109,1,176,144,13.816973,"\text{Not used}","int(1/(a + b*sin(c + d*x)^2)^3,x)","\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(3\,b^2+8\,a\,b\right)}{8\,a^2\,\left(a+b\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5\,b^2+8\,a\,b\right)}{8\,a\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4\,\left(a^2+2\,a\,b+b^2\right)+a^2+{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(2\,a^2+2\,b\,a\right)\right)}+\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)\,\left(a^2+2\,a\,b+b^2\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{5/2}}\right)\,\left(8\,a^2+8\,a\,b+3\,b^2\right)}{8\,a^{5/2}\,d\,{\left(a+b\right)}^{5/2}}","Not used",1,"((tan(c + d*x)^3*(8*a*b + 3*b^2))/(8*a^2*(a + b)) + (tan(c + d*x)*(8*a*b + 5*b^2))/(8*a*(2*a*b + a^2 + b^2)))/(d*(tan(c + d*x)^4*(2*a*b + a^2 + b^2) + a^2 + tan(c + d*x)^2*(2*a*b + 2*a^2))) + (atan((tan(c + d*x)*(2*a + 2*b)*(2*a*b + a^2 + b^2))/(2*a^(1/2)*(a + b)^(5/2)))*(8*a*b + 8*a^2 + 3*b^2))/(8*a^(5/2)*d*(a + b)^(5/2))","B"
110,1,251,196,15.241093,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + b*sin(c + d*x)^2)^3),x)","-\frac{\frac{1}{a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(8\,a^3+24\,a^2\,b+36\,a\,b^2+15\,b^3\right)}{8\,a^3\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(16\,a^3+48\,a^2\,b+60\,a\,b^2+25\,b^3\right)}{8\,a^2\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^5\,\left(a^2+2\,a\,b+b^2\right)+a^2\,\mathrm{tan}\left(c+d\,x\right)+{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(2\,a^2+2\,b\,a\right)\right)}-\frac{3\,b\,\mathrm{atan}\left(\frac{3\,b\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)\,\left(8\,a^2+12\,a\,b+5\,b^2\right)}{a^{7/2}\,{\left(a+b\right)}^{3/2}\,\left(24\,a^2\,b+36\,a\,b^2+15\,b^3\right)}\right)\,\left(8\,a^2+12\,a\,b+5\,b^2\right)}{8\,a^{7/2}\,d\,{\left(a+b\right)}^{5/2}}","Not used",1,"- (1/a + (tan(c + d*x)^4*(36*a*b^2 + 24*a^2*b + 8*a^3 + 15*b^3))/(8*a^3*(a + b)) + (tan(c + d*x)^2*(60*a*b^2 + 48*a^2*b + 16*a^3 + 25*b^3))/(8*a^2*(2*a*b + a^2 + b^2)))/(d*(tan(c + d*x)^5*(2*a*b + a^2 + b^2) + a^2*tan(c + d*x) + tan(c + d*x)^3*(2*a*b + 2*a^2))) - (3*b*atan((3*b*tan(c + d*x)*(2*a^4*b + a^5 + a^3*b^2)*(12*a*b + 8*a^2 + 5*b^2))/(a^(7/2)*(a + b)^(3/2)*(36*a*b^2 + 24*a^2*b + 15*b^3)))*(12*a*b + 8*a^2 + 5*b^2))/(8*a^(7/2)*d*(a + b)^(5/2))","B"
111,1,339,206,15.436023,"\text{Not used}","int(1/(a + b*sin(c + d*x)^2)^4,x)","\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(24\,a^2\,b+30\,a\,b^2+11\,b^3\right)}{16\,a\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(18\,a^2\,b+18\,a\,b^2+5\,b^3\right)}{6\,a^2\,\left(a^2+2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(24\,a^2\,b+18\,a\,b^2+5\,b^3\right)}{16\,a^3\,\left(a+b\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^6\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)+{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(3\,a^3+3\,b\,a^2\right)+{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(3\,a^3+6\,a^2\,b+3\,a\,b^2\right)+a^3\right)}+\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+b\right)\,\left(2\,a+2\,b\right)\,\left(8\,a^2+8\,a\,b+5\,b^2\right)\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{7/2}\,\left(16\,a^3+24\,a^2\,b+18\,a\,b^2+5\,b^3\right)}\right)\,\left(2\,a+b\right)\,\left(8\,a^2+8\,a\,b+5\,b^2\right)}{16\,a^{7/2}\,d\,{\left(a+b\right)}^{7/2}}","Not used",1,"((tan(c + d*x)*(30*a*b^2 + 24*a^2*b + 11*b^3))/(16*a*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) + (tan(c + d*x)^3*(18*a*b^2 + 18*a^2*b + 5*b^3))/(6*a^2*(2*a*b + a^2 + b^2)) + (tan(c + d*x)^5*(18*a*b^2 + 24*a^2*b + 5*b^3))/(16*a^3*(a + b)))/(d*(tan(c + d*x)^6*(3*a*b^2 + 3*a^2*b + a^3 + b^3) + tan(c + d*x)^2*(3*a^2*b + 3*a^3) + tan(c + d*x)^4*(3*a*b^2 + 6*a^2*b + 3*a^3) + a^3)) + (atan((tan(c + d*x)*(2*a + b)*(2*a + 2*b)*(8*a*b + 8*a^2 + 5*b^2)*(3*a*b^2 + 3*a^2*b + a^3 + b^3))/(2*a^(1/2)*(a + b)^(7/2)*(18*a*b^2 + 24*a^2*b + 16*a^3 + 5*b^3)))*(2*a + b)*(8*a*b + 8*a^2 + 5*b^2))/(16*a^(7/2)*d*(a + b)^(7/2))","B"
112,1,450,279,16.104325,"\text{Not used}","int(1/(a + b*sin(c + d*x)^2)^5,x)","\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^3\,b+480\,a^2\,b^2+352\,a\,b^3+93\,b^4\right)}{128\,a\,\left(a^4+4\,a^3\,b+6\,a^2\,b^2+4\,a\,b^3+b^4\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(2304\,a^3\,b+3744\,a^2\,b^2+2336\,a\,b^3+511\,b^4\right)}{384\,a^2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(2304\,a^3\,b+3168\,a^2\,b^2+1760\,a\,b^3+385\,b^4\right)}{384\,a^3\,\left(a^2+2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^7\,\left(256\,a^3\,b+288\,a^2\,b^2+160\,a\,b^3+35\,b^4\right)}{128\,a^4\,\left(a+b\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4\,\left(6\,a^4+12\,a^3\,b+6\,a^2\,b^2\right)+{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(4\,a^4+4\,b\,a^3\right)+{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(4\,a^4+12\,a^3\,b+12\,a^2\,b^2+4\,a\,b^3\right)+a^4+{\mathrm{tan}\left(c+d\,x\right)}^8\,\left(a^4+4\,a^3\,b+6\,a^2\,b^2+4\,a\,b^3+b^4\right)\right)}+\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)\,\left(a^4+4\,a^3\,b+6\,a^2\,b^2+4\,a\,b^3+b^4\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{9/2}}\right)\,\left(128\,a^4+256\,a^3\,b+288\,a^2\,b^2+160\,a\,b^3+35\,b^4\right)}{128\,a^{9/2}\,d\,{\left(a+b\right)}^{9/2}}","Not used",1,"((tan(c + d*x)*(352*a*b^3 + 256*a^3*b + 93*b^4 + 480*a^2*b^2))/(128*a*(4*a*b^3 + 4*a^3*b + a^4 + b^4 + 6*a^2*b^2)) + (tan(c + d*x)^3*(2336*a*b^3 + 2304*a^3*b + 511*b^4 + 3744*a^2*b^2))/(384*a^2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) + (tan(c + d*x)^5*(1760*a*b^3 + 2304*a^3*b + 385*b^4 + 3168*a^2*b^2))/(384*a^3*(2*a*b + a^2 + b^2)) + (tan(c + d*x)^7*(160*a*b^3 + 256*a^3*b + 35*b^4 + 288*a^2*b^2))/(128*a^4*(a + b)))/(d*(tan(c + d*x)^4*(12*a^3*b + 6*a^4 + 6*a^2*b^2) + tan(c + d*x)^2*(4*a^3*b + 4*a^4) + tan(c + d*x)^6*(4*a*b^3 + 12*a^3*b + 4*a^4 + 12*a^2*b^2) + a^4 + tan(c + d*x)^8*(4*a*b^3 + 4*a^3*b + a^4 + b^4 + 6*a^2*b^2))) + (atan((tan(c + d*x)*(2*a + 2*b)*(4*a*b^3 + 4*a^3*b + a^4 + b^4 + 6*a^2*b^2))/(2*a^(1/2)*(a + b)^(9/2)))*(160*a*b^3 + 256*a^3*b + 128*a^4 + 35*b^4 + 288*a^2*b^2))/(128*a^(9/2)*d*(a + b)^(9/2))","B"
113,1,18,11,13.376610,"\text{Not used}","int(sin(x)/(sin(x)^2 + 1)^(1/2),x)","\ln\left(\sqrt{{\sin\left(x\right)}^2+1}+\cos\left(x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}","Not used",1,"log(cos(x)*1i + (sin(x)^2 + 1)^(1/2))*1i","B"
114,0,-1,30,0.000000,"\text{Not used}","int(sin(x)*(sin(x)^2 + 1)^(1/2),x)","\int \sin\left(x\right)\,\sqrt{{\sin\left(x\right)}^2+1} \,d x","Not used",1,"int(sin(x)*(sin(x)^2 + 1)^(1/2), x)","F"
115,0,-1,15,0.000000,"\text{Not used}","int(sin(3*x + 7)/(sin(3*x + 7)^2 + 3)^(1/2),x)","\int \frac{\sin\left(3\,x+7\right)}{\sqrt{{\sin\left(3\,x+7\right)}^2+3}} \,d x","Not used",1,"int(sin(3*x + 7)/(sin(3*x + 7)^2 + 3)^(1/2), x)","F"
116,0,-1,53,0.000000,"\text{Not used}","int((a - a*sin(x)^2)^(5/2),x)","\int {\left(a-a\,{\sin\left(x\right)}^2\right)}^{5/2} \,d x","Not used",1,"int((a - a*sin(x)^2)^(5/2), x)","F"
117,0,-1,34,0.000000,"\text{Not used}","int((a - a*sin(x)^2)^(3/2),x)","\int {\left(a-a\,{\sin\left(x\right)}^2\right)}^{3/2} \,d x","Not used",1,"int((a - a*sin(x)^2)^(3/2), x)","F"
118,1,46,13,0.215861,"\text{Not used}","int((a - a*sin(x)^2)^(1/2),x)","\frac{\sqrt{2}\,\sqrt{a}\,\sqrt{\cos\left(2\,x\right)+1}\,\left(\cos\left(2\,x\right)-1+\sin\left(2\,x\right)\,1{}\mathrm{i}\right)}{2\,\left(\cos\left(2\,x\right)\,1{}\mathrm{i}-\sin\left(2\,x\right)+1{}\mathrm{i}\right)}","Not used",1,"(2^(1/2)*a^(1/2)*(cos(2*x) + 1)^(1/2)*(cos(2*x) + sin(2*x)*1i - 1))/(2*(cos(2*x)*1i - sin(2*x) + 1i))","B"
119,0,-1,16,0.000000,"\text{Not used}","int(1/(a - a*sin(x)^2)^(1/2),x)","\int \frac{1}{\sqrt{a-a\,{\sin\left(x\right)}^2}} \,d x","Not used",1,"int(1/(a - a*sin(x)^2)^(1/2), x)","F"
120,0,-1,42,0.000000,"\text{Not used}","int(1/(a - a*sin(x)^2)^(3/2),x)","\int \frac{1}{{\left(a-a\,{\sin\left(x\right)}^2\right)}^{3/2}} \,d x","Not used",1,"int(1/(a - a*sin(x)^2)^(3/2), x)","F"
121,0,-1,61,0.000000,"\text{Not used}","int(1/(a - a*sin(x)^2)^(5/2),x)","\int \frac{1}{{\left(a-a\,{\sin\left(x\right)}^2\right)}^{5/2}} \,d x","Not used",1,"int(1/(a - a*sin(x)^2)^(5/2), x)","F"
122,0,-1,125,0.000000,"\text{Not used}","int(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\sin\left(e+f\,x\right)}^3\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
123,0,-1,78,0.000000,"\text{Not used}","int(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2),x)","\int \sin\left(e+f\,x\right)\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
124,0,-1,83,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x),x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x), x)","F"
125,0,-1,84,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x)^3,x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{{\sin\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x)^3, x)","F"
126,0,-1,143,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x)^5,x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{{\sin\left(e+f\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x)^5, x)","F"
127,0,-1,259,0.000000,"\text{Not used}","int(sin(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\sin\left(e+f\,x\right)}^4\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(sin(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
128,0,-1,159,0.000000,"\text{Not used}","int(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\sin\left(e+f\,x\right)}^2\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
129,0,-1,51,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2),x)","\left\{\begin{array}{cl} \frac{\sqrt{a}\,\mathrm{E}\left(e+f\,x\middle|-\frac{b}{a}\right)}{f} & \text{\ if\ \ }0<a\\ \int \sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x & \text{\ if\ \ }\neg 0<a \end{array}\right.","Not used",1,"piecewise(0 < a, (a^(1/2)*ellipticE(e + f*x, -b/a))/f, ~0 < a, int((a + b*sin(e + f*x)^2)^(1/2), x))","F"
130,0,-1,174,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x)^2,x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x)^2, x)","F"
131,0,-1,234,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x)^4,x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{{\sin\left(e+f\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/sin(e + f*x)^4, x)","F"
132,0,-1,169,0.000000,"\text{Not used}","int(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\sin\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
133,0,-1,114,0.000000,"\text{Not used}","int(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2),x)","\int \sin\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
134,0,-1,122,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x),x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x), x)","F"
135,0,-1,128,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^3,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\sin\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^3, x)","F"
136,0,-1,128,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^5,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\sin\left(e+f\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^5, x)","F"
137,0,-1,197,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^7,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\sin\left(e+f\,x\right)}^7} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^7, x)","F"
138,0,-1,325,0.000000,"\text{Not used}","int(sin(e + f*x)^4*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\sin\left(e+f\,x\right)}^4\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(sin(e + f*x)^4*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
139,0,-1,218,0.000000,"\text{Not used}","int(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\sin\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
140,0,-1,154,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2),x)","\int {\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2), x)","F"
141,0,-1,181,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^2,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^2, x)","F"
142,0,-1,236,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^4,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\sin\left(e+f\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/sin(e + f*x)^4, x)","F"
143,0,-1,210,0.000000,"\text{Not used}","int((a + b*sin(c + d*x)^2)^(5/2),x)","\int {\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^{5/2} \,d x","Not used",1,"int((a + b*sin(c + d*x)^2)^(5/2), x)","F"
144,0,-1,83,0.000000,"\text{Not used}","int(sin(e + f*x)^3/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^3}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(sin(e + f*x)^3/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
145,0,-1,41,0.000000,"\text{Not used}","int(sin(e + f*x)/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{\sin\left(e+f\,x\right)}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(sin(e + f*x)/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
146,0,-1,41,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2)),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2)), x)","F"
147,0,-1,89,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^3\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2)), x)","F"
148,0,-1,206,0.000000,"\text{Not used}","int(sin(e + f*x)^4/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^4}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(sin(e + f*x)^4/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
149,0,-1,111,0.000000,"\text{Not used}","int(sin(e + f*x)^2/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^2}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(sin(e + f*x)^2/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
150,0,-1,51,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{1}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
151,0,-1,177,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2)), x)","F"
152,0,-1,244,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^4\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(sin(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2)), x)","F"
153,0,-1,79,0.000000,"\text{Not used}","int(sin(e + f*x)^3/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^3}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(sin(e + f*x)^3/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
154,1,119,34,15.179470,"\text{Not used}","int(sin(e + f*x)/(a + b*sin(e + f*x)^2)^(3/2),x)","-\frac{\sqrt{2}\,\sqrt{2\,a+b-b\,\cos\left(2\,e+2\,f\,x\right)}\,\left(4\,a\,\cos\left(e+f\,x\right)+b\,\cos\left(e+f\,x\right)-b\,\cos\left(3\,e+3\,f\,x\right)\right)}{f\,\left(a+b\right)\,\left(8\,a\,b+8\,a^2+3\,b^2-4\,b^2\,\cos\left(2\,e+2\,f\,x\right)+b^2\,\cos\left(4\,e+4\,f\,x\right)-8\,a\,b\,\cos\left(2\,e+2\,f\,x\right)\right)}","Not used",1,"-(2^(1/2)*(2*a + b - b*cos(2*e + 2*f*x))^(1/2)*(4*a*cos(e + f*x) + b*cos(e + f*x) - b*cos(3*e + 3*f*x)))/(f*(a + b)*(8*a*b + 8*a^2 + 3*b^2 - 4*b^2*cos(2*e + 2*f*x) + b^2*cos(4*e + 4*f*x) - 8*a*b*cos(2*e + 2*f*x)))","B"
155,0,-1,79,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2)),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2)), x)","F"
156,0,-1,134,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2)), x)","F"
157,0,-1,274,0.000000,"\text{Not used}","int(sin(e + f*x)^6/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^6}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(sin(e + f*x)^6/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
158,0,-1,202,0.000000,"\text{Not used}","int(sin(e + f*x)^4/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^4}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(sin(e + f*x)^4/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
159,0,-1,153,0.000000,"\text{Not used}","int(sin(e + f*x)^2/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^2}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(sin(e + f*x)^2/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
160,0,-1,101,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{1}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
161,0,-1,235,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2)), x)","F"
162,0,-1,137,0.000000,"\text{Not used}","int(sin(e + f*x)^5/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^5}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(sin(e + f*x)^5/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
163,1,176,81,20.866153,"\text{Not used}","int(sin(e + f*x)^3/(a + b*sin(e + f*x)^2)^(5/2),x)","\frac{2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)\,\sqrt{a+b\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,\left(a+3\,b-10\,a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+a\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-6\,b\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+3\,b\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\right)}{3\,f\,{\left(a+b\right)}^2\,{\left(b-4\,a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-2\,b\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+b\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\right)}^2}","Not used",1,"(2*exp(e*1i + f*x*1i)*(exp(e*2i + f*x*2i) + 1)*(a + b*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*(a + 3*b - 10*a*exp(e*2i + f*x*2i) + a*exp(e*4i + f*x*4i) - 6*b*exp(e*2i + f*x*2i) + 3*b*exp(e*4i + f*x*4i)))/(3*f*(a + b)^2*(b - 4*a*exp(e*2i + f*x*2i) - 2*b*exp(e*2i + f*x*2i) + b*exp(e*4i + f*x*4i))^2)","B"
164,1,159,73,20.795044,"\text{Not used}","int(sin(e + f*x)/(a + b*sin(e + f*x)^2)^(5/2),x)","\frac{4\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)\,\sqrt{a+b\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,\left(b-6\,a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-4\,b\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+b\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\right)}{3\,f\,{\left(a+b\right)}^2\,{\left(b-4\,a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-2\,b\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+b\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\right)}^2}","Not used",1,"(4*exp(e*1i + f*x*1i)*(exp(e*2i + f*x*2i) + 1)*(a + b*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*(b - 6*a*exp(e*2i + f*x*2i) - 4*b*exp(e*2i + f*x*2i) + b*exp(e*4i + f*x*4i)))/(3*f*(a + b)^2*(b - 4*a*exp(e*2i + f*x*2i) - 2*b*exp(e*2i + f*x*2i) + b*exp(e*4i + f*x*4i))^2)","B"
165,0,-1,129,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(5/2)),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(5/2)), x)","F"
166,0,-1,285,0.000000,"\text{Not used}","int(sin(e + f*x)^6/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^6}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(sin(e + f*x)^6/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
167,0,-1,269,0.000000,"\text{Not used}","int(sin(e + f*x)^4/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^4}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(sin(e + f*x)^4/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
168,0,-1,221,0.000000,"\text{Not used}","int(sin(e + f*x)^2/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^2}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(sin(e + f*x)^2/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
169,0,-1,223,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{1}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
170,0,-1,322,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(5/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^(5/2)), x)","F"
171,0,-1,122,0.000000,"\text{Not used}","int((d*sin(e + f*x))^m*(a + b*sin(e + f*x)^2)^p,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^m\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int((d*sin(e + f*x))^m*(a + b*sin(e + f*x)^2)^p, x)","F"
172,0,-1,220,0.000000,"\text{Not used}","int(sin(e + f*x)^5*(a + b*sin(e + f*x)^2)^p,x)","\int {\sin\left(e+f\,x\right)}^5\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(sin(e + f*x)^5*(a + b*sin(e + f*x)^2)^p, x)","F"
173,0,-1,131,0.000000,"\text{Not used}","int(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^p,x)","\int {\sin\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(sin(e + f*x)^3*(a + b*sin(e + f*x)^2)^p, x)","F"
174,0,-1,74,0.000000,"\text{Not used}","int(sin(e + f*x)*(a + b*sin(e + f*x)^2)^p,x)","\int \sin\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(sin(e + f*x)*(a + b*sin(e + f*x)^2)^p, x)","F"
175,0,-1,83,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/sin(e + f*x),x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/sin(e + f*x), x)","F"
176,0,-1,83,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/sin(e + f*x)^3,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{{\sin\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/sin(e + f*x)^3, x)","F"
177,0,-1,83,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/sin(e + f*x)^5,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{{\sin\left(e+f\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/sin(e + f*x)^5, x)","F"
178,0,-1,101,0.000000,"\text{Not used}","int(sin(e + f*x)^4*(a + b*sin(e + f*x)^2)^p,x)","\int {\sin\left(e+f\,x\right)}^4\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(sin(e + f*x)^4*(a + b*sin(e + f*x)^2)^p, x)","F"
179,0,-1,99,0.000000,"\text{Not used}","int(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^p,x)","\int {\sin\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(sin(e + f*x)^2*(a + b*sin(e + f*x)^2)^p, x)","F"
180,0,-1,97,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/sin(e + f*x)^2,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/sin(e + f*x)^2, x)","F"
181,0,-1,101,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/sin(e + f*x)^4,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{{\sin\left(e+f\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/sin(e + f*x)^4, x)","F"
182,1,1978,335,15.240576,"\text{Not used}","int(sin(c + d*x)^7/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(\frac{-12582912\,a^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-56623104\,a^{13}\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+150994944\,a^{12}\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)\,a^{11}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,679477248+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^2\,a^9\,b^8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,679477248-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^2\,a^{11}\,b^6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,42467328-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^2\,a^{13}\,b^4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,402653184+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^3\,a^8\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4586471424-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^3\,a^{12}\,b^6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,503316480+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^4\,a^7\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1911029760+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^4\,a^9\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1774190592-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^4\,a^{11}\,b^8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301989888-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^5\,a^4\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,18345885696+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^5\,a^6\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,17199267840+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^5\,a^8\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,32614907904+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^6\,a^5\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,9172942848+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^6\,a^7\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4416602112-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^7\,a^4\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,130459631616+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^7\,a^6\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,122305904640+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^2\,a^{10}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1613758464+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^2\,a^{12}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1073741824-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^3\,a^7\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4076863488+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^3\,a^9\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2420637696+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^3\,a^{11}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4831838208+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^4\,a^8\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2293235712+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^4\,a^{10}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11475615744-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^5\,a^5\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2293235712-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^5\,a^7\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27844411392+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^5\,a^9\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25367150592+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^6\,a^8\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,16307453952-{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^7\,a^5\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,40768634880+{\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}^7\,a^7\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,32614907904+\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)\,a^{15}\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,33554432-\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)\,a^{12}\,b^4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,70778880}{b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(729\,a^2\,b^{14}\,z^6-729\,b^{16}\,z^6+243\,a^4\,b^{10}\,z^4+a^{10},z,k\right)}{d}-\frac{\sin\left(2\,c+2\,d\,x\right)}{4\,b\,d}+\frac{\sin\left(4\,c+4\,d\,x\right)}{32\,b\,d}+\frac{a\,\cos\left(c+d\,x\right)}{b^2\,d}+\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{8\,b\,d}-\frac{\ln\left(\frac{-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{8\,b\,d}","Not used",1,"symsum(log((150994944*a^12*b^3*sin(c/2 + (d*x)/2) - 56623104*a^13*b^2*cos(c/2 + (d*x)/2) - 12582912*a^15*cos(c/2 + (d*x)/2) + 679477248*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)*a^11*b^5*sin(c/2 + (d*x)/2) + 679477248*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^2*a^9*b^8*cos(c/2 + (d*x)/2) - 42467328*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^2*a^11*b^6*cos(c/2 + (d*x)/2) - 402653184*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^2*a^13*b^4*cos(c/2 + (d*x)/2) + 4586471424*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^3*a^8*b^10*cos(c/2 + (d*x)/2) - 503316480*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^3*a^12*b^6*cos(c/2 + (d*x)/2) + 1911029760*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^4*a^7*b^12*cos(c/2 + (d*x)/2) + 1774190592*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^4*a^9*b^10*cos(c/2 + (d*x)/2) - 301989888*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^4*a^11*b^8*cos(c/2 + (d*x)/2) - 18345885696*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^5*a^4*b^16*cos(c/2 + (d*x)/2) + 17199267840*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^5*a^6*b^14*cos(c/2 + (d*x)/2) + 32614907904*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^5*a^8*b^12*cos(c/2 + (d*x)/2) + 9172942848*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^6*a^5*b^16*cos(c/2 + (d*x)/2) + 4416602112*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^6*a^7*b^14*cos(c/2 + (d*x)/2) - 130459631616*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^7*a^4*b^18*cos(c/2 + (d*x)/2) + 122305904640*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^7*a^6*b^16*cos(c/2 + (d*x)/2) + 1613758464*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^2*a^10*b^7*sin(c/2 + (d*x)/2) + 1073741824*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^2*a^12*b^5*sin(c/2 + (d*x)/2) - 4076863488*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^3*a^7*b^11*sin(c/2 + (d*x)/2) + 2420637696*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^3*a^9*b^9*sin(c/2 + (d*x)/2) + 4831838208*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^3*a^11*b^7*sin(c/2 + (d*x)/2) + 2293235712*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^4*a^8*b^11*sin(c/2 + (d*x)/2) + 11475615744*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^4*a^10*b^9*sin(c/2 + (d*x)/2) - 2293235712*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^5*a^5*b^15*sin(c/2 + (d*x)/2) - 27844411392*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^5*a^7*b^13*sin(c/2 + (d*x)/2) + 25367150592*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^5*a^9*b^11*sin(c/2 + (d*x)/2) + 16307453952*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^6*a^8*b^13*sin(c/2 + (d*x)/2) - 40768634880*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^7*a^5*b^17*sin(c/2 + (d*x)/2) + 32614907904*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)^7*a^7*b^15*sin(c/2 + (d*x)/2) + 33554432*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)*a^15*b*sin(c/2 + (d*x)/2) - 70778880*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k)*a^12*b^4*cos(c/2 + (d*x)/2))/(b^9*cos(c/2 + (d*x)/2)))*root(729*a^2*b^14*z^6 - 729*b^16*z^6 + 243*a^4*b^10*z^4 + a^10, z, k), k, 1, 6)/d + (log((cos(c/2 + (d*x)/2)*1i + sin(c/2 + (d*x)/2))/cos(c/2 + (d*x)/2))*3i)/(8*b*d) - (log((cos(c/2 + (d*x)/2)*1i - sin(c/2 + (d*x)/2))/cos(c/2 + (d*x)/2))*3i)/(8*b*d) - sin(2*c + 2*d*x)/(4*b*d) + sin(4*c + 4*d*x)/(32*b*d) + (a*cos(c + d*x))/(b^2*d)","B"
183,1,1962,273,14.465719,"\text{Not used}","int(sin(c + d*x)^5/(a + b*sin(c + d*x)^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,d}+\frac{\sum _{k=1}^6\ln\left(\frac{-16777216\,a^{11}+134217728\,a^9\,b^2-\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)\,a^8\,b^4\,402653184+50331648\,a^{10}\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^2\,a^7\,b^6\,2415919104+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^2\,a^9\,b^4\,914358272+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^3\,a^6\,b^8\,7247757312-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^3\,a^8\,b^6\,478150656+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^4\,a^5\,b^{10}\,10871635968-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^4\,a^7\,b^8\,21214789632-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^4\,a^9\,b^6\,301989888-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^5\,a^4\,b^{12}\,32614907904+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^5\,a^6\,b^{10}\,59567505408+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^5\,a^8\,b^8\,4529848320+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^6\,a^5\,b^{12}\,55717134336-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^6\,a^7\,b^{10}\,42127589376-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^7\,a^4\,b^{14}\,130459631616+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^7\,a^6\,b^{12}\,122305904640-\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)\,a^9\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,452984832+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^2\,a^8\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1509949440+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^2\,a^{10}\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,201326592-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^3\,a^7\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2717908992-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^3\,a^9\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2717908992+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^4\,a^6\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4076863488+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^4\,a^8\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,6039797760-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^5\,a^5\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4076863488-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^5\,a^7\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,679477248+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^6\,a^6\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,16307453952-{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^7\,a^5\,b^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,40768634880+{\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}^7\,a^7\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,32614907904+\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)\,a^{11}\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,33554432}{b^5}\right)\,\mathrm{root}\left(729\,a^2\,b^{10}\,z^6-729\,b^{12}\,z^6+243\,a^2\,b^8\,z^4-27\,a^4\,b^4\,z^2+a^6,z,k\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{2\,b\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,b\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(b*d + 2*b*d*tan(c/2 + (d*x)/2)^2 + b*d*tan(c/2 + (d*x)/2)^4) - tan(c/2 + (d*x)/2)/(b*d + 2*b*d*tan(c/2 + (d*x)/2)^2 + b*d*tan(c/2 + (d*x)/2)^4) + symsum(log((134217728*a^9*b^2 - 16777216*a^11 - 402653184*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)*a^8*b^4 + 50331648*a^10*b*tan(c/2 + (d*x)/2) - 2415919104*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^2*a^7*b^6 + 914358272*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^2*a^9*b^4 + 7247757312*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^3*a^6*b^8 - 478150656*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^3*a^8*b^6 + 10871635968*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^4*a^5*b^10 - 21214789632*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^4*a^7*b^8 - 301989888*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^4*a^9*b^6 - 32614907904*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^5*a^4*b^12 + 59567505408*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^5*a^6*b^10 + 4529848320*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^5*a^8*b^8 + 55717134336*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^6*a^5*b^12 - 42127589376*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^6*a^7*b^10 - 130459631616*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^7*a^4*b^14 + 122305904640*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^7*a^6*b^12 - 452984832*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)*a^9*b^3*tan(c/2 + (d*x)/2) + 1509949440*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^2*a^8*b^5*tan(c/2 + (d*x)/2) + 201326592*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^2*a^10*b^3*tan(c/2 + (d*x)/2) - 2717908992*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^3*a^7*b^7*tan(c/2 + (d*x)/2) - 2717908992*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^3*a^9*b^5*tan(c/2 + (d*x)/2) + 4076863488*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^4*a^6*b^9*tan(c/2 + (d*x)/2) + 6039797760*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^4*a^8*b^7*tan(c/2 + (d*x)/2) - 4076863488*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^5*a^5*b^11*tan(c/2 + (d*x)/2) - 679477248*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^5*a^7*b^9*tan(c/2 + (d*x)/2) + 16307453952*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^6*a^6*b^11*tan(c/2 + (d*x)/2) - 40768634880*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^7*a^5*b^13*tan(c/2 + (d*x)/2) + 32614907904*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)^7*a^7*b^11*tan(c/2 + (d*x)/2) + 33554432*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k)*a^11*b*tan(c/2 + (d*x)/2))/b^5)*root(729*a^2*b^10*z^6 - 729*b^12*z^6 + 243*a^2*b^8*z^4 - 27*a^4*b^4*z^2 + a^6, z, k), k, 1, 6)/d - (log(tan(c/2 + (d*x)/2) - 1i)*1i)/(2*b*d) + (log(tan(c/2 + (d*x)/2) + 1i)*1i)/(2*b*d)","B"
184,1,1672,259,14.901184,"\text{Not used}","int(sin(c + d*x)^3/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(-1073741824\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^2\,a^7\,b\,268435456+\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,134217728+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^2\,a^5\,b^3\,4831838208+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^3\,a^6\,b^3\,33722204160+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^4\,a^5\,b^5\,15703474176-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^4\,a^7\,b^3\,4831838208-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^5\,a^4\,b^7\,130459631616+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^5\,a^6\,b^5\,154014842880+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^6\,a^5\,b^7\,35332816896-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^6\,a^7\,b^5\,21743271936-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^7\,a^4\,b^9\,130459631616+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^7\,a^6\,b^7\,122305904640+\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)\,a^6\,b\,2013265920-\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3221225472-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^2\,a^6\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,18589155328-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^3\,a^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,17716740096+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^3\,a^7\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2818572288+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^4\,a^4\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,86973087744-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^4\,a^6\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,88181047296-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^5\,a^5\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30802968576+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^5\,a^7\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,18119393280+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^6\,a^4\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,86973087744-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^6\,a^6\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,70665633792-{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^7\,a^5\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,40768634880+{\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}^7\,a^7\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,32614907904\right)\,\mathrm{root}\left(729\,a^2\,b^6\,z^6-729\,b^8\,z^6+243\,a^2\,b^4\,z^4+27\,a^2\,b^2\,z^2+a^2,z,k\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{b\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b\,d}","Not used",1,"symsum(log(134217728*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)*a^7*tan(c/2 + (d*x)/2) - 268435456*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^2*a^7*b - 1073741824*a^6*tan(c/2 + (d*x)/2) + 4831838208*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^2*a^5*b^3 + 33722204160*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^3*a^6*b^3 + 15703474176*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^4*a^5*b^5 - 4831838208*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^4*a^7*b^3 - 130459631616*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^5*a^4*b^7 + 154014842880*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^5*a^6*b^5 + 35332816896*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^6*a^5*b^7 - 21743271936*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^6*a^7*b^5 - 130459631616*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^7*a^4*b^9 + 122305904640*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^7*a^6*b^7 + 2013265920*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)*a^6*b - 3221225472*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)*a^5*b^2*tan(c/2 + (d*x)/2) - 18589155328*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^2*a^6*b^2*tan(c/2 + (d*x)/2) - 17716740096*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^3*a^5*b^4*tan(c/2 + (d*x)/2) + 2818572288*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^3*a^7*b^2*tan(c/2 + (d*x)/2) + 86973087744*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^4*a^4*b^6*tan(c/2 + (d*x)/2) - 88181047296*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^4*a^6*b^4*tan(c/2 + (d*x)/2) - 30802968576*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^5*a^5*b^6*tan(c/2 + (d*x)/2) + 18119393280*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^5*a^7*b^4*tan(c/2 + (d*x)/2) + 86973087744*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^6*a^4*b^8*tan(c/2 + (d*x)/2) - 70665633792*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^6*a^6*b^6*tan(c/2 + (d*x)/2) - 40768634880*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^7*a^5*b^8*tan(c/2 + (d*x)/2) + 32614907904*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k)^7*a^7*b^6*tan(c/2 + (d*x)/2))*root(729*a^2*b^6*z^6 - 729*b^8*z^6 + 243*a^2*b^4*z^4 + 27*a^2*b^2*z^2 + a^2, z, k), k, 1, 6)/d - (log(tan(c/2 + (d*x)/2) - 1i)*1i)/(b*d) + (log(tan(c/2 + (d*x)/2) + 1i)*1i)/(b*d)","B"
185,1,652,267,16.121118,"\text{Not used}","int(sin(c + d*x)/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(-8192\,a^3\,b+{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^2\,a^3\,b^3\,294912+{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^3\,a^4\,b^3\,1548288+{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^4\,a^5\,b^3\,1990656-{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^5\,a^4\,b^5\,7962624+{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^5\,a^6\,b^3\,5971968+65536\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,196608+{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^2\,a^4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294912-{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^3\,a^3\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1769472+{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^3\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,221184+{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^4\,a^4\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2654208-{\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}^5\,a^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1990656\right)\,\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^2\,b^4\,d^6+243\,a^2\,b^2\,d^4+1,d,k\right)}{d}","Not used",1,"symsum(log(294912*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^2*a^3*b^3 - 8192*a^3*b + 1548288*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^3*a^4*b^3 + 1990656*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^4*a^5*b^3 - 7962624*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^5*a^4*b^5 + 5971968*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^5*a^6*b^3 + 65536*a^2*b^2*tan(c/2 + (d*x)/2) + 196608*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)*a^3*b^2*tan(c/2 + (d*x)/2) + 294912*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^2*a^4*b^2*tan(c/2 + (d*x)/2) - 1769472*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^3*a^3*b^4*tan(c/2 + (d*x)/2) + 221184*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^3*a^5*b^2*tan(c/2 + (d*x)/2) + 2654208*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^4*a^4*b^4*tan(c/2 + (d*x)/2) - 1990656*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k)^5*a^5*b^4*tan(c/2 + (d*x)/2))*root(729*a^4*b^2*d^6 - 729*a^2*b^4*d^6 + 243*a^2*b^2*d^4 + 1, d, k), k, 1, 6)/d","B"
186,1,1439,264,15.656018,"\text{Not used}","int(1/(sin(c + d*x)*(a + b*sin(c + d*x)^3)),x)","\frac{\sum _{k=1}^6\ln\left(98304\,b^5+\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1048576-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^2\,a^2\,b^5\,98304+{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^3\,a^3\,b^5\,5898240-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^4\,a^4\,b^5\,7962624-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^4\,a^6\,b^3\,663552-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^5\,a^5\,b^5\,5308416+{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^5\,a^7\,b^3\,10616832+{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^6\,a^6\,b^5\,7962624-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^6\,a^8\,b^3\,9953280-\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)\,a\,b^5\,589824-\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)\,a^2\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24576-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^2\,a\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3145728+{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^2\,a^3\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,466944-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^3\,a^2\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,18874368-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^3\,a^4\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3981312+{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^4\,a^3\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,56623104+{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^4\,a^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,20791296+{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^5\,a^4\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,84934656-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^5\,a^6\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,78962688-{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^6\,a^5\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,254803968+{\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}^6\,a^7\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,252813312\right)\,\mathrm{root}\left(729\,a^6\,b^2\,z^6-729\,a^8\,z^6-243\,a^4\,b^2\,z^4+27\,a^2\,b^2\,z^2-b^2,z,k\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}","Not used",1,"symsum(log(98304*b^5 + 1048576*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)*b^6*tan(c/2 + (d*x)/2) - 98304*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^2*a^2*b^5 + 5898240*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^3*a^3*b^5 - 7962624*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^4*a^4*b^5 - 663552*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^4*a^6*b^3 - 5308416*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^5*a^5*b^5 + 10616832*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^5*a^7*b^3 + 7962624*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^6*a^6*b^5 - 9953280*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^6*a^8*b^3 - 589824*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)*a*b^5 - 24576*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)*a^2*b^4*tan(c/2 + (d*x)/2) - 3145728*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^2*a*b^6*tan(c/2 + (d*x)/2) + 466944*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^2*a^3*b^4*tan(c/2 + (d*x)/2) - 18874368*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^3*a^2*b^6*tan(c/2 + (d*x)/2) - 3981312*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^3*a^4*b^4*tan(c/2 + (d*x)/2) + 56623104*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^4*a^3*b^6*tan(c/2 + (d*x)/2) + 20791296*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^4*a^5*b^4*tan(c/2 + (d*x)/2) + 84934656*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^5*a^4*b^6*tan(c/2 + (d*x)/2) - 78962688*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^5*a^6*b^4*tan(c/2 + (d*x)/2) - 254803968*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^6*a^5*b^6*tan(c/2 + (d*x)/2) + 252813312*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k)^6*a^7*b^4*tan(c/2 + (d*x)/2))*root(729*a^6*b^2*z^6 - 729*a^8*z^6 - 243*a^4*b^2*z^4 + 27*a^2*b^2*z^2 - b^2, z, k), k, 1, 6)/d + log(tan(c/2 + (d*x)/2))/(a*d)","B"
187,1,1573,287,15.034915,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + b*sin(c + d*x)^3)),x)","\frac{\sum _{k=1}^6\ln\left(-\frac{65536\,a\,b^9-262144\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)\,a^2\,b^9\,131072-\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)\,a^4\,b^7\,61440+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^2\,a^5\,b^7\,860160-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^3\,a^6\,b^7\,3244032-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^3\,a^8\,b^5\,1105920+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^4\,a^7\,b^7\,3538944+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^4\,a^9\,b^5\,3870720+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^5\,a^{10}\,b^5\,663552-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^5\,a^{12}\,b^3\,4976640-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^6\,a^{11}\,b^5\,7962624+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^6\,a^{13}\,b^3\,9953280+24576\,a^2\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)\,a^3\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,540672-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^2\,a^4\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7077888+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^2\,a^6\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,442368-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^3\,a^5\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2359296+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^3\,a^7\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7741440-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^4\,a^8\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,80953344+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^4\,a^{10}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1990656-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^5\,a^9\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31850496+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^5\,a^{11}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,26873856+{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^6\,a^{10}\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,254803968-{\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}^6\,a^{12}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,252813312}{a^5}\right)\,\mathrm{root}\left(729\,a^{10}\,b^2\,z^6-729\,a^{12}\,z^6-243\,a^8\,b^2\,z^4-27\,a^4\,b^4\,z^2-b^6,z,k\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}","Not used",1,"symsum(log(-(65536*a*b^9 - 262144*b^10*tan(c/2 + (d*x)/2) - 131072*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)*a^2*b^9 - 61440*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)*a^4*b^7 + 860160*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^2*a^5*b^7 - 3244032*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^3*a^6*b^7 - 1105920*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^3*a^8*b^5 + 3538944*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^4*a^7*b^7 + 3870720*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^4*a^9*b^5 + 663552*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^5*a^10*b^5 - 4976640*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^5*a^12*b^3 - 7962624*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^6*a^11*b^5 + 9953280*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^6*a^13*b^3 + 24576*a^2*b^8*tan(c/2 + (d*x)/2) + 540672*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)*a^3*b^8*tan(c/2 + (d*x)/2) - 7077888*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^2*a^4*b^8*tan(c/2 + (d*x)/2) + 442368*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^2*a^6*b^6*tan(c/2 + (d*x)/2) - 2359296*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^3*a^5*b^8*tan(c/2 + (d*x)/2) + 7741440*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^3*a^7*b^6*tan(c/2 + (d*x)/2) - 80953344*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^4*a^8*b^6*tan(c/2 + (d*x)/2) + 1990656*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^4*a^10*b^4*tan(c/2 + (d*x)/2) - 31850496*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^5*a^9*b^6*tan(c/2 + (d*x)/2) + 26873856*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^5*a^11*b^4*tan(c/2 + (d*x)/2) + 254803968*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^6*a^10*b^6*tan(c/2 + (d*x)/2) - 252813312*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k)^6*a^12*b^4*tan(c/2 + (d*x)/2))/a^5)*root(729*a^10*b^2*z^6 - 729*a^12*z^6 - 243*a^8*b^2*z^4 - 27*a^4*b^4*z^2 - b^6, z, k), k, 1, 6)/d - cot(c/2 + (d*x)/2)^2/(8*a*d) + tan(c/2 + (d*x)/2)^2/(8*a*d) + log(tan(c/2 + (d*x)/2))/(2*a*d)","B"
188,1,1560,344,14.598261,"\text{Not used}","int(1/(sin(c + d*x)^5*(a + b*sin(c + d*x)^3)),x)","\frac{\sum _{k=1}^6\ln\left(\frac{-3072\,a^3\,b^{11}+262144\,b^{14}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)\,a^4\,b^{11}\,155648-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^2\,a^5\,b^{11}\,393216+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^2\,a^7\,b^9\,774144-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^3\,a^8\,b^9\,2064384+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^3\,a^{10}\,b^7\,2073600-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^4\,a^{11}\,b^7\,9510912+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^4\,a^{13}\,b^5\,2737152+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^5\,a^{12}\,b^7\,10616832-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^5\,a^{14}\,b^5\,10285056+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^5\,a^{16}\,b^3\,3732480+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^6\,a^{15}\,b^5\,7962624-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^6\,a^{17}\,b^3\,9953280+98304\,a^2\,b^{12}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)\,a^3\,b^{12}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,262144+\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)\,a^5\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,165888-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^2\,a^6\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1327104+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^2\,a^8\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,165888+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^3\,a^7\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2359296-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^3\,a^9\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7077888+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^3\,a^{11}\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,82944+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^4\,a^{10}\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,81395712-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^4\,a^{12}\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1714176+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^5\,a^{13}\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27869184-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^5\,a^{15}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,23141376-{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^6\,a^{14}\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,254803968+{\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}^6\,a^{16}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,252813312}{a^9}\right)\,\mathrm{root}\left(729\,a^{14}\,b^2\,z^6-729\,a^{16}\,z^6-243\,a^{10}\,b^4\,z^4-b^{10},z,k\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}+\frac{b\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}","Not used",1,"symsum(log((262144*b^14*tan(c/2 + (d*x)/2) - 3072*a^3*b^11 + 155648*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)*a^4*b^11 - 393216*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^2*a^5*b^11 + 774144*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^2*a^7*b^9 - 2064384*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^3*a^8*b^9 + 2073600*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^3*a^10*b^7 - 9510912*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^4*a^11*b^7 + 2737152*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^4*a^13*b^5 + 10616832*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^5*a^12*b^7 - 10285056*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^5*a^14*b^5 + 3732480*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^5*a^16*b^3 + 7962624*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^6*a^15*b^5 - 9953280*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^6*a^17*b^3 + 98304*a^2*b^12*tan(c/2 + (d*x)/2) - 262144*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)*a^3*b^12*tan(c/2 + (d*x)/2) + 165888*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)*a^5*b^10*tan(c/2 + (d*x)/2) - 1327104*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^2*a^6*b^10*tan(c/2 + (d*x)/2) + 165888*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^2*a^8*b^8*tan(c/2 + (d*x)/2) + 2359296*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^3*a^7*b^10*tan(c/2 + (d*x)/2) - 7077888*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^3*a^9*b^8*tan(c/2 + (d*x)/2) + 82944*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^3*a^11*b^6*tan(c/2 + (d*x)/2) + 81395712*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^4*a^10*b^8*tan(c/2 + (d*x)/2) - 1714176*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^4*a^12*b^6*tan(c/2 + (d*x)/2) + 27869184*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^5*a^13*b^6*tan(c/2 + (d*x)/2) - 23141376*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^5*a^15*b^4*tan(c/2 + (d*x)/2) - 254803968*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^6*a^14*b^6*tan(c/2 + (d*x)/2) + 252813312*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k)^6*a^16*b^4*tan(c/2 + (d*x)/2))/a^9)*root(729*a^14*b^2*z^6 - 729*a^16*z^6 - 243*a^10*b^4*z^4 - b^10, z, k), k, 1, 6)/d - cot(c/2 + (d*x)/2)^2/(8*a*d) - cot(c/2 + (d*x)/2)^4/(64*a*d) + tan(c/2 + (d*x)/2)^2/(8*a*d) + tan(c/2 + (d*x)/2)^4/(64*a*d) + (3*log(tan(c/2 + (d*x)/2)))/(8*a*d) + (b*cot(c/2 + (d*x)/2))/(2*a^2*d) - (b*tan(c/2 + (d*x)/2))/(2*a^2*d)","B"
189,1,1800,293,14.583861,"\text{Not used}","int(sin(c + d*x)^6/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(\frac{1073741824\,a^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)\,a^{12}\,b^2\,2013265920-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^2\,a^{10}\,b^5\,4831838208+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^2\,a^{12}\,b^3\,268435456+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^3\,a^{10}\,b^6\,33722204160-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^4\,a^8\,b^9\,15703474176+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^4\,a^{10}\,b^7\,4831838208-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^5\,a^6\,b^{12}\,130459631616+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^5\,a^8\,b^{10}\,154014842880-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^6\,a^6\,b^{13}\,35332816896+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^6\,a^8\,b^{11}\,21743271936-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^7\,a^4\,b^{16}\,130459631616+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^7\,a^6\,b^{14}\,122305904640-\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)\,a^{11}\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3221225472+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^2\,a^{11}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,18589155328-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^3\,a^9\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,17716740096+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^3\,a^{11}\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2818572288-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^4\,a^7\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,86973087744+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^4\,a^9\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,88181047296-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^5\,a^7\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30802968576+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^5\,a^9\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,18119393280-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^6\,a^5\,b^{14}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,86973087744+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^6\,a^7\,b^{12}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,70665633792-{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^7\,a^5\,b^{15}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,40768634880+{\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}^7\,a^7\,b^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,32614907904+\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)\,a^{13}\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,134217728}{b^7}\right)\,\mathrm{root}\left(729\,a^2\,b^{12}\,z^6-729\,b^{14}\,z^6+243\,a^4\,b^8\,z^4+27\,a^6\,b^4\,z^2+a^8,z,k\right)}{d}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,d}-\frac{4}{3\,\left(b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,d\right)}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{b^2\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^2\,d}","Not used",1,"symsum(log((1073741824*a^13*tan(c/2 + (d*x)/2) + 2013265920*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)*a^12*b^2 - 4831838208*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^2*a^10*b^5 + 268435456*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^2*a^12*b^3 + 33722204160*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^3*a^10*b^6 - 15703474176*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^4*a^8*b^9 + 4831838208*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^4*a^10*b^7 - 130459631616*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^5*a^6*b^12 + 154014842880*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^5*a^8*b^10 - 35332816896*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^6*a^6*b^13 + 21743271936*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^6*a^8*b^11 - 130459631616*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^7*a^4*b^16 + 122305904640*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^7*a^6*b^14 - 3221225472*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)*a^11*b^3*tan(c/2 + (d*x)/2) + 18589155328*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^2*a^11*b^4*tan(c/2 + (d*x)/2) - 17716740096*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^3*a^9*b^7*tan(c/2 + (d*x)/2) + 2818572288*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^3*a^11*b^5*tan(c/2 + (d*x)/2) - 86973087744*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^4*a^7*b^10*tan(c/2 + (d*x)/2) + 88181047296*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^4*a^9*b^8*tan(c/2 + (d*x)/2) - 30802968576*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^5*a^7*b^11*tan(c/2 + (d*x)/2) + 18119393280*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^5*a^9*b^9*tan(c/2 + (d*x)/2) - 86973087744*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^6*a^5*b^14*tan(c/2 + (d*x)/2) + 70665633792*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^6*a^7*b^12*tan(c/2 + (d*x)/2) - 40768634880*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^7*a^5*b^15*tan(c/2 + (d*x)/2) + 32614907904*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)^7*a^7*b^13*tan(c/2 + (d*x)/2) + 134217728*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k)*a^13*b*tan(c/2 + (d*x)/2))/b^7)*root(729*a^2*b^12*z^6 - 729*b^14*z^6 + 243*a^4*b^8*z^4 + 27*a^6*b^4*z^2 + a^8, z, k), k, 1, 6)/d - (4*tan(c/2 + (d*x)/2)^2)/(b*d + 3*b*d*tan(c/2 + (d*x)/2)^2 + 3*b*d*tan(c/2 + (d*x)/2)^4 + b*d*tan(c/2 + (d*x)/2)^6) - 4/(3*(b*d + 3*b*d*tan(c/2 + (d*x)/2)^2 + 3*b*d*tan(c/2 + (d*x)/2)^4 + b*d*tan(c/2 + (d*x)/2)^6)) + (a*log(tan(c/2 + (d*x)/2) - 1i)*1i)/(b^2*d) - (a*log(tan(c/2 + (d*x)/2) + 1i)*1i)/(b^2*d)","B"
190,1,665,281,15.072174,"\text{Not used}","int(sin(c + d*x)^4/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(8192\,a^8\,b^5-{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^2\,a^6\,b^9\,294912+{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^3\,a^6\,b^{10}\,1548288-{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^4\,a^6\,b^{11}\,1990656-{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^5\,a^4\,b^{14}\,7962624+{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^5\,a^6\,b^{12}\,5971968-65536\,a^7\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)\,a^7\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,196608-{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^2\,a^7\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294912-{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^3\,a^5\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1769472+{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^3\,a^7\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,221184-{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^4\,a^5\,b^{12}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2654208-{\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}^5\,a^5\,b^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1990656\right)\,\mathrm{root}\left(729\,a^2\,b^8\,d^6-729\,b^{10}\,d^6+243\,a^2\,b^6\,d^4+a^4,d,k\right)}{d}-\frac{2}{b\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,d}","Not used",1,"symsum(log(8192*a^8*b^5 - 294912*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^2*a^6*b^9 + 1548288*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^3*a^6*b^10 - 1990656*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^4*a^6*b^11 - 7962624*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^5*a^4*b^14 + 5971968*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^5*a^6*b^12 - 65536*a^7*b^6*tan(c/2 + (d*x)/2) + 196608*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)*a^7*b^7*tan(c/2 + (d*x)/2) - 294912*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^2*a^7*b^8*tan(c/2 + (d*x)/2) - 1769472*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^3*a^5*b^11*tan(c/2 + (d*x)/2) + 221184*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^3*a^7*b^9*tan(c/2 + (d*x)/2) - 2654208*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^4*a^5*b^12*tan(c/2 + (d*x)/2) - 1990656*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k)^5*a^5*b^13*tan(c/2 + (d*x)/2))*root(729*a^2*b^8*d^6 - 729*b^10*d^6 + 243*a^2*b^6*d^4 + a^4, d, k), k, 1, 6)/d - 2/(b*d + b*d*tan(c/2 + (d*x)/2)^2)","B"
191,1,590,240,15.652443,"\text{Not used}","int(sin(c + d*x)^2/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(-\frac{8192\,a^4\,\left(-729\,a^2\,b^3-81\,a^2\,b^2\,\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)+243\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+324\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3\,\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)+162\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2\,{\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)}^2+36\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b\,{\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)}^3+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,{\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)}^4+972\,b^5+324\,b^4\,\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)-216\,b^3\,{\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)}^2-72\,b^2\,{\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)}^3+12\,b\,{\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)}^4+4\,{\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)}^5\right)}{{\mathrm{root}\left(d^6-27\,b^2\,d^4+243\,b^4\,d^2+729\,b^4\,\left(a^2-b^2\right),d,k\right)}^5}\right)\,\mathrm{root}\left(729\,a^2\,b^4\,d^6-729\,b^6\,d^6+243\,b^4\,d^4-27\,b^2\,d^2+1,d,k\right)}{d}","Not used",1,"symsum(log(-(8192*a^4*(12*b*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)^4 + 324*b^4*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k) + 972*b^5 + 4*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)^5 - 729*a^2*b^3 - 72*b^2*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)^3 - 216*b^3*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)^2 - 81*a^2*b^2*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k) + 243*a*b^4*tan(c/2 + (d*x)/2) + 3*a*tan(c/2 + (d*x)/2)*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)^4 + 162*a*b^2*tan(c/2 + (d*x)/2)*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)^2 + 36*a*b*tan(c/2 + (d*x)/2)*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)^3 + 324*a*tan(c/2 + (d*x)/2)*b^3*root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)))/root(d^6 - 27*b^2*d^4 + 243*b^4*d^2 + 729*b^4*(a^2 - b^2), d, k)^5)*root(729*a^2*b^4*d^6 - 729*b^6*d^6 + 243*b^4*d^4 - 27*b^2*d^2 + 1, d, k), k, 1, 6)/d","B"
192,1,609,245,15.883983,"\text{Not used}","int(1/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(-\frac{8192\,a\,b^3\,\left(-729\,a^5+243\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b-324\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)+972\,a^3\,b^2+a^3\,b\,\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)\,243-162\,a^3\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^2+648\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2\,\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)+216\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^2-72\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^3+36\,a\,b\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^3-9\,a\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^4+24\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^4-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^5\right)}{{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^5}\right)\,\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^6\,d^6-243\,a^4\,d^4-27\,a^2\,d^2-1,d,k\right)}{d}","Not used",1,"symsum(log(-(8192*a*b^3*(972*a^3*b^2 - 729*a^5 - 9*a*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^4 - 162*a^3*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^2 - 4*tan(c/2 + (d*x)/2)*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^5 + 243*a^4*b*tan(c/2 + (d*x)/2) - 324*tan(c/2 + (d*x)/2)*a^4*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k) + 24*b*tan(c/2 + (d*x)/2)*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^4 - 72*a^2*tan(c/2 + (d*x)/2)*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^3 + 36*a*b*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^3 + 243*b*a^3*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k) + 648*tan(c/2 + (d*x)/2)*a^2*b^2*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k) + 216*a^2*b*tan(c/2 + (d*x)/2)*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^2))/root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^5)*root(729*a^4*b^2*d^6 - 729*a^6*d^6 - 243*a^4*d^4 - 27*a^2*d^2 - 1, d, k), k, 1, 6)/d","B"
193,1,697,281,14.417419,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + b*sin(c + d*x)^3)),x)","\frac{\left(\sum _{k=1}^6\ln\left(8192\,a^7\,b^6-{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^2\,a^9\,b^6\,294912+{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^3\,a^{11}\,b^5\,1548288-{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^4\,a^{13}\,b^4\,1990656-{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^5\,a^{13}\,b^5\,7962624+{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^5\,a^{15}\,b^3\,5971968-65536\,a^6\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)\,a^8\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,196608-{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^2\,a^{10}\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294912-{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^3\,a^{10}\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1769472+{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^3\,a^{12}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,221184-{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^4\,a^{12}\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2654208-{\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)}^5\,a^{14}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1990656\right)\,\mathrm{root}\left(729\,a^8\,b^2\,d^6-729\,a^{10}\,d^6-243\,a^6\,b^2\,d^4-b^4,d,k\right)\right)-\frac{1}{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a}}{d}","Not used",1,"(symsum(log(8192*a^7*b^6 - 294912*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^2*a^9*b^6 + 1548288*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^3*a^11*b^5 - 1990656*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^4*a^13*b^4 - 7962624*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^5*a^13*b^5 + 5971968*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^5*a^15*b^3 - 65536*a^6*b^7*tan(c/2 + (d*x)/2) + 196608*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)*a^8*b^6*tan(c/2 + (d*x)/2) - 294912*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^2*a^10*b^5*tan(c/2 + (d*x)/2) - 1769472*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^3*a^10*b^6*tan(c/2 + (d*x)/2) + 221184*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^3*a^12*b^4*tan(c/2 + (d*x)/2) - 2654208*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^4*a^12*b^5*tan(c/2 + (d*x)/2) - 1990656*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k)^5*a^14*b^4*tan(c/2 + (d*x)/2))*root(729*a^8*b^2*d^6 - 729*a^10*d^6 - 243*a^6*b^2*d^4 - b^4, d, k), k, 1, 6) - 1/(2*a*tan(c/2 + (d*x)/2)) + tan(c/2 + (d*x)/2)/(2*a))/d","B"
194,1,1503,296,16.382587,"\text{Not used}","int(1/(sin(c + d*x)^4*(a + b*sin(c + d*x)^3)),x)","\frac{\sum _{k=1}^6\ln\left(\frac{98304\,b^{11}+\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)\,a^2\,b^{10}\,589824-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^2\,a^4\,b^9\,98304-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^3\,a^6\,b^8\,5898240-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^4\,a^8\,b^7\,7962624-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^4\,a^{10}\,b^5\,663552+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^5\,a^{10}\,b^6\,5308416-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^5\,a^{12}\,b^4\,10616832+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^6\,a^{12}\,b^5\,7962624-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^6\,a^{14}\,b^3\,9953280+\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)\,a^3\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24576-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^2\,a^3\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3145728+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^2\,a^5\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,466944+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^3\,a^5\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,18874368+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^3\,a^7\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3981312+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^4\,a^7\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,56623104+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^4\,a^9\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,20791296-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^5\,a^9\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,84934656+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^5\,a^{11}\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,78962688-{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^6\,a^{11}\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,254803968+{\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}^6\,a^{13}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,252813312-\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)\,a\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1048576}{a^6}\right)\,\mathrm{root}\left(729\,a^{12}\,b^2\,z^6-729\,a^{14}\,z^6-243\,a^8\,b^4\,z^4+27\,a^4\,b^6\,z^2-b^8,z,k\right)}{d}-\frac{a\,\left(\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}\right)+b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}","Not used",1,"symsum(log((98304*b^11 + 589824*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)*a^2*b^10 - 98304*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^2*a^4*b^9 - 5898240*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^3*a^6*b^8 - 7962624*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^4*a^8*b^7 - 663552*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^4*a^10*b^5 + 5308416*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^5*a^10*b^6 - 10616832*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^5*a^12*b^4 + 7962624*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^6*a^12*b^5 - 9953280*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^6*a^14*b^3 + 24576*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)*a^3*b^9*tan(c/2 + (d*x)/2) - 3145728*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^2*a^3*b^10*tan(c/2 + (d*x)/2) + 466944*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^2*a^5*b^8*tan(c/2 + (d*x)/2) + 18874368*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^3*a^5*b^9*tan(c/2 + (d*x)/2) + 3981312*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^3*a^7*b^7*tan(c/2 + (d*x)/2) + 56623104*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^4*a^7*b^8*tan(c/2 + (d*x)/2) + 20791296*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^4*a^9*b^6*tan(c/2 + (d*x)/2) - 84934656*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^5*a^9*b^7*tan(c/2 + (d*x)/2) + 78962688*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^5*a^11*b^5*tan(c/2 + (d*x)/2) - 254803968*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^6*a^11*b^6*tan(c/2 + (d*x)/2) + 252813312*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)^6*a^13*b^4*tan(c/2 + (d*x)/2) - 1048576*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k)*a*b^11*tan(c/2 + (d*x)/2))/a^6)*root(729*a^12*b^2*z^6 - 729*a^14*z^6 - 243*a^8*b^4*z^4 + 27*a^4*b^6*z^2 - b^8, z, k), k, 1, 6)/d - (a*((3*cot(c/2 + (d*x)/2))/8 - (3*tan(c/2 + (d*x)/2))/8 + cot(c/2 + (d*x)/2)^3/24 - tan(c/2 + (d*x)/2)^3/24) + b*log(tan(c/2 + (d*x)/2)))/(a^2*d)","B"
195,1,1067,177,14.438516,"\text{Not used}","int(sin(c + d*x)^9/(a - b*sin(c + d*x)^4),x)","\frac{{\cos\left(c+d\,x\right)}^5}{5\,b\,d}-\frac{2\,{\cos\left(c+d\,x\right)}^3}{3\,b\,d}+\frac{\cos\left(c+d\,x\right)\,\left(\frac{a-b}{b^2}+\frac{2}{b}\right)}{d}+\frac{\mathrm{atan}\left(-\frac{a^4\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^9}}{16\,\left(a\,b^9-b^{10}\right)}-\frac{a^3\,b^5}{16\,\left(a\,b^9-b^{10}\right)}}\,8{}\mathrm{i}}{\frac{2\,a^6\,b^7}{a\,b^9-b^{10}}+\frac{2\,a^3\,b^2\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}}+\frac{a^4\,b^9\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^9}}{16\,\left(a\,b^9-b^{10}\right)}-\frac{a^3\,b^5}{16\,\left(a\,b^9-b^{10}\right)}}\,8{}\mathrm{i}}{\frac{2\,a^6\,b^{16}}{a\,b^9-b^{10}}-\frac{2\,a^7\,b^{15}}{a\,b^9-b^{10}}+\frac{2\,a^3\,b^{11}\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}-\frac{2\,a^4\,b^{10}\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}}+\frac{a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^9}}{16\,\left(a\,b^9-b^{10}\right)}-\frac{a^3\,b^5}{16\,\left(a\,b^9-b^{10}\right)}}\,\sqrt{a^7\,b^9}\,8{}\mathrm{i}}{\frac{2\,a^6\,b^{16}}{a\,b^9-b^{10}}-\frac{2\,a^7\,b^{15}}{a\,b^9-b^{10}}+\frac{2\,a^3\,b^{11}\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}-\frac{2\,a^4\,b^{10}\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}}\right)\,\sqrt{-\frac{\sqrt{a^7\,b^9}+a^3\,b^5}{16\,\left(a\,b^9-b^{10}\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{a^4\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^9}}{16\,\left(a\,b^9-b^{10}\right)}-\frac{a^3\,b^5}{16\,\left(a\,b^9-b^{10}\right)}}\,8{}\mathrm{i}}{\frac{2\,a^6\,b^7}{a\,b^9-b^{10}}-\frac{2\,a^3\,b^2\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}}-\frac{a^4\,b^9\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^9}}{16\,\left(a\,b^9-b^{10}\right)}-\frac{a^3\,b^5}{16\,\left(a\,b^9-b^{10}\right)}}\,8{}\mathrm{i}}{\frac{2\,a^6\,b^{16}}{a\,b^9-b^{10}}-\frac{2\,a^7\,b^{15}}{a\,b^9-b^{10}}-\frac{2\,a^3\,b^{11}\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}+\frac{2\,a^4\,b^{10}\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}}+\frac{a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^9}}{16\,\left(a\,b^9-b^{10}\right)}-\frac{a^3\,b^5}{16\,\left(a\,b^9-b^{10}\right)}}\,\sqrt{a^7\,b^9}\,8{}\mathrm{i}}{\frac{2\,a^6\,b^{16}}{a\,b^9-b^{10}}-\frac{2\,a^7\,b^{15}}{a\,b^9-b^{10}}-\frac{2\,a^3\,b^{11}\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}+\frac{2\,a^4\,b^{10}\,\sqrt{a^7\,b^9}}{a\,b^9-b^{10}}}\right)\,\sqrt{\frac{\sqrt{a^7\,b^9}-a^3\,b^5}{16\,\left(a\,b^9-b^{10}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan((a^4*b^9*cos(c + d*x)*(- (a^7*b^9)^(1/2)/(16*(a*b^9 - b^10)) - (a^3*b^5)/(16*(a*b^9 - b^10)))^(1/2)*8i)/((2*a^6*b^16)/(a*b^9 - b^10) - (2*a^7*b^15)/(a*b^9 - b^10) + (2*a^3*b^11*(a^7*b^9)^(1/2))/(a*b^9 - b^10) - (2*a^4*b^10*(a^7*b^9)^(1/2))/(a*b^9 - b^10)) - (a^4*cos(c + d*x)*(- (a^7*b^9)^(1/2)/(16*(a*b^9 - b^10)) - (a^3*b^5)/(16*(a*b^9 - b^10)))^(1/2)*8i)/((2*a^6*b^7)/(a*b^9 - b^10) + (2*a^3*b^2*(a^7*b^9)^(1/2))/(a*b^9 - b^10)) + (a*b^4*cos(c + d*x)*(- (a^7*b^9)^(1/2)/(16*(a*b^9 - b^10)) - (a^3*b^5)/(16*(a*b^9 - b^10)))^(1/2)*(a^7*b^9)^(1/2)*8i)/((2*a^6*b^16)/(a*b^9 - b^10) - (2*a^7*b^15)/(a*b^9 - b^10) + (2*a^3*b^11*(a^7*b^9)^(1/2))/(a*b^9 - b^10) - (2*a^4*b^10*(a^7*b^9)^(1/2))/(a*b^9 - b^10)))*(-((a^7*b^9)^(1/2) + a^3*b^5)/(16*(a*b^9 - b^10)))^(1/2)*2i)/d - (atan((a^4*cos(c + d*x)*((a^7*b^9)^(1/2)/(16*(a*b^9 - b^10)) - (a^3*b^5)/(16*(a*b^9 - b^10)))^(1/2)*8i)/((2*a^6*b^7)/(a*b^9 - b^10) - (2*a^3*b^2*(a^7*b^9)^(1/2))/(a*b^9 - b^10)) - (a^4*b^9*cos(c + d*x)*((a^7*b^9)^(1/2)/(16*(a*b^9 - b^10)) - (a^3*b^5)/(16*(a*b^9 - b^10)))^(1/2)*8i)/((2*a^6*b^16)/(a*b^9 - b^10) - (2*a^7*b^15)/(a*b^9 - b^10) - (2*a^3*b^11*(a^7*b^9)^(1/2))/(a*b^9 - b^10) + (2*a^4*b^10*(a^7*b^9)^(1/2))/(a*b^9 - b^10)) + (a*b^4*cos(c + d*x)*((a^7*b^9)^(1/2)/(16*(a*b^9 - b^10)) - (a^3*b^5)/(16*(a*b^9 - b^10)))^(1/2)*(a^7*b^9)^(1/2)*8i)/((2*a^6*b^16)/(a*b^9 - b^10) - (2*a^7*b^15)/(a*b^9 - b^10) - (2*a^3*b^11*(a^7*b^9)^(1/2))/(a*b^9 - b^10) + (2*a^4*b^10*(a^7*b^9)^(1/2))/(a*b^9 - b^10)))*(((a^7*b^9)^(1/2) - a^3*b^5)/(16*(a*b^9 - b^10)))^(1/2)*2i)/d - (2*cos(c + d*x)^3)/(3*b*d) + cos(c + d*x)^5/(5*b*d) + (cos(c + d*x)*((a - b)/b^2 + 2/b))/d","B"
196,1,1119,148,14.269298,"\text{Not used}","int(sin(c + d*x)^7/(a - b*sin(c + d*x)^4),x)","\frac{\cos\left(c+d\,x\right)}{b\,d}-\frac{{\cos\left(c+d\,x\right)}^3}{3\,b\,d}+\frac{\mathrm{atan}\left(-\frac{a^3\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^5\,b^7}}{16\,\left(a\,b^7-b^8\right)}-\frac{a^2\,b^4}{16\,\left(a\,b^7-b^8\right)}}\,8{}\mathrm{i}}{\frac{2\,a^4}{b^2}+\frac{2\,a^4\,b^6}{a\,b^7-b^8}+\frac{2\,a^2\,b^2\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}}+\frac{a^3\,b^8\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^5\,b^7}}{16\,\left(a\,b^7-b^8\right)}-\frac{a^2\,b^4}{16\,\left(a\,b^7-b^8\right)}}\,8{}\mathrm{i}}{2\,a^4\,b^6-2\,a^5\,b^5+\frac{2\,a^4\,b^{14}}{a\,b^7-b^8}-\frac{2\,a^5\,b^{13}}{a\,b^7-b^8}+\frac{2\,a^2\,b^{10}\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}-\frac{2\,a^3\,b^9\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}}+\frac{a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^5\,b^7}}{16\,\left(a\,b^7-b^8\right)}-\frac{a^2\,b^4}{16\,\left(a\,b^7-b^8\right)}}\,\sqrt{a^5\,b^7}\,8{}\mathrm{i}}{2\,a^4\,b^6-2\,a^5\,b^5+\frac{2\,a^4\,b^{14}}{a\,b^7-b^8}-\frac{2\,a^5\,b^{13}}{a\,b^7-b^8}+\frac{2\,a^2\,b^{10}\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}-\frac{2\,a^3\,b^9\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^7}+a^2\,b^4}{16\,\left(a\,b^7-b^8\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{a^3\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^5\,b^7}}{16\,\left(a\,b^7-b^8\right)}-\frac{a^2\,b^4}{16\,\left(a\,b^7-b^8\right)}}\,8{}\mathrm{i}}{\frac{2\,a^4}{b^2}+\frac{2\,a^4\,b^6}{a\,b^7-b^8}-\frac{2\,a^2\,b^2\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}}-\frac{a^3\,b^8\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^5\,b^7}}{16\,\left(a\,b^7-b^8\right)}-\frac{a^2\,b^4}{16\,\left(a\,b^7-b^8\right)}}\,8{}\mathrm{i}}{2\,a^4\,b^6-2\,a^5\,b^5+\frac{2\,a^4\,b^{14}}{a\,b^7-b^8}-\frac{2\,a^5\,b^{13}}{a\,b^7-b^8}-\frac{2\,a^2\,b^{10}\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}+\frac{2\,a^3\,b^9\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}}+\frac{a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^5\,b^7}}{16\,\left(a\,b^7-b^8\right)}-\frac{a^2\,b^4}{16\,\left(a\,b^7-b^8\right)}}\,\sqrt{a^5\,b^7}\,8{}\mathrm{i}}{2\,a^4\,b^6-2\,a^5\,b^5+\frac{2\,a^4\,b^{14}}{a\,b^7-b^8}-\frac{2\,a^5\,b^{13}}{a\,b^7-b^8}-\frac{2\,a^2\,b^{10}\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}+\frac{2\,a^3\,b^9\,\sqrt{a^5\,b^7}}{a\,b^7-b^8}}\right)\,\sqrt{\frac{\sqrt{a^5\,b^7}-a^2\,b^4}{16\,\left(a\,b^7-b^8\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"cos(c + d*x)/(b*d) - cos(c + d*x)^3/(3*b*d) + (atan((a^3*b^8*cos(c + d*x)*(- (a^5*b^7)^(1/2)/(16*(a*b^7 - b^8)) - (a^2*b^4)/(16*(a*b^7 - b^8)))^(1/2)*8i)/(2*a^4*b^6 - 2*a^5*b^5 + (2*a^4*b^14)/(a*b^7 - b^8) - (2*a^5*b^13)/(a*b^7 - b^8) + (2*a^2*b^10*(a^5*b^7)^(1/2))/(a*b^7 - b^8) - (2*a^3*b^9*(a^5*b^7)^(1/2))/(a*b^7 - b^8)) - (a^3*cos(c + d*x)*(- (a^5*b^7)^(1/2)/(16*(a*b^7 - b^8)) - (a^2*b^4)/(16*(a*b^7 - b^8)))^(1/2)*8i)/((2*a^4)/b^2 + (2*a^4*b^6)/(a*b^7 - b^8) + (2*a^2*b^2*(a^5*b^7)^(1/2))/(a*b^7 - b^8)) + (a*b^4*cos(c + d*x)*(- (a^5*b^7)^(1/2)/(16*(a*b^7 - b^8)) - (a^2*b^4)/(16*(a*b^7 - b^8)))^(1/2)*(a^5*b^7)^(1/2)*8i)/(2*a^4*b^6 - 2*a^5*b^5 + (2*a^4*b^14)/(a*b^7 - b^8) - (2*a^5*b^13)/(a*b^7 - b^8) + (2*a^2*b^10*(a^5*b^7)^(1/2))/(a*b^7 - b^8) - (2*a^3*b^9*(a^5*b^7)^(1/2))/(a*b^7 - b^8)))*(-((a^5*b^7)^(1/2) + a^2*b^4)/(16*(a*b^7 - b^8)))^(1/2)*2i)/d - (atan((a^3*cos(c + d*x)*((a^5*b^7)^(1/2)/(16*(a*b^7 - b^8)) - (a^2*b^4)/(16*(a*b^7 - b^8)))^(1/2)*8i)/((2*a^4)/b^2 + (2*a^4*b^6)/(a*b^7 - b^8) - (2*a^2*b^2*(a^5*b^7)^(1/2))/(a*b^7 - b^8)) - (a^3*b^8*cos(c + d*x)*((a^5*b^7)^(1/2)/(16*(a*b^7 - b^8)) - (a^2*b^4)/(16*(a*b^7 - b^8)))^(1/2)*8i)/(2*a^4*b^6 - 2*a^5*b^5 + (2*a^4*b^14)/(a*b^7 - b^8) - (2*a^5*b^13)/(a*b^7 - b^8) - (2*a^2*b^10*(a^5*b^7)^(1/2))/(a*b^7 - b^8) + (2*a^3*b^9*(a^5*b^7)^(1/2))/(a*b^7 - b^8)) + (a*b^4*cos(c + d*x)*((a^5*b^7)^(1/2)/(16*(a*b^7 - b^8)) - (a^2*b^4)/(16*(a*b^7 - b^8)))^(1/2)*(a^5*b^7)^(1/2)*8i)/(2*a^4*b^6 - 2*a^5*b^5 + (2*a^4*b^14)/(a*b^7 - b^8) - (2*a^5*b^13)/(a*b^7 - b^8) - (2*a^2*b^10*(a^5*b^7)^(1/2))/(a*b^7 - b^8) + (2*a^3*b^9*(a^5*b^7)^(1/2))/(a*b^7 - b^8)))*(((a^5*b^7)^(1/2) - a^2*b^4)/(16*(a*b^7 - b^8)))^(1/2)*2i)/d","B"
197,1,1001,138,14.259682,"\text{Not used}","int(sin(c + d*x)^5/(a - b*sin(c + d*x)^4),x)","\frac{\cos\left(c+d\,x\right)}{b\,d}-\frac{2\,\mathrm{atanh}\left(\frac{8\,a^2\,b^7\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^5}}{16\,\left(a\,b^5-b^6\right)}-\frac{a\,b^3}{16\,\left(a\,b^5-b^6\right)}}}{\frac{2\,a^3\,b^{11}}{a\,b^5-b^6}-\frac{2\,a^4\,b^{10}}{a\,b^5-b^6}+\frac{2\,a^2\,b^8\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}-\frac{2\,a^3\,b^7\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}}-\frac{8\,a^2\,b\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^5}}{16\,\left(a\,b^5-b^6\right)}-\frac{a\,b^3}{16\,\left(a\,b^5-b^6\right)}}}{\frac{2\,a^3\,b^5}{a\,b^5-b^6}+\frac{2\,a^2\,b^2\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}}+\frac{8\,a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^5}}{16\,\left(a\,b^5-b^6\right)}-\frac{a\,b^3}{16\,\left(a\,b^5-b^6\right)}}\,\sqrt{a^3\,b^5}}{\frac{2\,a^3\,b^{11}}{a\,b^5-b^6}-\frac{2\,a^4\,b^{10}}{a\,b^5-b^6}+\frac{2\,a^2\,b^8\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}-\frac{2\,a^3\,b^7\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}}\right)\,\sqrt{-\frac{\sqrt{a^3\,b^5}+a\,b^3}{16\,\left(a\,b^5-b^6\right)}}}{d}+\frac{2\,\mathrm{atanh}\left(\frac{8\,a^2\,b\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^5}}{16\,\left(a\,b^5-b^6\right)}-\frac{a\,b^3}{16\,\left(a\,b^5-b^6\right)}}}{\frac{2\,a^3\,b^5}{a\,b^5-b^6}-\frac{2\,a^2\,b^2\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}}-\frac{8\,a^2\,b^7\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^5}}{16\,\left(a\,b^5-b^6\right)}-\frac{a\,b^3}{16\,\left(a\,b^5-b^6\right)}}}{\frac{2\,a^3\,b^{11}}{a\,b^5-b^6}-\frac{2\,a^4\,b^{10}}{a\,b^5-b^6}-\frac{2\,a^2\,b^8\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}+\frac{2\,a^3\,b^7\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}}+\frac{8\,a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^5}}{16\,\left(a\,b^5-b^6\right)}-\frac{a\,b^3}{16\,\left(a\,b^5-b^6\right)}}\,\sqrt{a^3\,b^5}}{\frac{2\,a^3\,b^{11}}{a\,b^5-b^6}-\frac{2\,a^4\,b^{10}}{a\,b^5-b^6}-\frac{2\,a^2\,b^8\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}+\frac{2\,a^3\,b^7\,\sqrt{a^3\,b^5}}{a\,b^5-b^6}}\right)\,\sqrt{\frac{\sqrt{a^3\,b^5}-a\,b^3}{16\,\left(a\,b^5-b^6\right)}}}{d}","Not used",1,"cos(c + d*x)/(b*d) - (2*atanh((8*a^2*b^7*cos(c + d*x)*(- (a^3*b^5)^(1/2)/(16*(a*b^5 - b^6)) - (a*b^3)/(16*(a*b^5 - b^6)))^(1/2))/((2*a^3*b^11)/(a*b^5 - b^6) - (2*a^4*b^10)/(a*b^5 - b^6) + (2*a^2*b^8*(a^3*b^5)^(1/2))/(a*b^5 - b^6) - (2*a^3*b^7*(a^3*b^5)^(1/2))/(a*b^5 - b^6)) - (8*a^2*b*cos(c + d*x)*(- (a^3*b^5)^(1/2)/(16*(a*b^5 - b^6)) - (a*b^3)/(16*(a*b^5 - b^6)))^(1/2))/((2*a^3*b^5)/(a*b^5 - b^6) + (2*a^2*b^2*(a^3*b^5)^(1/2))/(a*b^5 - b^6)) + (8*a*b^4*cos(c + d*x)*(- (a^3*b^5)^(1/2)/(16*(a*b^5 - b^6)) - (a*b^3)/(16*(a*b^5 - b^6)))^(1/2)*(a^3*b^5)^(1/2))/((2*a^3*b^11)/(a*b^5 - b^6) - (2*a^4*b^10)/(a*b^5 - b^6) + (2*a^2*b^8*(a^3*b^5)^(1/2))/(a*b^5 - b^6) - (2*a^3*b^7*(a^3*b^5)^(1/2))/(a*b^5 - b^6)))*(-((a^3*b^5)^(1/2) + a*b^3)/(16*(a*b^5 - b^6)))^(1/2))/d + (2*atanh((8*a^2*b*cos(c + d*x)*((a^3*b^5)^(1/2)/(16*(a*b^5 - b^6)) - (a*b^3)/(16*(a*b^5 - b^6)))^(1/2))/((2*a^3*b^5)/(a*b^5 - b^6) - (2*a^2*b^2*(a^3*b^5)^(1/2))/(a*b^5 - b^6)) - (8*a^2*b^7*cos(c + d*x)*((a^3*b^5)^(1/2)/(16*(a*b^5 - b^6)) - (a*b^3)/(16*(a*b^5 - b^6)))^(1/2))/((2*a^3*b^11)/(a*b^5 - b^6) - (2*a^4*b^10)/(a*b^5 - b^6) - (2*a^2*b^8*(a^3*b^5)^(1/2))/(a*b^5 - b^6) + (2*a^3*b^7*(a^3*b^5)^(1/2))/(a*b^5 - b^6)) + (8*a*b^4*cos(c + d*x)*((a^3*b^5)^(1/2)/(16*(a*b^5 - b^6)) - (a*b^3)/(16*(a*b^5 - b^6)))^(1/2)*(a^3*b^5)^(1/2))/((2*a^3*b^11)/(a*b^5 - b^6) - (2*a^4*b^10)/(a*b^5 - b^6) - (2*a^2*b^8*(a^3*b^5)^(1/2))/(a*b^5 - b^6) + (2*a^3*b^7*(a^3*b^5)^(1/2))/(a*b^5 - b^6)))*(((a^3*b^5)^(1/2) - a*b^3)/(16*(a*b^5 - b^6)))^(1/2))/d","B"
198,1,976,115,0.509231,"\text{Not used}","int(sin(c + d*x)^3/(a - b*sin(c + d*x)^4),x)","\frac{2\,\mathrm{atanh}\left(\frac{8\,a\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a\,b^3}}{16\,\left(a\,b^3-b^4\right)}-\frac{b^2}{16\,\left(a\,b^3-b^4\right)}}}{2\,a\,b+\frac{2\,a\,b^5}{a\,b^3-b^4}-\frac{2\,a\,b^3\,\sqrt{a\,b^3}}{a\,b^3-b^4}}-\frac{8\,a\,b^6\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a\,b^3}}{16\,\left(a\,b^3-b^4\right)}-\frac{b^2}{16\,\left(a\,b^3-b^4\right)}}}{2\,a\,b^5-2\,a^2\,b^4-\frac{2\,a^2\,b^8}{a\,b^3-b^4}+\frac{2\,a\,b^9}{a\,b^3-b^4}+\frac{2\,a^2\,b^6\,\sqrt{a\,b^3}}{a\,b^3-b^4}-\frac{2\,a\,b^7\,\sqrt{a\,b^3}}{a\,b^3-b^4}}+\frac{8\,a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{a\,b^3}\,\sqrt{\frac{\sqrt{a\,b^3}}{16\,\left(a\,b^3-b^4\right)}-\frac{b^2}{16\,\left(a\,b^3-b^4\right)}}}{2\,a\,b^5-2\,a^2\,b^4-\frac{2\,a^2\,b^8}{a\,b^3-b^4}+\frac{2\,a\,b^9}{a\,b^3-b^4}+\frac{2\,a^2\,b^6\,\sqrt{a\,b^3}}{a\,b^3-b^4}-\frac{2\,a\,b^7\,\sqrt{a\,b^3}}{a\,b^3-b^4}}\right)\,\sqrt{-\frac{b^2-\sqrt{a\,b^3}}{16\,\left(a\,b^3-b^4\right)}}}{d}-\frac{2\,\mathrm{atanh}\left(\frac{8\,a\,b^6\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{b^2}{16\,\left(a\,b^3-b^4\right)}-\frac{\sqrt{a\,b^3}}{16\,\left(a\,b^3-b^4\right)}}}{2\,a\,b^5-2\,a^2\,b^4-\frac{2\,a^2\,b^8}{a\,b^3-b^4}+\frac{2\,a\,b^9}{a\,b^3-b^4}-\frac{2\,a^2\,b^6\,\sqrt{a\,b^3}}{a\,b^3-b^4}+\frac{2\,a\,b^7\,\sqrt{a\,b^3}}{a\,b^3-b^4}}-\frac{8\,a\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{b^2}{16\,\left(a\,b^3-b^4\right)}-\frac{\sqrt{a\,b^3}}{16\,\left(a\,b^3-b^4\right)}}}{2\,a\,b+\frac{2\,a\,b^5}{a\,b^3-b^4}+\frac{2\,a\,b^3\,\sqrt{a\,b^3}}{a\,b^3-b^4}}+\frac{8\,a\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{a\,b^3}\,\sqrt{-\frac{b^2}{16\,\left(a\,b^3-b^4\right)}-\frac{\sqrt{a\,b^3}}{16\,\left(a\,b^3-b^4\right)}}}{2\,a\,b^5-2\,a^2\,b^4-\frac{2\,a^2\,b^8}{a\,b^3-b^4}+\frac{2\,a\,b^9}{a\,b^3-b^4}-\frac{2\,a^2\,b^6\,\sqrt{a\,b^3}}{a\,b^3-b^4}+\frac{2\,a\,b^7\,\sqrt{a\,b^3}}{a\,b^3-b^4}}\right)\,\sqrt{-\frac{b^2+\sqrt{a\,b^3}}{16\,\left(a\,b^3-b^4\right)}}}{d}","Not used",1,"(2*atanh((8*a*b^2*cos(c + d*x)*((a*b^3)^(1/2)/(16*(a*b^3 - b^4)) - b^2/(16*(a*b^3 - b^4)))^(1/2))/(2*a*b + (2*a*b^5)/(a*b^3 - b^4) - (2*a*b^3*(a*b^3)^(1/2))/(a*b^3 - b^4)) - (8*a*b^6*cos(c + d*x)*((a*b^3)^(1/2)/(16*(a*b^3 - b^4)) - b^2/(16*(a*b^3 - b^4)))^(1/2))/(2*a*b^5 - 2*a^2*b^4 - (2*a^2*b^8)/(a*b^3 - b^4) + (2*a*b^9)/(a*b^3 - b^4) + (2*a^2*b^6*(a*b^3)^(1/2))/(a*b^3 - b^4) - (2*a*b^7*(a*b^3)^(1/2))/(a*b^3 - b^4)) + (8*a*b^4*cos(c + d*x)*(a*b^3)^(1/2)*((a*b^3)^(1/2)/(16*(a*b^3 - b^4)) - b^2/(16*(a*b^3 - b^4)))^(1/2))/(2*a*b^5 - 2*a^2*b^4 - (2*a^2*b^8)/(a*b^3 - b^4) + (2*a*b^9)/(a*b^3 - b^4) + (2*a^2*b^6*(a*b^3)^(1/2))/(a*b^3 - b^4) - (2*a*b^7*(a*b^3)^(1/2))/(a*b^3 - b^4)))*(-(b^2 - (a*b^3)^(1/2))/(16*(a*b^3 - b^4)))^(1/2))/d - (2*atanh((8*a*b^6*cos(c + d*x)*(- b^2/(16*(a*b^3 - b^4)) - (a*b^3)^(1/2)/(16*(a*b^3 - b^4)))^(1/2))/(2*a*b^5 - 2*a^2*b^4 - (2*a^2*b^8)/(a*b^3 - b^4) + (2*a*b^9)/(a*b^3 - b^4) - (2*a^2*b^6*(a*b^3)^(1/2))/(a*b^3 - b^4) + (2*a*b^7*(a*b^3)^(1/2))/(a*b^3 - b^4)) - (8*a*b^2*cos(c + d*x)*(- b^2/(16*(a*b^3 - b^4)) - (a*b^3)^(1/2)/(16*(a*b^3 - b^4)))^(1/2))/(2*a*b + (2*a*b^5)/(a*b^3 - b^4) + (2*a*b^3*(a*b^3)^(1/2))/(a*b^3 - b^4)) + (8*a*b^4*cos(c + d*x)*(a*b^3)^(1/2)*(- b^2/(16*(a*b^3 - b^4)) - (a*b^3)^(1/2)/(16*(a*b^3 - b^4)))^(1/2))/(2*a*b^5 - 2*a^2*b^4 - (2*a^2*b^8)/(a*b^3 - b^4) + (2*a*b^9)/(a*b^3 - b^4) - (2*a^2*b^6*(a*b^3)^(1/2))/(a*b^3 - b^4) + (2*a*b^7*(a*b^3)^(1/2))/(a*b^3 - b^4)))*(-(b^2 + (a*b^3)^(1/2))/(16*(a*b^3 - b^4)))^(1/2))/d","B"
199,1,361,125,15.110501,"\text{Not used}","int(sin(c + d*x)/(a - b*sin(c + d*x)^4),x)","\frac{\ln\left(4\,a\,b^3\,\sqrt{\frac{1}{a\,b+\sqrt{a^3\,b}}}-4\,b^3\,\cos\left(c+d\,x\right)+\frac{4\,a\,b^4\,\cos\left(c+d\,x\right)}{a\,b+\sqrt{a^3\,b}}\right)\,\sqrt{-\frac{a\,b-\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^2\,b^2\right)}}}{d}+\frac{\ln\left(4\,b^3\,\cos\left(c+d\,x\right)-4\,a\,b^3\,\sqrt{\frac{1}{a\,b-\sqrt{a^3\,b}}}-\frac{4\,a\,b^4\,\cos\left(c+d\,x\right)}{a\,b-\sqrt{a^3\,b}}\right)\,\sqrt{-\frac{a\,b+\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^2\,b^2\right)}}}{d}-\frac{\ln\left(4\,b^3\,\cos\left(c+d\,x\right)+4\,a\,b^3\,\sqrt{\frac{1}{a\,b+\sqrt{a^3\,b}}}-\frac{4\,a\,b^4\,\cos\left(c+d\,x\right)}{a\,b+\sqrt{a^3\,b}}\right)\,\sqrt{\frac{1}{a\,b+\sqrt{a^3\,b}}}}{4\,d}-\frac{\ln\left(4\,b^3\,\cos\left(c+d\,x\right)+4\,a\,b^3\,\sqrt{\frac{1}{a\,b-\sqrt{a^3\,b}}}-\frac{4\,a\,b^4\,\cos\left(c+d\,x\right)}{a\,b-\sqrt{a^3\,b}}\right)\,\sqrt{\frac{1}{a\,b-\sqrt{a^3\,b}}}}{4\,d}","Not used",1,"(log(4*a*b^3*(1/(a*b + (a^3*b)^(1/2)))^(1/2) - 4*b^3*cos(c + d*x) + (4*a*b^4*cos(c + d*x))/(a*b + (a^3*b)^(1/2)))*(-(a*b - (a^3*b)^(1/2))/(16*(a^3*b - a^2*b^2)))^(1/2))/d + (log(4*b^3*cos(c + d*x) - 4*a*b^3*(1/(a*b - (a^3*b)^(1/2)))^(1/2) - (4*a*b^4*cos(c + d*x))/(a*b - (a^3*b)^(1/2)))*(-(a*b + (a^3*b)^(1/2))/(16*(a^3*b - a^2*b^2)))^(1/2))/d - (log(4*b^3*cos(c + d*x) + 4*a*b^3*(1/(a*b + (a^3*b)^(1/2)))^(1/2) - (4*a*b^4*cos(c + d*x))/(a*b + (a^3*b)^(1/2)))*(1/(a*b + (a^3*b)^(1/2)))^(1/2))/(4*d) - (log(4*b^3*cos(c + d*x) + 4*a*b^3*(1/(a*b - (a^3*b)^(1/2)))^(1/2) - (4*a*b^4*cos(c + d*x))/(a*b - (a^3*b)^(1/2)))*(1/(a*b - (a^3*b)^(1/2)))^(1/2))/(4*d)","B"
200,1,2031,136,15.361144,"\text{Not used}","int(1/(sin(c + d*x)*(a - b*sin(c + d*x)^4)),x)","-\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,\left(256\,a^4\,b^4-192\,a^3\,b^5+\cos\left(c+d\,x\right)\,\left(768\,a^4\,b^5-512\,a^5\,b^4\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)-144\,a^2\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}+12\,a\,b^5\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}+6\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,1{}\mathrm{i}+\left(\left(\left(\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,\left(192\,a^3\,b^5-256\,a^4\,b^4+\cos\left(c+d\,x\right)\,\left(768\,a^4\,b^5-512\,a^5\,b^4\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)-144\,a^2\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-12\,a\,b^5\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}+6\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,\left(256\,a^4\,b^4-192\,a^3\,b^5+\cos\left(c+d\,x\right)\,\left(768\,a^4\,b^5-512\,a^5\,b^4\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)-144\,a^2\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}+12\,a\,b^5\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}+6\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-\left(\left(\left(\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,\left(192\,a^3\,b^5-256\,a^4\,b^4+\cos\left(c+d\,x\right)\,\left(768\,a^4\,b^5-512\,a^5\,b^4\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)-144\,a^2\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-12\,a\,b^5\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}+6\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}}\right)\,\sqrt{\frac{a^2\,b+\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atanh}\left(\frac{32\,b^4\,\cos\left(c+d\,x\right)}{32\,b^4-\frac{18\,b^5}{a}}-\frac{18\,b^5\,\cos\left(c+d\,x\right)}{32\,a\,b^4-18\,b^5}\right)}{a\,d}-\frac{\mathrm{atan}\left(\frac{\left(6\,b^5\,\cos\left(c+d\,x\right)+\left(\left(\left(256\,a^4\,b^4-192\,a^3\,b^5+\cos\left(c+d\,x\right)\,\left(768\,a^4\,b^5-512\,a^5\,b^4\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-144\,a^2\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}+12\,a\,b^5\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,1{}\mathrm{i}+\left(6\,b^5\,\cos\left(c+d\,x\right)+\left(\left(\left(192\,a^3\,b^5-256\,a^4\,b^4+\cos\left(c+d\,x\right)\,\left(768\,a^4\,b^5-512\,a^5\,b^4\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-144\,a^2\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-12\,a\,b^5\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,1{}\mathrm{i}}{\left(6\,b^5\,\cos\left(c+d\,x\right)+\left(\left(\left(256\,a^4\,b^4-192\,a^3\,b^5+\cos\left(c+d\,x\right)\,\left(768\,a^4\,b^5-512\,a^5\,b^4\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-144\,a^2\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}+12\,a\,b^5\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-\left(6\,b^5\,\cos\left(c+d\,x\right)+\left(\left(\left(192\,a^3\,b^5-256\,a^4\,b^4+\cos\left(c+d\,x\right)\,\left(768\,a^4\,b^5-512\,a^5\,b^4\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-144\,a^2\,b^5\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}-12\,a\,b^5\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}}\right)\,\sqrt{\frac{a^2\,b-\sqrt{a^5\,b}}{16\,\left(a^4\,b-a^5\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- (atan(((((((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*(256*a^4*b^4 - 192*a^3*b^5 + cos(c + d*x)*(768*a^4*b^5 - 512*a^5*b^4)*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)) - 144*a^2*b^5*cos(c + d*x))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) + 12*a*b^5)*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) + 6*b^5*cos(c + d*x))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*1i + (((((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*(192*a^3*b^5 - 256*a^4*b^4 + cos(c + d*x)*(768*a^4*b^5 - 512*a^5*b^4)*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)) - 144*a^2*b^5*cos(c + d*x))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - 12*a*b^5)*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) + 6*b^5*cos(c + d*x))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*1i)/((((((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*(256*a^4*b^4 - 192*a^3*b^5 + cos(c + d*x)*(768*a^4*b^5 - 512*a^5*b^4)*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)) - 144*a^2*b^5*cos(c + d*x))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) + 12*a*b^5)*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) + 6*b^5*cos(c + d*x))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - (((((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*(192*a^3*b^5 - 256*a^4*b^4 + cos(c + d*x)*(768*a^4*b^5 - 512*a^5*b^4)*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)) - 144*a^2*b^5*cos(c + d*x))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - 12*a*b^5)*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) + 6*b^5*cos(c + d*x))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)))*((a^2*b + (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*2i)/d - atanh((32*b^4*cos(c + d*x))/(32*b^4 - (18*b^5)/a) - (18*b^5*cos(c + d*x))/(32*a*b^4 - 18*b^5))/(a*d) - (atan(((6*b^5*cos(c + d*x) + (((256*a^4*b^4 - 192*a^3*b^5 + cos(c + d*x)*(768*a^4*b^5 - 512*a^5*b^4)*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - 144*a^2*b^5*cos(c + d*x))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) + 12*a*b^5)*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*1i + (6*b^5*cos(c + d*x) + (((192*a^3*b^5 - 256*a^4*b^4 + cos(c + d*x)*(768*a^4*b^5 - 512*a^5*b^4)*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - 144*a^2*b^5*cos(c + d*x))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - 12*a*b^5)*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*1i)/((6*b^5*cos(c + d*x) + (((256*a^4*b^4 - 192*a^3*b^5 + cos(c + d*x)*(768*a^4*b^5 - 512*a^5*b^4)*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - 144*a^2*b^5*cos(c + d*x))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) + 12*a*b^5)*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - (6*b^5*cos(c + d*x) + (((192*a^3*b^5 - 256*a^4*b^4 + cos(c + d*x)*(768*a^4*b^5 - 512*a^5*b^4)*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - 144*a^2*b^5*cos(c + d*x))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2) - 12*a*b^5)*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)))*((a^2*b - (a^5*b)^(1/2))/(16*(a^4*b - a^5)))^(1/2)*2i)/d","B"
201,1,2779,184,15.186441,"\text{Not used}","int(1/(sin(c + d*x)^3*(a - b*sin(c + d*x)^4)),x)","\frac{\mathrm{atan}\left(\cos\left(c+d\,x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{d\,\left(2\,a-2\,a\,{\cos\left(c+d\,x\right)}^2\right)}-\frac{\cos\left(c+d\,x\right)}{d\,\left(2\,a-2\,a\,{\cos\left(c+d\,x\right)}^2\right)}-\frac{\mathrm{atan}\left(\cos\left(c+d\,x\right)\,1{}\mathrm{i}\right)\,{\cos\left(c+d\,x\right)}^2\,1{}\mathrm{i}}{d\,\left(2\,a-2\,a\,{\cos\left(c+d\,x\right)}^2\right)}+\frac{a\,\mathrm{atan}\left(\frac{a^{13}\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,2048{}\mathrm{i}+a^{10}\,b\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,64{}\mathrm{i}-a^{12}\,b\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,7168{}\mathrm{i}-a^4\,b^5\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,8{}\mathrm{i}+a^5\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,12{}\mathrm{i}-a^7\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,4{}\mathrm{i}+a^7\,b^4\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,320{}\mathrm{i}-a^8\,b^3\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,576{}\mathrm{i}+a^9\,b^2\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,192{}\mathrm{i}-a^{10}\,b^3\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,3072{}\mathrm{i}+a^{11}\,b^2\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,8192{}\mathrm{i}}{2\,b^3\,\sqrt{a^7\,b^3}+a^3\,b^5+a^5\,b^3-a\,b^2\,\sqrt{a^7\,b^3}+a^2\,b\,\sqrt{a^7\,b^3}}\right)\,\sqrt{\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,4{}\mathrm{i}}{d\,\left(2\,a-2\,a\,{\cos\left(c+d\,x\right)}^2\right)}+\frac{a\,\mathrm{atan}\left(\frac{a^{13}\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,2048{}\mathrm{i}+a^{10}\,b\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,64{}\mathrm{i}-a^{12}\,b\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,7168{}\mathrm{i}-a^4\,b^5\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,8{}\mathrm{i}+a^5\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,12{}\mathrm{i}-a^7\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,4{}\mathrm{i}+a^7\,b^4\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,320{}\mathrm{i}-a^8\,b^3\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,576{}\mathrm{i}+a^9\,b^2\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,192{}\mathrm{i}-a^{10}\,b^3\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,3072{}\mathrm{i}+a^{11}\,b^2\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,8192{}\mathrm{i}}{a^3\,b^5-2\,b^3\,\sqrt{a^7\,b^3}+a^5\,b^3+a\,b^2\,\sqrt{a^7\,b^3}-a^2\,b\,\sqrt{a^7\,b^3}}\right)\,\sqrt{-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,4{}\mathrm{i}}{d\,\left(2\,a-2\,a\,{\cos\left(c+d\,x\right)}^2\right)}-\frac{a\,{\cos\left(c+d\,x\right)}^2\,\mathrm{atan}\left(\frac{a^{13}\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,2048{}\mathrm{i}+a^{10}\,b\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,64{}\mathrm{i}-a^{12}\,b\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,7168{}\mathrm{i}-a^4\,b^5\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,8{}\mathrm{i}+a^5\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,12{}\mathrm{i}-a^7\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,4{}\mathrm{i}+a^7\,b^4\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,320{}\mathrm{i}-a^8\,b^3\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,576{}\mathrm{i}+a^9\,b^2\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,192{}\mathrm{i}-a^{10}\,b^3\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,3072{}\mathrm{i}+a^{11}\,b^2\,\cos\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,8192{}\mathrm{i}}{2\,b^3\,\sqrt{a^7\,b^3}+a^3\,b^5+a^5\,b^3-a\,b^2\,\sqrt{a^7\,b^3}+a^2\,b\,\sqrt{a^7\,b^3}}\right)\,\sqrt{\frac{\sqrt{a^7\,b^3}+a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,4{}\mathrm{i}}{d\,\left(2\,a-2\,a\,{\cos\left(c+d\,x\right)}^2\right)}-\frac{a\,{\cos\left(c+d\,x\right)}^2\,\mathrm{atan}\left(\frac{a^{13}\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,2048{}\mathrm{i}+a^{10}\,b\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,64{}\mathrm{i}-a^{12}\,b\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,7168{}\mathrm{i}-a^4\,b^5\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,8{}\mathrm{i}+a^5\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,12{}\mathrm{i}-a^7\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,4{}\mathrm{i}+a^7\,b^4\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,320{}\mathrm{i}-a^8\,b^3\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,576{}\mathrm{i}+a^9\,b^2\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{3/2}\,192{}\mathrm{i}-a^{10}\,b^3\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,3072{}\mathrm{i}+a^{11}\,b^2\,\cos\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}\right)}^{5/2}\,8192{}\mathrm{i}}{a^3\,b^5-2\,b^3\,\sqrt{a^7\,b^3}+a^5\,b^3+a\,b^2\,\sqrt{a^7\,b^3}-a^2\,b\,\sqrt{a^7\,b^3}}\right)\,\sqrt{-\frac{\sqrt{a^7\,b^3}-a^3\,b^2}{16\,a^6\,b-16\,a^7}}\,4{}\mathrm{i}}{d\,\left(2\,a-2\,a\,{\cos\left(c+d\,x\right)}^2\right)}","Not used",1,"(atan(cos(c + d*x)*1i)*1i)/(d*(2*a - 2*a*cos(c + d*x)^2)) - cos(c + d*x)/(d*(2*a - 2*a*cos(c + d*x)^2)) - (atan(cos(c + d*x)*1i)*cos(c + d*x)^2*1i)/(d*(2*a - 2*a*cos(c + d*x)^2)) + (a*atan((a^13*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*2048i + a^10*b*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*64i - a^12*b*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*7168i - a^4*b^5*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*8i + a^5*b^4*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*12i - a^7*b^2*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*4i + a^7*b^4*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*320i - a^8*b^3*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*576i + a^9*b^2*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*192i - a^10*b^3*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*3072i + a^11*b^2*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*8192i)/(2*b^3*(a^7*b^3)^(1/2) + a^3*b^5 + a^5*b^3 - a*b^2*(a^7*b^3)^(1/2) + a^2*b*(a^7*b^3)^(1/2)))*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*4i)/(d*(2*a - 2*a*cos(c + d*x)^2)) + (a*atan((a^13*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*2048i + a^10*b*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*64i - a^12*b*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*7168i - a^4*b^5*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*8i + a^5*b^4*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*12i - a^7*b^2*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*4i + a^7*b^4*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*320i - a^8*b^3*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*576i + a^9*b^2*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*192i - a^10*b^3*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*3072i + a^11*b^2*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*8192i)/(a^3*b^5 - 2*b^3*(a^7*b^3)^(1/2) + a^5*b^3 + a*b^2*(a^7*b^3)^(1/2) - a^2*b*(a^7*b^3)^(1/2)))*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*4i)/(d*(2*a - 2*a*cos(c + d*x)^2)) - (a*cos(c + d*x)^2*atan((a^13*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*2048i + a^10*b*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*64i - a^12*b*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*7168i - a^4*b^5*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*8i + a^5*b^4*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*12i - a^7*b^2*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*4i + a^7*b^4*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*320i - a^8*b^3*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*576i + a^9*b^2*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*192i - a^10*b^3*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*3072i + a^11*b^2*cos(c + d*x)*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*8192i)/(2*b^3*(a^7*b^3)^(1/2) + a^3*b^5 + a^5*b^3 - a*b^2*(a^7*b^3)^(1/2) + a^2*b*(a^7*b^3)^(1/2)))*(((a^7*b^3)^(1/2) + a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*4i)/(d*(2*a - 2*a*cos(c + d*x)^2)) - (a*cos(c + d*x)^2*atan((a^13*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*2048i + a^10*b*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*64i - a^12*b*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*7168i - a^4*b^5*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*8i + a^5*b^4*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*12i - a^7*b^2*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*4i + a^7*b^4*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*320i - a^8*b^3*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*576i + a^9*b^2*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(3/2)*192i - a^10*b^3*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*3072i + a^11*b^2*cos(c + d*x)*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(5/2)*8192i)/(a^3*b^5 - 2*b^3*(a^7*b^3)^(1/2) + a^5*b^3 + a*b^2*(a^7*b^3)^(1/2) - a^2*b*(a^7*b^3)^(1/2)))*(-((a^7*b^3)^(1/2) - a^3*b^2)/(16*a^6*b - 16*a^7))^(1/2)*4i)/(d*(2*a - 2*a*cos(c + d*x)^2))","B"
202,1,3692,229,15.516819,"\text{Not used}","int(1/(sin(c + d*x)^5*(a - b*sin(c + d*x)^4)),x)","\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{768\,a^3\,b^8-144\,a^5\,b^6}{64\,a^5}+\left(\left(\frac{6144\,a^9\,b^4+10240\,a^8\,b^5-12288\,a^7\,b^6}{64\,a^5}-\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\,1{}\mathrm{i}-\left(\left(\frac{768\,a^3\,b^8-144\,a^5\,b^6}{64\,a^5}+\left(\left(\frac{6144\,a^9\,b^4+10240\,a^8\,b^5-12288\,a^7\,b^6}{64\,a^5}+\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{768\,a^3\,b^8-144\,a^5\,b^6}{64\,a^5}+\left(\left(\frac{6144\,a^9\,b^4+10240\,a^8\,b^5-12288\,a^7\,b^6}{64\,a^5}-\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\left(\left(\frac{768\,a^3\,b^8-144\,a^5\,b^6}{64\,a^5}+\left(\left(\frac{6144\,a^9\,b^4+10240\,a^8\,b^5-12288\,a^7\,b^6}{64\,a^5}+\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{24\,b^9+9\,a\,b^8}{32\,a^5}}\right)\,\sqrt{\frac{\sqrt{a^9\,b^5}+a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{768\,a^3\,b^8-144\,a^5\,b^6}{64\,a^5}+\left(\left(\frac{6144\,a^9\,b^4+10240\,a^8\,b^5-12288\,a^7\,b^6}{64\,a^5}-\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\,1{}\mathrm{i}-\left(\left(\frac{768\,a^3\,b^8-144\,a^5\,b^6}{64\,a^5}+\left(\left(\frac{6144\,a^9\,b^4+10240\,a^8\,b^5-12288\,a^7\,b^6}{64\,a^5}+\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{768\,a^3\,b^8-144\,a^5\,b^6}{64\,a^5}+\left(\left(\frac{6144\,a^9\,b^4+10240\,a^8\,b^5-12288\,a^7\,b^6}{64\,a^5}-\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\left(\left(\frac{768\,a^3\,b^8-144\,a^5\,b^6}{64\,a^5}+\left(\left(\frac{6144\,a^9\,b^4+10240\,a^8\,b^5-12288\,a^7\,b^6}{64\,a^5}+\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}+\frac{24\,b^9+9\,a\,b^8}{32\,a^5}}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^5}-a^4\,b^3}{16\,\left(a^8\,b-a^9\right)}}\,2{}\mathrm{i}}{d}-\frac{\frac{5\,\cos\left(c+d\,x\right)}{8\,a}-\frac{3\,{\cos\left(c+d\,x\right)}^3}{8\,a}}{d\,\left({\cos\left(c+d\,x\right)}^4-{\cos\left(c+d\,x\right)}^2+{\sin\left(c+d\,x\right)}^2\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}-\frac{\left(\frac{12\,a^3\,b^8-\frac{9\,a^5\,b^6}{4}}{a^5}+\frac{\left(3\,a+8\,b\right)\,\left(\frac{\left(\frac{96\,a^9\,b^4+160\,a^8\,b^5-192\,a^7\,b^6}{a^5}-\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\left(3\,a+8\,b\right)}{256\,a^6}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}+\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)}{16\,a^2}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}\right)\,\left(3\,a+8\,b\right)\,1{}\mathrm{i}}{16\,a^2}+\frac{\left(\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}+\frac{\left(\frac{12\,a^3\,b^8-\frac{9\,a^5\,b^6}{4}}{a^5}+\frac{\left(3\,a+8\,b\right)\,\left(\frac{\left(\frac{96\,a^9\,b^4+160\,a^8\,b^5-192\,a^7\,b^6}{a^5}+\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\left(3\,a+8\,b\right)}{256\,a^6}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}-\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)}{16\,a^2}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}\right)\,\left(3\,a+8\,b\right)\,1{}\mathrm{i}}{16\,a^2}}{\frac{\frac{3\,b^9}{4}+\frac{9\,a\,b^8}{32}}{a^5}-\frac{\left(\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}-\frac{\left(\frac{12\,a^3\,b^8-\frac{9\,a^5\,b^6}{4}}{a^5}+\frac{\left(3\,a+8\,b\right)\,\left(\frac{\left(\frac{96\,a^9\,b^4+160\,a^8\,b^5-192\,a^7\,b^6}{a^5}-\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\left(3\,a+8\,b\right)}{256\,a^6}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}+\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)}{16\,a^2}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}+\frac{\left(\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^7+48\,a\,b^8+96\,b^9\right)}{16\,a^4}+\frac{\left(\frac{12\,a^3\,b^8-\frac{9\,a^5\,b^6}{4}}{a^5}+\frac{\left(3\,a+8\,b\right)\,\left(\frac{\left(\frac{96\,a^9\,b^4+160\,a^8\,b^5-192\,a^7\,b^6}{a^5}+\frac{\cos\left(c+d\,x\right)\,\left(12288\,a^8\,b^5-8192\,a^9\,b^4\right)\,\left(3\,a+8\,b\right)}{256\,a^6}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}-\frac{\cos\left(c+d\,x\right)\,\left(144\,a^6\,b^5+768\,a^5\,b^6+2304\,a^4\,b^7\right)}{16\,a^4}\right)}{16\,a^2}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}\right)\,\left(3\,a+8\,b\right)}{16\,a^2}}\right)\,\left(3\,a+8\,b\right)\,1{}\mathrm{i}}{8\,a^2\,d}","Not used",1,"(atan(((((768*a^3*b^8 - 144*a^5*b^6)/(64*a^5) + (((10240*a^8*b^5 - 12288*a^7*b^6 + 6144*a^9*b^4)/(64*a^5) - (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) - (cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2)*1i - (((768*a^3*b^8 - 144*a^5*b^6)/(64*a^5) + (((10240*a^8*b^5 - 12288*a^7*b^6 + 6144*a^9*b^4)/(64*a^5) + (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) - (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2)*1i)/((((768*a^3*b^8 - 144*a^5*b^6)/(64*a^5) + (((10240*a^8*b^5 - 12288*a^7*b^6 + 6144*a^9*b^4)/(64*a^5) - (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) - (cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (((768*a^3*b^8 - 144*a^5*b^6)/(64*a^5) + (((10240*a^8*b^5 - 12288*a^7*b^6 + 6144*a^9*b^4)/(64*a^5) + (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) - (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (9*a*b^8 + 24*b^9)/(32*a^5)))*(((a^9*b^5)^(1/2) + a^4*b^3)/(16*(a^8*b - a^9)))^(1/2)*2i)/d + (atan(((((768*a^3*b^8 - 144*a^5*b^6)/(64*a^5) + (((10240*a^8*b^5 - 12288*a^7*b^6 + 6144*a^9*b^4)/(64*a^5) - (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) - (cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2)*1i - (((768*a^3*b^8 - 144*a^5*b^6)/(64*a^5) + (((10240*a^8*b^5 - 12288*a^7*b^6 + 6144*a^9*b^4)/(64*a^5) + (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) - (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2)*1i)/((((768*a^3*b^8 - 144*a^5*b^6)/(64*a^5) + (((10240*a^8*b^5 - 12288*a^7*b^6 + 6144*a^9*b^4)/(64*a^5) - (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) - (cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (((768*a^3*b^8 - 144*a^5*b^6)/(64*a^5) + (((10240*a^8*b^5 - 12288*a^7*b^6 + 6144*a^9*b^4)/(64*a^5) + (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) - (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2) + (9*a*b^8 + 24*b^9)/(32*a^5)))*(-((a^9*b^5)^(1/2) - a^4*b^3)/(16*(a^8*b - a^9)))^(1/2)*2i)/d - ((5*cos(c + d*x))/(8*a) - (3*cos(c + d*x)^3)/(8*a))/(d*(cos(c + d*x)^4 - cos(c + d*x)^2 + sin(c + d*x)^2)) - (atan(((((cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4) - (((12*a^3*b^8 - (9*a^5*b^6)/4)/a^5 + ((3*a + 8*b)*((((160*a^8*b^5 - 192*a^7*b^6 + 96*a^9*b^4)/a^5 - (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(3*a + 8*b))/(256*a^6))*(3*a + 8*b))/(16*a^2) + (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4)))/(16*a^2))*(3*a + 8*b))/(16*a^2))*(3*a + 8*b)*1i)/(16*a^2) + (((cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4) + (((12*a^3*b^8 - (9*a^5*b^6)/4)/a^5 + ((3*a + 8*b)*((((160*a^8*b^5 - 192*a^7*b^6 + 96*a^9*b^4)/a^5 + (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(3*a + 8*b))/(256*a^6))*(3*a + 8*b))/(16*a^2) - (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4)))/(16*a^2))*(3*a + 8*b))/(16*a^2))*(3*a + 8*b)*1i)/(16*a^2))/(((9*a*b^8)/32 + (3*b^9)/4)/a^5 - (((cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4) - (((12*a^3*b^8 - (9*a^5*b^6)/4)/a^5 + ((3*a + 8*b)*((((160*a^8*b^5 - 192*a^7*b^6 + 96*a^9*b^4)/a^5 - (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(3*a + 8*b))/(256*a^6))*(3*a + 8*b))/(16*a^2) + (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4)))/(16*a^2))*(3*a + 8*b))/(16*a^2))*(3*a + 8*b))/(16*a^2) + (((cos(c + d*x)*(48*a*b^8 + 96*b^9 + 9*a^2*b^7))/(16*a^4) + (((12*a^3*b^8 - (9*a^5*b^6)/4)/a^5 + ((3*a + 8*b)*((((160*a^8*b^5 - 192*a^7*b^6 + 96*a^9*b^4)/a^5 + (cos(c + d*x)*(12288*a^8*b^5 - 8192*a^9*b^4)*(3*a + 8*b))/(256*a^6))*(3*a + 8*b))/(16*a^2) - (cos(c + d*x)*(2304*a^4*b^7 + 768*a^5*b^6 + 144*a^6*b^5))/(16*a^4)))/(16*a^2))*(3*a + 8*b))/(16*a^2))*(3*a + 8*b))/(16*a^2)))*(3*a + 8*b)*1i)/(8*a^2*d)","B"
203,1,5022,184,16.866580,"\text{Not used}","int(sin(c + d*x)^8/(a - b*sin(c + d*x)^4),x)","\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{12288\,a^6\,b^7-22528\,a^5\,b^8+8192\,a^4\,b^9+2048\,a^3\,b^{10}}{64\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{-768\,a^8\,b^3+1536\,a^7\,b^4-1648\,a^6\,b^5+112\,a^5\,b^6+624\,a^4\,b^7+144\,a^3\,b^8}{64\,b^5}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{12288\,a^6\,b^7-22528\,a^5\,b^8+8192\,a^4\,b^9+2048\,a^3\,b^{10}}{64\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{-768\,a^8\,b^3+1536\,a^7\,b^4-1648\,a^6\,b^5+112\,a^5\,b^6+624\,a^4\,b^7+144\,a^3\,b^8}{64\,b^5}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{12288\,a^6\,b^7-22528\,a^5\,b^8+8192\,a^4\,b^9+2048\,a^3\,b^{10}}{64\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{-768\,a^8\,b^3+1536\,a^7\,b^4-1648\,a^6\,b^5+112\,a^5\,b^6+624\,a^4\,b^7+144\,a^3\,b^8}{64\,b^5}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\left(\left(\left(\left(\frac{12288\,a^6\,b^7-22528\,a^5\,b^8+8192\,a^4\,b^9+2048\,a^3\,b^{10}}{64\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{-768\,a^8\,b^3+1536\,a^7\,b^4-1648\,a^6\,b^5+112\,a^5\,b^6+624\,a^4\,b^7+144\,a^3\,b^8}{64\,b^5}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{-216\,a^9+63\,a^8\,b+126\,a^7\,b^2+27\,a^6\,b^3}{32\,b^5}}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^9}+a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{12288\,a^6\,b^7-22528\,a^5\,b^8+8192\,a^4\,b^9+2048\,a^3\,b^{10}}{64\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{-768\,a^8\,b^3+1536\,a^7\,b^4-1648\,a^6\,b^5+112\,a^5\,b^6+624\,a^4\,b^7+144\,a^3\,b^8}{64\,b^5}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{12288\,a^6\,b^7-22528\,a^5\,b^8+8192\,a^4\,b^9+2048\,a^3\,b^{10}}{64\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{-768\,a^8\,b^3+1536\,a^7\,b^4-1648\,a^6\,b^5+112\,a^5\,b^6+624\,a^4\,b^7+144\,a^3\,b^8}{64\,b^5}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{12288\,a^6\,b^7-22528\,a^5\,b^8+8192\,a^4\,b^9+2048\,a^3\,b^{10}}{64\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{-768\,a^8\,b^3+1536\,a^7\,b^4-1648\,a^6\,b^5+112\,a^5\,b^6+624\,a^4\,b^7+144\,a^3\,b^8}{64\,b^5}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\left(\left(\left(\left(\frac{12288\,a^6\,b^7-22528\,a^5\,b^8+8192\,a^4\,b^9+2048\,a^3\,b^{10}}{64\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{-768\,a^8\,b^3+1536\,a^7\,b^4-1648\,a^6\,b^5+112\,a^5\,b^6+624\,a^4\,b^7+144\,a^3\,b^8}{64\,b^5}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}+\frac{-216\,a^9+63\,a^8\,b+126\,a^7\,b^2+27\,a^6\,b^3}{32\,b^5}}\right)\,\sqrt{\frac{\sqrt{a^5\,b^9}-a^3\,b^4}{16\,\left(a\,b^8-b^9\right)}}\,2{}\mathrm{i}}{d}+\frac{\frac{3\,\mathrm{tan}\left(c+d\,x\right)}{8\,b}+\frac{5\,{\mathrm{tan}\left(c+d\,x\right)}^3}{8\,b}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4+2\,{\mathrm{tan}\left(c+d\,x\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}-\frac{\left(\frac{-12\,a^8\,b^3+24\,a^7\,b^4-\frac{103\,a^6\,b^5}{4}+\frac{7\,a^5\,b^6}{4}+\frac{39\,a^4\,b^7}{4}+\frac{9\,a^3\,b^8}{4}}{b^5}+\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}-\frac{\left(\frac{192\,a^6\,b^7-352\,a^5\,b^8+128\,a^4\,b^9+32\,a^3\,b^{10}}{b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{256\,b^6}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,1{}\mathrm{i}}{16\,b^2}+\frac{\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}+\frac{\left(\frac{-12\,a^8\,b^3+24\,a^7\,b^4-\frac{103\,a^6\,b^5}{4}+\frac{7\,a^5\,b^6}{4}+\frac{39\,a^4\,b^7}{4}+\frac{9\,a^3\,b^8}{4}}{b^5}-\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}+\frac{\left(\frac{192\,a^6\,b^7-352\,a^5\,b^8+128\,a^4\,b^9+32\,a^3\,b^{10}}{b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{256\,b^6}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,1{}\mathrm{i}}{16\,b^2}}{\frac{-\frac{27\,a^9}{4}+\frac{63\,a^8\,b}{32}+\frac{63\,a^7\,b^2}{16}+\frac{27\,a^6\,b^3}{32}}{b^5}+\frac{\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}-\frac{\left(\frac{-12\,a^8\,b^3+24\,a^7\,b^4-\frac{103\,a^6\,b^5}{4}+\frac{7\,a^5\,b^6}{4}+\frac{39\,a^4\,b^7}{4}+\frac{9\,a^3\,b^8}{4}}{b^5}+\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}-\frac{\left(\frac{192\,a^6\,b^7-352\,a^5\,b^8+128\,a^4\,b^9+32\,a^3\,b^{10}}{b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{256\,b^6}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)}{16\,b^2}-\frac{\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-96\,a^9-336\,a^8\,b+71\,a^7\,b^2+259\,a^6\,b^3+93\,a^5\,b^4+9\,a^4\,b^5\right)}{16\,b^4}+\frac{\left(\frac{-12\,a^8\,b^3+24\,a^7\,b^4-\frac{103\,a^6\,b^5}{4}+\frac{7\,a^5\,b^6}{4}+\frac{39\,a^4\,b^7}{4}+\frac{9\,a^3\,b^8}{4}}{b^5}-\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2304\,a^7\,b^4+2048\,a^6\,b^5-5488\,a^5\,b^6-880\,a^4\,b^7+1584\,a^3\,b^8+432\,a^2\,b^9\right)}{16\,b^4}+\frac{\left(\frac{192\,a^6\,b^7-352\,a^5\,b^8+128\,a^4\,b^9+32\,a^3\,b^{10}}{b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{256\,b^6}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)}{16\,b^2}\right)}{16\,b^2}}\right)\,\left(a\,8{}\mathrm{i}+b\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^2\,d}","Not used",1,"(atan(((((((2048*a^3*b^10 + 8192*a^4*b^9 - 22528*a^5*b^8 + 12288*a^6*b^7)/(64*b^5) - (tan(c + d*x)*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (144*a^3*b^8 + 624*a^4*b^7 + 112*a^5*b^6 - 1648*a^6*b^5 + 1536*a^7*b^4 - 768*a^8*b^3)/(64*b^5))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*1i - (((((2048*a^3*b^10 + 8192*a^4*b^9 - 22528*a^5*b^8 + 12288*a^6*b^7)/(64*b^5) + (tan(c + d*x)*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (144*a^3*b^8 + 624*a^4*b^7 + 112*a^5*b^6 - 1648*a^6*b^5 + 1536*a^7*b^4 - 768*a^8*b^3)/(64*b^5))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*1i)/((((((2048*a^3*b^10 + 8192*a^4*b^9 - 22528*a^5*b^8 + 12288*a^6*b^7)/(64*b^5) - (tan(c + d*x)*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (144*a^3*b^8 + 624*a^4*b^7 + 112*a^5*b^6 - 1648*a^6*b^5 + 1536*a^7*b^4 - 768*a^8*b^3)/(64*b^5))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (((((2048*a^3*b^10 + 8192*a^4*b^9 - 22528*a^5*b^8 + 12288*a^6*b^7)/(64*b^5) + (tan(c + d*x)*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (144*a^3*b^8 + 624*a^4*b^7 + 112*a^5*b^6 - 1648*a^6*b^5 + 1536*a^7*b^4 - 768*a^8*b^3)/(64*b^5))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (63*a^8*b - 216*a^9 + 27*a^6*b^3 + 126*a^7*b^2)/(32*b^5)))*(-((a^5*b^9)^(1/2) + a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*2i)/d + (atan(((((((2048*a^3*b^10 + 8192*a^4*b^9 - 22528*a^5*b^8 + 12288*a^6*b^7)/(64*b^5) - (tan(c + d*x)*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (144*a^3*b^8 + 624*a^4*b^7 + 112*a^5*b^6 - 1648*a^6*b^5 + 1536*a^7*b^4 - 768*a^8*b^3)/(64*b^5))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*1i - (((((2048*a^3*b^10 + 8192*a^4*b^9 - 22528*a^5*b^8 + 12288*a^6*b^7)/(64*b^5) + (tan(c + d*x)*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (144*a^3*b^8 + 624*a^4*b^7 + 112*a^5*b^6 - 1648*a^6*b^5 + 1536*a^7*b^4 - 768*a^8*b^3)/(64*b^5))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*1i)/((((((2048*a^3*b^10 + 8192*a^4*b^9 - 22528*a^5*b^8 + 12288*a^6*b^7)/(64*b^5) - (tan(c + d*x)*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (144*a^3*b^8 + 624*a^4*b^7 + 112*a^5*b^6 - 1648*a^6*b^5 + 1536*a^7*b^4 - 768*a^8*b^3)/(64*b^5))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (((((2048*a^3*b^10 + 8192*a^4*b^9 - 22528*a^5*b^8 + 12288*a^6*b^7)/(64*b^5) + (tan(c + d*x)*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (144*a^3*b^8 + 624*a^4*b^7 + 112*a^5*b^6 - 1648*a^6*b^5 + 1536*a^7*b^4 - 768*a^8*b^3)/(64*b^5))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) - (tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2) + (63*a^8*b - 216*a^9 + 27*a^6*b^3 + 126*a^7*b^2)/(32*b^5)))*(((a^5*b^9)^(1/2) - a^3*b^4)/(16*(a*b^8 - b^9)))^(1/2)*2i)/d + ((3*tan(c + d*x))/(8*b) + (5*tan(c + d*x)^3)/(8*b))/(d*(2*tan(c + d*x)^2 + tan(c + d*x)^4 + 1)) + (atan((((a*8i + b*3i)*((tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4) - ((((9*a^3*b^8)/4 + (39*a^4*b^7)/4 + (7*a^5*b^6)/4 - (103*a^6*b^5)/4 + 24*a^7*b^4 - 12*a^8*b^3)/b^5 + (((tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4) - (((32*a^3*b^10 + 128*a^4*b^9 - 352*a^5*b^8 + 192*a^6*b^7)/b^5 - (tan(c + d*x)*(a*8i + b*3i)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(256*b^6))*(a*8i + b*3i))/(16*b^2))*(a*8i + b*3i))/(16*b^2))*(a*8i + b*3i))/(16*b^2))*1i)/(16*b^2) + ((a*8i + b*3i)*((tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4) + ((((9*a^3*b^8)/4 + (39*a^4*b^7)/4 + (7*a^5*b^6)/4 - (103*a^6*b^5)/4 + 24*a^7*b^4 - 12*a^8*b^3)/b^5 - (((tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4) + (((32*a^3*b^10 + 128*a^4*b^9 - 352*a^5*b^8 + 192*a^6*b^7)/b^5 + (tan(c + d*x)*(a*8i + b*3i)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(256*b^6))*(a*8i + b*3i))/(16*b^2))*(a*8i + b*3i))/(16*b^2))*(a*8i + b*3i))/(16*b^2))*1i)/(16*b^2))/(((63*a^8*b)/32 - (27*a^9)/4 + (27*a^6*b^3)/32 + (63*a^7*b^2)/16)/b^5 + ((a*8i + b*3i)*((tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4) - ((((9*a^3*b^8)/4 + (39*a^4*b^7)/4 + (7*a^5*b^6)/4 - (103*a^6*b^5)/4 + 24*a^7*b^4 - 12*a^8*b^3)/b^5 + (((tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4) - (((32*a^3*b^10 + 128*a^4*b^9 - 352*a^5*b^8 + 192*a^6*b^7)/b^5 - (tan(c + d*x)*(a*8i + b*3i)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(256*b^6))*(a*8i + b*3i))/(16*b^2))*(a*8i + b*3i))/(16*b^2))*(a*8i + b*3i))/(16*b^2)))/(16*b^2) - ((a*8i + b*3i)*((tan(c + d*x)*(9*a^4*b^5 - 96*a^9 - 336*a^8*b + 93*a^5*b^4 + 259*a^6*b^3 + 71*a^7*b^2))/(16*b^4) + ((((9*a^3*b^8)/4 + (39*a^4*b^7)/4 + (7*a^5*b^6)/4 - (103*a^6*b^5)/4 + 24*a^7*b^4 - 12*a^8*b^3)/b^5 - (((tan(c + d*x)*(432*a^2*b^9 + 1584*a^3*b^8 - 880*a^4*b^7 - 5488*a^5*b^6 + 2048*a^6*b^5 + 2304*a^7*b^4))/(16*b^4) + (((32*a^3*b^10 + 128*a^4*b^9 - 352*a^5*b^8 + 192*a^6*b^7)/b^5 + (tan(c + d*x)*(a*8i + b*3i)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(256*b^6))*(a*8i + b*3i))/(16*b^2))*(a*8i + b*3i))/(16*b^2))*(a*8i + b*3i))/(16*b^2)))/(16*b^2)))*(a*8i + b*3i)*1i)/(8*b^2*d)","B"
204,1,1273,155,16.401136,"\text{Not used}","int(sin(c + d*x)^6/(a - b*sin(c + d*x)^4),x)","\frac{\sin\left(2\,c+2\,d\,x\right)}{4\,b\,d}-\frac{\mathrm{atan}\left(\frac{\sin\left(c+d\,x\right)}{\cos\left(c+d\,x\right)}\right)}{2\,b\,d}-\frac{\mathrm{atan}\left(\frac{-b^{10}\,\sin\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{3/2}\,192{}\mathrm{i}-b^{12}\,\sin\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{5/2}\,3072{}\mathrm{i}+a\,b^7\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,4{}\mathrm{i}+a\,b^9\,\sin\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{3/2}\,192{}\mathrm{i}+a^2\,b^6\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,24{}\mathrm{i}+a^3\,b^5\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,4{}\mathrm{i}+a^4\,b^4\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,8{}\mathrm{i}+a^2\,b^8\,\sin\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{3/2}\,448{}\mathrm{i}+a^3\,b^7\,\sin\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{3/2}\,320{}\mathrm{i}+a^2\,b^{10}\,\sin\left(c+d\,x\right)\,{\left(-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{5/2}\,3072{}\mathrm{i}}{a^2\,b^5\,\cos\left(c+d\,x\right)+a^3\,b^4\,\cos\left(c+d\,x\right)-a^4\,b^3\,\cos\left(c+d\,x\right)+a^2\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}-2\,a\,b\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}}\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}+a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{-b^{10}\,\sin\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{3/2}\,192{}\mathrm{i}-b^{12}\,\sin\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{5/2}\,3072{}\mathrm{i}+a\,b^7\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,4{}\mathrm{i}+a\,b^9\,\sin\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{3/2}\,192{}\mathrm{i}+a^2\,b^6\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,24{}\mathrm{i}+a^3\,b^5\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,4{}\mathrm{i}+a^4\,b^4\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,8{}\mathrm{i}+a^2\,b^8\,\sin\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{3/2}\,448{}\mathrm{i}+a^3\,b^7\,\sin\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{3/2}\,320{}\mathrm{i}+a^2\,b^{10}\,\sin\left(c+d\,x\right)\,{\left(\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}\right)}^{5/2}\,3072{}\mathrm{i}}{a^2\,b^5\,\cos\left(c+d\,x\right)+a^3\,b^4\,\cos\left(c+d\,x\right)-a^4\,b^3\,\cos\left(c+d\,x\right)-a^2\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}+2\,a\,b\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}}\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}-a^2\,b^3}{16\,a\,b^6-16\,b^7}}\,2{}\mathrm{i}}{d}","Not used",1,"sin(2*c + 2*d*x)/(4*b*d) - (atan((a*b^7*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*4i - b^12*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(5/2)*3072i - b^10*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(3/2)*192i + a*b^9*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(3/2)*192i + a^2*b^6*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*24i + a^3*b^5*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*4i + a^4*b^4*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*8i + a^2*b^8*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(3/2)*448i + a^3*b^7*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(3/2)*320i + a^2*b^10*sin(c + d*x)*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(5/2)*3072i)/(a^2*b^5*cos(c + d*x) + a^3*b^4*cos(c + d*x) - a^4*b^3*cos(c + d*x) - a^2*cos(c + d*x)*(a^3*b^7)^(1/2) + 2*a*b*cos(c + d*x)*(a^3*b^7)^(1/2)))*(((a^3*b^7)^(1/2) - a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*2i)/d - (atan((a*b^7*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*4i - b^12*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(5/2)*3072i - b^10*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(3/2)*192i + a*b^9*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(3/2)*192i + a^2*b^6*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*24i + a^3*b^5*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*4i + a^4*b^4*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*8i + a^2*b^8*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(3/2)*448i + a^3*b^7*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(3/2)*320i + a^2*b^10*sin(c + d*x)*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(5/2)*3072i)/(a^2*b^5*cos(c + d*x) + a^3*b^4*cos(c + d*x) - a^4*b^3*cos(c + d*x) + a^2*cos(c + d*x)*(a^3*b^7)^(1/2) - 2*a*b*cos(c + d*x)*(a^3*b^7)^(1/2)))*(-((a^3*b^7)^(1/2) + a^2*b^3)/(16*a*b^6 - 16*b^7))^(1/2)*2i)/d - atan(sin(c + d*x)/cos(c + d*x))/(2*b*d)","B"
205,1,2991,127,16.274513,"\text{Not used}","int(sin(c + d*x)^4/(a - b*sin(c + d*x)^4),x)","-\frac{\mathrm{atan}\left(\frac{18\,a^5\,\mathrm{tan}\left(c+d\,x\right)}{18\,a^5-50\,a^4\,b+32\,a^3\,b^2}-\frac{50\,a^4\,\mathrm{tan}\left(c+d\,x\right)}{32\,a^3\,b-50\,a^4+\frac{18\,a^5}{b}}+\frac{32\,a^3\,b\,\mathrm{tan}\left(c+d\,x\right)}{32\,a^3\,b-50\,a^4+\frac{18\,a^5}{b}}\right)}{b\,d}-\frac{\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(\left(\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(320\,a^3\,b^5-64\,a^2\,b^6-448\,a^4\,b^4+192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+80\,a^4\,b^3-400\,a^3\,b^4+176\,a^2\,b^5\right)\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}+12\,a^5\,b-16\,a^2\,b^4+28\,a^3\,b^3-24\,a^4\,b^2\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5+18\,a^4\,b-20\,a^3\,b^2-4\,a^2\,b^3\right)\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(\left(\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(64\,a^2\,b^6-320\,a^3\,b^5+448\,a^4\,b^4-192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+80\,a^4\,b^3-400\,a^3\,b^4+176\,a^2\,b^5\right)\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}-12\,a^5\,b+16\,a^2\,b^4-28\,a^3\,b^3+24\,a^4\,b^2\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5+18\,a^4\,b-20\,a^3\,b^2-4\,a^2\,b^3\right)\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,1{}\mathrm{i}}{6\,a^3\,b-6\,a^4+\left(\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(\left(\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(320\,a^3\,b^5-64\,a^2\,b^6-448\,a^4\,b^4+192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+80\,a^4\,b^3-400\,a^3\,b^4+176\,a^2\,b^5\right)\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}+12\,a^5\,b-16\,a^2\,b^4+28\,a^3\,b^3-24\,a^4\,b^2\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5+18\,a^4\,b-20\,a^3\,b^2-4\,a^2\,b^3\right)\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}-\left(\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(\left(\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(64\,a^2\,b^6-320\,a^3\,b^5+448\,a^4\,b^4-192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+80\,a^4\,b^3-400\,a^3\,b^4+176\,a^2\,b^5\right)\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}-12\,a^5\,b+16\,a^2\,b^4-28\,a^3\,b^3+24\,a^4\,b^2\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5+18\,a^4\,b-20\,a^3\,b^2-4\,a^2\,b^3\right)\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}}\right)\,\sqrt{-\frac{a\,b^2-\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5+18\,a^4\,b-20\,a^3\,b^2-4\,a^2\,b^3\right)+\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(\left(\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+80\,a^4\,b^3-400\,a^3\,b^4+176\,a^2\,b^5\right)+\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(320\,a^3\,b^5-64\,a^2\,b^6-448\,a^4\,b^4+192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}+12\,a^5\,b-16\,a^2\,b^4+28\,a^3\,b^3-24\,a^4\,b^2\right)\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,1{}\mathrm{i}+\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5+18\,a^4\,b-20\,a^3\,b^2-4\,a^2\,b^3\right)+\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(\left(\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+80\,a^4\,b^3-400\,a^3\,b^4+176\,a^2\,b^5\right)+\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(64\,a^2\,b^6-320\,a^3\,b^5+448\,a^4\,b^4-192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}-12\,a^5\,b+16\,a^2\,b^4-28\,a^3\,b^3+24\,a^4\,b^2\right)\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5+18\,a^4\,b-20\,a^3\,b^2-4\,a^2\,b^3\right)+\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(\left(\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+80\,a^4\,b^3-400\,a^3\,b^4+176\,a^2\,b^5\right)+\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(320\,a^3\,b^5-64\,a^2\,b^6-448\,a^4\,b^4+192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}+12\,a^5\,b-16\,a^2\,b^4+28\,a^3\,b^3-24\,a^4\,b^2\right)\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}-\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5+18\,a^4\,b-20\,a^3\,b^2-4\,a^2\,b^3\right)+\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(\left(\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+80\,a^4\,b^3-400\,a^3\,b^4+176\,a^2\,b^5\right)+\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(64\,a^2\,b^6-320\,a^3\,b^5+448\,a^4\,b^4-192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}-12\,a^5\,b+16\,a^2\,b^4-28\,a^3\,b^3+24\,a^4\,b^2\right)\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}+6\,a^3\,b-6\,a^4}\right)\,\sqrt{-\frac{a\,b^2+\sqrt{a\,b^5}}{16\,\left(a\,b^4-b^5\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- atan((18*a^5*tan(c + d*x))/(18*a^5 - 50*a^4*b + 32*a^3*b^2) - (50*a^4*tan(c + d*x))/(32*a^3*b - 50*a^4 + (18*a^5)/b) + (32*a^3*b*tan(c + d*x))/(32*a^3*b - 50*a^4 + (18*a^5)/b))/(b*d) - (atan((((-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(((-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(320*a^3*b^5 - 64*a^2*b^6 - 448*a^4*b^4 + 192*a^5*b^3 + tan(c + d*x)*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) + tan(c + d*x)*(176*a^2*b^5 - 400*a^3*b^4 + 80*a^4*b^3 + 144*a^5*b^2))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) + 12*a^5*b - 16*a^2*b^4 + 28*a^3*b^3 - 24*a^4*b^2) + tan(c + d*x)*(18*a^4*b + 6*a^5 - 4*a^2*b^3 - 20*a^3*b^2))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*1i + ((-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(((-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(64*a^2*b^6 - 320*a^3*b^5 + 448*a^4*b^4 - 192*a^5*b^3 + tan(c + d*x)*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) + tan(c + d*x)*(176*a^2*b^5 - 400*a^3*b^4 + 80*a^4*b^3 + 144*a^5*b^2))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) - 12*a^5*b + 16*a^2*b^4 - 28*a^3*b^3 + 24*a^4*b^2) + tan(c + d*x)*(18*a^4*b + 6*a^5 - 4*a^2*b^3 - 20*a^3*b^2))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*1i)/(6*a^3*b - 6*a^4 + ((-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(((-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(320*a^3*b^5 - 64*a^2*b^6 - 448*a^4*b^4 + 192*a^5*b^3 + tan(c + d*x)*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) + tan(c + d*x)*(176*a^2*b^5 - 400*a^3*b^4 + 80*a^4*b^3 + 144*a^5*b^2))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) + 12*a^5*b - 16*a^2*b^4 + 28*a^3*b^3 - 24*a^4*b^2) + tan(c + d*x)*(18*a^4*b + 6*a^5 - 4*a^2*b^3 - 20*a^3*b^2))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) - ((-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(((-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(64*a^2*b^6 - 320*a^3*b^5 + 448*a^4*b^4 - 192*a^5*b^3 + tan(c + d*x)*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) + tan(c + d*x)*(176*a^2*b^5 - 400*a^3*b^4 + 80*a^4*b^3 + 144*a^5*b^2))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) - 12*a^5*b + 16*a^2*b^4 - 28*a^3*b^3 + 24*a^4*b^2) + tan(c + d*x)*(18*a^4*b + 6*a^5 - 4*a^2*b^3 - 20*a^3*b^2))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)))*(-(a*b^2 - (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*2i)/d - (atan(((tan(c + d*x)*(18*a^4*b + 6*a^5 - 4*a^2*b^3 - 20*a^3*b^2) + (-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*((tan(c + d*x)*(176*a^2*b^5 - 400*a^3*b^4 + 80*a^4*b^3 + 144*a^5*b^2) + (-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(320*a^3*b^5 - 64*a^2*b^6 - 448*a^4*b^4 + 192*a^5*b^3 + tan(c + d*x)*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) + 12*a^5*b - 16*a^2*b^4 + 28*a^3*b^3 - 24*a^4*b^2))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*1i + (tan(c + d*x)*(18*a^4*b + 6*a^5 - 4*a^2*b^3 - 20*a^3*b^2) + (-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*((tan(c + d*x)*(176*a^2*b^5 - 400*a^3*b^4 + 80*a^4*b^3 + 144*a^5*b^2) + (-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(64*a^2*b^6 - 320*a^3*b^5 + 448*a^4*b^4 - 192*a^5*b^3 + tan(c + d*x)*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) - 12*a^5*b + 16*a^2*b^4 - 28*a^3*b^3 + 24*a^4*b^2))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*1i)/((tan(c + d*x)*(18*a^4*b + 6*a^5 - 4*a^2*b^3 - 20*a^3*b^2) + (-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*((tan(c + d*x)*(176*a^2*b^5 - 400*a^3*b^4 + 80*a^4*b^3 + 144*a^5*b^2) + (-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(320*a^3*b^5 - 64*a^2*b^6 - 448*a^4*b^4 + 192*a^5*b^3 + tan(c + d*x)*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) + 12*a^5*b - 16*a^2*b^4 + 28*a^3*b^3 - 24*a^4*b^2))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) - (tan(c + d*x)*(18*a^4*b + 6*a^5 - 4*a^2*b^3 - 20*a^3*b^2) + (-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*((tan(c + d*x)*(176*a^2*b^5 - 400*a^3*b^4 + 80*a^4*b^3 + 144*a^5*b^2) + (-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(64*a^2*b^6 - 320*a^3*b^5 + 448*a^4*b^4 - 192*a^5*b^3 + tan(c + d*x)*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) - 12*a^5*b + 16*a^2*b^4 - 28*a^3*b^3 + 24*a^4*b^2))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2) + 6*a^3*b - 6*a^4))*(-(a*b^2 + (a*b^5)^(1/2))/(16*(a*b^4 - b^5)))^(1/2)*2i)/d","B"
206,1,443,125,16.186628,"\text{Not used}","int(sin(c + d*x)^2/(a - b*sin(c + d*x)^4),x)","\frac{\ln\left(a\,b-a^2-\frac{a\,\mathrm{tan}\left(c+d\,x\right)\,\left(a-b\right)\,\sqrt{-\frac{1}{a\,b+\sqrt{a\,b^3}}}\,\left(2\,a\,b^2+a\,\sqrt{a\,b^3}+b\,\sqrt{a\,b^3}\right)}{a\,b+\sqrt{a\,b^3}}\right)\,\sqrt{-\frac{1}{a\,b+\sqrt{a\,b^3}}}}{4\,d}-\frac{\ln\left(a\,b-a^2-\frac{a\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{a\,b-\sqrt{a\,b^3}}}\,\left(a-b\right)\,\left(a\,\sqrt{a\,b^3}-2\,a\,b^2+b\,\sqrt{a\,b^3}\right)}{a\,b-\sqrt{a\,b^3}}\right)\,\sqrt{\frac{a\,b+\sqrt{a\,b^3}}{16\,\left(a\,b^3-a^2\,b^2\right)}}}{d}+\frac{\ln\left(a\,b-a^2+\frac{a\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{a\,b-\sqrt{a\,b^3}}}\,\left(a-b\right)\,\left(a\,\sqrt{a\,b^3}-2\,a\,b^2+b\,\sqrt{a\,b^3}\right)}{a\,b-\sqrt{a\,b^3}}\right)\,\sqrt{-\frac{1}{a\,b-\sqrt{a\,b^3}}}}{4\,d}-\frac{\ln\left(a\,b-a^2+\frac{a\,\mathrm{tan}\left(c+d\,x\right)\,\left(a-b\right)\,\sqrt{-\frac{1}{a\,b+\sqrt{a\,b^3}}}\,\left(2\,a\,b^2+a\,\sqrt{a\,b^3}+b\,\sqrt{a\,b^3}\right)}{a\,b+\sqrt{a\,b^3}}\right)\,\sqrt{\frac{a\,b-\sqrt{a\,b^3}}{16\,\left(a\,b^3-a^2\,b^2\right)}}}{d}","Not used",1,"(log(a*b - a^2 - (a*tan(c + d*x)*(a - b)*(-1/(a*b + (a*b^3)^(1/2)))^(1/2)*(2*a*b^2 + a*(a*b^3)^(1/2) + b*(a*b^3)^(1/2)))/(a*b + (a*b^3)^(1/2)))*(-1/(a*b + (a*b^3)^(1/2)))^(1/2))/(4*d) - (log(a*b - a^2 - (a*tan(c + d*x)*(-1/(a*b - (a*b^3)^(1/2)))^(1/2)*(a - b)*(a*(a*b^3)^(1/2) - 2*a*b^2 + b*(a*b^3)^(1/2)))/(a*b - (a*b^3)^(1/2)))*((a*b + (a*b^3)^(1/2))/(16*(a*b^3 - a^2*b^2)))^(1/2))/d + (log(a*b - a^2 + (a*tan(c + d*x)*(-1/(a*b - (a*b^3)^(1/2)))^(1/2)*(a - b)*(a*(a*b^3)^(1/2) - 2*a*b^2 + b*(a*b^3)^(1/2)))/(a*b - (a*b^3)^(1/2)))*(-1/(a*b - (a*b^3)^(1/2)))^(1/2))/(4*d) - (log(a*b - a^2 + (a*tan(c + d*x)*(a - b)*(-1/(a*b + (a*b^3)^(1/2)))^(1/2)*(2*a*b^2 + a*(a*b^3)^(1/2) + b*(a*b^3)^(1/2)))/(a*b + (a*b^3)^(1/2)))*((a*b - (a*b^3)^(1/2))/(16*(a*b^3 - a^2*b^2)))^(1/2))/d","B"
207,1,671,115,14.994237,"\text{Not used}","int(1/(a - b*sin(c + d*x)^4),x)","\frac{\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}}\,4{}\mathrm{i}+a^5\,\mathrm{tan}\left(c+d\,x\right)\,{\left(-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}\right)}^{3/2}\,64{}\mathrm{i}+a^3\,\mathrm{tan}\left(c+d\,x\right)\,{\left(-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}\right)}^{3/2}\,\sqrt{a^3\,b}\,64{}\mathrm{i}+a^2\,b\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}}\,4{}\mathrm{i}-a^4\,b\,\mathrm{tan}\left(c+d\,x\right)\,{\left(-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}\right)}^{3/2}\,64{}\mathrm{i}+a\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}}\,\sqrt{a^3\,b}\,4{}\mathrm{i}+b\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}}\,\sqrt{a^3\,b}\,4{}\mathrm{i}-a^2\,b\,\mathrm{tan}\left(c+d\,x\right)\,{\left(-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}\right)}^{3/2}\,\sqrt{a^3\,b}\,64{}\mathrm{i}}{a\,b+\sqrt{a^3\,b}}\right)\,\sqrt{-\frac{1}{16\,a^2+16\,\sqrt{a^3\,b}}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}}\,4{}\mathrm{i}+a^5\,\mathrm{tan}\left(c+d\,x\right)\,{\left(-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}\right)}^{3/2}\,64{}\mathrm{i}-a^3\,\mathrm{tan}\left(c+d\,x\right)\,{\left(-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}\right)}^{3/2}\,\sqrt{a^3\,b}\,64{}\mathrm{i}+a^2\,b\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}}\,4{}\mathrm{i}-a^4\,b\,\mathrm{tan}\left(c+d\,x\right)\,{\left(-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}\right)}^{3/2}\,64{}\mathrm{i}-a\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}}\,\sqrt{a^3\,b}\,4{}\mathrm{i}-b\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}}\,\sqrt{a^3\,b}\,4{}\mathrm{i}+a^2\,b\,\mathrm{tan}\left(c+d\,x\right)\,{\left(-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}\right)}^{3/2}\,\sqrt{a^3\,b}\,64{}\mathrm{i}}{a\,b-\sqrt{a^3\,b}}\right)\,\sqrt{-\frac{1}{16\,a^2-16\,\sqrt{a^3\,b}}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan((a^3*tan(c + d*x)*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(1/2)*4i + a^5*tan(c + d*x)*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(3/2)*64i + a^3*tan(c + d*x)*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(3/2)*(a^3*b)^(1/2)*64i + a^2*b*tan(c + d*x)*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(1/2)*4i - a^4*b*tan(c + d*x)*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(3/2)*64i + a*tan(c + d*x)*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(1/2)*(a^3*b)^(1/2)*4i + b*tan(c + d*x)*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(1/2)*(a^3*b)^(1/2)*4i - a^2*b*tan(c + d*x)*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(3/2)*(a^3*b)^(1/2)*64i)/(a*b + (a^3*b)^(1/2)))*(-1/(16*a^2 + 16*(a^3*b)^(1/2)))^(1/2)*2i)/d + (atan((a^3*tan(c + d*x)*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(1/2)*4i + a^5*tan(c + d*x)*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(3/2)*64i - a^3*tan(c + d*x)*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(3/2)*(a^3*b)^(1/2)*64i + a^2*b*tan(c + d*x)*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(1/2)*4i - a^4*b*tan(c + d*x)*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(3/2)*64i - a*tan(c + d*x)*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(1/2)*(a^3*b)^(1/2)*4i - b*tan(c + d*x)*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(1/2)*(a^3*b)^(1/2)*4i + a^2*b*tan(c + d*x)*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(3/2)*(a^3*b)^(1/2)*64i)/(a*b - (a^3*b)^(1/2)))*(-1/(16*a^2 - 16*(a^3*b)^(1/2)))^(1/2)*2i)/d","B"
208,1,371,139,14.511509,"\text{Not used}","int(1/(sin(c + d*x)^2*(a - b*sin(c + d*x)^4)),x)","\frac{2\,\mathrm{atanh}\left(\frac{2\,\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4\,b^4-4\,a^6\,b^2\right)-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(\sqrt{a^5\,b^3}+a^3\,b\right)\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)}{16\,\left(a^5\,b-a^6\right)}\right)\,\sqrt{\frac{\sqrt{a^5\,b^3}+a^3\,b}{16\,\left(a^5\,b-a^6\right)}}}{2\,a^3\,b^4-2\,a^4\,b^3}\right)\,\sqrt{\frac{\sqrt{a^5\,b^3}+a^3\,b}{16\,\left(a^5\,b-a^6\right)}}}{d}+\frac{2\,\mathrm{atanh}\left(\frac{2\,\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4\,b^4-4\,a^6\,b^2\right)+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(\sqrt{a^5\,b^3}-a^3\,b\right)\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)}{16\,\left(a^5\,b-a^6\right)}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^3}-a^3\,b}{16\,\left(a^5\,b-a^6\right)}}}{2\,a^3\,b^4-2\,a^4\,b^3}\right)\,\sqrt{-\frac{\sqrt{a^5\,b^3}-a^3\,b}{16\,\left(a^5\,b-a^6\right)}}}{d}-\frac{\mathrm{cot}\left(c+d\,x\right)}{a\,d}","Not used",1,"(2*atanh((2*(tan(c + d*x)*(4*a^4*b^4 - 4*a^6*b^2) - (tan(c + d*x)*((a^5*b^3)^(1/2) + a^3*b)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2))/(16*(a^5*b - a^6)))*(((a^5*b^3)^(1/2) + a^3*b)/(16*(a^5*b - a^6)))^(1/2))/(2*a^3*b^4 - 2*a^4*b^3))*(((a^5*b^3)^(1/2) + a^3*b)/(16*(a^5*b - a^6)))^(1/2))/d + (2*atanh((2*(tan(c + d*x)*(4*a^4*b^4 - 4*a^6*b^2) + (tan(c + d*x)*((a^5*b^3)^(1/2) - a^3*b)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2))/(16*(a^5*b - a^6)))*(-((a^5*b^3)^(1/2) - a^3*b)/(16*(a^5*b - a^6)))^(1/2))/(2*a^3*b^4 - 2*a^4*b^3))*(-((a^5*b^3)^(1/2) - a^3*b)/(16*(a^5*b - a^6)))^(1/2))/d - cot(c + d*x)/(a*d)","B"
209,1,1670,149,15.554015,"\text{Not used}","int(1/(sin(c + d*x)^4*(a - b*sin(c + d*x)^4)),x)","-\frac{\frac{1}{3\,a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^2}{a}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^3}+\frac{\mathrm{atan}\left(\frac{\left(\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(16\,a^5\,b^4-32\,a^6\,b^3+16\,a^7\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3\,b^5-4\,a^5\,b^3\right)\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,1{}\mathrm{i}-\left(\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(16\,a^5\,b^4-32\,a^6\,b^3+16\,a^7\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3\,b^5-4\,a^5\,b^3\right)\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,1{}\mathrm{i}}{\left(\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(16\,a^5\,b^4-32\,a^6\,b^3+16\,a^7\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3\,b^5-4\,a^5\,b^3\right)\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}+\left(\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(16\,a^5\,b^4-32\,a^6\,b^3+16\,a^7\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3\,b^5-4\,a^5\,b^3\right)\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}-2\,a^2\,b^5+2\,a^3\,b^4}\right)\,\sqrt{\frac{\sqrt{a^7\,b^5}+a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(16\,a^5\,b^4-32\,a^6\,b^3+16\,a^7\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3\,b^5-4\,a^5\,b^3\right)\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,1{}\mathrm{i}-\left(\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(16\,a^5\,b^4-32\,a^6\,b^3+16\,a^7\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3\,b^5-4\,a^5\,b^3\right)\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(16\,a^5\,b^4-32\,a^6\,b^3+16\,a^7\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3\,b^5-4\,a^5\,b^3\right)\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}+\left(\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(16\,a^5\,b^4-32\,a^6\,b^3+16\,a^7\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,\left(64\,a^9\,b-128\,a^8\,b^2+64\,a^7\,b^3\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3\,b^5-4\,a^5\,b^3\right)\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}-2\,a^2\,b^5+2\,a^3\,b^4}\right)\,\sqrt{-\frac{\sqrt{a^7\,b^5}-a^4\,b^2}{16\,\left(a^7\,b-a^8\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan((((((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(16*a^5*b^4 - 32*a^6*b^3 + 16*a^7*b^2 + tan(c + d*x)*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2)) - tan(c + d*x)*(4*a^3*b^5 - 4*a^5*b^3))*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*1i - ((((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(16*a^5*b^4 - 32*a^6*b^3 + 16*a^7*b^2 - tan(c + d*x)*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2)) + tan(c + d*x)*(4*a^3*b^5 - 4*a^5*b^3))*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*1i)/(((((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(16*a^5*b^4 - 32*a^6*b^3 + 16*a^7*b^2 + tan(c + d*x)*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2)) - tan(c + d*x)*(4*a^3*b^5 - 4*a^5*b^3))*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2) + ((((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(16*a^5*b^4 - 32*a^6*b^3 + 16*a^7*b^2 - tan(c + d*x)*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2)) + tan(c + d*x)*(4*a^3*b^5 - 4*a^5*b^3))*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2) - 2*a^2*b^5 + 2*a^3*b^4))*(((a^7*b^5)^(1/2) + a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*2i)/d + (atan((((-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(16*a^5*b^4 - 32*a^6*b^3 + 16*a^7*b^2 + tan(c + d*x)*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2)) - tan(c + d*x)*(4*a^3*b^5 - 4*a^5*b^3))*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*1i - ((-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(16*a^5*b^4 - 32*a^6*b^3 + 16*a^7*b^2 - tan(c + d*x)*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2)) + tan(c + d*x)*(4*a^3*b^5 - 4*a^5*b^3))*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*1i)/(((-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(16*a^5*b^4 - 32*a^6*b^3 + 16*a^7*b^2 + tan(c + d*x)*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2)) - tan(c + d*x)*(4*a^3*b^5 - 4*a^5*b^3))*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2) + ((-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(16*a^5*b^4 - 32*a^6*b^3 + 16*a^7*b^2 - tan(c + d*x)*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*(64*a^9*b + 64*a^7*b^3 - 128*a^8*b^2)) + tan(c + d*x)*(4*a^3*b^5 - 4*a^5*b^3))*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2) - 2*a^2*b^5 + 2*a^3*b^4))*(-((a^7*b^5)^(1/2) - a^4*b^2)/(16*(a^7*b - a^8)))^(1/2)*2i)/d - (1/(3*a) + tan(c + d*x)^2/a)/(d*tan(c + d*x)^3)","B"
210,1,416,178,15.255866,"\text{Not used}","int(1/(sin(c + d*x)^6*(a - b*sin(c + d*x)^4)),x)","\frac{2\,\mathrm{atanh}\left(\frac{2\,\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^7\,b^6-4\,a^9\,b^4\right)-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(\sqrt{a^9\,b^7}+a^5\,b^3\right)\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)}{16\,\left(a^9\,b-a^{10}\right)}\right)\,\sqrt{\frac{\sqrt{a^9\,b^7}+a^5\,b^3}{16\,\left(a^9\,b-a^{10}\right)}}}{2\,a^5\,b^7-2\,a^6\,b^6}\right)\,\sqrt{\frac{\sqrt{a^9\,b^7}+a^5\,b^3}{16\,\left(a^9\,b-a^{10}\right)}}}{d}+\frac{2\,\mathrm{atanh}\left(\frac{2\,\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^7\,b^6-4\,a^9\,b^4\right)+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(\sqrt{a^9\,b^7}-a^5\,b^3\right)\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)}{16\,\left(a^9\,b-a^{10}\right)}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^7}-a^5\,b^3}{16\,\left(a^9\,b-a^{10}\right)}}}{2\,a^5\,b^7-2\,a^6\,b^6}\right)\,\sqrt{-\frac{\sqrt{a^9\,b^7}-a^5\,b^3}{16\,\left(a^9\,b-a^{10}\right)}}}{d}-\frac{\frac{1}{5\,a}+\frac{2\,{\mathrm{tan}\left(c+d\,x\right)}^2}{3\,a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(a+b\right)}{a^2}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^5}","Not used",1,"(2*atanh((2*(tan(c + d*x)*(4*a^7*b^6 - 4*a^9*b^4) - (tan(c + d*x)*((a^9*b^7)^(1/2) + a^5*b^3)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2))/(16*(a^9*b - a^10)))*(((a^9*b^7)^(1/2) + a^5*b^3)/(16*(a^9*b - a^10)))^(1/2))/(2*a^5*b^7 - 2*a^6*b^6))*(((a^9*b^7)^(1/2) + a^5*b^3)/(16*(a^9*b - a^10)))^(1/2))/d + (2*atanh((2*(tan(c + d*x)*(4*a^7*b^6 - 4*a^9*b^4) + (tan(c + d*x)*((a^9*b^7)^(1/2) - a^5*b^3)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2))/(16*(a^9*b - a^10)))*(-((a^9*b^7)^(1/2) - a^5*b^3)/(16*(a^9*b - a^10)))^(1/2))/(2*a^5*b^7 - 2*a^6*b^6))*(-((a^9*b^7)^(1/2) - a^5*b^3)/(16*(a^9*b - a^10)))^(1/2))/d - (1/(5*a) + (2*tan(c + d*x)^2)/(3*a) + (tan(c + d*x)^4*(a + b))/a^2)/(d*tan(c + d*x)^5)","B"
211,1,1704,197,17.077666,"\text{Not used}","int(1/(sin(c + d*x)^8*(a - b*sin(c + d*x)^4)),x)","-\frac{\frac{1}{7\,a}+\frac{3\,{\mathrm{tan}\left(c+d\,x\right)}^2}{5\,a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(a+b\right)}{a^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(3\,a+b\right)}{3\,a^2}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^7}+\frac{\mathrm{atan}\left(\frac{\left(\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(16\,a^9\,b^5-32\,a^{10}\,b^4+16\,a^{11}\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^6\,b^7-4\,a^8\,b^5\right)\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,1{}\mathrm{i}-\left(\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(16\,a^9\,b^5-32\,a^{10}\,b^4+16\,a^{11}\,b^3-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^6\,b^7-4\,a^8\,b^5\right)\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(16\,a^9\,b^5-32\,a^{10}\,b^4+16\,a^{11}\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^6\,b^7-4\,a^8\,b^5\right)\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}+\left(\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(16\,a^9\,b^5-32\,a^{10}\,b^4+16\,a^{11}\,b^3-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^6\,b^7-4\,a^8\,b^5\right)\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}-2\,a^4\,b^8+2\,a^5\,b^7}\right)\,\sqrt{\frac{\sqrt{a^{11}\,b^9}+a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(16\,a^9\,b^5-32\,a^{10}\,b^4+16\,a^{11}\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^6\,b^7-4\,a^8\,b^5\right)\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,1{}\mathrm{i}-\left(\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(16\,a^9\,b^5-32\,a^{10}\,b^4+16\,a^{11}\,b^3-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^6\,b^7-4\,a^8\,b^5\right)\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(16\,a^9\,b^5-32\,a^{10}\,b^4+16\,a^{11}\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^6\,b^7-4\,a^8\,b^5\right)\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}+\left(\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(16\,a^9\,b^5-32\,a^{10}\,b^4+16\,a^{11}\,b^3-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,\left(64\,a^{14}\,b-128\,a^{13}\,b^2+64\,a^{12}\,b^3\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^6\,b^7-4\,a^8\,b^5\right)\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}-2\,a^4\,b^8+2\,a^5\,b^7}\right)\,\sqrt{-\frac{\sqrt{a^{11}\,b^9}-a^6\,b^4}{16\,\left(a^{11}\,b-a^{12}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan((((((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(16*a^9*b^5 - 32*a^10*b^4 + 16*a^11*b^3 + tan(c + d*x)*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2)) - tan(c + d*x)*(4*a^6*b^7 - 4*a^8*b^5))*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*1i - ((((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(16*a^9*b^5 - 32*a^10*b^4 + 16*a^11*b^3 - tan(c + d*x)*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2)) + tan(c + d*x)*(4*a^6*b^7 - 4*a^8*b^5))*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*1i)/(((((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(16*a^9*b^5 - 32*a^10*b^4 + 16*a^11*b^3 + tan(c + d*x)*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2)) - tan(c + d*x)*(4*a^6*b^7 - 4*a^8*b^5))*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2) + ((((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(16*a^9*b^5 - 32*a^10*b^4 + 16*a^11*b^3 - tan(c + d*x)*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2)) + tan(c + d*x)*(4*a^6*b^7 - 4*a^8*b^5))*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2) - 2*a^4*b^8 + 2*a^5*b^7))*(((a^11*b^9)^(1/2) + a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*2i)/d + (atan((((-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(16*a^9*b^5 - 32*a^10*b^4 + 16*a^11*b^3 + tan(c + d*x)*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2)) - tan(c + d*x)*(4*a^6*b^7 - 4*a^8*b^5))*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*1i - ((-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(16*a^9*b^5 - 32*a^10*b^4 + 16*a^11*b^3 - tan(c + d*x)*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2)) + tan(c + d*x)*(4*a^6*b^7 - 4*a^8*b^5))*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*1i)/(((-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(16*a^9*b^5 - 32*a^10*b^4 + 16*a^11*b^3 + tan(c + d*x)*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2)) - tan(c + d*x)*(4*a^6*b^7 - 4*a^8*b^5))*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2) + ((-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(16*a^9*b^5 - 32*a^10*b^4 + 16*a^11*b^3 - tan(c + d*x)*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*(64*a^14*b + 64*a^12*b^3 - 128*a^13*b^2)) + tan(c + d*x)*(4*a^6*b^7 - 4*a^8*b^5))*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2) - 2*a^4*b^8 + 2*a^5*b^7))*(-((a^11*b^9)^(1/2) - a^6*b^4)/(16*(a^11*b - a^12)))^(1/2)*2i)/d - (1/(7*a) + (3*tan(c + d*x)^2)/(5*a) + (tan(c + d*x)^6*(a + b))/a^2 + (tan(c + d*x)^4*(3*a + b))/(3*a^2))/(d*tan(c + d*x)^7)","B"
212,1,3941,236,16.004169,"\text{Not used}","int(sin(c + d*x)^9/(a - b*sin(c + d*x)^4)^2,x)","-\frac{\cos\left(c+d\,x\right)}{b^2\,d}-\frac{\frac{\cos\left(c+d\,x\right)\,\left(a^2+b\,a\right)}{4\,\left(a-b\right)}-\frac{a\,b\,{\cos\left(c+d\,x\right)}^3}{4\,\left(a-b\right)}}{d\,\left(-b^3\,{\cos\left(c+d\,x\right)}^4+2\,b^3\,{\cos\left(c+d\,x\right)}^2-b^3+a\,b^2\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{1280\,a^4\,b^4-3072\,a^3\,b^5+1792\,a^2\,b^6}{64\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,\left(256\,a^3\,b^5-512\,a^2\,b^6+256\,a\,b^7\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-59\,a^3\,b+36\,a^2\,b^2\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{1280\,a^4\,b^4-3072\,a^3\,b^5+1792\,a^2\,b^6}{64\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,\left(256\,a^3\,b^5-512\,a^2\,b^6+256\,a\,b^7\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-59\,a^3\,b+36\,a^2\,b^2\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,1{}\mathrm{i}}{\frac{36\,a^3\,b-25\,a^4}{32\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\left(\left(\frac{1280\,a^4\,b^4-3072\,a^3\,b^5+1792\,a^2\,b^6}{64\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,\left(256\,a^3\,b^5-512\,a^2\,b^6+256\,a\,b^7\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-59\,a^3\,b+36\,a^2\,b^2\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}+\left(\left(\frac{1280\,a^4\,b^4-3072\,a^3\,b^5+1792\,a^2\,b^6}{64\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,\left(256\,a^3\,b^5-512\,a^2\,b^6+256\,a\,b^7\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-59\,a^3\,b+36\,a^2\,b^2\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}-36\,a\,b^7+47\,a^2\,b^6-15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{1280\,a^4\,b^4-3072\,a^3\,b^5+1792\,a^2\,b^6}{64\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,\left(256\,a^3\,b^5-512\,a^2\,b^6+256\,a\,b^7\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-59\,a^3\,b+36\,a^2\,b^2\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{1280\,a^4\,b^4-3072\,a^3\,b^5+1792\,a^2\,b^6}{64\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,\left(256\,a^3\,b^5-512\,a^2\,b^6+256\,a\,b^7\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-59\,a^3\,b+36\,a^2\,b^2\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,1{}\mathrm{i}}{\frac{36\,a^3\,b-25\,a^4}{32\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\left(\left(\frac{1280\,a^4\,b^4-3072\,a^3\,b^5+1792\,a^2\,b^6}{64\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,\left(256\,a^3\,b^5-512\,a^2\,b^6+256\,a\,b^7\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-59\,a^3\,b+36\,a^2\,b^2\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}+\left(\left(\frac{1280\,a^4\,b^4-3072\,a^3\,b^5+1792\,a^2\,b^6}{64\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,\left(256\,a^3\,b^5-512\,a^2\,b^6+256\,a\,b^7\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-59\,a^3\,b+36\,a^2\,b^2\right)}{4\,\left(a^2\,b-2\,a\,b^2+b^3\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^3\,b^9}+48\,b^2\,\sqrt{a^3\,b^9}+36\,a\,b^7-47\,a^2\,b^6+15\,a^3\,b^5-69\,a\,b\,\sqrt{a^3\,b^9}}{256\,\left(a^3\,b^9-3\,a^2\,b^{10}+3\,a\,b^{11}-b^{12}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- cos(c + d*x)/(b^2*d) - ((cos(c + d*x)*(a*b + a^2))/(4*(a - b)) - (a*b*cos(c + d*x)^3)/(4*(a - b)))/(d*(a*b^2 - b^3 + 2*b^3*cos(c + d*x)^2 - b^3*cos(c + d*x)^4)) - (atan(((((1792*a^2*b^6 - 3072*a^3*b^5 + 1280*a^4*b^4)/(64*(b^5 - 2*a*b^4 + a^2*b^3)) - (cos(c + d*x)*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*(256*a*b^7 - 512*a^2*b^6 + 256*a^3*b^5))/(4*(a^2*b - 2*a*b^2 + b^3)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) + (cos(c + d*x)*(25*a^4 - 59*a^3*b + 36*a^2*b^2))/(4*(a^2*b - 2*a*b^2 + b^3)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*1i - (((1792*a^2*b^6 - 3072*a^3*b^5 + 1280*a^4*b^4)/(64*(b^5 - 2*a*b^4 + a^2*b^3)) + (cos(c + d*x)*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*(256*a*b^7 - 512*a^2*b^6 + 256*a^3*b^5))/(4*(a^2*b - 2*a*b^2 + b^3)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) - (cos(c + d*x)*(25*a^4 - 59*a^3*b + 36*a^2*b^2))/(4*(a^2*b - 2*a*b^2 + b^3)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*1i)/((36*a^3*b - 25*a^4)/(32*(b^5 - 2*a*b^4 + a^2*b^3)) + (((1792*a^2*b^6 - 3072*a^3*b^5 + 1280*a^4*b^4)/(64*(b^5 - 2*a*b^4 + a^2*b^3)) - (cos(c + d*x)*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*(256*a*b^7 - 512*a^2*b^6 + 256*a^3*b^5))/(4*(a^2*b - 2*a*b^2 + b^3)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) + (cos(c + d*x)*(25*a^4 - 59*a^3*b + 36*a^2*b^2))/(4*(a^2*b - 2*a*b^2 + b^3)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) + (((1792*a^2*b^6 - 3072*a^3*b^5 + 1280*a^4*b^4)/(64*(b^5 - 2*a*b^4 + a^2*b^3)) + (cos(c + d*x)*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*(256*a*b^7 - 512*a^2*b^6 + 256*a^3*b^5))/(4*(a^2*b - 2*a*b^2 + b^3)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) - (cos(c + d*x)*(25*a^4 - 59*a^3*b + 36*a^2*b^2))/(4*(a^2*b - 2*a*b^2 + b^3)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)))*((25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) - 36*a*b^7 + 47*a^2*b^6 - 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*2i)/d - (atan(((((1792*a^2*b^6 - 3072*a^3*b^5 + 1280*a^4*b^4)/(64*(b^5 - 2*a*b^4 + a^2*b^3)) - (cos(c + d*x)*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*(256*a*b^7 - 512*a^2*b^6 + 256*a^3*b^5))/(4*(a^2*b - 2*a*b^2 + b^3)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) + (cos(c + d*x)*(25*a^4 - 59*a^3*b + 36*a^2*b^2))/(4*(a^2*b - 2*a*b^2 + b^3)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*1i - (((1792*a^2*b^6 - 3072*a^3*b^5 + 1280*a^4*b^4)/(64*(b^5 - 2*a*b^4 + a^2*b^3)) + (cos(c + d*x)*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*(256*a*b^7 - 512*a^2*b^6 + 256*a^3*b^5))/(4*(a^2*b - 2*a*b^2 + b^3)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) - (cos(c + d*x)*(25*a^4 - 59*a^3*b + 36*a^2*b^2))/(4*(a^2*b - 2*a*b^2 + b^3)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*1i)/((36*a^3*b - 25*a^4)/(32*(b^5 - 2*a*b^4 + a^2*b^3)) + (((1792*a^2*b^6 - 3072*a^3*b^5 + 1280*a^4*b^4)/(64*(b^5 - 2*a*b^4 + a^2*b^3)) - (cos(c + d*x)*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*(256*a*b^7 - 512*a^2*b^6 + 256*a^3*b^5))/(4*(a^2*b - 2*a*b^2 + b^3)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) + (cos(c + d*x)*(25*a^4 - 59*a^3*b + 36*a^2*b^2))/(4*(a^2*b - 2*a*b^2 + b^3)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) + (((1792*a^2*b^6 - 3072*a^3*b^5 + 1280*a^4*b^4)/(64*(b^5 - 2*a*b^4 + a^2*b^3)) + (cos(c + d*x)*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*(256*a*b^7 - 512*a^2*b^6 + 256*a^3*b^5))/(4*(a^2*b - 2*a*b^2 + b^3)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2) - (cos(c + d*x)*(25*a^4 - 59*a^3*b + 36*a^2*b^2))/(4*(a^2*b - 2*a*b^2 + b^3)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)))*(-(25*a^2*(a^3*b^9)^(1/2) + 48*b^2*(a^3*b^9)^(1/2) + 36*a*b^7 - 47*a^2*b^6 + 15*a^3*b^5 - 69*a*b*(a^3*b^9)^(1/2))/(256*(3*a*b^11 - b^12 - 3*a^2*b^10 + a^3*b^9)))^(1/2)*2i)/d","B"
213,1,3612,210,15.869914,"\text{Not used}","int(sin(c + d*x)^7/(a - b*sin(c + d*x)^4)^2,x)","\frac{\frac{a\,{\cos\left(c+d\,x\right)}^3}{4\,b\,\left(a-b\right)}-\frac{a\,\cos\left(c+d\,x\right)}{2\,b\,\left(a-b\right)}}{d\,\left(-b\,{\cos\left(c+d\,x\right)}^4+2\,b\,{\cos\left(c+d\,x\right)}^2+a-b\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{512\,a^3\,b^4-1536\,a^2\,b^5+1024\,a\,b^6}{64\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-23\,a^2\,b+16\,a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{512\,a^3\,b^4-1536\,a^2\,b^5+1024\,a\,b^6}{64\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-23\,a^2\,b+16\,a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{512\,a^3\,b^4-1536\,a^2\,b^5+1024\,a\,b^6}{64\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-23\,a^2\,b+16\,a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}+\left(\left(\frac{512\,a^3\,b^4-1536\,a^2\,b^5+1024\,a\,b^6}{64\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-23\,a^2\,b+16\,a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}-\frac{27\,a^3-84\,a^2\,b+64\,a\,b^2}{32\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}}\right)\,\sqrt{-\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}-15\,a\,b^5+16\,b^6+3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{512\,a^3\,b^4-1536\,a^2\,b^5+1024\,a\,b^6}{64\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-23\,a^2\,b+16\,a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{512\,a^3\,b^4-1536\,a^2\,b^5+1024\,a\,b^6}{64\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-23\,a^2\,b+16\,a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{512\,a^3\,b^4-1536\,a^2\,b^5+1024\,a\,b^6}{64\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-23\,a^2\,b+16\,a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}+\left(\left(\frac{512\,a^3\,b^4-1536\,a^2\,b^5+1024\,a\,b^6}{64\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-23\,a^2\,b+16\,a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}-\frac{27\,a^3-84\,a^2\,b+64\,a\,b^2}{32\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}}\right)\,\sqrt{\frac{9\,a^2\,\sqrt{a\,b^7}+24\,b^2\,\sqrt{a\,b^7}+15\,a\,b^5-16\,b^6-3\,a^2\,b^4-29\,a\,b\,\sqrt{a\,b^7}}{256\,\left(a^3\,b^7-3\,a^2\,b^8+3\,a\,b^9-b^{10}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"((a*cos(c + d*x)^3)/(4*b*(a - b)) - (a*cos(c + d*x))/(2*b*(a - b)))/(d*(a - b + 2*b*cos(c + d*x)^2 - b*cos(c + d*x)^4)) - (atan(((((1024*a*b^6 - 1536*a^2*b^5 + 512*a^3*b^4)/(64*(b^4 - 2*a*b^3 + a^2*b^2)) - (cos(c + d*x)*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) + (cos(c + d*x)*(16*a*b^2 - 23*a^2*b + 9*a^3))/(4*(a^2 - 2*a*b + b^2)))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*1i - (((1024*a*b^6 - 1536*a^2*b^5 + 512*a^3*b^4)/(64*(b^4 - 2*a*b^3 + a^2*b^2)) + (cos(c + d*x)*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) - (cos(c + d*x)*(16*a*b^2 - 23*a^2*b + 9*a^3))/(4*(a^2 - 2*a*b + b^2)))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*1i)/((((1024*a*b^6 - 1536*a^2*b^5 + 512*a^3*b^4)/(64*(b^4 - 2*a*b^3 + a^2*b^2)) - (cos(c + d*x)*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) + (cos(c + d*x)*(16*a*b^2 - 23*a^2*b + 9*a^3))/(4*(a^2 - 2*a*b + b^2)))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) + (((1024*a*b^6 - 1536*a^2*b^5 + 512*a^3*b^4)/(64*(b^4 - 2*a*b^3 + a^2*b^2)) + (cos(c + d*x)*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) - (cos(c + d*x)*(16*a*b^2 - 23*a^2*b + 9*a^3))/(4*(a^2 - 2*a*b + b^2)))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) - (64*a*b^2 - 84*a^2*b + 27*a^3)/(32*(b^4 - 2*a*b^3 + a^2*b^2))))*(-(9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) - 15*a*b^5 + 16*b^6 + 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*2i)/d - (atan(((((1024*a*b^6 - 1536*a^2*b^5 + 512*a^3*b^4)/(64*(b^4 - 2*a*b^3 + a^2*b^2)) - (cos(c + d*x)*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) + (cos(c + d*x)*(16*a*b^2 - 23*a^2*b + 9*a^3))/(4*(a^2 - 2*a*b + b^2)))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*1i - (((1024*a*b^6 - 1536*a^2*b^5 + 512*a^3*b^4)/(64*(b^4 - 2*a*b^3 + a^2*b^2)) + (cos(c + d*x)*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) - (cos(c + d*x)*(16*a*b^2 - 23*a^2*b + 9*a^3))/(4*(a^2 - 2*a*b + b^2)))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*1i)/((((1024*a*b^6 - 1536*a^2*b^5 + 512*a^3*b^4)/(64*(b^4 - 2*a*b^3 + a^2*b^2)) - (cos(c + d*x)*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) + (cos(c + d*x)*(16*a*b^2 - 23*a^2*b + 9*a^3))/(4*(a^2 - 2*a*b + b^2)))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) + (((1024*a*b^6 - 1536*a^2*b^5 + 512*a^3*b^4)/(64*(b^4 - 2*a*b^3 + a^2*b^2)) + (cos(c + d*x)*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) - (cos(c + d*x)*(16*a*b^2 - 23*a^2*b + 9*a^3))/(4*(a^2 - 2*a*b + b^2)))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2) - (64*a*b^2 - 84*a^2*b + 27*a^3)/(32*(b^4 - 2*a*b^3 + a^2*b^2))))*((9*a^2*(a*b^7)^(1/2) + 24*b^2*(a*b^7)^(1/2) + 15*a*b^5 - 16*b^6 - 3*a^2*b^4 - 29*a*b*(a*b^7)^(1/2))/(256*(3*a*b^9 - b^10 - 3*a^2*b^8 + a^3*b^7)))^(1/2)*2i)/d","B"
214,1,3839,217,16.630244,"\text{Not used}","int(sin(c + d*x)^5/(a - b*sin(c + d*x)^4)^2,x)","\frac{\frac{{\cos\left(c+d\,x\right)}^3}{4\,\left(a-b\right)}-\frac{\cos\left(c+d\,x\right)\,\left(a+b\right)}{4\,b\,\left(a-b\right)}}{d\,\left(-b\,{\cos\left(c+d\,x\right)}^4+2\,b\,{\cos\left(c+d\,x\right)}^2+a-b\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{256\,a^3\,b^2-1024\,a^2\,b^3+768\,a\,b^4}{64\,\left(a^2-2\,a\,b+b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(a^2\,b-3\,a\,b^2+4\,b^3\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,1{}\mathrm{i}-\left(\left(\frac{256\,a^3\,b^2-1024\,a^2\,b^3+768\,a\,b^4}{64\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(a^2\,b-3\,a\,b^2+4\,b^3\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{256\,a^3\,b^2-1024\,a^2\,b^3+768\,a\,b^4}{64\,\left(a^2-2\,a\,b+b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(a^2\,b-3\,a\,b^2+4\,b^3\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}-\frac{a-4\,b}{32\,\left(a^2-2\,a\,b+b^2\right)}+\left(\left(\frac{256\,a^3\,b^2-1024\,a^2\,b^3+768\,a\,b^4}{64\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(a^2\,b-3\,a\,b^2+4\,b^3\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}-4\,a\,b^5-a^2\,b^4+a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{256\,a^3\,b^2-1024\,a^2\,b^3+768\,a\,b^4}{64\,\left(a^2-2\,a\,b+b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(a^2\,b-3\,a\,b^2+4\,b^3\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,1{}\mathrm{i}-\left(\left(\frac{256\,a^3\,b^2-1024\,a^2\,b^3+768\,a\,b^4}{64\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(a^2\,b-3\,a\,b^2+4\,b^3\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{256\,a^3\,b^2-1024\,a^2\,b^3+768\,a\,b^4}{64\,\left(a^2-2\,a\,b+b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(a^2\,b-3\,a\,b^2+4\,b^3\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}-\frac{a-4\,b}{32\,\left(a^2-2\,a\,b+b^2\right)}+\left(\left(\frac{256\,a^3\,b^2-1024\,a^2\,b^3+768\,a\,b^4}{64\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(a^2\,b-3\,a\,b^2+4\,b^3\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+8\,b^2\,\sqrt{a^3\,b^5}+4\,a\,b^5+a^2\,b^4-a^3\,b^3-5\,a\,b\,\sqrt{a^3\,b^5}}{256\,\left(-a^5\,b^5+3\,a^4\,b^6-3\,a^3\,b^7+a^2\,b^8\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(cos(c + d*x)^3/(4*(a - b)) - (cos(c + d*x)*(a + b))/(4*b*(a - b)))/(d*(a - b + 2*b*cos(c + d*x)^2 - b*cos(c + d*x)^4)) - (atan(((((768*a*b^4 - 1024*a^2*b^3 + 256*a^3*b^2)/(64*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) + (cos(c + d*x)*(a^2*b - 3*a*b^2 + 4*b^3))/(4*(a^2 - 2*a*b + b^2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*1i - (((768*a*b^4 - 1024*a^2*b^3 + 256*a^3*b^2)/(64*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) - (cos(c + d*x)*(a^2*b - 3*a*b^2 + 4*b^3))/(4*(a^2 - 2*a*b + b^2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*1i)/((((768*a*b^4 - 1024*a^2*b^3 + 256*a^3*b^2)/(64*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) + (cos(c + d*x)*(a^2*b - 3*a*b^2 + 4*b^3))/(4*(a^2 - 2*a*b + b^2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) - (a - 4*b)/(32*(a^2 - 2*a*b + b^2)) + (((768*a*b^4 - 1024*a^2*b^3 + 256*a^3*b^2)/(64*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) - (cos(c + d*x)*(a^2*b - 3*a*b^2 + 4*b^3))/(4*(a^2 - 2*a*b + b^2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)))*(-(a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) - 4*a*b^5 - a^2*b^4 + a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*2i)/d - (atan(((((768*a*b^4 - 1024*a^2*b^3 + 256*a^3*b^2)/(64*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) + (cos(c + d*x)*(a^2*b - 3*a*b^2 + 4*b^3))/(4*(a^2 - 2*a*b + b^2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*1i - (((768*a*b^4 - 1024*a^2*b^3 + 256*a^3*b^2)/(64*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) - (cos(c + d*x)*(a^2*b - 3*a*b^2 + 4*b^3))/(4*(a^2 - 2*a*b + b^2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*1i)/((((768*a*b^4 - 1024*a^2*b^3 + 256*a^3*b^2)/(64*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) + (cos(c + d*x)*(a^2*b - 3*a*b^2 + 4*b^3))/(4*(a^2 - 2*a*b + b^2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) - (a - 4*b)/(32*(a^2 - 2*a*b + b^2)) + (((768*a*b^4 - 1024*a^2*b^3 + 256*a^3*b^2)/(64*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2) - (cos(c + d*x)*(a^2*b - 3*a*b^2 + 4*b^3))/(4*(a^2 - 2*a*b + b^2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)))*((a^2*(a^3*b^5)^(1/2) + 8*b^2*(a^3*b^5)^(1/2) + 4*a*b^5 + a^2*b^4 - a^3*b^3 - 5*a*b*(a^3*b^5)^(1/2))/(256*(a^2*b^8 - 3*a^3*b^7 + 3*a^4*b^6 - a^5*b^5)))^(1/2)*2i)/d","B"
215,1,3060,186,15.603248,"\text{Not used}","int(sin(c + d*x)^3/(a - b*sin(c + d*x)^4)^2,x)","\frac{\frac{{\cos\left(c+d\,x\right)}^3}{4\,\left(a-b\right)}-\frac{\cos\left(c+d\,x\right)}{2\,\left(a-b\right)}}{d\,\left(-b\,{\cos\left(c+d\,x\right)}^4+2\,b\,{\cos\left(c+d\,x\right)}^2+a-b\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{512\,a\,b^4-512\,a^2\,b^3}{64\,\left(a^2-2\,a\,b+b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(b^3+a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{512\,a\,b^4-512\,a^2\,b^3}{64\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(b^3+a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,1{}\mathrm{i}}{\frac{b}{32\,\left(a^2-2\,a\,b+b^2\right)}+\left(\left(\frac{512\,a\,b^4-512\,a^2\,b^3}{64\,\left(a^2-2\,a\,b+b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(b^3+a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}+\left(\left(\frac{512\,a\,b^4-512\,a^2\,b^3}{64\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(b^3+a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}+a\,b^3+3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{512\,a\,b^4-512\,a^2\,b^3}{64\,\left(a^2-2\,a\,b+b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(b^3+a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{512\,a\,b^4-512\,a^2\,b^3}{64\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(b^3+a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,1{}\mathrm{i}}{\frac{b}{32\,\left(a^2-2\,a\,b+b^2\right)}+\left(\left(\frac{512\,a\,b^4-512\,a^2\,b^3}{64\,\left(a^2-2\,a\,b+b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(b^3+a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}+\left(\left(\frac{512\,a\,b^4-512\,a^2\,b^3}{64\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,\left(256\,a^3\,b^4-512\,a^2\,b^5+256\,a\,b^6\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(b^3+a\,b^2\right)}{4\,\left(a^2-2\,a\,b+b^2\right)}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+3\,b\,\sqrt{a^3\,b^3}-a\,b^3-3\,a^2\,b^2}{256\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(cos(c + d*x)^3/(4*(a - b)) - cos(c + d*x)/(2*(a - b)))/(d*(a - b + 2*b*cos(c + d*x)^2 - b*cos(c + d*x)^4)) - (atan(((((512*a*b^4 - 512*a^2*b^3)/(64*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) + (cos(c + d*x)*(a*b^2 + b^3))/(4*(a^2 - 2*a*b + b^2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*1i - (((512*a*b^4 - 512*a^2*b^3)/(64*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) - (cos(c + d*x)*(a*b^2 + b^3))/(4*(a^2 - 2*a*b + b^2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*1i)/(b/(32*(a^2 - 2*a*b + b^2)) + (((512*a*b^4 - 512*a^2*b^3)/(64*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) + (cos(c + d*x)*(a*b^2 + b^3))/(4*(a^2 - 2*a*b + b^2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) + (((512*a*b^4 - 512*a^2*b^3)/(64*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) - (cos(c + d*x)*(a*b^2 + b^3))/(4*(a^2 - 2*a*b + b^2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)))*((a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) + a*b^3 + 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*2i)/d - (atan(((((512*a*b^4 - 512*a^2*b^3)/(64*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) + (cos(c + d*x)*(a*b^2 + b^3))/(4*(a^2 - 2*a*b + b^2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*1i - (((512*a*b^4 - 512*a^2*b^3)/(64*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) - (cos(c + d*x)*(a*b^2 + b^3))/(4*(a^2 - 2*a*b + b^2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*1i)/(b/(32*(a^2 - 2*a*b + b^2)) + (((512*a*b^4 - 512*a^2*b^3)/(64*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) + (cos(c + d*x)*(a*b^2 + b^3))/(4*(a^2 - 2*a*b + b^2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) + (((512*a*b^4 - 512*a^2*b^3)/(64*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*(256*a*b^6 - 512*a^2*b^5 + 256*a^3*b^4))/(4*(a^2 - 2*a*b + b^2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2) - (cos(c + d*x)*(a*b^2 + b^3))/(4*(a^2 - 2*a*b + b^2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)))*(-(a*(a^3*b^3)^(1/2) + 3*b*(a^3*b^3)^(1/2) - a*b^3 - 3*a^2*b^2)/(256*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)))^(1/2)*2i)/d","B"
216,1,3507,221,16.794183,"\text{Not used}","int(sin(c + d*x)/(a - b*sin(c + d*x)^4)^2,x)","\frac{\frac{b\,{\cos\left(c+d\,x\right)}^3}{4\,a\,\left(a-b\right)}-\frac{\cos\left(c+d\,x\right)\,\left(a+b\right)}{4\,a\,\left(a-b\right)}}{d\,\left(-b\,{\cos\left(c+d\,x\right)}^4+2\,b\,{\cos\left(c+d\,x\right)}^2+a-b\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{768\,a^5\,b^3-1024\,a^4\,b^4+256\,a^3\,b^5}{64\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(256\,a^5\,b^4-512\,a^4\,b^5+256\,a^3\,b^6\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^3-11\,a\,b^4+4\,b^5\right)}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}\,1{}\mathrm{i}-\left(\left(\frac{768\,a^5\,b^3-1024\,a^4\,b^4+256\,a^3\,b^5}{64\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(256\,a^5\,b^4-512\,a^4\,b^5+256\,a^3\,b^6\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^3-11\,a\,b^4+4\,b^5\right)}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}\,1{}\mathrm{i}}{\frac{9\,a\,b^3-4\,b^4}{32\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\left(\left(\frac{768\,a^5\,b^3-1024\,a^4\,b^4+256\,a^3\,b^5}{64\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(256\,a^5\,b^4-512\,a^4\,b^5+256\,a^3\,b^6\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^3-11\,a\,b^4+4\,b^5\right)}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}+\left(\left(\frac{768\,a^5\,b^3-1024\,a^4\,b^4+256\,a^3\,b^5}{64\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(256\,a^5\,b^4-512\,a^4\,b^5+256\,a^3\,b^6\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^3-11\,a\,b^4+4\,b^5\right)}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}\right)\,\sqrt{-\frac{15\,a^5\,b-9\,a\,\sqrt{a^9\,b}+5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{768\,a^5\,b^3-1024\,a^4\,b^4+256\,a^3\,b^5}{64\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(256\,a^5\,b^4-512\,a^4\,b^5+256\,a^3\,b^6\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^3-11\,a\,b^4+4\,b^5\right)}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}\,1{}\mathrm{i}-\left(\left(\frac{768\,a^5\,b^3-1024\,a^4\,b^4+256\,a^3\,b^5}{64\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(256\,a^5\,b^4-512\,a^4\,b^5+256\,a^3\,b^6\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^3-11\,a\,b^4+4\,b^5\right)}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}\,1{}\mathrm{i}}{\frac{9\,a\,b^3-4\,b^4}{32\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\left(\left(\frac{768\,a^5\,b^3-1024\,a^4\,b^4+256\,a^3\,b^5}{64\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(256\,a^5\,b^4-512\,a^4\,b^5+256\,a^3\,b^6\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^3-11\,a\,b^4+4\,b^5\right)}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}+\left(\left(\frac{768\,a^5\,b^3-1024\,a^4\,b^4+256\,a^3\,b^5}{64\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(256\,a^5\,b^4-512\,a^4\,b^5+256\,a^3\,b^6\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^2\,b^3-11\,a\,b^4+4\,b^5\right)}{4\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}}\right)\,\sqrt{-\frac{15\,a^5\,b+9\,a\,\sqrt{a^9\,b}-5\,b\,\sqrt{a^9\,b}+4\,a^3\,b^3-15\,a^4\,b^2}{256\,\left(a^9\,b-3\,a^8\,b^2+3\,a^7\,b^3-a^6\,b^4\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"((b*cos(c + d*x)^3)/(4*a*(a - b)) - (cos(c + d*x)*(a + b))/(4*a*(a - b)))/(d*(a - b + 2*b*cos(c + d*x)^2 - b*cos(c + d*x)^4)) + (atan(((((256*a^3*b^5 - 1024*a^4*b^4 + 768*a^5*b^3)/(64*(a^5 - 2*a^4*b + a^3*b^2)) - (cos(c + d*x)*(256*a^3*b^6 - 512*a^4*b^5 + 256*a^5*b^4)*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) + (cos(c + d*x)*(4*b^5 - 11*a*b^4 + 9*a^2*b^3))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2)*1i - (((256*a^3*b^5 - 1024*a^4*b^4 + 768*a^5*b^3)/(64*(a^5 - 2*a^4*b + a^3*b^2)) + (cos(c + d*x)*(256*a^3*b^6 - 512*a^4*b^5 + 256*a^5*b^4)*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) - (cos(c + d*x)*(4*b^5 - 11*a*b^4 + 9*a^2*b^3))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2)*1i)/((9*a*b^3 - 4*b^4)/(32*(a^5 - 2*a^4*b + a^3*b^2)) + (((256*a^3*b^5 - 1024*a^4*b^4 + 768*a^5*b^3)/(64*(a^5 - 2*a^4*b + a^3*b^2)) - (cos(c + d*x)*(256*a^3*b^6 - 512*a^4*b^5 + 256*a^5*b^4)*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) + (cos(c + d*x)*(4*b^5 - 11*a*b^4 + 9*a^2*b^3))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) + (((256*a^3*b^5 - 1024*a^4*b^4 + 768*a^5*b^3)/(64*(a^5 - 2*a^4*b + a^3*b^2)) + (cos(c + d*x)*(256*a^3*b^6 - 512*a^4*b^5 + 256*a^5*b^4)*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) - (cos(c + d*x)*(4*b^5 - 11*a*b^4 + 9*a^2*b^3))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2)))*(-(15*a^5*b - 9*a*(a^9*b)^(1/2) + 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2)*2i)/d + (atan(((((256*a^3*b^5 - 1024*a^4*b^4 + 768*a^5*b^3)/(64*(a^5 - 2*a^4*b + a^3*b^2)) - (cos(c + d*x)*(256*a^3*b^6 - 512*a^4*b^5 + 256*a^5*b^4)*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) + (cos(c + d*x)*(4*b^5 - 11*a*b^4 + 9*a^2*b^3))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2)*1i - (((256*a^3*b^5 - 1024*a^4*b^4 + 768*a^5*b^3)/(64*(a^5 - 2*a^4*b + a^3*b^2)) + (cos(c + d*x)*(256*a^3*b^6 - 512*a^4*b^5 + 256*a^5*b^4)*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) - (cos(c + d*x)*(4*b^5 - 11*a*b^4 + 9*a^2*b^3))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2)*1i)/((9*a*b^3 - 4*b^4)/(32*(a^5 - 2*a^4*b + a^3*b^2)) + (((256*a^3*b^5 - 1024*a^4*b^4 + 768*a^5*b^3)/(64*(a^5 - 2*a^4*b + a^3*b^2)) - (cos(c + d*x)*(256*a^3*b^6 - 512*a^4*b^5 + 256*a^5*b^4)*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) + (cos(c + d*x)*(4*b^5 - 11*a*b^4 + 9*a^2*b^3))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) + (((256*a^3*b^5 - 1024*a^4*b^4 + 768*a^5*b^3)/(64*(a^5 - 2*a^4*b + a^3*b^2)) + (cos(c + d*x)*(256*a^3*b^6 - 512*a^4*b^5 + 256*a^5*b^4)*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2) - (cos(c + d*x)*(4*b^5 - 11*a*b^4 + 9*a^2*b^3))/(4*(a^4 - 2*a^3*b + a^2*b^2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2)))*(-(15*a^5*b + 9*a*(a^9*b)^(1/2) - 5*b*(a^9*b)^(1/2) + 4*a^3*b^3 - 15*a^4*b^2)/(256*(a^9*b - a^6*b^4 + 3*a^7*b^3 - 3*a^8*b^2)))^(1/2)*2i)/d","B"
217,1,7491,325,17.549967,"\text{Not used}","int(1/(sin(c + d*x)*(a - b*sin(c + d*x)^4)^2),x)","\frac{\frac{b\,{\cos\left(c+d\,x\right)}^3}{4\,a\,\left(a-b\right)}-\frac{b\,\cos\left(c+d\,x\right)}{2\,a\,\left(a-b\right)}}{d\,\left(-b\,{\cos\left(c+d\,x\right)}^4+2\,b\,{\cos\left(c+d\,x\right)}^2+a-b\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{9776\,a^5\,b^5-10944\,a^4\,b^6+3072\,a^3\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\left(\left(\frac{-65536\,a^{10}\,b^4+172032\,a^9\,b^5-155648\,a^8\,b^6+49152\,a^7\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{9776\,a^5\,b^5-10944\,a^4\,b^6+3072\,a^3\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\left(\left(\frac{-65536\,a^{10}\,b^4+172032\,a^9\,b^5-155648\,a^8\,b^6+49152\,a^7\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{9776\,a^5\,b^5-10944\,a^4\,b^6+3072\,a^3\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\left(\left(\frac{-65536\,a^{10}\,b^4+172032\,a^9\,b^5-155648\,a^8\,b^6+49152\,a^7\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{125\,a\,b^5-80\,b^6}{128\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}+\left(\left(\frac{9776\,a^5\,b^5-10944\,a^4\,b^6+3072\,a^3\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\left(\left(\frac{-65536\,a^{10}\,b^4+172032\,a^9\,b^5-155648\,a^8\,b^6+49152\,a^7\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}+35\,a^6\,b+16\,a^4\,b^3-47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{9776\,a^5\,b^5-10944\,a^4\,b^6+3072\,a^3\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\left(\left(\frac{-65536\,a^{10}\,b^4+172032\,a^9\,b^5-155648\,a^8\,b^6+49152\,a^7\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{9776\,a^5\,b^5-10944\,a^4\,b^6+3072\,a^3\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\left(\left(\frac{-65536\,a^{10}\,b^4+172032\,a^9\,b^5-155648\,a^8\,b^6+49152\,a^7\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{9776\,a^5\,b^5-10944\,a^4\,b^6+3072\,a^3\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\left(\left(\frac{-65536\,a^{10}\,b^4+172032\,a^9\,b^5-155648\,a^8\,b^6+49152\,a^7\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{125\,a\,b^5-80\,b^6}{128\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}+\left(\left(\frac{9776\,a^5\,b^5-10944\,a^4\,b^6+3072\,a^3\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\left(\left(\frac{-65536\,a^{10}\,b^4+172032\,a^9\,b^5-155648\,a^8\,b^6+49152\,a^7\,b^7}{256\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{128\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}}\right)\,\sqrt{-\frac{25\,a^2\,\sqrt{a^9\,b}+8\,b^2\,\sqrt{a^9\,b}-35\,a^6\,b-16\,a^4\,b^3+47\,a^5\,b^2-29\,a\,b\,\sqrt{a^9\,b}}{256\,\left(-a^{11}+3\,a^{10}\,b-3\,a^9\,b^2+a^8\,b^3\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{\left(\frac{\frac{\frac{-256\,a^{10}\,b^4+672\,a^9\,b^5-608\,a^8\,b^6+192\,a^7\,b^7}{2\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{512\,a^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{2\,a^2}+\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{256\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{2\,a^2}-\frac{\frac{611\,a^5\,b^5}{16}-\frac{171\,a^4\,b^6}{4}+12\,a^3\,b^7}{2\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}\right)\,1{}\mathrm{i}}{2\,a^2}-\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)\,1{}\mathrm{i}}{256\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{a^2}-\frac{\frac{\left(\frac{\frac{\frac{-256\,a^{10}\,b^4+672\,a^9\,b^5-608\,a^8\,b^6+192\,a^7\,b^7}{2\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{512\,a^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{2\,a^2}-\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{256\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{2\,a^2}-\frac{\frac{611\,a^5\,b^5}{16}-\frac{171\,a^4\,b^6}{4}+12\,a^3\,b^7}{2\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}\right)\,1{}\mathrm{i}}{2\,a^2}+\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)\,1{}\mathrm{i}}{256\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{a^2}}{\frac{\frac{125\,a\,b^5}{128}-\frac{5\,b^6}{8}}{a^7-2\,a^6\,b+a^5\,b^2}+\frac{\frac{\frac{\frac{\frac{-256\,a^{10}\,b^4+672\,a^9\,b^5-608\,a^8\,b^6+192\,a^7\,b^7}{2\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{512\,a^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{2\,a^2}+\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{256\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{2\,a^2}-\frac{\frac{611\,a^5\,b^5}{16}-\frac{171\,a^4\,b^6}{4}+12\,a^3\,b^7}{2\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}}{2\,a^2}-\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{256\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{a^2}+\frac{\frac{\frac{\frac{\frac{-256\,a^{10}\,b^4+672\,a^9\,b^5-608\,a^8\,b^6+192\,a^7\,b^7}{2\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(-65536\,a^{11}\,b^4+229376\,a^{10}\,b^5-262144\,a^9\,b^6+98304\,a^8\,b^7\right)}{512\,a^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{2\,a^2}-\frac{\cos\left(c+d\,x\right)\,\left(29312\,a^6\,b^5-45440\,a^5\,b^6+18432\,a^4\,b^7\right)}{256\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{2\,a^2}-\frac{\frac{611\,a^5\,b^5}{16}-\frac{171\,a^4\,b^6}{4}+12\,a^3\,b^7}{2\,\left(a^7-2\,a^6\,b+a^5\,b^2\right)}}{2\,a^2}+\frac{\cos\left(c+d\,x\right)\,\left(1425\,a^2\,b^5-2048\,a\,b^6+768\,b^7\right)}{256\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{a^2}}\right)\,1{}\mathrm{i}}{a^2\,d}","Not used",1,"((b*cos(c + d*x)^3)/(4*a*(a - b)) - (b*cos(c + d*x))/(2*a*(a - b)))/(d*(a - b + 2*b*cos(c + d*x)^2 - b*cos(c + d*x)^4)) - (atan(((((3072*a^3*b^7 - 10944*a^4*b^6 + 9776*a^5*b^5)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (((49152*a^7*b^7 - 155648*a^8*b^6 + 172032*a^9*b^5 - 65536*a^10*b^4)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (cos(c + d*x)*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) + (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) + (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*1i - (((3072*a^3*b^7 - 10944*a^4*b^6 + 9776*a^5*b^5)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (((49152*a^7*b^7 - 155648*a^8*b^6 + 172032*a^9*b^5 - 65536*a^10*b^4)/(256*(a^7 - 2*a^6*b + a^5*b^2)) + (cos(c + d*x)*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*1i)/((((3072*a^3*b^7 - 10944*a^4*b^6 + 9776*a^5*b^5)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (((49152*a^7*b^7 - 155648*a^8*b^6 + 172032*a^9*b^5 - 65536*a^10*b^4)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (cos(c + d*x)*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) + (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) + (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (125*a*b^5 - 80*b^6)/(128*(a^7 - 2*a^6*b + a^5*b^2)) + (((3072*a^3*b^7 - 10944*a^4*b^6 + 9776*a^5*b^5)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (((49152*a^7*b^7 - 155648*a^8*b^6 + 172032*a^9*b^5 - 65536*a^10*b^4)/(256*(a^7 - 2*a^6*b + a^5*b^2)) + (cos(c + d*x)*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)))*((25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) + 35*a^6*b + 16*a^4*b^3 - 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*2i)/d - (atan(((((3072*a^3*b^7 - 10944*a^4*b^6 + 9776*a^5*b^5)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (((49152*a^7*b^7 - 155648*a^8*b^6 + 172032*a^9*b^5 - 65536*a^10*b^4)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (cos(c + d*x)*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) + (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) + (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*1i - (((3072*a^3*b^7 - 10944*a^4*b^6 + 9776*a^5*b^5)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (((49152*a^7*b^7 - 155648*a^8*b^6 + 172032*a^9*b^5 - 65536*a^10*b^4)/(256*(a^7 - 2*a^6*b + a^5*b^2)) + (cos(c + d*x)*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*1i)/((((3072*a^3*b^7 - 10944*a^4*b^6 + 9776*a^5*b^5)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (((49152*a^7*b^7 - 155648*a^8*b^6 + 172032*a^9*b^5 - 65536*a^10*b^4)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (cos(c + d*x)*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) + (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) + (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (125*a*b^5 - 80*b^6)/(128*(a^7 - 2*a^6*b + a^5*b^2)) + (((3072*a^3*b^7 - 10944*a^4*b^6 + 9776*a^5*b^5)/(256*(a^7 - 2*a^6*b + a^5*b^2)) - (((49152*a^7*b^7 - 155648*a^8*b^6 + 172032*a^9*b^5 - 65536*a^10*b^4)/(256*(a^7 - 2*a^6*b + a^5*b^2)) + (cos(c + d*x)*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2) - (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(128*(a^6 - 2*a^5*b + a^4*b^2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)))*(-(25*a^2*(a^9*b)^(1/2) + 8*b^2*(a^9*b)^(1/2) - 35*a^6*b - 16*a^4*b^3 + 47*a^5*b^2 - 29*a*b*(a^9*b)^(1/2))/(256*(3*a^10*b - a^11 + a^8*b^3 - 3*a^9*b^2)))^(1/2)*2i)/d - (atan((((((((192*a^7*b^7 - 608*a^8*b^6 + 672*a^9*b^5 - 256*a^10*b^4)/(2*(a^7 - 2*a^6*b + a^5*b^2)) - (cos(c + d*x)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(512*a^2*(a^6 - 2*a^5*b + a^4*b^2)))/(2*a^2) + (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(256*(a^6 - 2*a^5*b + a^4*b^2)))/(2*a^2) - (12*a^3*b^7 - (171*a^4*b^6)/4 + (611*a^5*b^5)/16)/(2*(a^7 - 2*a^6*b + a^5*b^2)))*1i)/(2*a^2) - (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5)*1i)/(256*(a^6 - 2*a^5*b + a^4*b^2)))/a^2 - ((((((192*a^7*b^7 - 608*a^8*b^6 + 672*a^9*b^5 - 256*a^10*b^4)/(2*(a^7 - 2*a^6*b + a^5*b^2)) + (cos(c + d*x)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(512*a^2*(a^6 - 2*a^5*b + a^4*b^2)))/(2*a^2) - (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(256*(a^6 - 2*a^5*b + a^4*b^2)))/(2*a^2) - (12*a^3*b^7 - (171*a^4*b^6)/4 + (611*a^5*b^5)/16)/(2*(a^7 - 2*a^6*b + a^5*b^2)))*1i)/(2*a^2) + (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5)*1i)/(256*(a^6 - 2*a^5*b + a^4*b^2)))/a^2)/(((125*a*b^5)/128 - (5*b^6)/8)/(a^7 - 2*a^6*b + a^5*b^2) + (((((192*a^7*b^7 - 608*a^8*b^6 + 672*a^9*b^5 - 256*a^10*b^4)/(2*(a^7 - 2*a^6*b + a^5*b^2)) - (cos(c + d*x)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(512*a^2*(a^6 - 2*a^5*b + a^4*b^2)))/(2*a^2) + (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(256*(a^6 - 2*a^5*b + a^4*b^2)))/(2*a^2) - (12*a^3*b^7 - (171*a^4*b^6)/4 + (611*a^5*b^5)/16)/(2*(a^7 - 2*a^6*b + a^5*b^2)))/(2*a^2) - (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(256*(a^6 - 2*a^5*b + a^4*b^2)))/a^2 + (((((192*a^7*b^7 - 608*a^8*b^6 + 672*a^9*b^5 - 256*a^10*b^4)/(2*(a^7 - 2*a^6*b + a^5*b^2)) + (cos(c + d*x)*(98304*a^8*b^7 - 262144*a^9*b^6 + 229376*a^10*b^5 - 65536*a^11*b^4))/(512*a^2*(a^6 - 2*a^5*b + a^4*b^2)))/(2*a^2) - (cos(c + d*x)*(18432*a^4*b^7 - 45440*a^5*b^6 + 29312*a^6*b^5))/(256*(a^6 - 2*a^5*b + a^4*b^2)))/(2*a^2) - (12*a^3*b^7 - (171*a^4*b^6)/4 + (611*a^5*b^5)/16)/(2*(a^7 - 2*a^6*b + a^5*b^2)))/(2*a^2) + (cos(c + d*x)*(768*b^7 - 2048*a*b^6 + 1425*a^2*b^5))/(256*(a^6 - 2*a^5*b + a^4*b^2)))/a^2))*1i)/(a^2*d)","B"
218,1,7640,320,17.601871,"\text{Not used}","int(sin(c + d*x)^8/(a - b*sin(c + d*x)^4)^2,x)","-\frac{\mathrm{atan}\left(\frac{\frac{\frac{\frac{\left(\frac{\left(-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{512\,b^2\,\left(a\,b^4-b^5\right)}+\frac{\left(192\,a^6\,b^7-656\,a^5\,b^8+816\,a^4\,b^9-432\,a^3\,b^{10}+80\,a^2\,b^{11}\right)\,1{}\mathrm{i}}{2\,\left(a\,b^5-b^6\right)}\right)\,1{}\mathrm{i}}{2\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)\,1{}\mathrm{i}}{256\,\left(a\,b^4-b^5\right)}\right)\,1{}\mathrm{i}}{2\,b^2}+\frac{\left(12\,a^6\,b^3-\frac{255\,a^5\,b^4}{4}+\frac{417\,a^4\,b^5}{4}-69\,a^3\,b^6+20\,a^2\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a\,b^5-b^6\right)}}{2\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{256\,\left(a\,b^4-b^5\right)}}{b^2}-\frac{\frac{\frac{\left(\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{512\,b^2\,\left(a\,b^4-b^5\right)}+\frac{\left(192\,a^6\,b^7-656\,a^5\,b^8+816\,a^4\,b^9-432\,a^3\,b^{10}+80\,a^2\,b^{11}\right)\,1{}\mathrm{i}}{2\,\left(a\,b^5-b^6\right)}\right)\,1{}\mathrm{i}}{2\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)\,1{}\mathrm{i}}{256\,\left(a\,b^4-b^5\right)}\right)\,1{}\mathrm{i}}{2\,b^2}+\frac{\left(12\,a^6\,b^3-\frac{255\,a^5\,b^4}{4}+\frac{417\,a^4\,b^5}{4}-69\,a^3\,b^6+20\,a^2\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a\,b^5-b^6\right)}}{2\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{256\,\left(a\,b^4-b^5\right)}}{b^2}}{\frac{\frac{\left(\frac{\left(\frac{\left(-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{512\,b^2\,\left(a\,b^4-b^5\right)}+\frac{\left(192\,a^6\,b^7-656\,a^5\,b^8+816\,a^4\,b^9-432\,a^3\,b^{10}+80\,a^2\,b^{11}\right)\,1{}\mathrm{i}}{2\,\left(a\,b^5-b^6\right)}\right)\,1{}\mathrm{i}}{2\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)\,1{}\mathrm{i}}{256\,\left(a\,b^4-b^5\right)}\right)\,1{}\mathrm{i}}{2\,b^2}+\frac{\left(12\,a^6\,b^3-\frac{255\,a^5\,b^4}{4}+\frac{417\,a^4\,b^5}{4}-69\,a^3\,b^6+20\,a^2\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a\,b^5-b^6\right)}\right)\,1{}\mathrm{i}}{2\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)\,1{}\mathrm{i}}{256\,\left(a\,b^4-b^5\right)}}{b^2}+\frac{\frac{\left(\frac{\left(\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{512\,b^2\,\left(a\,b^4-b^5\right)}+\frac{\left(192\,a^6\,b^7-656\,a^5\,b^8+816\,a^4\,b^9-432\,a^3\,b^{10}+80\,a^2\,b^{11}\right)\,1{}\mathrm{i}}{2\,\left(a\,b^5-b^6\right)}\right)\,1{}\mathrm{i}}{2\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)\,1{}\mathrm{i}}{256\,\left(a\,b^4-b^5\right)}\right)\,1{}\mathrm{i}}{2\,b^2}+\frac{\left(12\,a^6\,b^3-\frac{255\,a^5\,b^4}{4}+\frac{417\,a^4\,b^5}{4}-69\,a^3\,b^6+20\,a^2\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a\,b^5-b^6\right)}\right)\,1{}\mathrm{i}}{2\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)\,1{}\mathrm{i}}{256\,\left(a\,b^4-b^5\right)}}{b^2}-\frac{\frac{41\,a^5}{8}-\frac{2049\,a^4\,b}{128}+\frac{25\,a^3\,b^2}{2}}{a\,b^5-b^6}}\right)}{b^2\,d}-\frac{\frac{a\,{\mathrm{tan}\left(c+d\,x\right)}^3}{2\,b\,\left(a-b\right)}+\frac{a\,\mathrm{tan}\left(c+d\,x\right)}{4\,b\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^4+2\,a\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3072\,a^6\,b^3-16320\,a^5\,b^4+26688\,a^4\,b^5-17664\,a^3\,b^6+5120\,a^2\,b^7}{256\,\left(a\,b^5-b^6\right)}+\left(\left(\frac{49152\,a^6\,b^7-167936\,a^5\,b^8+208896\,a^4\,b^9-110592\,a^3\,b^{10}+20480\,a^2\,b^{11}}{256\,\left(a\,b^5-b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3072\,a^6\,b^3-16320\,a^5\,b^4+26688\,a^4\,b^5-17664\,a^3\,b^6+5120\,a^2\,b^7}{256\,\left(a\,b^5-b^6\right)}+\left(\left(\frac{49152\,a^6\,b^7-167936\,a^5\,b^8+208896\,a^4\,b^9-110592\,a^3\,b^{10}+20480\,a^2\,b^{11}}{256\,\left(a\,b^5-b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3072\,a^6\,b^3-16320\,a^5\,b^4+26688\,a^4\,b^5-17664\,a^3\,b^6+5120\,a^2\,b^7}{256\,\left(a\,b^5-b^6\right)}+\left(\left(\frac{49152\,a^6\,b^7-167936\,a^5\,b^8+208896\,a^4\,b^9-110592\,a^3\,b^{10}+20480\,a^2\,b^{11}}{256\,\left(a\,b^5-b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\left(\left(\frac{3072\,a^6\,b^3-16320\,a^5\,b^4+26688\,a^4\,b^5-17664\,a^3\,b^6+5120\,a^2\,b^7}{256\,\left(a\,b^5-b^6\right)}+\left(\left(\frac{49152\,a^6\,b^7-167936\,a^5\,b^8+208896\,a^4\,b^9-110592\,a^3\,b^{10}+20480\,a^2\,b^{11}}{256\,\left(a\,b^5-b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{656\,a^5-2049\,a^4\,b+1600\,a^3\,b^2}{128\,\left(a\,b^5-b^6\right)}}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}-35\,a\,b^6+47\,a^2\,b^5-16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3072\,a^6\,b^3-16320\,a^5\,b^4+26688\,a^4\,b^5-17664\,a^3\,b^6+5120\,a^2\,b^7}{256\,\left(a\,b^5-b^6\right)}+\left(\left(\frac{49152\,a^6\,b^7-167936\,a^5\,b^8+208896\,a^4\,b^9-110592\,a^3\,b^{10}+20480\,a^2\,b^{11}}{256\,\left(a\,b^5-b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3072\,a^6\,b^3-16320\,a^5\,b^4+26688\,a^4\,b^5-17664\,a^3\,b^6+5120\,a^2\,b^7}{256\,\left(a\,b^5-b^6\right)}+\left(\left(\frac{49152\,a^6\,b^7-167936\,a^5\,b^8+208896\,a^4\,b^9-110592\,a^3\,b^{10}+20480\,a^2\,b^{11}}{256\,\left(a\,b^5-b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3072\,a^6\,b^3-16320\,a^5\,b^4+26688\,a^4\,b^5-17664\,a^3\,b^6+5120\,a^2\,b^7}{256\,\left(a\,b^5-b^6\right)}+\left(\left(\frac{49152\,a^6\,b^7-167936\,a^5\,b^8+208896\,a^4\,b^9-110592\,a^3\,b^{10}+20480\,a^2\,b^{11}}{256\,\left(a\,b^5-b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\left(\left(\frac{3072\,a^6\,b^3-16320\,a^5\,b^4+26688\,a^4\,b^5-17664\,a^3\,b^6+5120\,a^2\,b^7}{256\,\left(a\,b^5-b^6\right)}+\left(\left(\frac{49152\,a^6\,b^7-167936\,a^5\,b^8+208896\,a^4\,b^9-110592\,a^3\,b^{10}+20480\,a^2\,b^{11}}{256\,\left(a\,b^5-b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,\left(-98304\,a^6\,b^8+196608\,a^5\,b^9-196608\,a^3\,b^{11}+98304\,a^2\,b^{12}\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-18432\,a^6\,b^4+20864\,a^5\,b^5+54912\,a^4\,b^6-84864\,a^3\,b^7+21376\,a^2\,b^8\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(768\,a^6-5295\,a^4\,b^2+4832\,a^3\,b^3+800\,a^2\,b^4\right)}{128\,\left(a\,b^4-b^5\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}-\frac{656\,a^5-2049\,a^4\,b+1600\,a^3\,b^2}{128\,\left(a\,b^5-b^6\right)}}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a\,b^9}+25\,b^2\,\sqrt{a\,b^9}+35\,a\,b^6-47\,a^2\,b^5+16\,a^3\,b^4-29\,a\,b\,\sqrt{a\,b^9}}{256\,\left(a^3\,b^8-3\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((((5120*a^2*b^7 - 17664*a^3*b^6 + 26688*a^4*b^5 - 16320*a^5*b^4 + 3072*a^6*b^3)/(256*(a*b^5 - b^6)) + (((20480*a^2*b^11 - 110592*a^3*b^10 + 208896*a^4*b^9 - 167936*a^5*b^8 + 49152*a^6*b^7)/(256*(a*b^5 - b^6)) - (tan(c + d*x)*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*1i - (((5120*a^2*b^7 - 17664*a^3*b^6 + 26688*a^4*b^5 - 16320*a^5*b^4 + 3072*a^6*b^3)/(256*(a*b^5 - b^6)) + (((20480*a^2*b^11 - 110592*a^3*b^10 + 208896*a^4*b^9 - 167936*a^5*b^8 + 49152*a^6*b^7)/(256*(a*b^5 - b^6)) + (tan(c + d*x)*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*1i)/((((5120*a^2*b^7 - 17664*a^3*b^6 + 26688*a^4*b^5 - 16320*a^5*b^4 + 3072*a^6*b^3)/(256*(a*b^5 - b^6)) + (((20480*a^2*b^11 - 110592*a^3*b^10 + 208896*a^4*b^9 - 167936*a^5*b^8 + 49152*a^6*b^7)/(256*(a*b^5 - b^6)) - (tan(c + d*x)*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (((5120*a^2*b^7 - 17664*a^3*b^6 + 26688*a^4*b^5 - 16320*a^5*b^4 + 3072*a^6*b^3)/(256*(a*b^5 - b^6)) + (((20480*a^2*b^11 - 110592*a^3*b^10 + 208896*a^4*b^9 - 167936*a^5*b^8 + 49152*a^6*b^7)/(256*(a*b^5 - b^6)) + (tan(c + d*x)*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(128*(a*b^4 - b^5)))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (656*a^5 - 2049*a^4*b + 1600*a^3*b^2)/(128*(a*b^5 - b^6))))*((8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) - 35*a*b^6 + 47*a^2*b^5 - 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*2i)/d + (atan(((((5120*a^2*b^7 - 17664*a^3*b^6 + 26688*a^4*b^5 - 16320*a^5*b^4 + 3072*a^6*b^3)/(256*(a*b^5 - b^6)) + (((20480*a^2*b^11 - 110592*a^3*b^10 + 208896*a^4*b^9 - 167936*a^5*b^8 + 49152*a^6*b^7)/(256*(a*b^5 - b^6)) - (tan(c + d*x)*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*1i - (((5120*a^2*b^7 - 17664*a^3*b^6 + 26688*a^4*b^5 - 16320*a^5*b^4 + 3072*a^6*b^3)/(256*(a*b^5 - b^6)) + (((20480*a^2*b^11 - 110592*a^3*b^10 + 208896*a^4*b^9 - 167936*a^5*b^8 + 49152*a^6*b^7)/(256*(a*b^5 - b^6)) + (tan(c + d*x)*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*1i)/((((5120*a^2*b^7 - 17664*a^3*b^6 + 26688*a^4*b^5 - 16320*a^5*b^4 + 3072*a^6*b^3)/(256*(a*b^5 - b^6)) + (((20480*a^2*b^11 - 110592*a^3*b^10 + 208896*a^4*b^9 - 167936*a^5*b^8 + 49152*a^6*b^7)/(256*(a*b^5 - b^6)) - (tan(c + d*x)*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (((5120*a^2*b^7 - 17664*a^3*b^6 + 26688*a^4*b^5 - 16320*a^5*b^4 + 3072*a^6*b^3)/(256*(a*b^5 - b^6)) + (((20480*a^2*b^11 - 110592*a^3*b^10 + 208896*a^4*b^9 - 167936*a^5*b^8 + 49152*a^6*b^7)/(256*(a*b^5 - b^6)) + (tan(c + d*x)*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) + (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(128*(a*b^4 - b^5)))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2) - (656*a^5 - 2049*a^4*b + 1600*a^3*b^2)/(128*(a*b^5 - b^6))))*(-(8*a^2*(a*b^9)^(1/2) + 25*b^2*(a*b^9)^(1/2) + 35*a*b^6 - 47*a^2*b^5 + 16*a^3*b^4 - 29*a*b*(a*b^9)^(1/2))/(256*(3*a*b^10 - b^11 - 3*a^2*b^9 + a^3*b^8)))^(1/2)*2i)/d - atan((((((((((80*a^2*b^11 - 432*a^3*b^10 + 816*a^4*b^9 - 656*a^5*b^8 + 192*a^6*b^7)*1i)/(2*(a*b^5 - b^6)) - (tan(c + d*x)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(512*b^2*(a*b^4 - b^5)))*1i)/(2*b^2) + (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4)*1i)/(256*(a*b^4 - b^5)))*1i)/(2*b^2) + ((20*a^2*b^7 - 69*a^3*b^6 + (417*a^4*b^5)/4 - (255*a^5*b^4)/4 + 12*a^6*b^3)*1i)/(2*(a*b^5 - b^6)))/(2*b^2) - (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(256*(a*b^4 - b^5)))/b^2 - ((((((((80*a^2*b^11 - 432*a^3*b^10 + 816*a^4*b^9 - 656*a^5*b^8 + 192*a^6*b^7)*1i)/(2*(a*b^5 - b^6)) + (tan(c + d*x)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(512*b^2*(a*b^4 - b^5)))*1i)/(2*b^2) - (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4)*1i)/(256*(a*b^4 - b^5)))*1i)/(2*b^2) + ((20*a^2*b^7 - 69*a^3*b^6 + (417*a^4*b^5)/4 - (255*a^5*b^4)/4 + 12*a^6*b^3)*1i)/(2*(a*b^5 - b^6)))/(2*b^2) + (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2))/(256*(a*b^4 - b^5)))/b^2)/((((((((((80*a^2*b^11 - 432*a^3*b^10 + 816*a^4*b^9 - 656*a^5*b^8 + 192*a^6*b^7)*1i)/(2*(a*b^5 - b^6)) - (tan(c + d*x)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(512*b^2*(a*b^4 - b^5)))*1i)/(2*b^2) + (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4)*1i)/(256*(a*b^4 - b^5)))*1i)/(2*b^2) + ((20*a^2*b^7 - 69*a^3*b^6 + (417*a^4*b^5)/4 - (255*a^5*b^4)/4 + 12*a^6*b^3)*1i)/(2*(a*b^5 - b^6)))*1i)/(2*b^2) - (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2)*1i)/(256*(a*b^4 - b^5)))/b^2 + (((((((((80*a^2*b^11 - 432*a^3*b^10 + 816*a^4*b^9 - 656*a^5*b^8 + 192*a^6*b^7)*1i)/(2*(a*b^5 - b^6)) + (tan(c + d*x)*(98304*a^2*b^12 - 196608*a^3*b^11 + 196608*a^5*b^9 - 98304*a^6*b^8))/(512*b^2*(a*b^4 - b^5)))*1i)/(2*b^2) - (tan(c + d*x)*(21376*a^2*b^8 - 84864*a^3*b^7 + 54912*a^4*b^6 + 20864*a^5*b^5 - 18432*a^6*b^4)*1i)/(256*(a*b^4 - b^5)))*1i)/(2*b^2) + ((20*a^2*b^7 - 69*a^3*b^6 + (417*a^4*b^5)/4 - (255*a^5*b^4)/4 + 12*a^6*b^3)*1i)/(2*(a*b^5 - b^6)))*1i)/(2*b^2) + (tan(c + d*x)*(768*a^6 + 800*a^2*b^4 + 4832*a^3*b^3 - 5295*a^4*b^2)*1i)/(256*(a*b^4 - b^5)))/b^2 - ((41*a^5)/8 - (2049*a^4*b)/128 + (25*a^3*b^2)/2)/(a*b^5 - b^6)))/(b^2*d) - ((a*tan(c + d*x)^3)/(2*b*(a - b)) + (a*tan(c + d*x))/(4*b*(a - b)))/(d*(a + 2*a*tan(c + d*x)^2 + tan(c + d*x)^4*(a - b)))","B"
219,1,3400,233,16.544869,"\text{Not used}","int(sin(c + d*x)^6/(a - b*sin(c + d*x)^4)^2,x)","-\frac{\frac{a\,\mathrm{tan}\left(c+d\,x\right)}{4\,\left(a\,b-b^2\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(a+b\right)}{4\,\left(a\,b-b^2\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^4+2\,a\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{256\,a^4\,b^3-512\,a^3\,b^4+256\,a^2\,b^5}{64\,\left(a\,b^3-b^4\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,\left(-256\,a^5\,b^3+768\,a^4\,b^4-768\,a^3\,b^5+256\,a^2\,b^6\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-15\,a^3\,b+10\,a^2\,b^2+9\,a\,b^3\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,1{}\mathrm{i}-\left(\left(\frac{256\,a^4\,b^3-512\,a^3\,b^4+256\,a^2\,b^5}{64\,\left(a\,b^3-b^4\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,\left(-256\,a^5\,b^3+768\,a^4\,b^4-768\,a^3\,b^5+256\,a^2\,b^6\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-15\,a^3\,b+10\,a^2\,b^2+9\,a\,b^3\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,1{}\mathrm{i}}{\frac{4\,a^3-21\,a^2\,b+27\,a\,b^2}{32\,\left(a\,b^3-b^4\right)}+\left(\left(\frac{256\,a^4\,b^3-512\,a^3\,b^4+256\,a^2\,b^5}{64\,\left(a\,b^3-b^4\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,\left(-256\,a^5\,b^3+768\,a^4\,b^4-768\,a^3\,b^5+256\,a^2\,b^6\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-15\,a^3\,b+10\,a^2\,b^2+9\,a\,b^3\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}+\left(\left(\frac{256\,a^4\,b^3-512\,a^3\,b^4+256\,a^2\,b^5}{64\,\left(a\,b^3-b^4\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,\left(-256\,a^5\,b^3+768\,a^4\,b^4-768\,a^3\,b^5+256\,a^2\,b^6\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-15\,a^3\,b+10\,a^2\,b^2+9\,a\,b^3\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}}\right)\,\sqrt{\frac{15\,a\,b^5-5\,a\,\sqrt{a\,b^9}+9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{256\,a^4\,b^3-512\,a^3\,b^4+256\,a^2\,b^5}{64\,\left(a\,b^3-b^4\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,\left(-256\,a^5\,b^3+768\,a^4\,b^4-768\,a^3\,b^5+256\,a^2\,b^6\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-15\,a^3\,b+10\,a^2\,b^2+9\,a\,b^3\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,1{}\mathrm{i}-\left(\left(\frac{256\,a^4\,b^3-512\,a^3\,b^4+256\,a^2\,b^5}{64\,\left(a\,b^3-b^4\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,\left(-256\,a^5\,b^3+768\,a^4\,b^4-768\,a^3\,b^5+256\,a^2\,b^6\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-15\,a^3\,b+10\,a^2\,b^2+9\,a\,b^3\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,1{}\mathrm{i}}{\frac{4\,a^3-21\,a^2\,b+27\,a\,b^2}{32\,\left(a\,b^3-b^4\right)}+\left(\left(\frac{256\,a^4\,b^3-512\,a^3\,b^4+256\,a^2\,b^5}{64\,\left(a\,b^3-b^4\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,\left(-256\,a^5\,b^3+768\,a^4\,b^4-768\,a^3\,b^5+256\,a^2\,b^6\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-15\,a^3\,b+10\,a^2\,b^2+9\,a\,b^3\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}+\left(\left(\frac{256\,a^4\,b^3-512\,a^3\,b^4+256\,a^2\,b^5}{64\,\left(a\,b^3-b^4\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,\left(-256\,a^5\,b^3+768\,a^4\,b^4-768\,a^3\,b^5+256\,a^2\,b^6\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-15\,a^3\,b+10\,a^2\,b^2+9\,a\,b^3\right)}{4\,\left(a\,b^2-b^3\right)}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}}\right)\,\sqrt{\frac{15\,a\,b^5+5\,a\,\sqrt{a\,b^9}-9\,b\,\sqrt{a\,b^9}-15\,a^2\,b^4+4\,a^3\,b^3}{256\,\left(-a^4\,b^6+3\,a^3\,b^7-3\,a^2\,b^8+a\,b^9\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((((256*a^2*b^5 - 512*a^3*b^4 + 256*a^4*b^3)/(64*(a*b^3 - b^4)) - (tan(c + d*x)*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*(256*a^2*b^6 - 768*a^3*b^5 + 768*a^4*b^4 - 256*a^5*b^3))/(4*(a*b^2 - b^3)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) + (tan(c + d*x)*(9*a*b^3 - 15*a^3*b + 4*a^4 + 10*a^2*b^2))/(4*(a*b^2 - b^3)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*1i - (((256*a^2*b^5 - 512*a^3*b^4 + 256*a^4*b^3)/(64*(a*b^3 - b^4)) + (tan(c + d*x)*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*(256*a^2*b^6 - 768*a^3*b^5 + 768*a^4*b^4 - 256*a^5*b^3))/(4*(a*b^2 - b^3)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) - (tan(c + d*x)*(9*a*b^3 - 15*a^3*b + 4*a^4 + 10*a^2*b^2))/(4*(a*b^2 - b^3)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*1i)/((27*a*b^2 - 21*a^2*b + 4*a^3)/(32*(a*b^3 - b^4)) + (((256*a^2*b^5 - 512*a^3*b^4 + 256*a^4*b^3)/(64*(a*b^3 - b^4)) - (tan(c + d*x)*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*(256*a^2*b^6 - 768*a^3*b^5 + 768*a^4*b^4 - 256*a^5*b^3))/(4*(a*b^2 - b^3)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) + (tan(c + d*x)*(9*a*b^3 - 15*a^3*b + 4*a^4 + 10*a^2*b^2))/(4*(a*b^2 - b^3)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) + (((256*a^2*b^5 - 512*a^3*b^4 + 256*a^4*b^3)/(64*(a*b^3 - b^4)) + (tan(c + d*x)*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*(256*a^2*b^6 - 768*a^3*b^5 + 768*a^4*b^4 - 256*a^5*b^3))/(4*(a*b^2 - b^3)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) - (tan(c + d*x)*(9*a*b^3 - 15*a^3*b + 4*a^4 + 10*a^2*b^2))/(4*(a*b^2 - b^3)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)))*((15*a*b^5 - 5*a*(a*b^9)^(1/2) + 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*2i)/d + (atan(((((256*a^2*b^5 - 512*a^3*b^4 + 256*a^4*b^3)/(64*(a*b^3 - b^4)) - (tan(c + d*x)*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*(256*a^2*b^6 - 768*a^3*b^5 + 768*a^4*b^4 - 256*a^5*b^3))/(4*(a*b^2 - b^3)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) + (tan(c + d*x)*(9*a*b^3 - 15*a^3*b + 4*a^4 + 10*a^2*b^2))/(4*(a*b^2 - b^3)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*1i - (((256*a^2*b^5 - 512*a^3*b^4 + 256*a^4*b^3)/(64*(a*b^3 - b^4)) + (tan(c + d*x)*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*(256*a^2*b^6 - 768*a^3*b^5 + 768*a^4*b^4 - 256*a^5*b^3))/(4*(a*b^2 - b^3)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) - (tan(c + d*x)*(9*a*b^3 - 15*a^3*b + 4*a^4 + 10*a^2*b^2))/(4*(a*b^2 - b^3)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*1i)/((27*a*b^2 - 21*a^2*b + 4*a^3)/(32*(a*b^3 - b^4)) + (((256*a^2*b^5 - 512*a^3*b^4 + 256*a^4*b^3)/(64*(a*b^3 - b^4)) - (tan(c + d*x)*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*(256*a^2*b^6 - 768*a^3*b^5 + 768*a^4*b^4 - 256*a^5*b^3))/(4*(a*b^2 - b^3)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) + (tan(c + d*x)*(9*a*b^3 - 15*a^3*b + 4*a^4 + 10*a^2*b^2))/(4*(a*b^2 - b^3)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) + (((256*a^2*b^5 - 512*a^3*b^4 + 256*a^4*b^3)/(64*(a*b^3 - b^4)) + (tan(c + d*x)*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*(256*a^2*b^6 - 768*a^3*b^5 + 768*a^4*b^4 - 256*a^5*b^3))/(4*(a*b^2 - b^3)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2) - (tan(c + d*x)*(9*a*b^3 - 15*a^3*b + 4*a^4 + 10*a^2*b^2))/(4*(a*b^2 - b^3)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)))*((15*a*b^5 + 5*a*(a*b^9)^(1/2) - 9*b*(a*b^9)^(1/2) - 15*a^2*b^4 + 4*a^3*b^3)/(256*(a*b^9 - 3*a^2*b^8 + 3*a^3*b^7 - a^4*b^6)))^(1/2)*2i)/d - ((a*tan(c + d*x))/(4*(a*b - b^2)) + (tan(c + d*x)^3*(a + b))/(4*(a*b - b^2)))/(d*(a + 2*a*tan(c + d*x)^2 + tan(c + d*x)^4*(a - b)))","B"
220,1,2980,195,15.989901,"\text{Not used}","int(sin(c + d*x)^4/(a - b*sin(c + d*x)^4)^2,x)","-\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{2\,\left(a-b\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)}{4\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^4+2\,a\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{128\,a^3\,b-256\,a^2\,b^2+128\,a\,b^3}{32\,\left(a-b\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,\left(256\,a^5\,b-768\,a^4\,b^2+768\,a^3\,b^3-256\,a^2\,b^4\right)}{4\,\left(a-b\right)}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2+6\,a\,b+b^2\right)}{4\,\left(a-b\right)}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{128\,a^3\,b-256\,a^2\,b^2+128\,a\,b^3}{32\,\left(a-b\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,\left(256\,a^5\,b-768\,a^4\,b^2+768\,a^3\,b^3-256\,a^2\,b^4\right)}{4\,\left(a-b\right)}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2+6\,a\,b+b^2\right)}{4\,\left(a-b\right)}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{128\,a^3\,b-256\,a^2\,b^2+128\,a\,b^3}{32\,\left(a-b\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,\left(256\,a^5\,b-768\,a^4\,b^2+768\,a^3\,b^3-256\,a^2\,b^4\right)}{4\,\left(a-b\right)}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2+6\,a\,b+b^2\right)}{4\,\left(a-b\right)}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}+\left(\left(\frac{128\,a^3\,b-256\,a^2\,b^2+128\,a\,b^3}{32\,\left(a-b\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,\left(256\,a^5\,b-768\,a^4\,b^2+768\,a^3\,b^3-256\,a^2\,b^4\right)}{4\,\left(a-b\right)}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2+6\,a\,b+b^2\right)}{4\,\left(a-b\right)}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}-\frac{1}{16\,\left(a-b\right)}}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{128\,a^3\,b-256\,a^2\,b^2+128\,a\,b^3}{32\,\left(a-b\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,\left(256\,a^5\,b-768\,a^4\,b^2+768\,a^3\,b^3-256\,a^2\,b^4\right)}{4\,\left(a-b\right)}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2+6\,a\,b+b^2\right)}{4\,\left(a-b\right)}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{128\,a^3\,b-256\,a^2\,b^2+128\,a\,b^3}{32\,\left(a-b\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,\left(256\,a^5\,b-768\,a^4\,b^2+768\,a^3\,b^3-256\,a^2\,b^4\right)}{4\,\left(a-b\right)}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2+6\,a\,b+b^2\right)}{4\,\left(a-b\right)}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{128\,a^3\,b-256\,a^2\,b^2+128\,a\,b^3}{32\,\left(a-b\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,\left(256\,a^5\,b-768\,a^4\,b^2+768\,a^3\,b^3-256\,a^2\,b^4\right)}{4\,\left(a-b\right)}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2+6\,a\,b+b^2\right)}{4\,\left(a-b\right)}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}+\left(\left(\frac{128\,a^3\,b-256\,a^2\,b^2+128\,a\,b^3}{32\,\left(a-b\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,\left(256\,a^5\,b-768\,a^4\,b^2+768\,a^3\,b^3-256\,a^2\,b^4\right)}{4\,\left(a-b\right)}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a^2+6\,a\,b+b^2\right)}{4\,\left(a-b\right)}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}-\frac{1}{16\,\left(a-b\right)}}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{256\,\left(-a^6\,b^2+3\,a^5\,b^3-3\,a^4\,b^4+a^3\,b^5\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- (atan(((((128*a*b^3 + 128*a^3*b - 256*a^2*b^2)/(32*(a - b)) - (tan(c + d*x)*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*(256*a^5*b - 256*a^2*b^4 + 768*a^3*b^3 - 768*a^4*b^2))/(4*(a - b)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) - (tan(c + d*x)*(6*a*b + a^2 + b^2))/(4*(a - b)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*1i - (((128*a*b^3 + 128*a^3*b - 256*a^2*b^2)/(32*(a - b)) + (tan(c + d*x)*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*(256*a^5*b - 256*a^2*b^4 + 768*a^3*b^3 - 768*a^4*b^2))/(4*(a - b)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) + (tan(c + d*x)*(6*a*b + a^2 + b^2))/(4*(a - b)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*1i)/((((128*a*b^3 + 128*a^3*b - 256*a^2*b^2)/(32*(a - b)) - (tan(c + d*x)*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*(256*a^5*b - 256*a^2*b^4 + 768*a^3*b^3 - 768*a^4*b^2))/(4*(a - b)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) - (tan(c + d*x)*(6*a*b + a^2 + b^2))/(4*(a - b)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) + (((128*a*b^3 + 128*a^3*b - 256*a^2*b^2)/(32*(a - b)) + (tan(c + d*x)*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*(256*a^5*b - 256*a^2*b^4 + 768*a^3*b^3 - 768*a^4*b^2))/(4*(a - b)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) + (tan(c + d*x)*(6*a*b + a^2 + b^2))/(4*(a - b)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) - 1/(16*(a - b))))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*2i)/d - (atan(((((128*a*b^3 + 128*a^3*b - 256*a^2*b^2)/(32*(a - b)) - (tan(c + d*x)*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*(256*a^5*b - 256*a^2*b^4 + 768*a^3*b^3 - 768*a^4*b^2))/(4*(a - b)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) - (tan(c + d*x)*(6*a*b + a^2 + b^2))/(4*(a - b)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*1i - (((128*a*b^3 + 128*a^3*b - 256*a^2*b^2)/(32*(a - b)) + (tan(c + d*x)*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*(256*a^5*b - 256*a^2*b^4 + 768*a^3*b^3 - 768*a^4*b^2))/(4*(a - b)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) + (tan(c + d*x)*(6*a*b + a^2 + b^2))/(4*(a - b)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*1i)/((((128*a*b^3 + 128*a^3*b - 256*a^2*b^2)/(32*(a - b)) - (tan(c + d*x)*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*(256*a^5*b - 256*a^2*b^4 + 768*a^3*b^3 - 768*a^4*b^2))/(4*(a - b)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) - (tan(c + d*x)*(6*a*b + a^2 + b^2))/(4*(a - b)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) + (((128*a*b^3 + 128*a^3*b - 256*a^2*b^2)/(32*(a - b)) + (tan(c + d*x)*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*(256*a^5*b - 256*a^2*b^4 + 768*a^3*b^3 - 768*a^4*b^2))/(4*(a - b)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) + (tan(c + d*x)*(6*a*b + a^2 + b^2))/(4*(a - b)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2) - 1/(16*(a - b))))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(256*(a^3*b^5 - 3*a^4*b^4 + 3*a^5*b^3 - a^6*b^2)))^(1/2)*2i)/d - (tan(c + d*x)^3/(2*(a - b)) + tan(c + d*x)/(4*(a - b)))/(d*(a + 2*a*tan(c + d*x)^2 + tan(c + d*x)^4*(a - b)))","B"
221,1,3842,219,17.349481,"\text{Not used}","int(sin(c + d*x)^2/(a - b*sin(c + d*x)^4)^2,x)","-\frac{\frac{\mathrm{tan}\left(c+d\,x\right)}{4\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(a+b\right)}{4\,a\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^4+2\,a\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{256\,a^5\,b-512\,a^4\,b^2+256\,a^3\,b^3}{64\,\left(a^2\,b-a^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,\left(256\,a^6\,b-768\,a^5\,b^2+768\,a^4\,b^3-256\,a^3\,b^4\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3+9\,a^2\,b-6\,a\,b^2+b^3\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{256\,a^5\,b-512\,a^4\,b^2+256\,a^3\,b^3}{64\,\left(a^2\,b-a^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,\left(256\,a^6\,b-768\,a^5\,b^2+768\,a^4\,b^3-256\,a^3\,b^4\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3+9\,a^2\,b-6\,a\,b^2+b^3\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{256\,a^5\,b-512\,a^4\,b^2+256\,a^3\,b^3}{64\,\left(a^2\,b-a^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,\left(256\,a^6\,b-768\,a^5\,b^2+768\,a^4\,b^3-256\,a^3\,b^4\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3+9\,a^2\,b-6\,a\,b^2+b^3\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}-\frac{12\,a^2-7\,a\,b+b^2}{32\,\left(a^2\,b-a^3\right)}+\left(\left(\frac{256\,a^5\,b-512\,a^4\,b^2+256\,a^3\,b^3}{64\,\left(a^2\,b-a^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,\left(256\,a^6\,b-768\,a^5\,b^2+768\,a^4\,b^3-256\,a^3\,b^4\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3+9\,a^2\,b-6\,a\,b^2+b^3\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}}\right)\,\sqrt{-\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}-4\,a^5\,b+a^3\,b^3-a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{256\,a^5\,b-512\,a^4\,b^2+256\,a^3\,b^3}{64\,\left(a^2\,b-a^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,\left(256\,a^6\,b-768\,a^5\,b^2+768\,a^4\,b^3-256\,a^3\,b^4\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3+9\,a^2\,b-6\,a\,b^2+b^3\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{256\,a^5\,b-512\,a^4\,b^2+256\,a^3\,b^3}{64\,\left(a^2\,b-a^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,\left(256\,a^6\,b-768\,a^5\,b^2+768\,a^4\,b^3-256\,a^3\,b^4\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3+9\,a^2\,b-6\,a\,b^2+b^3\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{256\,a^5\,b-512\,a^4\,b^2+256\,a^3\,b^3}{64\,\left(a^2\,b-a^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,\left(256\,a^6\,b-768\,a^5\,b^2+768\,a^4\,b^3-256\,a^3\,b^4\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3+9\,a^2\,b-6\,a\,b^2+b^3\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}-\frac{12\,a^2-7\,a\,b+b^2}{32\,\left(a^2\,b-a^3\right)}+\left(\left(\frac{256\,a^5\,b-512\,a^4\,b^2+256\,a^3\,b^3}{64\,\left(a^2\,b-a^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,\left(256\,a^6\,b-768\,a^5\,b^2+768\,a^4\,b^3-256\,a^3\,b^4\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3+9\,a^2\,b-6\,a\,b^2+b^3\right)}{4\,\left(a\,b-a^2\right)}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}}\right)\,\sqrt{\frac{8\,a^2\,\sqrt{a^5\,b^3}+b^2\,\sqrt{a^5\,b^3}+4\,a^5\,b-a^3\,b^3+a^4\,b^2-5\,a\,b\,\sqrt{a^5\,b^3}}{256\,\left(-a^8\,b^2+3\,a^7\,b^3-3\,a^6\,b^4+a^5\,b^5\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- (tan(c + d*x)/(4*(a - b)) + (tan(c + d*x)^3*(a + b))/(4*a*(a - b)))/(d*(a + 2*a*tan(c + d*x)^2 + tan(c + d*x)^4*(a - b))) - (atan(((((256*a^5*b + 256*a^3*b^3 - 512*a^4*b^2)/(64*(a^2*b - a^3)) - (tan(c + d*x)*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*(256*a^6*b - 256*a^3*b^4 + 768*a^4*b^3 - 768*a^5*b^2))/(4*(a*b - a^2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) - (tan(c + d*x)*(9*a^2*b - 6*a*b^2 + 4*a^3 + b^3))/(4*(a*b - a^2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*1i - (((256*a^5*b + 256*a^3*b^3 - 512*a^4*b^2)/(64*(a^2*b - a^3)) + (tan(c + d*x)*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*(256*a^6*b - 256*a^3*b^4 + 768*a^4*b^3 - 768*a^5*b^2))/(4*(a*b - a^2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) + (tan(c + d*x)*(9*a^2*b - 6*a*b^2 + 4*a^3 + b^3))/(4*(a*b - a^2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*1i)/((((256*a^5*b + 256*a^3*b^3 - 512*a^4*b^2)/(64*(a^2*b - a^3)) - (tan(c + d*x)*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*(256*a^6*b - 256*a^3*b^4 + 768*a^4*b^3 - 768*a^5*b^2))/(4*(a*b - a^2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) - (tan(c + d*x)*(9*a^2*b - 6*a*b^2 + 4*a^3 + b^3))/(4*(a*b - a^2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) - (12*a^2 - 7*a*b + b^2)/(32*(a^2*b - a^3)) + (((256*a^5*b + 256*a^3*b^3 - 512*a^4*b^2)/(64*(a^2*b - a^3)) + (tan(c + d*x)*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*(256*a^6*b - 256*a^3*b^4 + 768*a^4*b^3 - 768*a^5*b^2))/(4*(a*b - a^2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) + (tan(c + d*x)*(9*a^2*b - 6*a*b^2 + 4*a^3 + b^3))/(4*(a*b - a^2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)))*(-(8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) - 4*a^5*b + a^3*b^3 - a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*2i)/d - (atan(((((256*a^5*b + 256*a^3*b^3 - 512*a^4*b^2)/(64*(a^2*b - a^3)) - (tan(c + d*x)*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*(256*a^6*b - 256*a^3*b^4 + 768*a^4*b^3 - 768*a^5*b^2))/(4*(a*b - a^2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) - (tan(c + d*x)*(9*a^2*b - 6*a*b^2 + 4*a^3 + b^3))/(4*(a*b - a^2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*1i - (((256*a^5*b + 256*a^3*b^3 - 512*a^4*b^2)/(64*(a^2*b - a^3)) + (tan(c + d*x)*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*(256*a^6*b - 256*a^3*b^4 + 768*a^4*b^3 - 768*a^5*b^2))/(4*(a*b - a^2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) + (tan(c + d*x)*(9*a^2*b - 6*a*b^2 + 4*a^3 + b^3))/(4*(a*b - a^2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*1i)/((((256*a^5*b + 256*a^3*b^3 - 512*a^4*b^2)/(64*(a^2*b - a^3)) - (tan(c + d*x)*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*(256*a^6*b - 256*a^3*b^4 + 768*a^4*b^3 - 768*a^5*b^2))/(4*(a*b - a^2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) - (tan(c + d*x)*(9*a^2*b - 6*a*b^2 + 4*a^3 + b^3))/(4*(a*b - a^2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) - (12*a^2 - 7*a*b + b^2)/(32*(a^2*b - a^3)) + (((256*a^5*b + 256*a^3*b^3 - 512*a^4*b^2)/(64*(a^2*b - a^3)) + (tan(c + d*x)*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*(256*a^6*b - 256*a^3*b^4 + 768*a^4*b^3 - 768*a^5*b^2))/(4*(a*b - a^2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2) + (tan(c + d*x)*(9*a^2*b - 6*a*b^2 + 4*a^3 + b^3))/(4*(a*b - a^2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)))*((8*a^2*(a^5*b^3)^(1/2) + b^2*(a^5*b^3)^(1/2) + 4*a^5*b - a^3*b^3 + a^4*b^2 - 5*a*b*(a^5*b^3)^(1/2))/(256*(a^5*b^5 - 3*a^6*b^4 + 3*a^7*b^3 - a^8*b^2)))^(1/2)*2i)/d","B"
222,1,3675,210,16.516184,"\text{Not used}","int(1/(a - b*sin(c + d*x)^4)^2,x)","-\frac{\frac{b\,{\mathrm{tan}\left(c+d\,x\right)}^3}{2\,a\,\left(a-b\right)}+\frac{b\,\mathrm{tan}\left(c+d\,x\right)}{4\,a\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^4+2\,a\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{512\,a^6\,b-1408\,a^5\,b^2+1280\,a^4\,b^3-384\,a^3\,b^4}{32\,\left(a^3\,b-a^4\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,\left(256\,a^7\,b-768\,a^6\,b^2+768\,a^5\,b^3-256\,a^4\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^3\,b+9\,a^2\,b^2-26\,a\,b^3+9\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{512\,a^6\,b-1408\,a^5\,b^2+1280\,a^4\,b^3-384\,a^3\,b^4}{32\,\left(a^3\,b-a^4\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,\left(256\,a^7\,b-768\,a^6\,b^2+768\,a^5\,b^3-256\,a^4\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^3\,b+9\,a^2\,b^2-26\,a\,b^3+9\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,1{}\mathrm{i}}{\frac{32\,a^2\,b-34\,a\,b^2+9\,b^3}{16\,\left(a^3\,b-a^4\right)}+\left(\left(\frac{512\,a^6\,b-1408\,a^5\,b^2+1280\,a^4\,b^3-384\,a^3\,b^4}{32\,\left(a^3\,b-a^4\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,\left(256\,a^7\,b-768\,a^6\,b^2+768\,a^5\,b^3-256\,a^4\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^3\,b+9\,a^2\,b^2-26\,a\,b^3+9\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}+\left(\left(\frac{512\,a^6\,b-1408\,a^5\,b^2+1280\,a^4\,b^3-384\,a^3\,b^4}{32\,\left(a^3\,b-a^4\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,\left(256\,a^7\,b-768\,a^6\,b^2+768\,a^5\,b^3-256\,a^4\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^3\,b+9\,a^2\,b^2-26\,a\,b^3+9\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}}\right)\,\sqrt{\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}-15\,a^5\,b+16\,a^6+3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{512\,a^6\,b-1408\,a^5\,b^2+1280\,a^4\,b^3-384\,a^3\,b^4}{32\,\left(a^3\,b-a^4\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,\left(256\,a^7\,b-768\,a^6\,b^2+768\,a^5\,b^3-256\,a^4\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^3\,b+9\,a^2\,b^2-26\,a\,b^3+9\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{512\,a^6\,b-1408\,a^5\,b^2+1280\,a^4\,b^3-384\,a^3\,b^4}{32\,\left(a^3\,b-a^4\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,\left(256\,a^7\,b-768\,a^6\,b^2+768\,a^5\,b^3-256\,a^4\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^3\,b+9\,a^2\,b^2-26\,a\,b^3+9\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,1{}\mathrm{i}}{\frac{32\,a^2\,b-34\,a\,b^2+9\,b^3}{16\,\left(a^3\,b-a^4\right)}+\left(\left(\frac{512\,a^6\,b-1408\,a^5\,b^2+1280\,a^4\,b^3-384\,a^3\,b^4}{32\,\left(a^3\,b-a^4\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,\left(256\,a^7\,b-768\,a^6\,b^2+768\,a^5\,b^3-256\,a^4\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^3\,b+9\,a^2\,b^2-26\,a\,b^3+9\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}+\left(\left(\frac{512\,a^6\,b-1408\,a^5\,b^2+1280\,a^4\,b^3-384\,a^3\,b^4}{32\,\left(a^3\,b-a^4\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,\left(256\,a^7\,b-768\,a^6\,b^2+768\,a^5\,b^3-256\,a^4\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^3\,b+9\,a^2\,b^2-26\,a\,b^3+9\,b^4\right)}{4\,\left(a^2\,b-a^3\right)}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}}\right)\,\sqrt{-\frac{24\,a^2\,\sqrt{a^7\,b}+9\,b^2\,\sqrt{a^7\,b}+15\,a^5\,b-16\,a^6-3\,a^4\,b^2-29\,a\,b\,\sqrt{a^7\,b}}{256\,\left(-a^{10}+3\,a^9\,b-3\,a^8\,b^2+a^7\,b^3\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- (atan(((((512*a^6*b - 384*a^3*b^4 + 1280*a^4*b^3 - 1408*a^5*b^2)/(32*(a^3*b - a^4)) - (tan(c + d*x)*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*(256*a^7*b - 256*a^4*b^4 + 768*a^5*b^3 - 768*a^6*b^2))/(4*(a^2*b - a^3)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) - (tan(c + d*x)*(16*a^3*b - 26*a*b^3 + 9*b^4 + 9*a^2*b^2))/(4*(a^2*b - a^3)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*1i - (((512*a^6*b - 384*a^3*b^4 + 1280*a^4*b^3 - 1408*a^5*b^2)/(32*(a^3*b - a^4)) + (tan(c + d*x)*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*(256*a^7*b - 256*a^4*b^4 + 768*a^5*b^3 - 768*a^6*b^2))/(4*(a^2*b - a^3)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) + (tan(c + d*x)*(16*a^3*b - 26*a*b^3 + 9*b^4 + 9*a^2*b^2))/(4*(a^2*b - a^3)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*1i)/((32*a^2*b - 34*a*b^2 + 9*b^3)/(16*(a^3*b - a^4)) + (((512*a^6*b - 384*a^3*b^4 + 1280*a^4*b^3 - 1408*a^5*b^2)/(32*(a^3*b - a^4)) - (tan(c + d*x)*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*(256*a^7*b - 256*a^4*b^4 + 768*a^5*b^3 - 768*a^6*b^2))/(4*(a^2*b - a^3)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) - (tan(c + d*x)*(16*a^3*b - 26*a*b^3 + 9*b^4 + 9*a^2*b^2))/(4*(a^2*b - a^3)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) + (((512*a^6*b - 384*a^3*b^4 + 1280*a^4*b^3 - 1408*a^5*b^2)/(32*(a^3*b - a^4)) + (tan(c + d*x)*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*(256*a^7*b - 256*a^4*b^4 + 768*a^5*b^3 - 768*a^6*b^2))/(4*(a^2*b - a^3)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) + (tan(c + d*x)*(16*a^3*b - 26*a*b^3 + 9*b^4 + 9*a^2*b^2))/(4*(a^2*b - a^3)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)))*((24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) - 15*a^5*b + 16*a^6 + 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*2i)/d - (atan(((((512*a^6*b - 384*a^3*b^4 + 1280*a^4*b^3 - 1408*a^5*b^2)/(32*(a^3*b - a^4)) - (tan(c + d*x)*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*(256*a^7*b - 256*a^4*b^4 + 768*a^5*b^3 - 768*a^6*b^2))/(4*(a^2*b - a^3)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) - (tan(c + d*x)*(16*a^3*b - 26*a*b^3 + 9*b^4 + 9*a^2*b^2))/(4*(a^2*b - a^3)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*1i - (((512*a^6*b - 384*a^3*b^4 + 1280*a^4*b^3 - 1408*a^5*b^2)/(32*(a^3*b - a^4)) + (tan(c + d*x)*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*(256*a^7*b - 256*a^4*b^4 + 768*a^5*b^3 - 768*a^6*b^2))/(4*(a^2*b - a^3)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) + (tan(c + d*x)*(16*a^3*b - 26*a*b^3 + 9*b^4 + 9*a^2*b^2))/(4*(a^2*b - a^3)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*1i)/((32*a^2*b - 34*a*b^2 + 9*b^3)/(16*(a^3*b - a^4)) + (((512*a^6*b - 384*a^3*b^4 + 1280*a^4*b^3 - 1408*a^5*b^2)/(32*(a^3*b - a^4)) - (tan(c + d*x)*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*(256*a^7*b - 256*a^4*b^4 + 768*a^5*b^3 - 768*a^6*b^2))/(4*(a^2*b - a^3)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) - (tan(c + d*x)*(16*a^3*b - 26*a*b^3 + 9*b^4 + 9*a^2*b^2))/(4*(a^2*b - a^3)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) + (((512*a^6*b - 384*a^3*b^4 + 1280*a^4*b^3 - 1408*a^5*b^2)/(32*(a^3*b - a^4)) + (tan(c + d*x)*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*(256*a^7*b - 256*a^4*b^4 + 768*a^5*b^3 - 768*a^6*b^2))/(4*(a^2*b - a^3)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2) + (tan(c + d*x)*(16*a^3*b - 26*a*b^3 + 9*b^4 + 9*a^2*b^2))/(4*(a^2*b - a^3)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)))*(-(24*a^2*(a^7*b)^(1/2) + 9*b^2*(a^7*b)^(1/2) + 15*a^5*b - 16*a^6 - 3*a^4*b^2 - 29*a*b*(a^7*b)^(1/2))/(256*(3*a^9*b - a^10 + a^7*b^3 - 3*a^8*b^2)))^(1/2)*2i)/d - ((b*tan(c + d*x)^3)/(2*a*(a - b)) + (b*tan(c + d*x))/(4*a*(a - b)))/(d*(a + 2*a*tan(c + d*x)^2 + tan(c + d*x)^4*(a - b)))","B"
223,1,4411,236,18.289589,"\text{Not used}","int(1/(sin(c + d*x)^2*(a - b*sin(c + d*x)^4)^2),x)","-\frac{\frac{1}{a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(4\,a^2-7\,a\,b+5\,b^2\right)}{4\,a^2\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(8\,a-7\,b\right)}{4\,a\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^5+2\,a\,{\mathrm{tan}\left(c+d\,x\right)}^3+a\,\mathrm{tan}\left(c+d\,x\right)\right)}+\frac{\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(4096\,a^{10}\,b^8-24576\,a^{11}\,b^7+61440\,a^{12}\,b^6-81920\,a^{13}\,b^5+61440\,a^{14}\,b^4-24576\,a^{15}\,b^3+4096\,a^{16}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(65536\,a^{19}\,b-458752\,a^{18}\,b^2+1376256\,a^{17}\,b^3-2293760\,a^{16}\,b^4+2293760\,a^{15}\,b^5-1376256\,a^{14}\,b^6+458752\,a^{13}\,b^7-65536\,a^{12}\,b^8\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(9216\,a^{14}\,b^2-36608\,a^{13}\,b^3+40448\,a^{12}\,b^4+26368\,a^{11}\,b^5-100352\,a^{10}\,b^6+93952\,a^9\,b^7-39424\,a^8\,b^8+6400\,a^7\,b^9\right)\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,1{}\mathrm{i}-\left(\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(4096\,a^{10}\,b^8-24576\,a^{11}\,b^7+61440\,a^{12}\,b^6-81920\,a^{13}\,b^5+61440\,a^{14}\,b^4-24576\,a^{15}\,b^3+4096\,a^{16}\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(65536\,a^{19}\,b-458752\,a^{18}\,b^2+1376256\,a^{17}\,b^3-2293760\,a^{16}\,b^4+2293760\,a^{15}\,b^5-1376256\,a^{14}\,b^6+458752\,a^{13}\,b^7-65536\,a^{12}\,b^8\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(9216\,a^{14}\,b^2-36608\,a^{13}\,b^3+40448\,a^{12}\,b^4+26368\,a^{11}\,b^5-100352\,a^{10}\,b^6+93952\,a^9\,b^7-39424\,a^8\,b^8+6400\,a^7\,b^9\right)\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(4096\,a^{10}\,b^8-24576\,a^{11}\,b^7+61440\,a^{12}\,b^6-81920\,a^{13}\,b^5+61440\,a^{14}\,b^4-24576\,a^{15}\,b^3+4096\,a^{16}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(65536\,a^{19}\,b-458752\,a^{18}\,b^2+1376256\,a^{17}\,b^3-2293760\,a^{16}\,b^4+2293760\,a^{15}\,b^5-1376256\,a^{14}\,b^6+458752\,a^{13}\,b^7-65536\,a^{12}\,b^8\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(9216\,a^{14}\,b^2-36608\,a^{13}\,b^3+40448\,a^{12}\,b^4+26368\,a^{11}\,b^5-100352\,a^{10}\,b^6+93952\,a^9\,b^7-39424\,a^8\,b^8+6400\,a^7\,b^9\right)\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}+\left(\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(4096\,a^{10}\,b^8-24576\,a^{11}\,b^7+61440\,a^{12}\,b^6-81920\,a^{13}\,b^5+61440\,a^{14}\,b^4-24576\,a^{15}\,b^3+4096\,a^{16}\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(65536\,a^{19}\,b-458752\,a^{18}\,b^2+1376256\,a^{17}\,b^3-2293760\,a^{16}\,b^4+2293760\,a^{15}\,b^5-1376256\,a^{14}\,b^6+458752\,a^{13}\,b^7-65536\,a^{12}\,b^8\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(9216\,a^{14}\,b^2-36608\,a^{13}\,b^3+40448\,a^{12}\,b^4+26368\,a^{11}\,b^5-100352\,a^{10}\,b^6+93952\,a^9\,b^7-39424\,a^8\,b^8+6400\,a^7\,b^9\right)\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}-4000\,a^5\,b^9+27360\,a^6\,b^8-77504\,a^7\,b^7+116416\,a^8\,b^6-97824\,a^9\,b^5+43616\,a^{10}\,b^4-8064\,a^{11}\,b^3}\right)\,\sqrt{-\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}-36\,a^7\,b-15\,a^5\,b^3+47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(4096\,a^{10}\,b^8-24576\,a^{11}\,b^7+61440\,a^{12}\,b^6-81920\,a^{13}\,b^5+61440\,a^{14}\,b^4-24576\,a^{15}\,b^3+4096\,a^{16}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(65536\,a^{19}\,b-458752\,a^{18}\,b^2+1376256\,a^{17}\,b^3-2293760\,a^{16}\,b^4+2293760\,a^{15}\,b^5-1376256\,a^{14}\,b^6+458752\,a^{13}\,b^7-65536\,a^{12}\,b^8\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(9216\,a^{14}\,b^2-36608\,a^{13}\,b^3+40448\,a^{12}\,b^4+26368\,a^{11}\,b^5-100352\,a^{10}\,b^6+93952\,a^9\,b^7-39424\,a^8\,b^8+6400\,a^7\,b^9\right)\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,1{}\mathrm{i}-\left(\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(4096\,a^{10}\,b^8-24576\,a^{11}\,b^7+61440\,a^{12}\,b^6-81920\,a^{13}\,b^5+61440\,a^{14}\,b^4-24576\,a^{15}\,b^3+4096\,a^{16}\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(65536\,a^{19}\,b-458752\,a^{18}\,b^2+1376256\,a^{17}\,b^3-2293760\,a^{16}\,b^4+2293760\,a^{15}\,b^5-1376256\,a^{14}\,b^6+458752\,a^{13}\,b^7-65536\,a^{12}\,b^8\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(9216\,a^{14}\,b^2-36608\,a^{13}\,b^3+40448\,a^{12}\,b^4+26368\,a^{11}\,b^5-100352\,a^{10}\,b^6+93952\,a^9\,b^7-39424\,a^8\,b^8+6400\,a^7\,b^9\right)\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,1{}\mathrm{i}}{\left(\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(4096\,a^{10}\,b^8-24576\,a^{11}\,b^7+61440\,a^{12}\,b^6-81920\,a^{13}\,b^5+61440\,a^{14}\,b^4-24576\,a^{15}\,b^3+4096\,a^{16}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(65536\,a^{19}\,b-458752\,a^{18}\,b^2+1376256\,a^{17}\,b^3-2293760\,a^{16}\,b^4+2293760\,a^{15}\,b^5-1376256\,a^{14}\,b^6+458752\,a^{13}\,b^7-65536\,a^{12}\,b^8\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(9216\,a^{14}\,b^2-36608\,a^{13}\,b^3+40448\,a^{12}\,b^4+26368\,a^{11}\,b^5-100352\,a^{10}\,b^6+93952\,a^9\,b^7-39424\,a^8\,b^8+6400\,a^7\,b^9\right)\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}+\left(\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(4096\,a^{10}\,b^8-24576\,a^{11}\,b^7+61440\,a^{12}\,b^6-81920\,a^{13}\,b^5+61440\,a^{14}\,b^4-24576\,a^{15}\,b^3+4096\,a^{16}\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,\left(65536\,a^{19}\,b-458752\,a^{18}\,b^2+1376256\,a^{17}\,b^3-2293760\,a^{16}\,b^4+2293760\,a^{15}\,b^5-1376256\,a^{14}\,b^6+458752\,a^{13}\,b^7-65536\,a^{12}\,b^8\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(9216\,a^{14}\,b^2-36608\,a^{13}\,b^3+40448\,a^{12}\,b^4+26368\,a^{11}\,b^5-100352\,a^{10}\,b^6+93952\,a^9\,b^7-39424\,a^8\,b^8+6400\,a^7\,b^9\right)\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}-4000\,a^5\,b^9+27360\,a^6\,b^8-77504\,a^7\,b^7+116416\,a^8\,b^6-97824\,a^9\,b^5+43616\,a^{10}\,b^4-8064\,a^{11}\,b^3}\right)\,\sqrt{\frac{48\,a^2\,\sqrt{a^9\,b^3}+25\,b^2\,\sqrt{a^9\,b^3}+36\,a^7\,b+15\,a^5\,b^3-47\,a^6\,b^2-69\,a\,b\,\sqrt{a^9\,b^3}}{256\,\left(-a^{12}+3\,a^{11}\,b-3\,a^{10}\,b^2+a^9\,b^3\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan((((-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(4096*a^10*b^8 - 24576*a^11*b^7 + 61440*a^12*b^6 - 81920*a^13*b^5 + 61440*a^14*b^4 - 24576*a^15*b^3 + 4096*a^16*b^2 + tan(c + d*x)*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(65536*a^19*b - 65536*a^12*b^8 + 458752*a^13*b^7 - 1376256*a^14*b^6 + 2293760*a^15*b^5 - 2293760*a^16*b^4 + 1376256*a^17*b^3 - 458752*a^18*b^2)) + tan(c + d*x)*(6400*a^7*b^9 - 39424*a^8*b^8 + 93952*a^9*b^7 - 100352*a^10*b^6 + 26368*a^11*b^5 + 40448*a^12*b^4 - 36608*a^13*b^3 + 9216*a^14*b^2))*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*1i - ((-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(4096*a^10*b^8 - 24576*a^11*b^7 + 61440*a^12*b^6 - 81920*a^13*b^5 + 61440*a^14*b^4 - 24576*a^15*b^3 + 4096*a^16*b^2 - tan(c + d*x)*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(65536*a^19*b - 65536*a^12*b^8 + 458752*a^13*b^7 - 1376256*a^14*b^6 + 2293760*a^15*b^5 - 2293760*a^16*b^4 + 1376256*a^17*b^3 - 458752*a^18*b^2)) - tan(c + d*x)*(6400*a^7*b^9 - 39424*a^8*b^8 + 93952*a^9*b^7 - 100352*a^10*b^6 + 26368*a^11*b^5 + 40448*a^12*b^4 - 36608*a^13*b^3 + 9216*a^14*b^2))*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*1i)/(((-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(4096*a^10*b^8 - 24576*a^11*b^7 + 61440*a^12*b^6 - 81920*a^13*b^5 + 61440*a^14*b^4 - 24576*a^15*b^3 + 4096*a^16*b^2 + tan(c + d*x)*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(65536*a^19*b - 65536*a^12*b^8 + 458752*a^13*b^7 - 1376256*a^14*b^6 + 2293760*a^15*b^5 - 2293760*a^16*b^4 + 1376256*a^17*b^3 - 458752*a^18*b^2)) + tan(c + d*x)*(6400*a^7*b^9 - 39424*a^8*b^8 + 93952*a^9*b^7 - 100352*a^10*b^6 + 26368*a^11*b^5 + 40448*a^12*b^4 - 36608*a^13*b^3 + 9216*a^14*b^2))*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2) + ((-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(4096*a^10*b^8 - 24576*a^11*b^7 + 61440*a^12*b^6 - 81920*a^13*b^5 + 61440*a^14*b^4 - 24576*a^15*b^3 + 4096*a^16*b^2 - tan(c + d*x)*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(65536*a^19*b - 65536*a^12*b^8 + 458752*a^13*b^7 - 1376256*a^14*b^6 + 2293760*a^15*b^5 - 2293760*a^16*b^4 + 1376256*a^17*b^3 - 458752*a^18*b^2)) - tan(c + d*x)*(6400*a^7*b^9 - 39424*a^8*b^8 + 93952*a^9*b^7 - 100352*a^10*b^6 + 26368*a^11*b^5 + 40448*a^12*b^4 - 36608*a^13*b^3 + 9216*a^14*b^2))*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2) - 4000*a^5*b^9 + 27360*a^6*b^8 - 77504*a^7*b^7 + 116416*a^8*b^6 - 97824*a^9*b^5 + 43616*a^10*b^4 - 8064*a^11*b^3))*(-(48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) - 36*a^7*b - 15*a^5*b^3 + 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*2i)/d - (1/a + (tan(c + d*x)^4*(4*a^2 - 7*a*b + 5*b^2))/(4*a^2*(a - b)) + (tan(c + d*x)^2*(8*a - 7*b))/(4*a*(a - b)))/(d*(a*tan(c + d*x) + 2*a*tan(c + d*x)^3 + tan(c + d*x)^5*(a - b))) + (atan(((((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(4096*a^10*b^8 - 24576*a^11*b^7 + 61440*a^12*b^6 - 81920*a^13*b^5 + 61440*a^14*b^4 - 24576*a^15*b^3 + 4096*a^16*b^2 + tan(c + d*x)*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(65536*a^19*b - 65536*a^12*b^8 + 458752*a^13*b^7 - 1376256*a^14*b^6 + 2293760*a^15*b^5 - 2293760*a^16*b^4 + 1376256*a^17*b^3 - 458752*a^18*b^2)) + tan(c + d*x)*(6400*a^7*b^9 - 39424*a^8*b^8 + 93952*a^9*b^7 - 100352*a^10*b^6 + 26368*a^11*b^5 + 40448*a^12*b^4 - 36608*a^13*b^3 + 9216*a^14*b^2))*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*1i - (((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(4096*a^10*b^8 - 24576*a^11*b^7 + 61440*a^12*b^6 - 81920*a^13*b^5 + 61440*a^14*b^4 - 24576*a^15*b^3 + 4096*a^16*b^2 - tan(c + d*x)*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(65536*a^19*b - 65536*a^12*b^8 + 458752*a^13*b^7 - 1376256*a^14*b^6 + 2293760*a^15*b^5 - 2293760*a^16*b^4 + 1376256*a^17*b^3 - 458752*a^18*b^2)) - tan(c + d*x)*(6400*a^7*b^9 - 39424*a^8*b^8 + 93952*a^9*b^7 - 100352*a^10*b^6 + 26368*a^11*b^5 + 40448*a^12*b^4 - 36608*a^13*b^3 + 9216*a^14*b^2))*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*1i)/((((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(4096*a^10*b^8 - 24576*a^11*b^7 + 61440*a^12*b^6 - 81920*a^13*b^5 + 61440*a^14*b^4 - 24576*a^15*b^3 + 4096*a^16*b^2 + tan(c + d*x)*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(65536*a^19*b - 65536*a^12*b^8 + 458752*a^13*b^7 - 1376256*a^14*b^6 + 2293760*a^15*b^5 - 2293760*a^16*b^4 + 1376256*a^17*b^3 - 458752*a^18*b^2)) + tan(c + d*x)*(6400*a^7*b^9 - 39424*a^8*b^8 + 93952*a^9*b^7 - 100352*a^10*b^6 + 26368*a^11*b^5 + 40448*a^12*b^4 - 36608*a^13*b^3 + 9216*a^14*b^2))*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2) + (((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(4096*a^10*b^8 - 24576*a^11*b^7 + 61440*a^12*b^6 - 81920*a^13*b^5 + 61440*a^14*b^4 - 24576*a^15*b^3 + 4096*a^16*b^2 - tan(c + d*x)*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*(65536*a^19*b - 65536*a^12*b^8 + 458752*a^13*b^7 - 1376256*a^14*b^6 + 2293760*a^15*b^5 - 2293760*a^16*b^4 + 1376256*a^17*b^3 - 458752*a^18*b^2)) - tan(c + d*x)*(6400*a^7*b^9 - 39424*a^8*b^8 + 93952*a^9*b^7 - 100352*a^10*b^6 + 26368*a^11*b^5 + 40448*a^12*b^4 - 36608*a^13*b^3 + 9216*a^14*b^2))*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2) - 4000*a^5*b^9 + 27360*a^6*b^8 - 77504*a^7*b^7 + 116416*a^8*b^6 - 97824*a^9*b^5 + 43616*a^10*b^4 - 8064*a^11*b^3))*((48*a^2*(a^9*b^3)^(1/2) + 25*b^2*(a^9*b^3)^(1/2) + 36*a^7*b + 15*a^5*b^3 - 47*a^6*b^2 - 69*a*b*(a^9*b^3)^(1/2))/(256*(3*a^11*b - a^12 + a^9*b^3 - 3*a^10*b^2)))^(1/2)*2i)/d","B"
224,1,6675,315,19.294310,"\text{Not used}","int(sin(c + d*x)^9/(a - b*sin(c + d*x)^4)^3,x)","\frac{\frac{{\cos\left(c+d\,x\right)}^7\,\left(2\,a-5\,b\right)}{16\,\left(a^2-2\,a\,b+b^2\right)}+\frac{3\,{\cos\left(c+d\,x\right)}^5\,\left(-3\,a^2+a\,b+10\,b^2\right)}{32\,b\,\left(a^2-2\,a\,b+b^2\right)}-\frac{5\,\cos\left(c+d\,x\right)\,\left(-a^2+3\,a\,b+2\,b^2\right)}{32\,b^2\,\left(a-b\right)}-\frac{3\,{\cos\left(c+d\,x\right)}^3\,\left(-3\,a^2+2\,a\,b+5\,b^2\right)}{16\,b\,{\left(a-b\right)}^2}}{d\,\left(a^2-2\,a\,b+b^2+{\cos\left(c+d\,x\right)}^2\,\left(4\,a\,b-4\,b^2\right)-{\cos\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,b^2\right)-4\,b^2\,{\cos\left(c+d\,x\right)}^6+b^2\,{\cos\left(c+d\,x\right)}^8\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{40960\,a^5\,b^4-204800\,a^4\,b^5+466944\,a^3\,b^6-483328\,a^2\,b^7+180224\,a\,b^8}{16384\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,\left(16384\,a^5\,b^5-65536\,a^4\,b^6+98304\,a^3\,b^7-65536\,a^2\,b^8+16384\,a\,b^9\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-94\,a^3\,b+161\,a^2\,b^2-164\,a\,b^3+144\,b^4\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{40960\,a^5\,b^4-204800\,a^4\,b^5+466944\,a^3\,b^6-483328\,a^2\,b^7+180224\,a\,b^8}{16384\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,\left(16384\,a^5\,b^5-65536\,a^4\,b^6+98304\,a^3\,b^7-65536\,a^2\,b^8+16384\,a\,b^9\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-94\,a^3\,b+161\,a^2\,b^2-164\,a\,b^3+144\,b^4\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{40960\,a^5\,b^4-204800\,a^4\,b^5+466944\,a^3\,b^6-483328\,a^2\,b^7+180224\,a\,b^8}{16384\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,\left(16384\,a^5\,b^5-65536\,a^4\,b^6+98304\,a^3\,b^7-65536\,a^2\,b^8+16384\,a\,b^9\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-94\,a^3\,b+161\,a^2\,b^2-164\,a\,b^3+144\,b^4\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}+\left(\left(\frac{40960\,a^5\,b^4-204800\,a^4\,b^5+466944\,a^3\,b^6-483328\,a^2\,b^7+180224\,a\,b^8}{16384\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,\left(16384\,a^5\,b^5-65536\,a^4\,b^6+98304\,a^3\,b^7-65536\,a^2\,b^8+16384\,a\,b^9\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-94\,a^3\,b+161\,a^2\,b^2-164\,a\,b^3+144\,b^4\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}-\frac{50\,a^3-277\,a^2\,b+668\,a\,b^2-720\,b^3}{8192\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}}\right)\,\sqrt{-\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}-144\,a\,b^9-76\,a^2\,b^8+155\,a^3\,b^7-94\,a^4\,b^6+15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{40960\,a^5\,b^4-204800\,a^4\,b^5+466944\,a^3\,b^6-483328\,a^2\,b^7+180224\,a\,b^8}{16384\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,\left(16384\,a^5\,b^5-65536\,a^4\,b^6+98304\,a^3\,b^7-65536\,a^2\,b^8+16384\,a\,b^9\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-94\,a^3\,b+161\,a^2\,b^2-164\,a\,b^3+144\,b^4\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{40960\,a^5\,b^4-204800\,a^4\,b^5+466944\,a^3\,b^6-483328\,a^2\,b^7+180224\,a\,b^8}{16384\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,\left(16384\,a^5\,b^5-65536\,a^4\,b^6+98304\,a^3\,b^7-65536\,a^2\,b^8+16384\,a\,b^9\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-94\,a^3\,b+161\,a^2\,b^2-164\,a\,b^3+144\,b^4\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{40960\,a^5\,b^4-204800\,a^4\,b^5+466944\,a^3\,b^6-483328\,a^2\,b^7+180224\,a\,b^8}{16384\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,\left(16384\,a^5\,b^5-65536\,a^4\,b^6+98304\,a^3\,b^7-65536\,a^2\,b^8+16384\,a\,b^9\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-94\,a^3\,b+161\,a^2\,b^2-164\,a\,b^3+144\,b^4\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}+\left(\left(\frac{40960\,a^5\,b^4-204800\,a^4\,b^5+466944\,a^3\,b^6-483328\,a^2\,b^7+180224\,a\,b^8}{16384\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,\left(16384\,a^5\,b^5-65536\,a^4\,b^6+98304\,a^3\,b^7-65536\,a^2\,b^8+16384\,a\,b^9\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^4-94\,a^3\,b+161\,a^2\,b^2-164\,a\,b^3+144\,b^4\right)}{256\,\left(a^4\,b-4\,a^3\,b^2+6\,a^2\,b^3-4\,a\,b^4+b^5\right)}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}-\frac{50\,a^3-277\,a^2\,b+668\,a\,b^2-720\,b^3}{8192\,\left(a^4\,b^3-4\,a^3\,b^4+6\,a^2\,b^5-4\,a\,b^6+b^7\right)}}\right)\,\sqrt{\frac{25\,a^4\,\sqrt{a^3\,b^9}+384\,b^4\,\sqrt{a^3\,b^9}+144\,a\,b^9+76\,a^2\,b^8-155\,a^3\,b^7+94\,a^4\,b^6-15\,a^5\,b^5+349\,a^2\,b^2\,\sqrt{a^3\,b^9}-480\,a\,b^3\,\sqrt{a^3\,b^9}-134\,a^3\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^7\,b^9+5\,a^6\,b^{10}-10\,a^5\,b^{11}+10\,a^4\,b^{12}-5\,a^3\,b^{13}+a^2\,b^{14}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"((cos(c + d*x)^7*(2*a - 5*b))/(16*(a^2 - 2*a*b + b^2)) + (3*cos(c + d*x)^5*(a*b - 3*a^2 + 10*b^2))/(32*b*(a^2 - 2*a*b + b^2)) - (5*cos(c + d*x)*(3*a*b - a^2 + 2*b^2))/(32*b^2*(a - b)) - (3*cos(c + d*x)^3*(2*a*b - 3*a^2 + 5*b^2))/(16*b*(a - b)^2))/(d*(a^2 - 2*a*b + b^2 + cos(c + d*x)^2*(4*a*b - 4*b^2) - cos(c + d*x)^4*(2*a*b - 6*b^2) - 4*b^2*cos(c + d*x)^6 + b^2*cos(c + d*x)^8)) + (atan(((((180224*a*b^8 - 483328*a^2*b^7 + 466944*a^3*b^6 - 204800*a^4*b^5 + 40960*a^5*b^4)/(16384*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3)) - (cos(c + d*x)*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*(16384*a*b^9 - 65536*a^2*b^8 + 98304*a^3*b^7 - 65536*a^4*b^6 + 16384*a^5*b^5))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) + (cos(c + d*x)*(25*a^4 - 94*a^3*b - 164*a*b^3 + 144*b^4 + 161*a^2*b^2))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*1i - (((180224*a*b^8 - 483328*a^2*b^7 + 466944*a^3*b^6 - 204800*a^4*b^5 + 40960*a^5*b^4)/(16384*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3)) + (cos(c + d*x)*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*(16384*a*b^9 - 65536*a^2*b^8 + 98304*a^3*b^7 - 65536*a^4*b^6 + 16384*a^5*b^5))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) - (cos(c + d*x)*(25*a^4 - 94*a^3*b - 164*a*b^3 + 144*b^4 + 161*a^2*b^2))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*1i)/((((180224*a*b^8 - 483328*a^2*b^7 + 466944*a^3*b^6 - 204800*a^4*b^5 + 40960*a^5*b^4)/(16384*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3)) - (cos(c + d*x)*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*(16384*a*b^9 - 65536*a^2*b^8 + 98304*a^3*b^7 - 65536*a^4*b^6 + 16384*a^5*b^5))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) + (cos(c + d*x)*(25*a^4 - 94*a^3*b - 164*a*b^3 + 144*b^4 + 161*a^2*b^2))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) + (((180224*a*b^8 - 483328*a^2*b^7 + 466944*a^3*b^6 - 204800*a^4*b^5 + 40960*a^5*b^4)/(16384*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3)) + (cos(c + d*x)*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*(16384*a*b^9 - 65536*a^2*b^8 + 98304*a^3*b^7 - 65536*a^4*b^6 + 16384*a^5*b^5))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) - (cos(c + d*x)*(25*a^4 - 94*a^3*b - 164*a*b^3 + 144*b^4 + 161*a^2*b^2))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) - (668*a*b^2 - 277*a^2*b + 50*a^3 - 720*b^3)/(8192*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3))))*(-(25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) - 144*a*b^9 - 76*a^2*b^8 + 155*a^3*b^7 - 94*a^4*b^6 + 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*2i)/d + (atan(((((180224*a*b^8 - 483328*a^2*b^7 + 466944*a^3*b^6 - 204800*a^4*b^5 + 40960*a^5*b^4)/(16384*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3)) - (cos(c + d*x)*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*(16384*a*b^9 - 65536*a^2*b^8 + 98304*a^3*b^7 - 65536*a^4*b^6 + 16384*a^5*b^5))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) + (cos(c + d*x)*(25*a^4 - 94*a^3*b - 164*a*b^3 + 144*b^4 + 161*a^2*b^2))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*1i - (((180224*a*b^8 - 483328*a^2*b^7 + 466944*a^3*b^6 - 204800*a^4*b^5 + 40960*a^5*b^4)/(16384*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3)) + (cos(c + d*x)*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*(16384*a*b^9 - 65536*a^2*b^8 + 98304*a^3*b^7 - 65536*a^4*b^6 + 16384*a^5*b^5))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) - (cos(c + d*x)*(25*a^4 - 94*a^3*b - 164*a*b^3 + 144*b^4 + 161*a^2*b^2))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*1i)/((((180224*a*b^8 - 483328*a^2*b^7 + 466944*a^3*b^6 - 204800*a^4*b^5 + 40960*a^5*b^4)/(16384*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3)) - (cos(c + d*x)*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*(16384*a*b^9 - 65536*a^2*b^8 + 98304*a^3*b^7 - 65536*a^4*b^6 + 16384*a^5*b^5))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) + (cos(c + d*x)*(25*a^4 - 94*a^3*b - 164*a*b^3 + 144*b^4 + 161*a^2*b^2))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) + (((180224*a*b^8 - 483328*a^2*b^7 + 466944*a^3*b^6 - 204800*a^4*b^5 + 40960*a^5*b^4)/(16384*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3)) + (cos(c + d*x)*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*(16384*a*b^9 - 65536*a^2*b^8 + 98304*a^3*b^7 - 65536*a^4*b^6 + 16384*a^5*b^5))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) - (cos(c + d*x)*(25*a^4 - 94*a^3*b - 164*a*b^3 + 144*b^4 + 161*a^2*b^2))/(256*(a^4*b - 4*a*b^4 + b^5 + 6*a^2*b^3 - 4*a^3*b^2)))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2) - (668*a*b^2 - 277*a^2*b + 50*a^3 - 720*b^3)/(8192*(b^7 - 4*a*b^6 + 6*a^2*b^5 - 4*a^3*b^4 + a^4*b^3))))*((25*a^4*(a^3*b^9)^(1/2) + 384*b^4*(a^3*b^9)^(1/2) + 144*a*b^9 + 76*a^2*b^8 - 155*a^3*b^7 + 94*a^4*b^6 - 15*a^5*b^5 + 349*a^2*b^2*(a^3*b^9)^(1/2) - 480*a*b^3*(a^3*b^9)^(1/2) - 134*a^3*b*(a^3*b^9)^(1/2))/(16384*(a^2*b^14 - 5*a^3*b^13 + 10*a^4*b^12 - 10*a^5*b^11 + 5*a^6*b^10 - a^7*b^9)))^(1/2)*2i)/d","B"
225,1,5824,290,19.618110,"\text{Not used}","int(sin(c + d*x)^7/(a - b*sin(c + d*x)^4)^3,x)","\frac{\frac{3\,{\cos\left(c+d\,x\right)}^7\,\left(a-3\,b\right)}{32\,\left(a^2-2\,a\,b+b^2\right)}-\frac{{\cos\left(c+d\,x\right)}^5\,\left(11\,a-35\,b\right)}{32\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\cos\left(c+d\,x\right)}^3\,\left(a^2+18\,a\,b-43\,b^2\right)}{32\,b\,{\left(a-b\right)}^2}-\frac{\cos\left(c+d\,x\right)\,\left(3\,a+17\,b\right)}{32\,b\,\left(a-b\right)}}{d\,\left(a^2-2\,a\,b+b^2+{\cos\left(c+d\,x\right)}^2\,\left(4\,a\,b-4\,b^2\right)-{\cos\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,b^2\right)-4\,b^2\,{\cos\left(c+d\,x\right)}^6+b^2\,{\cos\left(c+d\,x\right)}^8\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(-16384\,a^4\,b^4+114688\,a^3\,b^5-180224\,a^2\,b^6+81920\,a\,b^7\right)}{32768\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,\left(16384\,a^5\,b^4-65536\,a^4\,b^5+98304\,a^3\,b^6-65536\,a^2\,b^7+16384\,a\,b^8\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-54\,a^2\,b+81\,a\,b^2+36\,b^3\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(-16384\,a^4\,b^4+114688\,a^3\,b^5-180224\,a^2\,b^6+81920\,a\,b^7\right)}{32768\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,\left(16384\,a^5\,b^4-65536\,a^4\,b^5+98304\,a^3\,b^6-65536\,a^2\,b^7+16384\,a\,b^8\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-54\,a^2\,b+81\,a\,b^2+36\,b^3\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3\,\left(-16384\,a^4\,b^4+114688\,a^3\,b^5-180224\,a^2\,b^6+81920\,a\,b^7\right)}{32768\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,\left(16384\,a^5\,b^4-65536\,a^4\,b^5+98304\,a^3\,b^6-65536\,a^2\,b^7+16384\,a\,b^8\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-54\,a^2\,b+81\,a\,b^2+36\,b^3\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}+\left(\left(\frac{3\,\left(-16384\,a^4\,b^4+114688\,a^3\,b^5-180224\,a^2\,b^6+81920\,a\,b^7\right)}{32768\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,\left(16384\,a^5\,b^4-65536\,a^4\,b^5+98304\,a^3\,b^6-65536\,a^2\,b^7+16384\,a\,b^8\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-54\,a^2\,b+81\,a\,b^2+36\,b^3\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}+\frac{3\,\left(9\,a^2-63\,a\,b+108\,b^2\right)}{16384\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}}\right)\,\sqrt{\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}+4\,a\,b^7+21\,a^2\,b^6-10\,a^3\,b^5+a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(-16384\,a^4\,b^4+114688\,a^3\,b^5-180224\,a^2\,b^6+81920\,a\,b^7\right)}{32768\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,\left(16384\,a^5\,b^4-65536\,a^4\,b^5+98304\,a^3\,b^6-65536\,a^2\,b^7+16384\,a\,b^8\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-54\,a^2\,b+81\,a\,b^2+36\,b^3\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(-16384\,a^4\,b^4+114688\,a^3\,b^5-180224\,a^2\,b^6+81920\,a\,b^7\right)}{32768\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,\left(16384\,a^5\,b^4-65536\,a^4\,b^5+98304\,a^3\,b^6-65536\,a^2\,b^7+16384\,a\,b^8\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-54\,a^2\,b+81\,a\,b^2+36\,b^3\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3\,\left(-16384\,a^4\,b^4+114688\,a^3\,b^5-180224\,a^2\,b^6+81920\,a\,b^7\right)}{32768\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,\left(16384\,a^5\,b^4-65536\,a^4\,b^5+98304\,a^3\,b^6-65536\,a^2\,b^7+16384\,a\,b^8\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-54\,a^2\,b+81\,a\,b^2+36\,b^3\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}+\left(\left(\frac{3\,\left(-16384\,a^4\,b^4+114688\,a^3\,b^5-180224\,a^2\,b^6+81920\,a\,b^7\right)}{32768\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,\left(16384\,a^5\,b^4-65536\,a^4\,b^5+98304\,a^3\,b^6-65536\,a^2\,b^7+16384\,a\,b^8\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^3-54\,a^2\,b+81\,a\,b^2+36\,b^3\right)}{256\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}+\frac{3\,\left(9\,a^2-63\,a\,b+108\,b^2\right)}{16384\,\left(a^4\,b^2-4\,a^3\,b^3+6\,a^2\,b^4-4\,a\,b^5+b^6\right)}}\right)\,\sqrt{-\frac{9\,\left(a^3\,\sqrt{a^3\,b^7}+16\,b^3\,\sqrt{a^3\,b^7}-4\,a\,b^7-21\,a^2\,b^6+10\,a^3\,b^5-a^4\,b^4+5\,a\,b^2\,\sqrt{a^3\,b^7}-6\,a^2\,b\,\sqrt{a^3\,b^7}\right)}{16384\,\left(-a^7\,b^7+5\,a^6\,b^8-10\,a^5\,b^9+10\,a^4\,b^{10}-5\,a^3\,b^{11}+a^2\,b^{12}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"((3*cos(c + d*x)^7*(a - 3*b))/(32*(a^2 - 2*a*b + b^2)) - (cos(c + d*x)^5*(11*a - 35*b))/(32*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)^3*(18*a*b + a^2 - 43*b^2))/(32*b*(a - b)^2) - (cos(c + d*x)*(3*a + 17*b))/(32*b*(a - b)))/(d*(a^2 - 2*a*b + b^2 + cos(c + d*x)^2*(4*a*b - 4*b^2) - cos(c + d*x)^4*(2*a*b - 6*b^2) - 4*b^2*cos(c + d*x)^6 + b^2*cos(c + d*x)^8)) + (atan(((((3*(81920*a*b^7 - 180224*a^2*b^6 + 114688*a^3*b^5 - 16384*a^4*b^4))/(32768*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2)) - (cos(c + d*x)*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*(16384*a*b^8 - 65536*a^2*b^7 + 98304*a^3*b^6 - 65536*a^4*b^5 + 16384*a^5*b^4))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) + (cos(c + d*x)*(81*a*b^2 - 54*a^2*b + 9*a^3 + 36*b^3))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*1i - (((3*(81920*a*b^7 - 180224*a^2*b^6 + 114688*a^3*b^5 - 16384*a^4*b^4))/(32768*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2)) + (cos(c + d*x)*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*(16384*a*b^8 - 65536*a^2*b^7 + 98304*a^3*b^6 - 65536*a^4*b^5 + 16384*a^5*b^4))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) - (cos(c + d*x)*(81*a*b^2 - 54*a^2*b + 9*a^3 + 36*b^3))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*1i)/((((3*(81920*a*b^7 - 180224*a^2*b^6 + 114688*a^3*b^5 - 16384*a^4*b^4))/(32768*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2)) - (cos(c + d*x)*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*(16384*a*b^8 - 65536*a^2*b^7 + 98304*a^3*b^6 - 65536*a^4*b^5 + 16384*a^5*b^4))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) + (cos(c + d*x)*(81*a*b^2 - 54*a^2*b + 9*a^3 + 36*b^3))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) + (((3*(81920*a*b^7 - 180224*a^2*b^6 + 114688*a^3*b^5 - 16384*a^4*b^4))/(32768*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2)) + (cos(c + d*x)*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*(16384*a*b^8 - 65536*a^2*b^7 + 98304*a^3*b^6 - 65536*a^4*b^5 + 16384*a^5*b^4))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) - (cos(c + d*x)*(81*a*b^2 - 54*a^2*b + 9*a^3 + 36*b^3))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) + (3*(9*a^2 - 63*a*b + 108*b^2))/(16384*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2))))*((9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) + 4*a*b^7 + 21*a^2*b^6 - 10*a^3*b^5 + a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*2i)/d + (atan(((((3*(81920*a*b^7 - 180224*a^2*b^6 + 114688*a^3*b^5 - 16384*a^4*b^4))/(32768*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2)) - (cos(c + d*x)*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*(16384*a*b^8 - 65536*a^2*b^7 + 98304*a^3*b^6 - 65536*a^4*b^5 + 16384*a^5*b^4))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) + (cos(c + d*x)*(81*a*b^2 - 54*a^2*b + 9*a^3 + 36*b^3))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*1i - (((3*(81920*a*b^7 - 180224*a^2*b^6 + 114688*a^3*b^5 - 16384*a^4*b^4))/(32768*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2)) + (cos(c + d*x)*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*(16384*a*b^8 - 65536*a^2*b^7 + 98304*a^3*b^6 - 65536*a^4*b^5 + 16384*a^5*b^4))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) - (cos(c + d*x)*(81*a*b^2 - 54*a^2*b + 9*a^3 + 36*b^3))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*1i)/((((3*(81920*a*b^7 - 180224*a^2*b^6 + 114688*a^3*b^5 - 16384*a^4*b^4))/(32768*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2)) - (cos(c + d*x)*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*(16384*a*b^8 - 65536*a^2*b^7 + 98304*a^3*b^6 - 65536*a^4*b^5 + 16384*a^5*b^4))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) + (cos(c + d*x)*(81*a*b^2 - 54*a^2*b + 9*a^3 + 36*b^3))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) + (((3*(81920*a*b^7 - 180224*a^2*b^6 + 114688*a^3*b^5 - 16384*a^4*b^4))/(32768*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2)) + (cos(c + d*x)*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*(16384*a*b^8 - 65536*a^2*b^7 + 98304*a^3*b^6 - 65536*a^4*b^5 + 16384*a^5*b^4))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) - (cos(c + d*x)*(81*a*b^2 - 54*a^2*b + 9*a^3 + 36*b^3))/(256*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2) + (3*(9*a^2 - 63*a*b + 108*b^2))/(16384*(b^6 - 4*a*b^5 + 6*a^2*b^4 - 4*a^3*b^3 + a^4*b^2))))*(-(9*(a^3*(a^3*b^7)^(1/2) + 16*b^3*(a^3*b^7)^(1/2) - 4*a*b^7 - 21*a^2*b^6 + 10*a^3*b^5 - a^4*b^4 + 5*a*b^2*(a^3*b^7)^(1/2) - 6*a^2*b*(a^3*b^7)^(1/2)))/(16384*(a^2*b^12 - 5*a^3*b^11 + 10*a^4*b^10 - 10*a^5*b^9 + 5*a^6*b^8 - a^7*b^7)))^(1/2)*2i)/d","B"
226,1,6362,313,20.152906,"\text{Not used}","int(sin(c + d*x)^5/(a - b*sin(c + d*x)^4)^3,x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^3\,\left(-5\,a^2+14\,a\,b+3\,b^2\right)}{16\,a\,{\left(a-b\right)}^2}-\frac{{\cos\left(c+d\,x\right)}^5\,\left(-a^2+19\,a\,b+6\,b^2\right)}{32\,a\,\left(a^2-2\,a\,b+b^2\right)}+\frac{b\,{\cos\left(c+d\,x\right)}^7\,\left(2\,a+b\right)}{16\,a\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\cos\left(c+d\,x\right)\,\left(3\,a^2+15\,a\,b+2\,b^2\right)}{32\,a\,b\,\left(a-b\right)}}{d\,\left(a^2-2\,a\,b+b^2+{\cos\left(c+d\,x\right)}^2\,\left(4\,a\,b-4\,b^2\right)-{\cos\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,b^2\right)-4\,b^2\,{\cos\left(c+d\,x\right)}^6+b^2\,{\cos\left(c+d\,x\right)}^8\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{24576\,a^7\,b^2-188416\,a^6\,b^3+319488\,a^5\,b^4-172032\,a^4\,b^5+16384\,a^3\,b^6}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b-62\,a^3\,b^2+209\,a^2\,b^3-100\,a\,b^4+16\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{24576\,a^7\,b^2-188416\,a^6\,b^3+319488\,a^5\,b^4-172032\,a^4\,b^5+16384\,a^3\,b^6}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b-62\,a^3\,b^2+209\,a^2\,b^3-100\,a\,b^4+16\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{24576\,a^7\,b^2-188416\,a^6\,b^3+319488\,a^5\,b^4-172032\,a^4\,b^5+16384\,a^3\,b^6}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b-62\,a^3\,b^2+209\,a^2\,b^3-100\,a\,b^4+16\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}+\left(\left(\frac{24576\,a^7\,b^2-188416\,a^6\,b^3+319488\,a^5\,b^4-172032\,a^4\,b^5+16384\,a^3\,b^6}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b-62\,a^3\,b^2+209\,a^2\,b^3-100\,a\,b^4+16\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}+\frac{-18\,a^3+143\,a^2\,b+44\,a\,b^2-16\,b^3}{8192\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\right)\,\sqrt{\frac{80\,b^3\,\sqrt{a^9\,b^5}-9\,a^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3-301\,a\,b^2\,\sqrt{a^9\,b^5}+86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{24576\,a^7\,b^2-188416\,a^6\,b^3+319488\,a^5\,b^4-172032\,a^4\,b^5+16384\,a^3\,b^6}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b-62\,a^3\,b^2+209\,a^2\,b^3-100\,a\,b^4+16\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{24576\,a^7\,b^2-188416\,a^6\,b^3+319488\,a^5\,b^4-172032\,a^4\,b^5+16384\,a^3\,b^6}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b-62\,a^3\,b^2+209\,a^2\,b^3-100\,a\,b^4+16\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{24576\,a^7\,b^2-188416\,a^6\,b^3+319488\,a^5\,b^4-172032\,a^4\,b^5+16384\,a^3\,b^6}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b-62\,a^3\,b^2+209\,a^2\,b^3-100\,a\,b^4+16\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}+\left(\left(\frac{24576\,a^7\,b^2-188416\,a^6\,b^3+319488\,a^5\,b^4-172032\,a^4\,b^5+16384\,a^3\,b^6}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(9\,a^4\,b-62\,a^3\,b^2+209\,a^2\,b^3-100\,a\,b^4+16\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}+\frac{-18\,a^3+143\,a^2\,b+44\,a\,b^2-16\,b^3}{8192\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\right)\,\sqrt{\frac{9\,a^3\,\sqrt{a^9\,b^5}-80\,b^3\,\sqrt{a^9\,b^5}+16\,a^3\,b^7-116\,a^4\,b^6+229\,a^5\,b^5+30\,a^6\,b^4-15\,a^7\,b^3+301\,a\,b^2\,\sqrt{a^9\,b^5}-86\,a^2\,b\,\sqrt{a^9\,b^5}}{16384\,\left(-a^{11}\,b^5+5\,a^{10}\,b^6-10\,a^9\,b^7+10\,a^8\,b^8-5\,a^7\,b^9+a^6\,b^{10}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- ((cos(c + d*x)^3*(14*a*b - 5*a^2 + 3*b^2))/(16*a*(a - b)^2) - (cos(c + d*x)^5*(19*a*b - a^2 + 6*b^2))/(32*a*(a^2 - 2*a*b + b^2)) + (b*cos(c + d*x)^7*(2*a + b))/(16*a*(a^2 - 2*a*b + b^2)) + (cos(c + d*x)*(15*a*b + 3*a^2 + 2*b^2))/(32*a*b*(a - b)))/(d*(a^2 - 2*a*b + b^2 + cos(c + d*x)^2*(4*a*b - 4*b^2) - cos(c + d*x)^4*(2*a*b - 6*b^2) - 4*b^2*cos(c + d*x)^6 + b^2*cos(c + d*x)^8)) - (atan(((((16384*a^3*b^6 - 172032*a^4*b^5 + 319488*a^5*b^4 - 188416*a^6*b^3 + 24576*a^7*b^2)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) - (cos(c + d*x)*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) + (cos(c + d*x)*(9*a^4*b - 100*a*b^4 + 16*b^5 + 209*a^2*b^3 - 62*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*1i - (((16384*a^3*b^6 - 172032*a^4*b^5 + 319488*a^5*b^4 - 188416*a^6*b^3 + 24576*a^7*b^2)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) + (cos(c + d*x)*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) - (cos(c + d*x)*(9*a^4*b - 100*a*b^4 + 16*b^5 + 209*a^2*b^3 - 62*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*1i)/((((16384*a^3*b^6 - 172032*a^4*b^5 + 319488*a^5*b^4 - 188416*a^6*b^3 + 24576*a^7*b^2)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) - (cos(c + d*x)*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) + (cos(c + d*x)*(9*a^4*b - 100*a*b^4 + 16*b^5 + 209*a^2*b^3 - 62*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) + (((16384*a^3*b^6 - 172032*a^4*b^5 + 319488*a^5*b^4 - 188416*a^6*b^3 + 24576*a^7*b^2)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) + (cos(c + d*x)*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) - (cos(c + d*x)*(9*a^4*b - 100*a*b^4 + 16*b^5 + 209*a^2*b^3 - 62*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) + (44*a*b^2 + 143*a^2*b - 18*a^3 - 16*b^3)/(8192*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2))))*((80*b^3*(a^9*b^5)^(1/2) - 9*a^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 - 301*a*b^2*(a^9*b^5)^(1/2) + 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*2i)/d - (atan(((((16384*a^3*b^6 - 172032*a^4*b^5 + 319488*a^5*b^4 - 188416*a^6*b^3 + 24576*a^7*b^2)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) - (cos(c + d*x)*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) + (cos(c + d*x)*(9*a^4*b - 100*a*b^4 + 16*b^5 + 209*a^2*b^3 - 62*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*1i - (((16384*a^3*b^6 - 172032*a^4*b^5 + 319488*a^5*b^4 - 188416*a^6*b^3 + 24576*a^7*b^2)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) + (cos(c + d*x)*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) - (cos(c + d*x)*(9*a^4*b - 100*a*b^4 + 16*b^5 + 209*a^2*b^3 - 62*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*1i)/((((16384*a^3*b^6 - 172032*a^4*b^5 + 319488*a^5*b^4 - 188416*a^6*b^3 + 24576*a^7*b^2)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) - (cos(c + d*x)*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) + (cos(c + d*x)*(9*a^4*b - 100*a*b^4 + 16*b^5 + 209*a^2*b^3 - 62*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) + (((16384*a^3*b^6 - 172032*a^4*b^5 + 319488*a^5*b^4 - 188416*a^6*b^3 + 24576*a^7*b^2)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) + (cos(c + d*x)*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) - (cos(c + d*x)*(9*a^4*b - 100*a*b^4 + 16*b^5 + 209*a^2*b^3 - 62*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2) + (44*a*b^2 + 143*a^2*b - 18*a^3 - 16*b^3)/(8192*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2))))*((9*a^3*(a^9*b^5)^(1/2) - 80*b^3*(a^9*b^5)^(1/2) + 16*a^3*b^7 - 116*a^4*b^6 + 229*a^5*b^5 + 30*a^6*b^4 - 15*a^7*b^3 + 301*a*b^2*(a^9*b^5)^(1/2) - 86*a^2*b*(a^9*b^5)^(1/2))/(16384*(a^6*b^10 - 5*a^7*b^9 + 10*a^8*b^8 - 10*a^9*b^7 + 5*a^10*b^6 - a^11*b^5)))^(1/2)*2i)/d","B"
227,1,5566,288,19.278188,"\text{Not used}","int(sin(c + d*x)^3/(a - b*sin(c + d*x)^4)^3,x)","-\frac{\frac{3\,{\cos\left(c+d\,x\right)}^3\,\left(-3\,a^2+10\,a\,b+b^2\right)}{32\,a\,{\left(a-b\right)}^2}+\frac{\cos\left(c+d\,x\right)\,\left(19\,a+b\right)}{32\,a\,\left(a-b\right)}-\frac{3\,b\,{\cos\left(c+d\,x\right)}^5\,\left(7\,a+b\right)}{32\,a\,\left(a^2-2\,a\,b+b^2\right)}+\frac{b\,{\cos\left(c+d\,x\right)}^7\,\left(5\,a+b\right)}{32\,a\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(a^2-2\,a\,b+b^2+{\cos\left(c+d\,x\right)}^2\,\left(4\,a\,b-4\,b^2\right)-{\cos\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,b^2\right)-4\,b^2\,{\cos\left(c+d\,x\right)}^6+b^2\,{\cos\left(c+d\,x\right)}^8\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-212992\,a^6\,b^3+442368\,a^5\,b^4-245760\,a^4\,b^5+16384\,a^3\,b^6}{32768\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^3\,b^2+74\,a^2\,b^3-31\,a\,b^4+4\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-212992\,a^6\,b^3+442368\,a^5\,b^4-245760\,a^4\,b^5+16384\,a^3\,b^6}{32768\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^3\,b^2+74\,a^2\,b^3-31\,a\,b^4+4\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-212992\,a^6\,b^3+442368\,a^5\,b^4-245760\,a^4\,b^5+16384\,a^3\,b^6}{32768\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^3\,b^2+74\,a^2\,b^3-31\,a\,b^4+4\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}+\left(\left(\frac{-212992\,a^6\,b^3+442368\,a^5\,b^4-245760\,a^4\,b^5+16384\,a^3\,b^6}{32768\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^3\,b^2+74\,a^2\,b^3-31\,a\,b^4+4\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}+\frac{125\,a^2\,b+5\,a\,b^2-4\,b^3}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\right)\,\sqrt{\frac{35\,b^2\,\sqrt{a^9\,b^3}-25\,a^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2-154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-212992\,a^6\,b^3+442368\,a^5\,b^4-245760\,a^4\,b^5+16384\,a^3\,b^6}{32768\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^3\,b^2+74\,a^2\,b^3-31\,a\,b^4+4\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-212992\,a^6\,b^3+442368\,a^5\,b^4-245760\,a^4\,b^5+16384\,a^3\,b^6}{32768\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^3\,b^2+74\,a^2\,b^3-31\,a\,b^4+4\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-212992\,a^6\,b^3+442368\,a^5\,b^4-245760\,a^4\,b^5+16384\,a^3\,b^6}{32768\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(25\,a^3\,b^2+74\,a^2\,b^3-31\,a\,b^4+4\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}+\left(\left(\frac{-212992\,a^6\,b^3+442368\,a^5\,b^4-245760\,a^4\,b^5+16384\,a^3\,b^6}{32768\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,\left(16384\,a^7\,b^4-65536\,a^6\,b^5+98304\,a^5\,b^6-65536\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(25\,a^3\,b^2+74\,a^2\,b^3-31\,a\,b^4+4\,b^5\right)}{256\,\left(a^6-4\,a^5\,b+6\,a^4\,b^2-4\,a^3\,b^3+a^2\,b^4\right)}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}+\frac{125\,a^2\,b+5\,a\,b^2-4\,b^3}{16384\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\right)\,\sqrt{\frac{25\,a^2\,\sqrt{a^9\,b^3}-35\,b^2\,\sqrt{a^9\,b^3}+4\,a^3\,b^5-35\,a^4\,b^4+70\,a^5\,b^3+105\,a^6\,b^2+154\,a\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{11}\,b^3+5\,a^{10}\,b^4-10\,a^9\,b^5+10\,a^8\,b^6-5\,a^7\,b^7+a^6\,b^8\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- (atan(((((16384*a^3*b^6 - 245760*a^4*b^5 + 442368*a^5*b^4 - 212992*a^6*b^3)/(32768*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) - (cos(c + d*x)*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) + (cos(c + d*x)*(4*b^5 - 31*a*b^4 + 74*a^2*b^3 + 25*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*1i - (((16384*a^3*b^6 - 245760*a^4*b^5 + 442368*a^5*b^4 - 212992*a^6*b^3)/(32768*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) + (cos(c + d*x)*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) - (cos(c + d*x)*(4*b^5 - 31*a*b^4 + 74*a^2*b^3 + 25*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*1i)/((((16384*a^3*b^6 - 245760*a^4*b^5 + 442368*a^5*b^4 - 212992*a^6*b^3)/(32768*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) - (cos(c + d*x)*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) + (cos(c + d*x)*(4*b^5 - 31*a*b^4 + 74*a^2*b^3 + 25*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) + (((16384*a^3*b^6 - 245760*a^4*b^5 + 442368*a^5*b^4 - 212992*a^6*b^3)/(32768*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) + (cos(c + d*x)*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) - (cos(c + d*x)*(4*b^5 - 31*a*b^4 + 74*a^2*b^3 + 25*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) + (5*a*b^2 + 125*a^2*b - 4*b^3)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2))))*((35*b^2*(a^9*b^3)^(1/2) - 25*a^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 - 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*2i)/d - (atan(((((16384*a^3*b^6 - 245760*a^4*b^5 + 442368*a^5*b^4 - 212992*a^6*b^3)/(32768*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) - (cos(c + d*x)*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) + (cos(c + d*x)*(4*b^5 - 31*a*b^4 + 74*a^2*b^3 + 25*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*1i - (((16384*a^3*b^6 - 245760*a^4*b^5 + 442368*a^5*b^4 - 212992*a^6*b^3)/(32768*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) + (cos(c + d*x)*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) - (cos(c + d*x)*(4*b^5 - 31*a*b^4 + 74*a^2*b^3 + 25*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*1i)/((((16384*a^3*b^6 - 245760*a^4*b^5 + 442368*a^5*b^4 - 212992*a^6*b^3)/(32768*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) - (cos(c + d*x)*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) + (cos(c + d*x)*(4*b^5 - 31*a*b^4 + 74*a^2*b^3 + 25*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) + (((16384*a^3*b^6 - 245760*a^4*b^5 + 442368*a^5*b^4 - 212992*a^6*b^3)/(32768*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)) + (cos(c + d*x)*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*(16384*a^3*b^8 - 65536*a^4*b^7 + 98304*a^5*b^6 - 65536*a^6*b^5 + 16384*a^7*b^4))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) - (cos(c + d*x)*(4*b^5 - 31*a*b^4 + 74*a^2*b^3 + 25*a^3*b^2))/(256*(a^6 - 4*a^5*b + a^2*b^4 - 4*a^3*b^3 + 6*a^4*b^2)))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2) + (5*a*b^2 + 125*a^2*b - 4*b^3)/(16384*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2))))*((25*a^2*(a^9*b^3)^(1/2) - 35*b^2*(a^9*b^3)^(1/2) + 4*a^3*b^5 - 35*a^4*b^4 + 70*a^5*b^3 + 105*a^6*b^2 + 154*a*b*(a^9*b^3)^(1/2))/(16384*(a^6*b^8 - 5*a^7*b^7 + 10*a^8*b^6 - 10*a^9*b^5 + 5*a^10*b^4 - a^11*b^3)))^(1/2)*2i)/d - ((3*cos(c + d*x)^3*(10*a*b - 3*a^2 + b^2))/(32*a*(a - b)^2) + (cos(c + d*x)*(19*a + b))/(32*a*(a - b)) - (3*b*cos(c + d*x)^5*(7*a + b))/(32*a*(a^2 - 2*a*b + b^2)) + (b*cos(c + d*x)^7*(5*a + b))/(32*a*(a^2 - 2*a*b + b^2)))/(d*(a^2 - 2*a*b + b^2 + cos(c + d*x)^2*(4*a*b - 4*b^2) - cos(c + d*x)^4*(2*a*b - 6*b^2) - 4*b^2*cos(c + d*x)^6 + b^2*cos(c + d*x)^8))","B"
228,1,5753,313,18.909884,"\text{Not used}","int(sin(c + d*x)/(a - b*sin(c + d*x)^4)^3,x)","-\frac{\frac{\cos\left(c+d\,x\right)\,\left(11\,a^2+15\,a\,b-6\,b^2\right)}{32\,a^2\,\left(a-b\right)}-\frac{{\cos\left(c+d\,x\right)}^3\,\left(a^2\,b-22\,a\,b^2+9\,b^3\right)}{16\,a^2\,{\left(a-b\right)}^2}+\frac{3\,b\,{\cos\left(c+d\,x\right)}^7\,\left(2\,a\,b-b^2\right)}{16\,a^2\,\left(a^2-2\,a\,b+b^2\right)}-\frac{b\,{\cos\left(c+d\,x\right)}^5\,\left(7\,a^2+35\,a\,b-18\,b^2\right)}{32\,a^2\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(a^2-2\,a\,b+b^2+{\cos\left(c+d\,x\right)}^2\,\left(4\,a\,b-4\,b^2\right)-{\cos\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,b^2\right)-4\,b^2\,{\cos\left(c+d\,x\right)}^6+b^2\,{\cos\left(c+d\,x\right)}^8\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(57344\,a^9\,b^3-155648\,a^8\,b^4+155648\,a^7\,b^5-73728\,a^6\,b^6+16384\,a^5\,b^7\right)}{16384\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,\left(16384\,a^9\,b^4-65536\,a^8\,b^5+98304\,a^7\,b^6-65536\,a^6\,b^7+16384\,a^5\,b^8\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(441\,a^4\,b^3-990\,a^3\,b^4+1089\,a^2\,b^5-612\,a\,b^6+144\,b^7\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(57344\,a^9\,b^3-155648\,a^8\,b^4+155648\,a^7\,b^5-73728\,a^6\,b^6+16384\,a^5\,b^7\right)}{16384\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,\left(16384\,a^9\,b^4-65536\,a^8\,b^5+98304\,a^7\,b^6-65536\,a^6\,b^7+16384\,a^5\,b^8\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(441\,a^4\,b^3-990\,a^3\,b^4+1089\,a^2\,b^5-612\,a\,b^6+144\,b^7\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,1{}\mathrm{i}}{\frac{3\,\left(882\,a^3\,b^3-1233\,a^2\,b^4+684\,a\,b^5-144\,b^6\right)}{8192\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}+\left(\left(\frac{3\,\left(57344\,a^9\,b^3-155648\,a^8\,b^4+155648\,a^7\,b^5-73728\,a^6\,b^6+16384\,a^5\,b^7\right)}{16384\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,\left(16384\,a^9\,b^4-65536\,a^8\,b^5+98304\,a^7\,b^6-65536\,a^6\,b^7+16384\,a^5\,b^8\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(441\,a^4\,b^3-990\,a^3\,b^4+1089\,a^2\,b^5-612\,a\,b^6+144\,b^7\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}+\left(\left(\frac{3\,\left(57344\,a^9\,b^3-155648\,a^8\,b^4+155648\,a^7\,b^5-73728\,a^6\,b^6+16384\,a^5\,b^7\right)}{16384\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,\left(16384\,a^9\,b^4-65536\,a^8\,b^5+98304\,a^7\,b^6-65536\,a^6\,b^7+16384\,a^5\,b^8\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(441\,a^4\,b^3-990\,a^3\,b^4+1089\,a^2\,b^5-612\,a\,b^6+144\,b^7\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}}\right)\,\sqrt{\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}-105\,a^9\,b-16\,a^5\,b^5+84\,a^6\,b^4-189\,a^7\,b^3+210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(57344\,a^9\,b^3-155648\,a^8\,b^4+155648\,a^7\,b^5-73728\,a^6\,b^6+16384\,a^5\,b^7\right)}{16384\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,\left(16384\,a^9\,b^4-65536\,a^8\,b^5+98304\,a^7\,b^6-65536\,a^6\,b^7+16384\,a^5\,b^8\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(441\,a^4\,b^3-990\,a^3\,b^4+1089\,a^2\,b^5-612\,a\,b^6+144\,b^7\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(57344\,a^9\,b^3-155648\,a^8\,b^4+155648\,a^7\,b^5-73728\,a^6\,b^6+16384\,a^5\,b^7\right)}{16384\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,\left(16384\,a^9\,b^4-65536\,a^8\,b^5+98304\,a^7\,b^6-65536\,a^6\,b^7+16384\,a^5\,b^8\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(441\,a^4\,b^3-990\,a^3\,b^4+1089\,a^2\,b^5-612\,a\,b^6+144\,b^7\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,1{}\mathrm{i}}{\frac{3\,\left(882\,a^3\,b^3-1233\,a^2\,b^4+684\,a\,b^5-144\,b^6\right)}{8192\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}+\left(\left(\frac{3\,\left(57344\,a^9\,b^3-155648\,a^8\,b^4+155648\,a^7\,b^5-73728\,a^6\,b^6+16384\,a^5\,b^7\right)}{16384\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,\left(16384\,a^9\,b^4-65536\,a^8\,b^5+98304\,a^7\,b^6-65536\,a^6\,b^7+16384\,a^5\,b^8\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(441\,a^4\,b^3-990\,a^3\,b^4+1089\,a^2\,b^5-612\,a\,b^6+144\,b^7\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}+\left(\left(\frac{3\,\left(57344\,a^9\,b^3-155648\,a^8\,b^4+155648\,a^7\,b^5-73728\,a^6\,b^6+16384\,a^5\,b^7\right)}{16384\,\left(a^{10}-4\,a^9\,b+6\,a^8\,b^2-4\,a^7\,b^3+a^6\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,\left(16384\,a^9\,b^4-65536\,a^8\,b^5+98304\,a^7\,b^6-65536\,a^6\,b^7+16384\,a^5\,b^8\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(441\,a^4\,b^3-990\,a^3\,b^4+1089\,a^2\,b^5-612\,a\,b^6+144\,b^7\right)}{256\,\left(a^8-4\,a^7\,b+6\,a^6\,b^2-4\,a^5\,b^3+a^4\,b^4\right)}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}}\right)\,\sqrt{-\frac{9\,\left(49\,a^2\,\sqrt{a^{15}\,b}+21\,b^2\,\sqrt{a^{15}\,b}+105\,a^9\,b+16\,a^5\,b^5-84\,a^6\,b^4+189\,a^7\,b^3-210\,a^8\,b^2-54\,a\,b\,\sqrt{a^{15}\,b}\right)}{16384\,\left(a^{15}\,b-5\,a^{14}\,b^2+10\,a^{13}\,b^3-10\,a^{12}\,b^4+5\,a^{11}\,b^5-a^{10}\,b^6\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((((3*(16384*a^5*b^7 - 73728*a^6*b^6 + 155648*a^7*b^5 - 155648*a^8*b^4 + 57344*a^9*b^3))/(16384*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) - (cos(c + d*x)*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*(16384*a^5*b^8 - 65536*a^6*b^7 + 98304*a^7*b^6 - 65536*a^8*b^5 + 16384*a^9*b^4))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) + (cos(c + d*x)*(144*b^7 - 612*a*b^6 + 1089*a^2*b^5 - 990*a^3*b^4 + 441*a^4*b^3))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*1i - (((3*(16384*a^5*b^7 - 73728*a^6*b^6 + 155648*a^7*b^5 - 155648*a^8*b^4 + 57344*a^9*b^3))/(16384*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) + (cos(c + d*x)*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*(16384*a^5*b^8 - 65536*a^6*b^7 + 98304*a^7*b^6 - 65536*a^8*b^5 + 16384*a^9*b^4))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) - (cos(c + d*x)*(144*b^7 - 612*a*b^6 + 1089*a^2*b^5 - 990*a^3*b^4 + 441*a^4*b^3))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*1i)/((3*(684*a*b^5 - 144*b^6 - 1233*a^2*b^4 + 882*a^3*b^3))/(8192*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) + (((3*(16384*a^5*b^7 - 73728*a^6*b^6 + 155648*a^7*b^5 - 155648*a^8*b^4 + 57344*a^9*b^3))/(16384*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) - (cos(c + d*x)*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*(16384*a^5*b^8 - 65536*a^6*b^7 + 98304*a^7*b^6 - 65536*a^8*b^5 + 16384*a^9*b^4))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) + (cos(c + d*x)*(144*b^7 - 612*a*b^6 + 1089*a^2*b^5 - 990*a^3*b^4 + 441*a^4*b^3))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) + (((3*(16384*a^5*b^7 - 73728*a^6*b^6 + 155648*a^7*b^5 - 155648*a^8*b^4 + 57344*a^9*b^3))/(16384*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) + (cos(c + d*x)*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*(16384*a^5*b^8 - 65536*a^6*b^7 + 98304*a^7*b^6 - 65536*a^8*b^5 + 16384*a^9*b^4))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) - (cos(c + d*x)*(144*b^7 - 612*a*b^6 + 1089*a^2*b^5 - 990*a^3*b^4 + 441*a^4*b^3))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)))*((9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) - 105*a^9*b - 16*a^5*b^5 + 84*a^6*b^4 - 189*a^7*b^3 + 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*2i)/d - ((cos(c + d*x)*(15*a*b + 11*a^2 - 6*b^2))/(32*a^2*(a - b)) - (cos(c + d*x)^3*(a^2*b - 22*a*b^2 + 9*b^3))/(16*a^2*(a - b)^2) + (3*b*cos(c + d*x)^7*(2*a*b - b^2))/(16*a^2*(a^2 - 2*a*b + b^2)) - (b*cos(c + d*x)^5*(35*a*b + 7*a^2 - 18*b^2))/(32*a^2*(a^2 - 2*a*b + b^2)))/(d*(a^2 - 2*a*b + b^2 + cos(c + d*x)^2*(4*a*b - 4*b^2) - cos(c + d*x)^4*(2*a*b - 6*b^2) - 4*b^2*cos(c + d*x)^6 + b^2*cos(c + d*x)^8)) + (atan(((((3*(16384*a^5*b^7 - 73728*a^6*b^6 + 155648*a^7*b^5 - 155648*a^8*b^4 + 57344*a^9*b^3))/(16384*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) - (cos(c + d*x)*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*(16384*a^5*b^8 - 65536*a^6*b^7 + 98304*a^7*b^6 - 65536*a^8*b^5 + 16384*a^9*b^4))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) + (cos(c + d*x)*(144*b^7 - 612*a*b^6 + 1089*a^2*b^5 - 990*a^3*b^4 + 441*a^4*b^3))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*1i - (((3*(16384*a^5*b^7 - 73728*a^6*b^6 + 155648*a^7*b^5 - 155648*a^8*b^4 + 57344*a^9*b^3))/(16384*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) + (cos(c + d*x)*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*(16384*a^5*b^8 - 65536*a^6*b^7 + 98304*a^7*b^6 - 65536*a^8*b^5 + 16384*a^9*b^4))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) - (cos(c + d*x)*(144*b^7 - 612*a*b^6 + 1089*a^2*b^5 - 990*a^3*b^4 + 441*a^4*b^3))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*1i)/((3*(684*a*b^5 - 144*b^6 - 1233*a^2*b^4 + 882*a^3*b^3))/(8192*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) + (((3*(16384*a^5*b^7 - 73728*a^6*b^6 + 155648*a^7*b^5 - 155648*a^8*b^4 + 57344*a^9*b^3))/(16384*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) - (cos(c + d*x)*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*(16384*a^5*b^8 - 65536*a^6*b^7 + 98304*a^7*b^6 - 65536*a^8*b^5 + 16384*a^9*b^4))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) + (cos(c + d*x)*(144*b^7 - 612*a*b^6 + 1089*a^2*b^5 - 990*a^3*b^4 + 441*a^4*b^3))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) + (((3*(16384*a^5*b^7 - 73728*a^6*b^6 + 155648*a^7*b^5 - 155648*a^8*b^4 + 57344*a^9*b^3))/(16384*(a^10 - 4*a^9*b + a^6*b^4 - 4*a^7*b^3 + 6*a^8*b^2)) + (cos(c + d*x)*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*(16384*a^5*b^8 - 65536*a^6*b^7 + 98304*a^7*b^6 - 65536*a^8*b^5 + 16384*a^9*b^4))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2) - (cos(c + d*x)*(144*b^7 - 612*a*b^6 + 1089*a^2*b^5 - 990*a^3*b^4 + 441*a^4*b^3))/(256*(a^8 - 4*a^7*b + a^4*b^4 - 4*a^5*b^3 + 6*a^6*b^2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)))*(-(9*(49*a^2*(a^15*b)^(1/2) + 21*b^2*(a^15*b)^(1/2) + 105*a^9*b + 16*a^5*b^5 - 84*a^6*b^4 + 189*a^7*b^3 - 210*a^8*b^2 - 54*a*b*(a^15*b)^(1/2)))/(16384*(a^15*b - a^10*b^6 + 5*a^11*b^5 - 10*a^12*b^4 + 10*a^13*b^3 - 5*a^14*b^2)))^(1/2)*2i)/d","B"
229,1,12247,617,20.834752,"\text{Not used}","int(1/(sin(c + d*x)*(a - b*sin(c + d*x)^4)^3),x)","-\frac{\frac{5\,\cos\left(c+d\,x\right)\,\left(7\,a\,b-3\,b^2\right)}{32\,a^2\,\left(a-b\right)}-\frac{{\cos\left(c+d\,x\right)}^3\,\left(17\,a^2\,b-78\,a\,b^2+37\,b^3\right)}{32\,a^2\,{\left(a-b\right)}^2}-\frac{{\cos\left(c+d\,x\right)}^5\,\left(53\,a\,b^2-29\,b^3\right)}{32\,a^2\,{\left(a-b\right)}^2}+\frac{b\,{\cos\left(c+d\,x\right)}^7\,\left(13\,a\,b-7\,b^2\right)}{32\,a^2\,{\left(a-b\right)}^2}}{d\,\left(a^2-2\,a\,b+b^2+{\cos\left(c+d\,x\right)}^2\,\left(4\,a\,b-4\,b^2\right)-{\cos\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,b^2\right)-4\,b^2\,{\cos\left(c+d\,x\right)}^6+b^2\,{\cos\left(c+d\,x\right)}^8\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{\left(\frac{\frac{\frac{-256\,a^{16}\,b^4+1158\,a^{15}\,b^5-2154\,a^{14}\,b^6+2050\,a^{13}\,b^7-990\,a^{12}\,b^8+192\,a^{11}\,b^9}{2\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{2097152\,a^3\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{2\,a^3}+\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{1048576\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{2\,a^3}-\frac{\frac{546059\,a^9\,b^5}{8192}-\frac{1290253\,a^8\,b^6}{8192}+\frac{307961\,a^7\,b^7}{2048}-\frac{4311\,a^6\,b^8}{64}+12\,a^5\,b^9}{2\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,1{}\mathrm{i}}{2\,a^3}-\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)\,1{}\mathrm{i}}{1048576\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{a^3}-\frac{\frac{\left(\frac{\frac{\frac{-256\,a^{16}\,b^4+1158\,a^{15}\,b^5-2154\,a^{14}\,b^6+2050\,a^{13}\,b^7-990\,a^{12}\,b^8+192\,a^{11}\,b^9}{2\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{2097152\,a^3\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{2\,a^3}-\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{1048576\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{2\,a^3}-\frac{\frac{546059\,a^9\,b^5}{8192}-\frac{1290253\,a^8\,b^6}{8192}+\frac{307961\,a^7\,b^7}{2048}-\frac{4311\,a^6\,b^8}{64}+12\,a^5\,b^9}{2\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,1{}\mathrm{i}}{2\,a^3}+\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)\,1{}\mathrm{i}}{1048576\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{a^3}}{\frac{\frac{\frac{\frac{\frac{-256\,a^{16}\,b^4+1158\,a^{15}\,b^5-2154\,a^{14}\,b^6+2050\,a^{13}\,b^7-990\,a^{12}\,b^8+192\,a^{11}\,b^9}{2\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{2097152\,a^3\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{2\,a^3}+\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{1048576\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{2\,a^3}-\frac{\frac{546059\,a^9\,b^5}{8192}-\frac{1290253\,a^8\,b^6}{8192}+\frac{307961\,a^7\,b^7}{2048}-\frac{4311\,a^6\,b^8}{64}+12\,a^5\,b^9}{2\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}}{2\,a^3}-\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{1048576\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{a^3}+\frac{\frac{\frac{\frac{\frac{-256\,a^{16}\,b^4+1158\,a^{15}\,b^5-2154\,a^{14}\,b^6+2050\,a^{13}\,b^7-990\,a^{12}\,b^8+192\,a^{11}\,b^9}{2\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{2097152\,a^3\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{2\,a^3}-\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{1048576\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{2\,a^3}-\frac{\frac{546059\,a^9\,b^5}{8192}-\frac{1290253\,a^8\,b^6}{8192}+\frac{307961\,a^7\,b^7}{2048}-\frac{4311\,a^6\,b^8}{64}+12\,a^5\,b^9}{2\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}}{2\,a^3}+\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{1048576\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}}{a^3}+\frac{\frac{1184625\,a^3\,b^5}{524288}-\frac{271845\,a^2\,b^6}{65536}+\frac{90009\,a\,b^7}{32768}-\frac{81\,b^8}{128}}{a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4}}\right)\,1{}\mathrm{i}}{a^3\,d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{-268435456\,a^{16}\,b^4+1214251008\,a^{15}\,b^5-2258632704\,a^{14}\,b^6+2149580800\,a^{13}\,b^7-1038090240\,a^{12}\,b^8+201326592\,a^{11}\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{69895552\,a^9\,b^5-165152384\,a^8\,b^6+157676032\,a^7\,b^7-70631424\,a^6\,b^8+12582912\,a^5\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{-268435456\,a^{16}\,b^4+1214251008\,a^{15}\,b^5-2258632704\,a^{14}\,b^6+2149580800\,a^{13}\,b^7-1038090240\,a^{12}\,b^8+201326592\,a^{11}\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{69895552\,a^9\,b^5-165152384\,a^8\,b^6+157676032\,a^7\,b^7-70631424\,a^6\,b^8+12582912\,a^5\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{-268435456\,a^{16}\,b^4+1214251008\,a^{15}\,b^5-2258632704\,a^{14}\,b^6+2149580800\,a^{13}\,b^7-1038090240\,a^{12}\,b^8+201326592\,a^{11}\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{69895552\,a^9\,b^5-165152384\,a^8\,b^6+157676032\,a^7\,b^7-70631424\,a^6\,b^8+12582912\,a^5\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\left(\left(\left(\left(\frac{-268435456\,a^{16}\,b^4+1214251008\,a^{15}\,b^5-2258632704\,a^{14}\,b^6+2149580800\,a^{13}\,b^7-1038090240\,a^{12}\,b^8+201326592\,a^{11}\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{69895552\,a^9\,b^5-165152384\,a^8\,b^6+157676032\,a^7\,b^7-70631424\,a^6\,b^8+12582912\,a^5\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{1184625\,a^3\,b^5-2174760\,a^2\,b^6+1440144\,a\,b^7-331776\,b^8}{524288\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}}\right)\,\sqrt{-\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}-3465\,a^{10}\,b-1024\,a^6\,b^5+5084\,a^7\,b^4-10045\,a^8\,b^3+9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{-268435456\,a^{16}\,b^4+1214251008\,a^{15}\,b^5-2258632704\,a^{14}\,b^6+2149580800\,a^{13}\,b^7-1038090240\,a^{12}\,b^8+201326592\,a^{11}\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{69895552\,a^9\,b^5-165152384\,a^8\,b^6+157676032\,a^7\,b^7-70631424\,a^6\,b^8+12582912\,a^5\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{-268435456\,a^{16}\,b^4+1214251008\,a^{15}\,b^5-2258632704\,a^{14}\,b^6+2149580800\,a^{13}\,b^7-1038090240\,a^{12}\,b^8+201326592\,a^{11}\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{69895552\,a^9\,b^5-165152384\,a^8\,b^6+157676032\,a^7\,b^7-70631424\,a^6\,b^8+12582912\,a^5\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{-268435456\,a^{16}\,b^4+1214251008\,a^{15}\,b^5-2258632704\,a^{14}\,b^6+2149580800\,a^{13}\,b^7-1038090240\,a^{12}\,b^8+201326592\,a^{11}\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}-\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{69895552\,a^9\,b^5-165152384\,a^8\,b^6+157676032\,a^7\,b^7-70631424\,a^6\,b^8+12582912\,a^5\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\left(\left(\left(\left(\frac{-268435456\,a^{16}\,b^4+1214251008\,a^{15}\,b^5-2258632704\,a^{14}\,b^6+2149580800\,a^{13}\,b^7-1038090240\,a^{12}\,b^8+201326592\,a^{11}\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}+\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,\left(-268435456\,a^{17}\,b^4+1476395008\,a^{16}\,b^5-3221225472\,a^{15}\,b^6+3489660928\,a^{14}\,b^7-1879048192\,a^{13}\,b^8+402653184\,a^{12}\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{\cos\left(c+d\,x\right)\,\left(163684352\,a^{10}\,b^5-489406464\,a^9\,b^6+592748544\,a^8\,b^7-337215488\,a^7\,b^8+75497472\,a^6\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}-\frac{69895552\,a^9\,b^5-165152384\,a^8\,b^6+157676032\,a^7\,b^7-70631424\,a^6\,b^8+12582912\,a^5\,b^9}{1048576\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{\cos\left(c+d\,x\right)\,\left(8247825\,a^4\,b^5-23076232\,a^3\,b^6+26453264\,a^2\,b^7-14417920\,a\,b^8+3145728\,b^9\right)}{524288\,\left(a^{12}-4\,a^{11}\,b+6\,a^{10}\,b^2-4\,a^9\,b^3+a^8\,b^4\right)}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}+\frac{1184625\,a^3\,b^5-2174760\,a^2\,b^6+1440144\,a\,b^7-331776\,b^8}{524288\,\left(a^{14}-4\,a^{13}\,b+6\,a^{12}\,b^2-4\,a^{11}\,b^3+a^{10}\,b^4\right)}}\right)\,\sqrt{\frac{2025\,a^4\,\sqrt{a^{13}\,b}+384\,b^4\,\sqrt{a^{13}\,b}+3465\,a^{10}\,b+1024\,a^6\,b^5-5084\,a^7\,b^4+10045\,a^8\,b^3-9306\,a^9\,b^2-2000\,a\,b^3\,\sqrt{a^{13}\,b}-4694\,a^3\,b\,\sqrt{a^{13}\,b}+4429\,a^2\,b^2\,\sqrt{a^{13}\,b}}{16384\,\left(-a^{17}+5\,a^{16}\,b-10\,a^{15}\,b^2+10\,a^{14}\,b^3-5\,a^{13}\,b^4+a^{12}\,b^5\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- ((5*cos(c + d*x)*(7*a*b - 3*b^2))/(32*a^2*(a - b)) - (cos(c + d*x)^3*(17*a^2*b - 78*a*b^2 + 37*b^3))/(32*a^2*(a - b)^2) - (cos(c + d*x)^5*(53*a*b^2 - 29*b^3))/(32*a^2*(a - b)^2) + (b*cos(c + d*x)^7*(13*a*b - 7*b^2))/(32*a^2*(a - b)^2))/(d*(a^2 - 2*a*b + b^2 + cos(c + d*x)^2*(4*a*b - 4*b^2) - cos(c + d*x)^4*(2*a*b - 6*b^2) - 4*b^2*cos(c + d*x)^6 + b^2*cos(c + d*x)^8)) - (atan((((((((192*a^11*b^9 - 990*a^12*b^8 + 2050*a^13*b^7 - 2154*a^14*b^6 + 1158*a^15*b^5 - 256*a^16*b^4)/(2*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) - (cos(c + d*x)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(2097152*a^3*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/(2*a^3) + (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(1048576*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/(2*a^3) - (12*a^5*b^9 - (4311*a^6*b^8)/64 + (307961*a^7*b^7)/2048 - (1290253*a^8*b^6)/8192 + (546059*a^9*b^5)/8192)/(2*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*1i)/(2*a^3) - (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5)*1i)/(1048576*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/a^3 - ((((((192*a^11*b^9 - 990*a^12*b^8 + 2050*a^13*b^7 - 2154*a^14*b^6 + 1158*a^15*b^5 - 256*a^16*b^4)/(2*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) + (cos(c + d*x)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(2097152*a^3*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/(2*a^3) - (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(1048576*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/(2*a^3) - (12*a^5*b^9 - (4311*a^6*b^8)/64 + (307961*a^7*b^7)/2048 - (1290253*a^8*b^6)/8192 + (546059*a^9*b^5)/8192)/(2*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*1i)/(2*a^3) + (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5)*1i)/(1048576*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/a^3)/((((((192*a^11*b^9 - 990*a^12*b^8 + 2050*a^13*b^7 - 2154*a^14*b^6 + 1158*a^15*b^5 - 256*a^16*b^4)/(2*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) - (cos(c + d*x)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(2097152*a^3*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/(2*a^3) + (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(1048576*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/(2*a^3) - (12*a^5*b^9 - (4311*a^6*b^8)/64 + (307961*a^7*b^7)/2048 - (1290253*a^8*b^6)/8192 + (546059*a^9*b^5)/8192)/(2*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))/(2*a^3) - (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(1048576*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/a^3 + (((((192*a^11*b^9 - 990*a^12*b^8 + 2050*a^13*b^7 - 2154*a^14*b^6 + 1158*a^15*b^5 - 256*a^16*b^4)/(2*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) + (cos(c + d*x)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(2097152*a^3*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/(2*a^3) - (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(1048576*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/(2*a^3) - (12*a^5*b^9 - (4311*a^6*b^8)/64 + (307961*a^7*b^7)/2048 - (1290253*a^8*b^6)/8192 + (546059*a^9*b^5)/8192)/(2*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))/(2*a^3) + (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(1048576*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))/a^3 + ((90009*a*b^7)/32768 - (81*b^8)/128 - (271845*a^2*b^6)/65536 + (1184625*a^3*b^5)/524288)/(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*1i)/(a^3*d) - (atan(((((((201326592*a^11*b^9 - 1038090240*a^12*b^8 + 2149580800*a^13*b^7 - 2258632704*a^14*b^6 + 1214251008*a^15*b^5 - 268435456*a^16*b^4)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) - (cos(c + d*x)*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (12582912*a^5*b^9 - 70631424*a^6*b^8 + 157676032*a^7*b^7 - 165152384*a^8*b^6 + 69895552*a^9*b^5)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*1i - (((((201326592*a^11*b^9 - 1038090240*a^12*b^8 + 2149580800*a^13*b^7 - 2258632704*a^14*b^6 + 1214251008*a^15*b^5 - 268435456*a^16*b^4)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) + (cos(c + d*x)*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (12582912*a^5*b^9 - 70631424*a^6*b^8 + 157676032*a^7*b^7 - 165152384*a^8*b^6 + 69895552*a^9*b^5)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*1i)/((((((201326592*a^11*b^9 - 1038090240*a^12*b^8 + 2149580800*a^13*b^7 - 2258632704*a^14*b^6 + 1214251008*a^15*b^5 - 268435456*a^16*b^4)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) - (cos(c + d*x)*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (12582912*a^5*b^9 - 70631424*a^6*b^8 + 157676032*a^7*b^7 - 165152384*a^8*b^6 + 69895552*a^9*b^5)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (((((201326592*a^11*b^9 - 1038090240*a^12*b^8 + 2149580800*a^13*b^7 - 2258632704*a^14*b^6 + 1214251008*a^15*b^5 - 268435456*a^16*b^4)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) + (cos(c + d*x)*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (12582912*a^5*b^9 - 70631424*a^6*b^8 + 157676032*a^7*b^7 - 165152384*a^8*b^6 + 69895552*a^9*b^5)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (1440144*a*b^7 - 331776*b^8 - 2174760*a^2*b^6 + 1184625*a^3*b^5)/(524288*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2))))*(-(2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) - 3465*a^10*b - 1024*a^6*b^5 + 5084*a^7*b^4 - 10045*a^8*b^3 + 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*2i)/d - (atan(((((((201326592*a^11*b^9 - 1038090240*a^12*b^8 + 2149580800*a^13*b^7 - 2258632704*a^14*b^6 + 1214251008*a^15*b^5 - 268435456*a^16*b^4)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) - (cos(c + d*x)*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (12582912*a^5*b^9 - 70631424*a^6*b^8 + 157676032*a^7*b^7 - 165152384*a^8*b^6 + 69895552*a^9*b^5)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*1i - (((((201326592*a^11*b^9 - 1038090240*a^12*b^8 + 2149580800*a^13*b^7 - 2258632704*a^14*b^6 + 1214251008*a^15*b^5 - 268435456*a^16*b^4)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) + (cos(c + d*x)*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (12582912*a^5*b^9 - 70631424*a^6*b^8 + 157676032*a^7*b^7 - 165152384*a^8*b^6 + 69895552*a^9*b^5)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*1i)/((((((201326592*a^11*b^9 - 1038090240*a^12*b^8 + 2149580800*a^13*b^7 - 2258632704*a^14*b^6 + 1214251008*a^15*b^5 - 268435456*a^16*b^4)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) - (cos(c + d*x)*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (12582912*a^5*b^9 - 70631424*a^6*b^8 + 157676032*a^7*b^7 - 165152384*a^8*b^6 + 69895552*a^9*b^5)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (((((201326592*a^11*b^9 - 1038090240*a^12*b^8 + 2149580800*a^13*b^7 - 2258632704*a^14*b^6 + 1214251008*a^15*b^5 - 268435456*a^16*b^4)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)) + (cos(c + d*x)*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*(402653184*a^12*b^9 - 1879048192*a^13*b^8 + 3489660928*a^14*b^7 - 3221225472*a^15*b^6 + 1476395008*a^16*b^5 - 268435456*a^17*b^4))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (cos(c + d*x)*(75497472*a^6*b^9 - 337215488*a^7*b^8 + 592748544*a^8*b^7 - 489406464*a^9*b^6 + 163684352*a^10*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) - (12582912*a^5*b^9 - 70631424*a^6*b^8 + 157676032*a^7*b^7 - 165152384*a^8*b^6 + 69895552*a^9*b^5)/(1048576*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (cos(c + d*x)*(3145728*b^9 - 14417920*a*b^8 + 26453264*a^2*b^7 - 23076232*a^3*b^6 + 8247825*a^4*b^5))/(524288*(a^12 - 4*a^11*b + a^8*b^4 - 4*a^9*b^3 + 6*a^10*b^2)))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2) + (1440144*a*b^7 - 331776*b^8 - 2174760*a^2*b^6 + 1184625*a^3*b^5)/(524288*(a^14 - 4*a^13*b + a^10*b^4 - 4*a^11*b^3 + 6*a^12*b^2))))*((2025*a^4*(a^13*b)^(1/2) + 384*b^4*(a^13*b)^(1/2) + 3465*a^10*b + 1024*a^6*b^5 - 5084*a^7*b^4 + 10045*a^8*b^3 - 9306*a^9*b^2 - 2000*a*b^3*(a^13*b)^(1/2) - 4694*a^3*b*(a^13*b)^(1/2) + 4429*a^2*b^2*(a^13*b)^(1/2))/(16384*(5*a^16*b - a^17 + a^12*b^5 - 5*a^13*b^4 + 10*a^14*b^3 - 10*a^15*b^2)))^(1/2)*2i)/d","B"
230,1,5508,319,19.648385,"\text{Not used}","int(sin(c + d*x)^8/(a - b*sin(c + d*x)^4)^3,x)","-\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^7\,\left(a+19\,b\right)}{32\,\left(a\,b-b^2\right)}+\frac{3\,{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(a^2+7\,b\,a\right)}{32\,\left(a^2\,b-2\,a\,b^2+b^3\right)}+\frac{a\,\mathrm{tan}\left(c+d\,x\right)\,\left(a+5\,b\right)}{32\,\left(a^2\,b-2\,a\,b^2+b^3\right)}+\frac{3\,{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(a^2+10\,a\,b-3\,b^2\right)}{32\,\left(a-b\right)\,\left(a\,b-b^2\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2-{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,a^2\right)-{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(4\,a\,b-4\,a^2\right)+4\,a^2\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{16384\,a^5\,b^3+32768\,a^4\,b^4-196608\,a^3\,b^5+229376\,a^2\,b^6-81920\,a\,b^7}{32768\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,\left(-16384\,a^7\,b^3+81920\,a^6\,b^4-163840\,a^5\,b^5+163840\,a^4\,b^6-81920\,a^3\,b^7+16384\,a^2\,b^8\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-35\,a^3\,b+35\,a^2\,b^2+259\,a\,b^3+25\,b^4\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{16384\,a^5\,b^3+32768\,a^4\,b^4-196608\,a^3\,b^5+229376\,a^2\,b^6-81920\,a\,b^7}{32768\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,\left(-16384\,a^7\,b^3+81920\,a^6\,b^4-163840\,a^5\,b^5+163840\,a^4\,b^6-81920\,a^3\,b^7+16384\,a^2\,b^8\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-35\,a^3\,b+35\,a^2\,b^2+259\,a\,b^3+25\,b^4\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,1{}\mathrm{i}}{\frac{4\,a^2-77\,a\,b+325\,b^2}{16384\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}+\left(\left(\frac{16384\,a^5\,b^3+32768\,a^4\,b^4-196608\,a^3\,b^5+229376\,a^2\,b^6-81920\,a\,b^7}{32768\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,\left(-16384\,a^7\,b^3+81920\,a^6\,b^4-163840\,a^5\,b^5+163840\,a^4\,b^6-81920\,a^3\,b^7+16384\,a^2\,b^8\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-35\,a^3\,b+35\,a^2\,b^2+259\,a\,b^3+25\,b^4\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}+\left(\left(\frac{16384\,a^5\,b^3+32768\,a^4\,b^4-196608\,a^3\,b^5+229376\,a^2\,b^6-81920\,a\,b^7}{32768\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,\left(-16384\,a^7\,b^3+81920\,a^6\,b^4-163840\,a^5\,b^5+163840\,a^4\,b^6-81920\,a^3\,b^7+16384\,a^2\,b^8\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-35\,a^3\,b+35\,a^2\,b^2+259\,a\,b^3+25\,b^4\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}}\right)\,\sqrt{\frac{25\,b^2\,\sqrt{a^3\,b^9}-35\,a^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3+154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{16384\,a^5\,b^3+32768\,a^4\,b^4-196608\,a^3\,b^5+229376\,a^2\,b^6-81920\,a\,b^7}{32768\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,\left(-16384\,a^7\,b^3+81920\,a^6\,b^4-163840\,a^5\,b^5+163840\,a^4\,b^6-81920\,a^3\,b^7+16384\,a^2\,b^8\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-35\,a^3\,b+35\,a^2\,b^2+259\,a\,b^3+25\,b^4\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{16384\,a^5\,b^3+32768\,a^4\,b^4-196608\,a^3\,b^5+229376\,a^2\,b^6-81920\,a\,b^7}{32768\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,\left(-16384\,a^7\,b^3+81920\,a^6\,b^4-163840\,a^5\,b^5+163840\,a^4\,b^6-81920\,a^3\,b^7+16384\,a^2\,b^8\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-35\,a^3\,b+35\,a^2\,b^2+259\,a\,b^3+25\,b^4\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,1{}\mathrm{i}}{\frac{4\,a^2-77\,a\,b+325\,b^2}{16384\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}+\left(\left(\frac{16384\,a^5\,b^3+32768\,a^4\,b^4-196608\,a^3\,b^5+229376\,a^2\,b^6-81920\,a\,b^7}{32768\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,\left(-16384\,a^7\,b^3+81920\,a^6\,b^4-163840\,a^5\,b^5+163840\,a^4\,b^6-81920\,a^3\,b^7+16384\,a^2\,b^8\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-35\,a^3\,b+35\,a^2\,b^2+259\,a\,b^3+25\,b^4\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}+\left(\left(\frac{16384\,a^5\,b^3+32768\,a^4\,b^4-196608\,a^3\,b^5+229376\,a^2\,b^6-81920\,a\,b^7}{32768\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,\left(-16384\,a^7\,b^3+81920\,a^6\,b^4-163840\,a^5\,b^5+163840\,a^4\,b^6-81920\,a^3\,b^7+16384\,a^2\,b^8\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4-35\,a^3\,b+35\,a^2\,b^2+259\,a\,b^3+25\,b^4\right)}{256\,\left(a^3\,b^2-3\,a^2\,b^3+3\,a\,b^4-b^5\right)}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}}\right)\,\sqrt{\frac{35\,a^2\,\sqrt{a^3\,b^9}-25\,b^2\,\sqrt{a^3\,b^9}+105\,a^2\,b^6+70\,a^3\,b^5-35\,a^4\,b^4+4\,a^5\,b^3-154\,a\,b\,\sqrt{a^3\,b^9}}{16384\,\left(-a^8\,b^6+5\,a^7\,b^7-10\,a^6\,b^8+10\,a^5\,b^9-5\,a^4\,b^{10}+a^3\,b^{11}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((((229376*a^2*b^6 - 81920*a*b^7 - 196608*a^3*b^5 + 32768*a^4*b^4 + 16384*a^5*b^3)/(32768*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) - (tan(c + d*x)*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*(16384*a^2*b^8 - 81920*a^3*b^7 + 163840*a^4*b^6 - 163840*a^5*b^5 + 81920*a^6*b^4 - 16384*a^7*b^3))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) + (tan(c + d*x)*(259*a*b^3 - 35*a^3*b + 4*a^4 + 25*b^4 + 35*a^2*b^2))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*1i - (((229376*a^2*b^6 - 81920*a*b^7 - 196608*a^3*b^5 + 32768*a^4*b^4 + 16384*a^5*b^3)/(32768*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) + (tan(c + d*x)*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*(16384*a^2*b^8 - 81920*a^3*b^7 + 163840*a^4*b^6 - 163840*a^5*b^5 + 81920*a^6*b^4 - 16384*a^7*b^3))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) - (tan(c + d*x)*(259*a*b^3 - 35*a^3*b + 4*a^4 + 25*b^4 + 35*a^2*b^2))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*1i)/((4*a^2 - 77*a*b + 325*b^2)/(16384*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) + (((229376*a^2*b^6 - 81920*a*b^7 - 196608*a^3*b^5 + 32768*a^4*b^4 + 16384*a^5*b^3)/(32768*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) - (tan(c + d*x)*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*(16384*a^2*b^8 - 81920*a^3*b^7 + 163840*a^4*b^6 - 163840*a^5*b^5 + 81920*a^6*b^4 - 16384*a^7*b^3))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) + (tan(c + d*x)*(259*a*b^3 - 35*a^3*b + 4*a^4 + 25*b^4 + 35*a^2*b^2))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) + (((229376*a^2*b^6 - 81920*a*b^7 - 196608*a^3*b^5 + 32768*a^4*b^4 + 16384*a^5*b^3)/(32768*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) + (tan(c + d*x)*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*(16384*a^2*b^8 - 81920*a^3*b^7 + 163840*a^4*b^6 - 163840*a^5*b^5 + 81920*a^6*b^4 - 16384*a^7*b^3))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) - (tan(c + d*x)*(259*a*b^3 - 35*a^3*b + 4*a^4 + 25*b^4 + 35*a^2*b^2))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)))*((25*b^2*(a^3*b^9)^(1/2) - 35*a^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 + 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*2i)/d - ((tan(c + d*x)^7*(a + 19*b))/(32*(a*b - b^2)) + (3*tan(c + d*x)^3*(7*a*b + a^2))/(32*(a^2*b - 2*a*b^2 + b^3)) + (a*tan(c + d*x)*(a + 5*b))/(32*(a^2*b - 2*a*b^2 + b^3)) + (3*tan(c + d*x)^5*(10*a*b + a^2 - 3*b^2))/(32*(a - b)*(a*b - b^2)))/(d*(tan(c + d*x)^8*(a^2 - 2*a*b + b^2) + a^2 - tan(c + d*x)^4*(2*a*b - 6*a^2) - tan(c + d*x)^6*(4*a*b - 4*a^2) + 4*a^2*tan(c + d*x)^2)) + (atan(((((229376*a^2*b^6 - 81920*a*b^7 - 196608*a^3*b^5 + 32768*a^4*b^4 + 16384*a^5*b^3)/(32768*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) - (tan(c + d*x)*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*(16384*a^2*b^8 - 81920*a^3*b^7 + 163840*a^4*b^6 - 163840*a^5*b^5 + 81920*a^6*b^4 - 16384*a^7*b^3))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) + (tan(c + d*x)*(259*a*b^3 - 35*a^3*b + 4*a^4 + 25*b^4 + 35*a^2*b^2))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*1i - (((229376*a^2*b^6 - 81920*a*b^7 - 196608*a^3*b^5 + 32768*a^4*b^4 + 16384*a^5*b^3)/(32768*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) + (tan(c + d*x)*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*(16384*a^2*b^8 - 81920*a^3*b^7 + 163840*a^4*b^6 - 163840*a^5*b^5 + 81920*a^6*b^4 - 16384*a^7*b^3))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) - (tan(c + d*x)*(259*a*b^3 - 35*a^3*b + 4*a^4 + 25*b^4 + 35*a^2*b^2))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*1i)/((4*a^2 - 77*a*b + 325*b^2)/(16384*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) + (((229376*a^2*b^6 - 81920*a*b^7 - 196608*a^3*b^5 + 32768*a^4*b^4 + 16384*a^5*b^3)/(32768*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) - (tan(c + d*x)*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*(16384*a^2*b^8 - 81920*a^3*b^7 + 163840*a^4*b^6 - 163840*a^5*b^5 + 81920*a^6*b^4 - 16384*a^7*b^3))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) + (tan(c + d*x)*(259*a*b^3 - 35*a^3*b + 4*a^4 + 25*b^4 + 35*a^2*b^2))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) + (((229376*a^2*b^6 - 81920*a*b^7 - 196608*a^3*b^5 + 32768*a^4*b^4 + 16384*a^5*b^3)/(32768*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) + (tan(c + d*x)*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*(16384*a^2*b^8 - 81920*a^3*b^7 + 163840*a^4*b^6 - 163840*a^5*b^5 + 81920*a^6*b^4 - 16384*a^7*b^3))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2) - (tan(c + d*x)*(259*a*b^3 - 35*a^3*b + 4*a^4 + 25*b^4 + 35*a^2*b^2))/(256*(3*a*b^4 - b^5 - 3*a^2*b^3 + a^3*b^2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)))*((35*a^2*(a^3*b^9)^(1/2) - 25*b^2*(a^3*b^9)^(1/2) + 105*a^2*b^6 + 70*a^3*b^5 - 35*a^4*b^4 + 4*a^5*b^3 - 154*a*b*(a^3*b^9)^(1/2))/(16384*(a^3*b^11 - 5*a^4*b^10 + 10*a^5*b^9 - 10*a^6*b^8 + 5*a^7*b^7 - a^8*b^6)))^(1/2)*2i)/d","B"
231,1,6391,343,20.336749,"\text{Not used}","int(sin(c + d*x)^6/(a - b*sin(c + d*x)^4)^3,x)","-\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(6\,a^2+19\,a\,b-b^2\right)}{32\,\left(a^2\,b-2\,a\,b^2+b^3\right)}+\frac{a\,\mathrm{tan}\left(c+d\,x\right)\,\left(a+2\,b\right)}{16\,\left(a^2\,b-2\,a\,b^2+b^3\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^7\,\left(2\,a^2+15\,a\,b+3\,b^2\right)}{32\,a\,\left(a\,b-b^2\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(3\,a^2+14\,a\,b-5\,b^2\right)}{16\,\left(a-b\right)\,\left(a\,b-b^2\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2-{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,a^2\right)-{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(4\,a\,b-4\,a^2\right)+4\,a^2\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-32768\,a^7\,b^3+32768\,a^6\,b^4+98304\,a^5\,b^5-163840\,a^4\,b^6+65536\,a^3\,b^7}{32768\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,\left(-16384\,a^8\,b^3+81920\,a^7\,b^4-163840\,a^6\,b^5+163840\,a^5\,b^6-81920\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^5-116\,a^4\,b+149\,a^3\,b^2+331\,a^2\,b^3-101\,a\,b^4+9\,b^5\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-32768\,a^7\,b^3+32768\,a^6\,b^4+98304\,a^5\,b^5-163840\,a^4\,b^6+65536\,a^3\,b^7}{32768\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,\left(-16384\,a^8\,b^3+81920\,a^7\,b^4-163840\,a^6\,b^5+163840\,a^5\,b^6-81920\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^5-116\,a^4\,b+149\,a^3\,b^2+331\,a^2\,b^3-101\,a\,b^4+9\,b^5\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-32768\,a^7\,b^3+32768\,a^6\,b^4+98304\,a^5\,b^5-163840\,a^4\,b^6+65536\,a^3\,b^7}{32768\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,\left(-16384\,a^8\,b^3+81920\,a^7\,b^4-163840\,a^6\,b^5+163840\,a^5\,b^6-81920\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^5-116\,a^4\,b+149\,a^3\,b^2+331\,a^2\,b^3-101\,a\,b^4+9\,b^5\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}-\frac{32\,a^4-424\,a^3\,b+1358\,a^2\,b^2-381\,a\,b^3+27\,b^4}{16384\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}+\left(\left(\frac{-32768\,a^7\,b^3+32768\,a^6\,b^4+98304\,a^5\,b^5-163840\,a^4\,b^6+65536\,a^3\,b^7}{32768\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,\left(-16384\,a^8\,b^3+81920\,a^7\,b^4-163840\,a^6\,b^5+163840\,a^5\,b^6-81920\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^5-116\,a^4\,b+149\,a^3\,b^2+331\,a^2\,b^3-101\,a\,b^4+9\,b^5\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}}\right)\,\sqrt{\frac{9\,b^3\,\sqrt{a^5\,b^9}-80\,a^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3-86\,a\,b^2\,\sqrt{a^5\,b^9}+301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-32768\,a^7\,b^3+32768\,a^6\,b^4+98304\,a^5\,b^5-163840\,a^4\,b^6+65536\,a^3\,b^7}{32768\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,\left(-16384\,a^8\,b^3+81920\,a^7\,b^4-163840\,a^6\,b^5+163840\,a^5\,b^6-81920\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^5-116\,a^4\,b+149\,a^3\,b^2+331\,a^2\,b^3-101\,a\,b^4+9\,b^5\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-32768\,a^7\,b^3+32768\,a^6\,b^4+98304\,a^5\,b^5-163840\,a^4\,b^6+65536\,a^3\,b^7}{32768\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,\left(-16384\,a^8\,b^3+81920\,a^7\,b^4-163840\,a^6\,b^5+163840\,a^5\,b^6-81920\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^5-116\,a^4\,b+149\,a^3\,b^2+331\,a^2\,b^3-101\,a\,b^4+9\,b^5\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-32768\,a^7\,b^3+32768\,a^6\,b^4+98304\,a^5\,b^5-163840\,a^4\,b^6+65536\,a^3\,b^7}{32768\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,\left(-16384\,a^8\,b^3+81920\,a^7\,b^4-163840\,a^6\,b^5+163840\,a^5\,b^6-81920\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^5-116\,a^4\,b+149\,a^3\,b^2+331\,a^2\,b^3-101\,a\,b^4+9\,b^5\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}-\frac{32\,a^4-424\,a^3\,b+1358\,a^2\,b^2-381\,a\,b^3+27\,b^4}{16384\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}+\left(\left(\frac{-32768\,a^7\,b^3+32768\,a^6\,b^4+98304\,a^5\,b^5-163840\,a^4\,b^6+65536\,a^3\,b^7}{32768\,\left(-a^5\,b^3+3\,a^4\,b^4-3\,a^3\,b^5+a^2\,b^6\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,\left(-16384\,a^8\,b^3+81920\,a^7\,b^4-163840\,a^6\,b^5+163840\,a^5\,b^6-81920\,a^4\,b^7+16384\,a^3\,b^8\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^5-116\,a^4\,b+149\,a^3\,b^2+331\,a^2\,b^3-101\,a\,b^4+9\,b^5\right)}{256\,\left(-a^4\,b^2+3\,a^3\,b^3-3\,a^2\,b^4+a\,b^5\right)}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}}\right)\,\sqrt{\frac{80\,a^3\,\sqrt{a^5\,b^9}-9\,b^3\,\sqrt{a^5\,b^9}-15\,a^3\,b^7+30\,a^4\,b^6+229\,a^5\,b^5-116\,a^6\,b^4+16\,a^7\,b^3+86\,a\,b^2\,\sqrt{a^5\,b^9}-301\,a^2\,b\,\sqrt{a^5\,b^9}}{16384\,\left(-a^{10}\,b^6+5\,a^9\,b^7-10\,a^8\,b^8+10\,a^7\,b^9-5\,a^6\,b^{10}+a^5\,b^{11}\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- ((tan(c + d*x)^3*(19*a*b + 6*a^2 - b^2))/(32*(a^2*b - 2*a*b^2 + b^3)) + (a*tan(c + d*x)*(a + 2*b))/(16*(a^2*b - 2*a*b^2 + b^3)) + (tan(c + d*x)^7*(15*a*b + 2*a^2 + 3*b^2))/(32*a*(a*b - b^2)) + (tan(c + d*x)^5*(14*a*b + 3*a^2 - 5*b^2))/(16*(a - b)*(a*b - b^2)))/(d*(tan(c + d*x)^8*(a^2 - 2*a*b + b^2) + a^2 - tan(c + d*x)^4*(2*a*b - 6*a^2) - tan(c + d*x)^6*(4*a*b - 4*a^2) + 4*a^2*tan(c + d*x)^2)) - (atan(((((65536*a^3*b^7 - 163840*a^4*b^6 + 98304*a^5*b^5 + 32768*a^6*b^4 - 32768*a^7*b^3)/(32768*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) - (tan(c + d*x)*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*(16384*a^3*b^8 - 81920*a^4*b^7 + 163840*a^5*b^6 - 163840*a^6*b^5 + 81920*a^7*b^4 - 16384*a^8*b^3))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) + (tan(c + d*x)*(16*a^5 - 116*a^4*b - 101*a*b^4 + 9*b^5 + 331*a^2*b^3 + 149*a^3*b^2))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*1i - (((65536*a^3*b^7 - 163840*a^4*b^6 + 98304*a^5*b^5 + 32768*a^6*b^4 - 32768*a^7*b^3)/(32768*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) + (tan(c + d*x)*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*(16384*a^3*b^8 - 81920*a^4*b^7 + 163840*a^5*b^6 - 163840*a^6*b^5 + 81920*a^7*b^4 - 16384*a^8*b^3))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) - (tan(c + d*x)*(16*a^5 - 116*a^4*b - 101*a*b^4 + 9*b^5 + 331*a^2*b^3 + 149*a^3*b^2))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*1i)/((((65536*a^3*b^7 - 163840*a^4*b^6 + 98304*a^5*b^5 + 32768*a^6*b^4 - 32768*a^7*b^3)/(32768*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) - (tan(c + d*x)*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*(16384*a^3*b^8 - 81920*a^4*b^7 + 163840*a^5*b^6 - 163840*a^6*b^5 + 81920*a^7*b^4 - 16384*a^8*b^3))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) + (tan(c + d*x)*(16*a^5 - 116*a^4*b - 101*a*b^4 + 9*b^5 + 331*a^2*b^3 + 149*a^3*b^2))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) - (32*a^4 - 424*a^3*b - 381*a*b^3 + 27*b^4 + 1358*a^2*b^2)/(16384*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) + (((65536*a^3*b^7 - 163840*a^4*b^6 + 98304*a^5*b^5 + 32768*a^6*b^4 - 32768*a^7*b^3)/(32768*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) + (tan(c + d*x)*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*(16384*a^3*b^8 - 81920*a^4*b^7 + 163840*a^5*b^6 - 163840*a^6*b^5 + 81920*a^7*b^4 - 16384*a^8*b^3))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) - (tan(c + d*x)*(16*a^5 - 116*a^4*b - 101*a*b^4 + 9*b^5 + 331*a^2*b^3 + 149*a^3*b^2))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)))*((9*b^3*(a^5*b^9)^(1/2) - 80*a^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 - 86*a*b^2*(a^5*b^9)^(1/2) + 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*2i)/d - (atan(((((65536*a^3*b^7 - 163840*a^4*b^6 + 98304*a^5*b^5 + 32768*a^6*b^4 - 32768*a^7*b^3)/(32768*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) - (tan(c + d*x)*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*(16384*a^3*b^8 - 81920*a^4*b^7 + 163840*a^5*b^6 - 163840*a^6*b^5 + 81920*a^7*b^4 - 16384*a^8*b^3))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) + (tan(c + d*x)*(16*a^5 - 116*a^4*b - 101*a*b^4 + 9*b^5 + 331*a^2*b^3 + 149*a^3*b^2))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*1i - (((65536*a^3*b^7 - 163840*a^4*b^6 + 98304*a^5*b^5 + 32768*a^6*b^4 - 32768*a^7*b^3)/(32768*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) + (tan(c + d*x)*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*(16384*a^3*b^8 - 81920*a^4*b^7 + 163840*a^5*b^6 - 163840*a^6*b^5 + 81920*a^7*b^4 - 16384*a^8*b^3))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) - (tan(c + d*x)*(16*a^5 - 116*a^4*b - 101*a*b^4 + 9*b^5 + 331*a^2*b^3 + 149*a^3*b^2))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*1i)/((((65536*a^3*b^7 - 163840*a^4*b^6 + 98304*a^5*b^5 + 32768*a^6*b^4 - 32768*a^7*b^3)/(32768*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) - (tan(c + d*x)*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*(16384*a^3*b^8 - 81920*a^4*b^7 + 163840*a^5*b^6 - 163840*a^6*b^5 + 81920*a^7*b^4 - 16384*a^8*b^3))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) + (tan(c + d*x)*(16*a^5 - 116*a^4*b - 101*a*b^4 + 9*b^5 + 331*a^2*b^3 + 149*a^3*b^2))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) - (32*a^4 - 424*a^3*b - 381*a*b^3 + 27*b^4 + 1358*a^2*b^2)/(16384*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) + (((65536*a^3*b^7 - 163840*a^4*b^6 + 98304*a^5*b^5 + 32768*a^6*b^4 - 32768*a^7*b^3)/(32768*(a^2*b^6 - 3*a^3*b^5 + 3*a^4*b^4 - a^5*b^3)) + (tan(c + d*x)*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*(16384*a^3*b^8 - 81920*a^4*b^7 + 163840*a^5*b^6 - 163840*a^6*b^5 + 81920*a^7*b^4 - 16384*a^8*b^3))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2) - (tan(c + d*x)*(16*a^5 - 116*a^4*b - 101*a*b^4 + 9*b^5 + 331*a^2*b^3 + 149*a^3*b^2))/(256*(a*b^5 - 3*a^2*b^4 + 3*a^3*b^3 - a^4*b^2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)))*((80*a^3*(a^5*b^9)^(1/2) - 9*b^3*(a^5*b^9)^(1/2) - 15*a^3*b^7 + 30*a^4*b^6 + 229*a^5*b^5 - 116*a^6*b^4 + 16*a^7*b^3 + 86*a*b^2*(a^5*b^9)^(1/2) - 301*a^2*b*(a^5*b^9)^(1/2))/(16384*(a^5*b^11 - 5*a^6*b^10 + 10*a^7*b^9 - 10*a^8*b^8 + 5*a^9*b^7 - a^10*b^6)))^(1/2)*2i)/d","B"
232,1,5892,313,19.498783,"\text{Not used}","int(sin(c + d*x)^4/(a - b*sin(c + d*x)^4)^3,x)","-\frac{\frac{3\,\mathrm{tan}\left(c+d\,x\right)\,\left(3\,a-b\right)}{32\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(35\,a-11\,b\right)}{32\,\left(a^2-2\,a\,b+b^2\right)}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(-43\,a^2+18\,a\,b+b^2\right)}{32\,a\,{\left(a-b\right)}^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^7\,\left(17\,a+3\,b\right)}{32\,a\,\left(a-b\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2-{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,a^2\right)-{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(4\,a\,b-4\,a^2\right)+4\,a^2\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(49152\,a^7\,b-163840\,a^6\,b^2+196608\,a^5\,b^3-98304\,a^4\,b^4+16384\,a^3\,b^5\right)}{32768\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,\left(16384\,a^9\,b-81920\,a^8\,b^2+163840\,a^7\,b^3-163840\,a^6\,b^4+81920\,a^5\,b^5-16384\,a^4\,b^6\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(36\,a^4+333\,a^3\,b-45\,a^2\,b^2-45\,a\,b^3+9\,b^4\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(49152\,a^7\,b-163840\,a^6\,b^2+196608\,a^5\,b^3-98304\,a^4\,b^4+16384\,a^3\,b^5\right)}{32768\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,\left(16384\,a^9\,b-81920\,a^8\,b^2+163840\,a^7\,b^3-163840\,a^6\,b^4+81920\,a^5\,b^5-16384\,a^4\,b^6\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(36\,a^4+333\,a^3\,b-45\,a^2\,b^2-45\,a\,b^3+9\,b^4\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3\,\left(49152\,a^7\,b-163840\,a^6\,b^2+196608\,a^5\,b^3-98304\,a^4\,b^4+16384\,a^3\,b^5\right)}{32768\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,\left(16384\,a^9\,b-81920\,a^8\,b^2+163840\,a^7\,b^3-163840\,a^6\,b^4+81920\,a^5\,b^5-16384\,a^4\,b^6\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(36\,a^4+333\,a^3\,b-45\,a^2\,b^2-45\,a\,b^3+9\,b^4\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}-\frac{3\,\left(180\,a^2-81\,a\,b+9\,b^2\right)}{16384\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\left(\left(\frac{3\,\left(49152\,a^7\,b-163840\,a^6\,b^2+196608\,a^5\,b^3-98304\,a^4\,b^4+16384\,a^3\,b^5\right)}{32768\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,\left(16384\,a^9\,b-81920\,a^8\,b^2+163840\,a^7\,b^3-163840\,a^6\,b^4+81920\,a^5\,b^5-16384\,a^4\,b^6\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(36\,a^4+333\,a^3\,b-45\,a^2\,b^2-45\,a\,b^3+9\,b^4\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}}\right)\,\sqrt{\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}+4\,a^7\,b+a^4\,b^4-10\,a^5\,b^3+21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(49152\,a^7\,b-163840\,a^6\,b^2+196608\,a^5\,b^3-98304\,a^4\,b^4+16384\,a^3\,b^5\right)}{32768\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,\left(16384\,a^9\,b-81920\,a^8\,b^2+163840\,a^7\,b^3-163840\,a^6\,b^4+81920\,a^5\,b^5-16384\,a^4\,b^6\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(36\,a^4+333\,a^3\,b-45\,a^2\,b^2-45\,a\,b^3+9\,b^4\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(49152\,a^7\,b-163840\,a^6\,b^2+196608\,a^5\,b^3-98304\,a^4\,b^4+16384\,a^3\,b^5\right)}{32768\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,\left(16384\,a^9\,b-81920\,a^8\,b^2+163840\,a^7\,b^3-163840\,a^6\,b^4+81920\,a^5\,b^5-16384\,a^4\,b^6\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(36\,a^4+333\,a^3\,b-45\,a^2\,b^2-45\,a\,b^3+9\,b^4\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3\,\left(49152\,a^7\,b-163840\,a^6\,b^2+196608\,a^5\,b^3-98304\,a^4\,b^4+16384\,a^3\,b^5\right)}{32768\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,\left(16384\,a^9\,b-81920\,a^8\,b^2+163840\,a^7\,b^3-163840\,a^6\,b^4+81920\,a^5\,b^5-16384\,a^4\,b^6\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(36\,a^4+333\,a^3\,b-45\,a^2\,b^2-45\,a\,b^3+9\,b^4\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}-\frac{3\,\left(180\,a^2-81\,a\,b+9\,b^2\right)}{16384\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\left(\left(\frac{3\,\left(49152\,a^7\,b-163840\,a^6\,b^2+196608\,a^5\,b^3-98304\,a^4\,b^4+16384\,a^3\,b^5\right)}{32768\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,\left(16384\,a^9\,b-81920\,a^8\,b^2+163840\,a^7\,b^3-163840\,a^6\,b^4+81920\,a^5\,b^5-16384\,a^4\,b^6\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(36\,a^4+333\,a^3\,b-45\,a^2\,b^2-45\,a\,b^3+9\,b^4\right)}{256\,\left(-a^5+3\,a^4\,b-3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}}\right)\,\sqrt{-\frac{9\,\left(16\,a^3\,\sqrt{a^7\,b^3}+b^3\,\sqrt{a^7\,b^3}-4\,a^7\,b-a^4\,b^4+10\,a^5\,b^3-21\,a^6\,b^2-6\,a\,b^2\,\sqrt{a^7\,b^3}+5\,a^2\,b\,\sqrt{a^7\,b^3}\right)}{16384\,\left(-a^{12}\,b^2+5\,a^{11}\,b^3-10\,a^{10}\,b^4+10\,a^9\,b^5-5\,a^8\,b^6+a^7\,b^7\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- (atan(((((3*(49152*a^7*b + 16384*a^3*b^5 - 98304*a^4*b^4 + 196608*a^5*b^3 - 163840*a^6*b^2))/(32768*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) - (tan(c + d*x)*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*(16384*a^9*b - 16384*a^4*b^6 + 81920*a^5*b^5 - 163840*a^6*b^4 + 163840*a^7*b^3 - 81920*a^8*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) - (tan(c + d*x)*(333*a^3*b - 45*a*b^3 + 36*a^4 + 9*b^4 - 45*a^2*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*1i - (((3*(49152*a^7*b + 16384*a^3*b^5 - 98304*a^4*b^4 + 196608*a^5*b^3 - 163840*a^6*b^2))/(32768*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (tan(c + d*x)*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*(16384*a^9*b - 16384*a^4*b^6 + 81920*a^5*b^5 - 163840*a^6*b^4 + 163840*a^7*b^3 - 81920*a^8*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) + (tan(c + d*x)*(333*a^3*b - 45*a*b^3 + 36*a^4 + 9*b^4 - 45*a^2*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*1i)/((((3*(49152*a^7*b + 16384*a^3*b^5 - 98304*a^4*b^4 + 196608*a^5*b^3 - 163840*a^6*b^2))/(32768*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) - (tan(c + d*x)*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*(16384*a^9*b - 16384*a^4*b^6 + 81920*a^5*b^5 - 163840*a^6*b^4 + 163840*a^7*b^3 - 81920*a^8*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) - (tan(c + d*x)*(333*a^3*b - 45*a*b^3 + 36*a^4 + 9*b^4 - 45*a^2*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) - (3*(180*a^2 - 81*a*b + 9*b^2))/(16384*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (((3*(49152*a^7*b + 16384*a^3*b^5 - 98304*a^4*b^4 + 196608*a^5*b^3 - 163840*a^6*b^2))/(32768*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (tan(c + d*x)*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*(16384*a^9*b - 16384*a^4*b^6 + 81920*a^5*b^5 - 163840*a^6*b^4 + 163840*a^7*b^3 - 81920*a^8*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) + (tan(c + d*x)*(333*a^3*b - 45*a*b^3 + 36*a^4 + 9*b^4 - 45*a^2*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)))*((9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) + 4*a^7*b + a^4*b^4 - 10*a^5*b^3 + 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*2i)/d - (atan(((((3*(49152*a^7*b + 16384*a^3*b^5 - 98304*a^4*b^4 + 196608*a^5*b^3 - 163840*a^6*b^2))/(32768*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) - (tan(c + d*x)*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*(16384*a^9*b - 16384*a^4*b^6 + 81920*a^5*b^5 - 163840*a^6*b^4 + 163840*a^7*b^3 - 81920*a^8*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) - (tan(c + d*x)*(333*a^3*b - 45*a*b^3 + 36*a^4 + 9*b^4 - 45*a^2*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*1i - (((3*(49152*a^7*b + 16384*a^3*b^5 - 98304*a^4*b^4 + 196608*a^5*b^3 - 163840*a^6*b^2))/(32768*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (tan(c + d*x)*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*(16384*a^9*b - 16384*a^4*b^6 + 81920*a^5*b^5 - 163840*a^6*b^4 + 163840*a^7*b^3 - 81920*a^8*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) + (tan(c + d*x)*(333*a^3*b - 45*a*b^3 + 36*a^4 + 9*b^4 - 45*a^2*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*1i)/((((3*(49152*a^7*b + 16384*a^3*b^5 - 98304*a^4*b^4 + 196608*a^5*b^3 - 163840*a^6*b^2))/(32768*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) - (tan(c + d*x)*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*(16384*a^9*b - 16384*a^4*b^6 + 81920*a^5*b^5 - 163840*a^6*b^4 + 163840*a^7*b^3 - 81920*a^8*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) - (tan(c + d*x)*(333*a^3*b - 45*a*b^3 + 36*a^4 + 9*b^4 - 45*a^2*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) - (3*(180*a^2 - 81*a*b + 9*b^2))/(16384*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (((3*(49152*a^7*b + 16384*a^3*b^5 - 98304*a^4*b^4 + 196608*a^5*b^3 - 163840*a^6*b^2))/(32768*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (tan(c + d*x)*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*(16384*a^9*b - 16384*a^4*b^6 + 81920*a^5*b^5 - 163840*a^6*b^4 + 163840*a^7*b^3 - 81920*a^8*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2) + (tan(c + d*x)*(333*a^3*b - 45*a*b^3 + 36*a^4 + 9*b^4 - 45*a^2*b^2))/(256*(3*a^4*b - a^5 + a^2*b^3 - 3*a^3*b^2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)))*(-(9*(16*a^3*(a^7*b^3)^(1/2) + b^3*(a^7*b^3)^(1/2) - 4*a^7*b - a^4*b^4 + 10*a^5*b^3 - 21*a^6*b^2 - 6*a*b^2*(a^7*b^3)^(1/2) + 5*a^2*b*(a^7*b^3)^(1/2)))/(16384*(a^7*b^7 - 5*a^8*b^6 + 10*a^9*b^5 - 10*a^10*b^4 + 5*a^11*b^3 - a^12*b^2)))^(1/2)*2i)/d - ((3*tan(c + d*x)*(3*a - b))/(32*(a^2 - 2*a*b + b^2)) + (tan(c + d*x)^3*(35*a - 11*b))/(32*(a^2 - 2*a*b + b^2)) - (tan(c + d*x)^5*(18*a*b - 43*a^2 + b^2))/(32*a*(a - b)^2) + (tan(c + d*x)^7*(17*a + 3*b))/(32*a*(a - b)))/(d*(tan(c + d*x)^8*(a^2 - 2*a*b + b^2) + a^2 - tan(c + d*x)^4*(2*a*b - 6*a^2) - tan(c + d*x)^6*(4*a*b - 4*a^2) + 4*a^2*tan(c + d*x)^2))","B"
233,1,6646,347,19.904630,"\text{Not used}","int(sin(c + d*x)^2/(a - b*sin(c + d*x)^4)^3,x)","-\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5\,a-2\,b\right)}{16\,\left(a^2-2\,a\,b+b^2\right)}+\frac{3\,{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(10\,a^2+a\,b-3\,b^2\right)}{32\,a\,\left(a^2-2\,a\,b+b^2\right)}+\frac{5\,{\mathrm{tan}\left(c+d\,x\right)}^7\,\left(2\,a^2+3\,a\,b-b^2\right)}{32\,a^2\,\left(a-b\right)}+\frac{3\,{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(5\,a^2+2\,a\,b-3\,b^2\right)}{16\,a\,{\left(a-b\right)}^2}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2-{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,a^2\right)-{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(4\,a\,b-4\,a^2\right)+4\,a^2\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{163840\,a^9\,b-557056\,a^8\,b^2+688128\,a^7\,b^3-360448\,a^6\,b^4+65536\,a^5\,b^5}{32768\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,\left(16384\,a^{10}\,b-81920\,a^9\,b^2+163840\,a^8\,b^3-163840\,a^7\,b^4+81920\,a^6\,b^5-16384\,a^5\,b^6\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5+460\,a^4\,b-635\,a^3\,b^2+443\,a^2\,b^3-149\,a\,b^4+25\,b^5\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,1{}\mathrm{i}-\left(\left(\frac{163840\,a^9\,b-557056\,a^8\,b^2+688128\,a^7\,b^3-360448\,a^6\,b^4+65536\,a^5\,b^5}{32768\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,\left(16384\,a^{10}\,b-81920\,a^9\,b^2+163840\,a^8\,b^3-163840\,a^7\,b^4+81920\,a^6\,b^5-16384\,a^5\,b^6\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5+460\,a^4\,b-635\,a^3\,b^2+443\,a^2\,b^3-149\,a\,b^4+25\,b^5\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{163840\,a^9\,b-557056\,a^8\,b^2+688128\,a^7\,b^3-360448\,a^6\,b^4+65536\,a^5\,b^5}{32768\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,\left(16384\,a^{10}\,b-81920\,a^9\,b^2+163840\,a^8\,b^3-163840\,a^7\,b^4+81920\,a^6\,b^5-16384\,a^5\,b^6\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5+460\,a^4\,b-635\,a^3\,b^2+443\,a^2\,b^3-149\,a\,b^4+25\,b^5\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}-\frac{3168\,a^4-3832\,a^3\,b+2410\,a^2\,b^2-755\,a\,b^3+125\,b^4}{16384\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}+\left(\left(\frac{163840\,a^9\,b-557056\,a^8\,b^2+688128\,a^7\,b^3-360448\,a^6\,b^4+65536\,a^5\,b^5}{32768\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,\left(16384\,a^{10}\,b-81920\,a^9\,b^2+163840\,a^8\,b^3-163840\,a^7\,b^4+81920\,a^6\,b^5-16384\,a^5\,b^6\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5+460\,a^4\,b-635\,a^3\,b^2+443\,a^2\,b^3-149\,a\,b^4+25\,b^5\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}}\right)\,\sqrt{-\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}-144\,a^9\,b+15\,a^5\,b^5-94\,a^6\,b^4+155\,a^7\,b^3-76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{163840\,a^9\,b-557056\,a^8\,b^2+688128\,a^7\,b^3-360448\,a^6\,b^4+65536\,a^5\,b^5}{32768\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,\left(16384\,a^{10}\,b-81920\,a^9\,b^2+163840\,a^8\,b^3-163840\,a^7\,b^4+81920\,a^6\,b^5-16384\,a^5\,b^6\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5+460\,a^4\,b-635\,a^3\,b^2+443\,a^2\,b^3-149\,a\,b^4+25\,b^5\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,1{}\mathrm{i}-\left(\left(\frac{163840\,a^9\,b-557056\,a^8\,b^2+688128\,a^7\,b^3-360448\,a^6\,b^4+65536\,a^5\,b^5}{32768\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,\left(16384\,a^{10}\,b-81920\,a^9\,b^2+163840\,a^8\,b^3-163840\,a^7\,b^4+81920\,a^6\,b^5-16384\,a^5\,b^6\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5+460\,a^4\,b-635\,a^3\,b^2+443\,a^2\,b^3-149\,a\,b^4+25\,b^5\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{163840\,a^9\,b-557056\,a^8\,b^2+688128\,a^7\,b^3-360448\,a^6\,b^4+65536\,a^5\,b^5}{32768\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,\left(16384\,a^{10}\,b-81920\,a^9\,b^2+163840\,a^8\,b^3-163840\,a^7\,b^4+81920\,a^6\,b^5-16384\,a^5\,b^6\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5+460\,a^4\,b-635\,a^3\,b^2+443\,a^2\,b^3-149\,a\,b^4+25\,b^5\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}-\frac{3168\,a^4-3832\,a^3\,b+2410\,a^2\,b^2-755\,a\,b^3+125\,b^4}{16384\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}+\left(\left(\frac{163840\,a^9\,b-557056\,a^8\,b^2+688128\,a^7\,b^3-360448\,a^6\,b^4+65536\,a^5\,b^5}{32768\,\left(-a^8+3\,a^7\,b-3\,a^6\,b^2+a^5\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,\left(16384\,a^{10}\,b-81920\,a^9\,b^2+163840\,a^8\,b^3-163840\,a^7\,b^4+81920\,a^6\,b^5-16384\,a^5\,b^6\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5+460\,a^4\,b-635\,a^3\,b^2+443\,a^2\,b^3-149\,a\,b^4+25\,b^5\right)}{256\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}}\right)\,\sqrt{\frac{384\,a^4\,\sqrt{a^9\,b^3}+25\,b^4\,\sqrt{a^9\,b^3}+144\,a^9\,b-15\,a^5\,b^5+94\,a^6\,b^4-155\,a^7\,b^3+76\,a^8\,b^2+349\,a^2\,b^2\,\sqrt{a^9\,b^3}-134\,a\,b^3\,\sqrt{a^9\,b^3}-480\,a^3\,b\,\sqrt{a^9\,b^3}}{16384\,\left(-a^{14}\,b^2+5\,a^{13}\,b^3-10\,a^{12}\,b^4+10\,a^{11}\,b^5-5\,a^{10}\,b^6+a^9\,b^7\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- ((tan(c + d*x)*(5*a - 2*b))/(16*(a^2 - 2*a*b + b^2)) + (3*tan(c + d*x)^3*(a*b + 10*a^2 - 3*b^2))/(32*a*(a^2 - 2*a*b + b^2)) + (5*tan(c + d*x)^7*(3*a*b + 2*a^2 - b^2))/(32*a^2*(a - b)) + (3*tan(c + d*x)^5*(2*a*b + 5*a^2 - 3*b^2))/(16*a*(a - b)^2))/(d*(tan(c + d*x)^8*(a^2 - 2*a*b + b^2) + a^2 - tan(c + d*x)^4*(2*a*b - 6*a^2) - tan(c + d*x)^6*(4*a*b - 4*a^2) + 4*a^2*tan(c + d*x)^2)) - (atan(((((163840*a^9*b + 65536*a^5*b^5 - 360448*a^6*b^4 + 688128*a^7*b^3 - 557056*a^8*b^2)/(32768*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) - (tan(c + d*x)*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*(16384*a^10*b - 16384*a^5*b^6 + 81920*a^6*b^5 - 163840*a^7*b^4 + 163840*a^8*b^3 - 81920*a^9*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) - (tan(c + d*x)*(460*a^4*b - 149*a*b^4 + 144*a^5 + 25*b^5 + 443*a^2*b^3 - 635*a^3*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*1i - (((163840*a^9*b + 65536*a^5*b^5 - 360448*a^6*b^4 + 688128*a^7*b^3 - 557056*a^8*b^2)/(32768*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) + (tan(c + d*x)*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*(16384*a^10*b - 16384*a^5*b^6 + 81920*a^6*b^5 - 163840*a^7*b^4 + 163840*a^8*b^3 - 81920*a^9*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) + (tan(c + d*x)*(460*a^4*b - 149*a*b^4 + 144*a^5 + 25*b^5 + 443*a^2*b^3 - 635*a^3*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*1i)/((((163840*a^9*b + 65536*a^5*b^5 - 360448*a^6*b^4 + 688128*a^7*b^3 - 557056*a^8*b^2)/(32768*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) - (tan(c + d*x)*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*(16384*a^10*b - 16384*a^5*b^6 + 81920*a^6*b^5 - 163840*a^7*b^4 + 163840*a^8*b^3 - 81920*a^9*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) - (tan(c + d*x)*(460*a^4*b - 149*a*b^4 + 144*a^5 + 25*b^5 + 443*a^2*b^3 - 635*a^3*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) - (3168*a^4 - 3832*a^3*b - 755*a*b^3 + 125*b^4 + 2410*a^2*b^2)/(16384*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) + (((163840*a^9*b + 65536*a^5*b^5 - 360448*a^6*b^4 + 688128*a^7*b^3 - 557056*a^8*b^2)/(32768*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) + (tan(c + d*x)*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*(16384*a^10*b - 16384*a^5*b^6 + 81920*a^6*b^5 - 163840*a^7*b^4 + 163840*a^8*b^3 - 81920*a^9*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) + (tan(c + d*x)*(460*a^4*b - 149*a*b^4 + 144*a^5 + 25*b^5 + 443*a^2*b^3 - 635*a^3*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)))*(-(384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) - 144*a^9*b + 15*a^5*b^5 - 94*a^6*b^4 + 155*a^7*b^3 - 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*2i)/d - (atan(((((163840*a^9*b + 65536*a^5*b^5 - 360448*a^6*b^4 + 688128*a^7*b^3 - 557056*a^8*b^2)/(32768*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) - (tan(c + d*x)*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*(16384*a^10*b - 16384*a^5*b^6 + 81920*a^6*b^5 - 163840*a^7*b^4 + 163840*a^8*b^3 - 81920*a^9*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) - (tan(c + d*x)*(460*a^4*b - 149*a*b^4 + 144*a^5 + 25*b^5 + 443*a^2*b^3 - 635*a^3*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*1i - (((163840*a^9*b + 65536*a^5*b^5 - 360448*a^6*b^4 + 688128*a^7*b^3 - 557056*a^8*b^2)/(32768*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) + (tan(c + d*x)*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*(16384*a^10*b - 16384*a^5*b^6 + 81920*a^6*b^5 - 163840*a^7*b^4 + 163840*a^8*b^3 - 81920*a^9*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) + (tan(c + d*x)*(460*a^4*b - 149*a*b^4 + 144*a^5 + 25*b^5 + 443*a^2*b^3 - 635*a^3*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*1i)/((((163840*a^9*b + 65536*a^5*b^5 - 360448*a^6*b^4 + 688128*a^7*b^3 - 557056*a^8*b^2)/(32768*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) - (tan(c + d*x)*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*(16384*a^10*b - 16384*a^5*b^6 + 81920*a^6*b^5 - 163840*a^7*b^4 + 163840*a^8*b^3 - 81920*a^9*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) - (tan(c + d*x)*(460*a^4*b - 149*a*b^4 + 144*a^5 + 25*b^5 + 443*a^2*b^3 - 635*a^3*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) - (3168*a^4 - 3832*a^3*b - 755*a*b^3 + 125*b^4 + 2410*a^2*b^2)/(16384*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) + (((163840*a^9*b + 65536*a^5*b^5 - 360448*a^6*b^4 + 688128*a^7*b^3 - 557056*a^8*b^2)/(32768*(3*a^7*b - a^8 + a^5*b^3 - 3*a^6*b^2)) + (tan(c + d*x)*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*(16384*a^10*b - 16384*a^5*b^6 + 81920*a^6*b^5 - 163840*a^7*b^4 + 163840*a^8*b^3 - 81920*a^9*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2) + (tan(c + d*x)*(460*a^4*b - 149*a*b^4 + 144*a^5 + 25*b^5 + 443*a^2*b^3 - 635*a^3*b^2))/(256*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)))*((384*a^4*(a^9*b^3)^(1/2) + 25*b^4*(a^9*b^3)^(1/2) + 144*a^9*b - 15*a^5*b^5 + 94*a^6*b^4 - 155*a^7*b^3 + 76*a^8*b^2 + 349*a^2*b^2*(a^9*b^3)^(1/2) - 134*a*b^3*(a^9*b^3)^(1/2) - 480*a^3*b*(a^9*b^3)^(1/2))/(16384*(a^9*b^7 - 5*a^10*b^6 + 10*a^11*b^5 - 10*a^12*b^4 + 5*a^13*b^3 - a^14*b^2)))^(1/2)*2i)/d","B"
234,1,6267,319,19.666187,"\text{Not used}","int(1/(a - b*sin(c + d*x)^4)^3,x)","-\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(83\,a^2\,b-66\,a\,b^2+7\,b^3\right)}{32\,a^2\,{\left(a-b\right)}^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^7\,\left(33\,a\,b-13\,b^2\right)}{32\,a^2\,\left(a-b\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(17\,a\,b-11\,b^2\right)}{32\,a\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(67\,a\,b-43\,b^2\right)}{32\,a\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2-{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(2\,a\,b-6\,a^2\right)-{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(4\,a\,b-4\,a^2\right)+4\,a^2\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{524288\,a^{10}\,b-2342912\,a^9\,b^2+4227072\,a^8\,b^3-3866624\,a^7\,b^4+1802240\,a^6\,b^5-344064\,a^5\,b^6}{32768\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,\left(16384\,a^{11}\,b-81920\,a^{10}\,b^2+163840\,a^9\,b^3-163840\,a^8\,b^4+81920\,a^7\,b^5-16384\,a^6\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^5\,b+4\,a^4\,b^2-3139\,a^3\,b^3+4099\,a^2\,b^4-2141\,a\,b^5+441\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{524288\,a^{10}\,b-2342912\,a^9\,b^2+4227072\,a^8\,b^3-3866624\,a^7\,b^4+1802240\,a^6\,b^5-344064\,a^5\,b^6}{32768\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,\left(16384\,a^{11}\,b-81920\,a^{10}\,b^2+163840\,a^9\,b^3-163840\,a^8\,b^4+81920\,a^7\,b^5-16384\,a^6\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^5\,b+4\,a^4\,b^2-3139\,a^3\,b^3+4099\,a^2\,b^4-2141\,a\,b^5+441\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{524288\,a^{10}\,b-2342912\,a^9\,b^2+4227072\,a^8\,b^3-3866624\,a^7\,b^4+1802240\,a^6\,b^5-344064\,a^5\,b^6}{32768\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,\left(16384\,a^{11}\,b-81920\,a^{10}\,b^2+163840\,a^9\,b^3-163840\,a^8\,b^4+81920\,a^7\,b^5-16384\,a^6\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^5\,b+4\,a^4\,b^2-3139\,a^3\,b^3+4099\,a^2\,b^4-2141\,a\,b^5+441\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}+\left(\left(\frac{524288\,a^{10}\,b-2342912\,a^9\,b^2+4227072\,a^8\,b^3-3866624\,a^7\,b^4+1802240\,a^6\,b^5-344064\,a^5\,b^6}{32768\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,\left(16384\,a^{11}\,b-81920\,a^{10}\,b^2+163840\,a^9\,b^3-163840\,a^8\,b^4+81920\,a^7\,b^5-16384\,a^6\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^5\,b+4\,a^4\,b^2-3139\,a^3\,b^3+4099\,a^2\,b^4-2141\,a\,b^5+441\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}+\frac{32768\,a^4\,b-70784\,a^3\,b^2+65572\,a^2\,b^3-29581\,a\,b^4+5733\,b^5}{16384\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}}\right)\,\sqrt{\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}-1916\,a^9\,b+1024\,a^{10}+105\,a^6\,b^4-570\,a^7\,b^3+1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{524288\,a^{10}\,b-2342912\,a^9\,b^2+4227072\,a^8\,b^3-3866624\,a^7\,b^4+1802240\,a^6\,b^5-344064\,a^5\,b^6}{32768\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,\left(16384\,a^{11}\,b-81920\,a^{10}\,b^2+163840\,a^9\,b^3-163840\,a^8\,b^4+81920\,a^7\,b^5-16384\,a^6\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^5\,b+4\,a^4\,b^2-3139\,a^3\,b^3+4099\,a^2\,b^4-2141\,a\,b^5+441\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{524288\,a^{10}\,b-2342912\,a^9\,b^2+4227072\,a^8\,b^3-3866624\,a^7\,b^4+1802240\,a^6\,b^5-344064\,a^5\,b^6}{32768\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,\left(16384\,a^{11}\,b-81920\,a^{10}\,b^2+163840\,a^9\,b^3-163840\,a^8\,b^4+81920\,a^7\,b^5-16384\,a^6\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^5\,b+4\,a^4\,b^2-3139\,a^3\,b^3+4099\,a^2\,b^4-2141\,a\,b^5+441\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{524288\,a^{10}\,b-2342912\,a^9\,b^2+4227072\,a^8\,b^3-3866624\,a^7\,b^4+1802240\,a^6\,b^5-344064\,a^5\,b^6}{32768\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,\left(16384\,a^{11}\,b-81920\,a^{10}\,b^2+163840\,a^9\,b^3-163840\,a^8\,b^4+81920\,a^7\,b^5-16384\,a^6\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^5\,b+4\,a^4\,b^2-3139\,a^3\,b^3+4099\,a^2\,b^4-2141\,a\,b^5+441\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}+\left(\left(\frac{524288\,a^{10}\,b-2342912\,a^9\,b^2+4227072\,a^8\,b^3-3866624\,a^7\,b^4+1802240\,a^6\,b^5-344064\,a^5\,b^6}{32768\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,\left(16384\,a^{11}\,b-81920\,a^{10}\,b^2+163840\,a^9\,b^3-163840\,a^8\,b^4+81920\,a^7\,b^5-16384\,a^6\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^5\,b+4\,a^4\,b^2-3139\,a^3\,b^3+4099\,a^2\,b^4-2141\,a\,b^5+441\,b^6\right)}{256\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}+\frac{32768\,a^4\,b-70784\,a^3\,b^2+65572\,a^2\,b^3-29581\,a\,b^4+5733\,b^5}{16384\,\left(-a^9+3\,a^8\,b-3\,a^7\,b^2+a^6\,b^3\right)}}\right)\,\sqrt{-\frac{1920\,a^4\,\sqrt{a^{11}\,b}+441\,b^4\,\sqrt{a^{11}\,b}+1916\,a^9\,b-1024\,a^{10}-105\,a^6\,b^4+570\,a^7\,b^3-1501\,a^8\,b^2-2246\,a\,b^3\,\sqrt{a^{11}\,b}-4640\,a^3\,b\,\sqrt{a^{11}\,b}+4669\,a^2\,b^2\,\sqrt{a^{11}\,b}}{16384\,\left(-a^{16}+5\,a^{15}\,b-10\,a^{14}\,b^2+10\,a^{13}\,b^3-5\,a^{12}\,b^4+a^{11}\,b^5\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"- ((tan(c + d*x)^5*(83*a^2*b - 66*a*b^2 + 7*b^3))/(32*a^2*(a - b)^2) + (tan(c + d*x)^7*(33*a*b - 13*b^2))/(32*a^2*(a - b)) + (tan(c + d*x)*(17*a*b - 11*b^2))/(32*a*(a^2 - 2*a*b + b^2)) + (tan(c + d*x)^3*(67*a*b - 43*b^2))/(32*a*(a^2 - 2*a*b + b^2)))/(d*(tan(c + d*x)^8*(a^2 - 2*a*b + b^2) + a^2 - tan(c + d*x)^4*(2*a*b - 6*a^2) - tan(c + d*x)^6*(4*a*b - 4*a^2) + 4*a^2*tan(c + d*x)^2)) - (atan(((((524288*a^10*b - 344064*a^5*b^6 + 1802240*a^6*b^5 - 3866624*a^7*b^4 + 4227072*a^8*b^3 - 2342912*a^9*b^2)/(32768*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2)) - (tan(c + d*x)*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*(16384*a^11*b - 16384*a^6*b^6 + 81920*a^7*b^5 - 163840*a^8*b^4 + 163840*a^9*b^3 - 81920*a^10*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) - (tan(c + d*x)*(1024*a^5*b - 2141*a*b^5 + 441*b^6 + 4099*a^2*b^4 - 3139*a^3*b^3 + 4*a^4*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*1i - (((524288*a^10*b - 344064*a^5*b^6 + 1802240*a^6*b^5 - 3866624*a^7*b^4 + 4227072*a^8*b^3 - 2342912*a^9*b^2)/(32768*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2)) + (tan(c + d*x)*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*(16384*a^11*b - 16384*a^6*b^6 + 81920*a^7*b^5 - 163840*a^8*b^4 + 163840*a^9*b^3 - 81920*a^10*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) + (tan(c + d*x)*(1024*a^5*b - 2141*a*b^5 + 441*b^6 + 4099*a^2*b^4 - 3139*a^3*b^3 + 4*a^4*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*1i)/((((524288*a^10*b - 344064*a^5*b^6 + 1802240*a^6*b^5 - 3866624*a^7*b^4 + 4227072*a^8*b^3 - 2342912*a^9*b^2)/(32768*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2)) - (tan(c + d*x)*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*(16384*a^11*b - 16384*a^6*b^6 + 81920*a^7*b^5 - 163840*a^8*b^4 + 163840*a^9*b^3 - 81920*a^10*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) - (tan(c + d*x)*(1024*a^5*b - 2141*a*b^5 + 441*b^6 + 4099*a^2*b^4 - 3139*a^3*b^3 + 4*a^4*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) + (((524288*a^10*b - 344064*a^5*b^6 + 1802240*a^6*b^5 - 3866624*a^7*b^4 + 4227072*a^8*b^3 - 2342912*a^9*b^2)/(32768*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2)) + (tan(c + d*x)*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*(16384*a^11*b - 16384*a^6*b^6 + 81920*a^7*b^5 - 163840*a^8*b^4 + 163840*a^9*b^3 - 81920*a^10*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) + (tan(c + d*x)*(1024*a^5*b - 2141*a*b^5 + 441*b^6 + 4099*a^2*b^4 - 3139*a^3*b^3 + 4*a^4*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) + (32768*a^4*b - 29581*a*b^4 + 5733*b^5 + 65572*a^2*b^3 - 70784*a^3*b^2)/(16384*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2))))*((1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) - 1916*a^9*b + 1024*a^10 + 105*a^6*b^4 - 570*a^7*b^3 + 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*2i)/d - (atan(((((524288*a^10*b - 344064*a^5*b^6 + 1802240*a^6*b^5 - 3866624*a^7*b^4 + 4227072*a^8*b^3 - 2342912*a^9*b^2)/(32768*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2)) - (tan(c + d*x)*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*(16384*a^11*b - 16384*a^6*b^6 + 81920*a^7*b^5 - 163840*a^8*b^4 + 163840*a^9*b^3 - 81920*a^10*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) - (tan(c + d*x)*(1024*a^5*b - 2141*a*b^5 + 441*b^6 + 4099*a^2*b^4 - 3139*a^3*b^3 + 4*a^4*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*1i - (((524288*a^10*b - 344064*a^5*b^6 + 1802240*a^6*b^5 - 3866624*a^7*b^4 + 4227072*a^8*b^3 - 2342912*a^9*b^2)/(32768*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2)) + (tan(c + d*x)*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*(16384*a^11*b - 16384*a^6*b^6 + 81920*a^7*b^5 - 163840*a^8*b^4 + 163840*a^9*b^3 - 81920*a^10*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) + (tan(c + d*x)*(1024*a^5*b - 2141*a*b^5 + 441*b^6 + 4099*a^2*b^4 - 3139*a^3*b^3 + 4*a^4*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*1i)/((((524288*a^10*b - 344064*a^5*b^6 + 1802240*a^6*b^5 - 3866624*a^7*b^4 + 4227072*a^8*b^3 - 2342912*a^9*b^2)/(32768*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2)) - (tan(c + d*x)*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*(16384*a^11*b - 16384*a^6*b^6 + 81920*a^7*b^5 - 163840*a^8*b^4 + 163840*a^9*b^3 - 81920*a^10*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) - (tan(c + d*x)*(1024*a^5*b - 2141*a*b^5 + 441*b^6 + 4099*a^2*b^4 - 3139*a^3*b^3 + 4*a^4*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) + (((524288*a^10*b - 344064*a^5*b^6 + 1802240*a^6*b^5 - 3866624*a^7*b^4 + 4227072*a^8*b^3 - 2342912*a^9*b^2)/(32768*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2)) + (tan(c + d*x)*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*(16384*a^11*b - 16384*a^6*b^6 + 81920*a^7*b^5 - 163840*a^8*b^4 + 163840*a^9*b^3 - 81920*a^10*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) + (tan(c + d*x)*(1024*a^5*b - 2141*a*b^5 + 441*b^6 + 4099*a^2*b^4 - 3139*a^3*b^3 + 4*a^4*b^2))/(256*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2) + (32768*a^4*b - 29581*a*b^4 + 5733*b^5 + 65572*a^2*b^3 - 70784*a^3*b^2)/(16384*(3*a^8*b - a^9 + a^6*b^3 - 3*a^7*b^2))))*(-(1920*a^4*(a^11*b)^(1/2) + 441*b^4*(a^11*b)^(1/2) + 1916*a^9*b - 1024*a^10 - 105*a^6*b^4 + 570*a^7*b^3 - 1501*a^8*b^2 - 2246*a*b^3*(a^11*b)^(1/2) - 4640*a^3*b*(a^11*b)^(1/2) + 4669*a^2*b^2*(a^11*b)^(1/2))/(16384*(5*a^15*b - a^16 + a^11*b^5 - 5*a^12*b^4 + 10*a^13*b^3 - 10*a^14*b^2)))^(1/2)*2i)/d","B"
235,1,7364,357,20.801432,"\text{Not used}","int(1/(sin(c + d*x)^2*(a - b*sin(c + d*x)^4)^3),x)","-\frac{\frac{1}{a}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(64\,a^2-119\,a\,b+58\,b^2\right)}{16\,a\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^8\,\left(32\,a^3-78\,a^2\,b+111\,a\,b^2-45\,b^3\right)}{32\,a^3\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(64\,a^3-165\,a^2\,b+190\,a\,b^2-77\,b^3\right)}{16\,a^2\,{\left(a-b\right)}^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(192\,a^3-394\,a^2\,b+307\,a\,b^2-81\,b^3\right)}{32\,a^2\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^9\,\left(a^2-2\,a\,b+b^2\right)+a^2\,\mathrm{tan}\left(c+d\,x\right)-{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(2\,a\,b-6\,a^2\right)-{\mathrm{tan}\left(c+d\,x\right)}^7\,\left(4\,a\,b-4\,a^2\right)+4\,a^2\,{\mathrm{tan}\left(c+d\,x\right)}^3\right)}+\frac{\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2315255808\,a^{15}\,b^{12}-201326592\,a^{14}\,b^{13}-12079595520\,a^{16}\,b^{11}+37748736000\,a^{17}\,b^{10}-78517370880\,a^{18}\,b^9+114152177664\,a^{19}\,b^8-118380036096\,a^{20}\,b^7+87577067520\,a^{21}\,b^6-45298483200\,a^{22}\,b^5+15602810880\,a^{23}\,b^4-3221225472\,a^{24}\,b^3+301989888\,a^{25}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2147483648\,a^{29}\,b-25769803776\,a^{28}\,b^2+141733920768\,a^{27}\,b^3-472446402560\,a^{26}\,b^4+1063004405760\,a^{25}\,b^5-1700807049216\,a^{24}\,b^6+1984274890752\,a^{23}\,b^7-1700807049216\,a^{22}\,b^8+1063004405760\,a^{21}\,b^9-472446402560\,a^{20}\,b^{10}+141733920768\,a^{19}\,b^{11}-25769803776\,a^{18}\,b^{12}+2147483648\,a^{17}\,b^{13}\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(471859200\,a^{22}\,b^2-3779592192\,a^{21}\,b^3+12354453504\,a^{20}\,b^4-18454413312\,a^{19}\,b^5+484835328\,a^{18}\,b^6+51536461824\,a^{17}\,b^7-108421447680\,a^{16}\,b^8+125505110016\,a^{15}\,b^9-94402510848\,a^{14}\,b^{10}+47520940032\,a^{13}\,b^{11}-15574892544\,a^{12}\,b^{12}+3024617472\,a^{11}\,b^{13}-265420800\,a^{10}\,b^{14}\right)\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(201326592\,a^{14}\,b^{13}-2315255808\,a^{15}\,b^{12}+12079595520\,a^{16}\,b^{11}-37748736000\,a^{17}\,b^{10}+78517370880\,a^{18}\,b^9-114152177664\,a^{19}\,b^8+118380036096\,a^{20}\,b^7-87577067520\,a^{21}\,b^6+45298483200\,a^{22}\,b^5-15602810880\,a^{23}\,b^4+3221225472\,a^{24}\,b^3-301989888\,a^{25}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2147483648\,a^{29}\,b-25769803776\,a^{28}\,b^2+141733920768\,a^{27}\,b^3-472446402560\,a^{26}\,b^4+1063004405760\,a^{25}\,b^5-1700807049216\,a^{24}\,b^6+1984274890752\,a^{23}\,b^7-1700807049216\,a^{22}\,b^8+1063004405760\,a^{21}\,b^9-472446402560\,a^{20}\,b^{10}+141733920768\,a^{19}\,b^{11}-25769803776\,a^{18}\,b^{12}+2147483648\,a^{17}\,b^{13}\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(471859200\,a^{22}\,b^2-3779592192\,a^{21}\,b^3+12354453504\,a^{20}\,b^4-18454413312\,a^{19}\,b^5+484835328\,a^{18}\,b^6+51536461824\,a^{17}\,b^7-108421447680\,a^{16}\,b^8+125505110016\,a^{15}\,b^9-94402510848\,a^{14}\,b^{10}+47520940032\,a^{13}\,b^{11}-15574892544\,a^{12}\,b^{12}+3024617472\,a^{11}\,b^{13}-265420800\,a^{10}\,b^{14}\right)\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2315255808\,a^{15}\,b^{12}-201326592\,a^{14}\,b^{13}-12079595520\,a^{16}\,b^{11}+37748736000\,a^{17}\,b^{10}-78517370880\,a^{18}\,b^9+114152177664\,a^{19}\,b^8-118380036096\,a^{20}\,b^7+87577067520\,a^{21}\,b^6-45298483200\,a^{22}\,b^5+15602810880\,a^{23}\,b^4-3221225472\,a^{24}\,b^3+301989888\,a^{25}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2147483648\,a^{29}\,b-25769803776\,a^{28}\,b^2+141733920768\,a^{27}\,b^3-472446402560\,a^{26}\,b^4+1063004405760\,a^{25}\,b^5-1700807049216\,a^{24}\,b^6+1984274890752\,a^{23}\,b^7-1700807049216\,a^{22}\,b^8+1063004405760\,a^{21}\,b^9-472446402560\,a^{20}\,b^{10}+141733920768\,a^{19}\,b^{11}-25769803776\,a^{18}\,b^{12}+2147483648\,a^{17}\,b^{13}\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(471859200\,a^{22}\,b^2-3779592192\,a^{21}\,b^3+12354453504\,a^{20}\,b^4-18454413312\,a^{19}\,b^5+484835328\,a^{18}\,b^6+51536461824\,a^{17}\,b^7-108421447680\,a^{16}\,b^8+125505110016\,a^{15}\,b^9-94402510848\,a^{14}\,b^{10}+47520940032\,a^{13}\,b^{11}-15574892544\,a^{12}\,b^{12}+3024617472\,a^{11}\,b^{13}-265420800\,a^{10}\,b^{14}\right)\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}-\left(\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(201326592\,a^{14}\,b^{13}-2315255808\,a^{15}\,b^{12}+12079595520\,a^{16}\,b^{11}-37748736000\,a^{17}\,b^{10}+78517370880\,a^{18}\,b^9-114152177664\,a^{19}\,b^8+118380036096\,a^{20}\,b^7-87577067520\,a^{21}\,b^6+45298483200\,a^{22}\,b^5-15602810880\,a^{23}\,b^4+3221225472\,a^{24}\,b^3-301989888\,a^{25}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2147483648\,a^{29}\,b-25769803776\,a^{28}\,b^2+141733920768\,a^{27}\,b^3-472446402560\,a^{26}\,b^4+1063004405760\,a^{25}\,b^5-1700807049216\,a^{24}\,b^6+1984274890752\,a^{23}\,b^7-1700807049216\,a^{22}\,b^8+1063004405760\,a^{21}\,b^9-472446402560\,a^{20}\,b^{10}+141733920768\,a^{19}\,b^{11}-25769803776\,a^{18}\,b^{12}+2147483648\,a^{17}\,b^{13}\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(471859200\,a^{22}\,b^2-3779592192\,a^{21}\,b^3+12354453504\,a^{20}\,b^4-18454413312\,a^{19}\,b^5+484835328\,a^{18}\,b^6+51536461824\,a^{17}\,b^7-108421447680\,a^{16}\,b^8+125505110016\,a^{15}\,b^9-94402510848\,a^{14}\,b^{10}+47520940032\,a^{13}\,b^{11}-15574892544\,a^{12}\,b^{12}+3024617472\,a^{11}\,b^{13}-265420800\,a^{10}\,b^{14}\right)\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}+186624000\,a^7\,b^{14}-2227875840\,a^8\,b^{13}+12162465792\,a^9\,b^{12}-40050892800\,a^{10}\,b^{11}+88332816384\,a^{11}\,b^{10}-136918204416\,a^{12}\,b^9+152103813120\,a^{13}\,b^8-121034760192\,a^{14}\,b^7+67571435520\,a^{15}\,b^6-25193631744\,a^{16}\,b^5+5643288576\,a^{17}\,b^4-575078400\,a^{18}\,b^3}\right)\,\sqrt{-\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}-400\,a^{11}\,b-105\,a^7\,b^5+530\,a^8\,b^4-1085\,a^9\,b^3+1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2315255808\,a^{15}\,b^{12}-201326592\,a^{14}\,b^{13}-12079595520\,a^{16}\,b^{11}+37748736000\,a^{17}\,b^{10}-78517370880\,a^{18}\,b^9+114152177664\,a^{19}\,b^8-118380036096\,a^{20}\,b^7+87577067520\,a^{21}\,b^6-45298483200\,a^{22}\,b^5+15602810880\,a^{23}\,b^4-3221225472\,a^{24}\,b^3+301989888\,a^{25}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2147483648\,a^{29}\,b-25769803776\,a^{28}\,b^2+141733920768\,a^{27}\,b^3-472446402560\,a^{26}\,b^4+1063004405760\,a^{25}\,b^5-1700807049216\,a^{24}\,b^6+1984274890752\,a^{23}\,b^7-1700807049216\,a^{22}\,b^8+1063004405760\,a^{21}\,b^9-472446402560\,a^{20}\,b^{10}+141733920768\,a^{19}\,b^{11}-25769803776\,a^{18}\,b^{12}+2147483648\,a^{17}\,b^{13}\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(471859200\,a^{22}\,b^2-3779592192\,a^{21}\,b^3+12354453504\,a^{20}\,b^4-18454413312\,a^{19}\,b^5+484835328\,a^{18}\,b^6+51536461824\,a^{17}\,b^7-108421447680\,a^{16}\,b^8+125505110016\,a^{15}\,b^9-94402510848\,a^{14}\,b^{10}+47520940032\,a^{13}\,b^{11}-15574892544\,a^{12}\,b^{12}+3024617472\,a^{11}\,b^{13}-265420800\,a^{10}\,b^{14}\right)\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,1{}\mathrm{i}+\left(\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(201326592\,a^{14}\,b^{13}-2315255808\,a^{15}\,b^{12}+12079595520\,a^{16}\,b^{11}-37748736000\,a^{17}\,b^{10}+78517370880\,a^{18}\,b^9-114152177664\,a^{19}\,b^8+118380036096\,a^{20}\,b^7-87577067520\,a^{21}\,b^6+45298483200\,a^{22}\,b^5-15602810880\,a^{23}\,b^4+3221225472\,a^{24}\,b^3-301989888\,a^{25}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2147483648\,a^{29}\,b-25769803776\,a^{28}\,b^2+141733920768\,a^{27}\,b^3-472446402560\,a^{26}\,b^4+1063004405760\,a^{25}\,b^5-1700807049216\,a^{24}\,b^6+1984274890752\,a^{23}\,b^7-1700807049216\,a^{22}\,b^8+1063004405760\,a^{21}\,b^9-472446402560\,a^{20}\,b^{10}+141733920768\,a^{19}\,b^{11}-25769803776\,a^{18}\,b^{12}+2147483648\,a^{17}\,b^{13}\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(471859200\,a^{22}\,b^2-3779592192\,a^{21}\,b^3+12354453504\,a^{20}\,b^4-18454413312\,a^{19}\,b^5+484835328\,a^{18}\,b^6+51536461824\,a^{17}\,b^7-108421447680\,a^{16}\,b^8+125505110016\,a^{15}\,b^9-94402510848\,a^{14}\,b^{10}+47520940032\,a^{13}\,b^{11}-15574892544\,a^{12}\,b^{12}+3024617472\,a^{11}\,b^{13}-265420800\,a^{10}\,b^{14}\right)\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,1{}\mathrm{i}}{\left(\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2315255808\,a^{15}\,b^{12}-201326592\,a^{14}\,b^{13}-12079595520\,a^{16}\,b^{11}+37748736000\,a^{17}\,b^{10}-78517370880\,a^{18}\,b^9+114152177664\,a^{19}\,b^8-118380036096\,a^{20}\,b^7+87577067520\,a^{21}\,b^6-45298483200\,a^{22}\,b^5+15602810880\,a^{23}\,b^4-3221225472\,a^{24}\,b^3+301989888\,a^{25}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2147483648\,a^{29}\,b-25769803776\,a^{28}\,b^2+141733920768\,a^{27}\,b^3-472446402560\,a^{26}\,b^4+1063004405760\,a^{25}\,b^5-1700807049216\,a^{24}\,b^6+1984274890752\,a^{23}\,b^7-1700807049216\,a^{22}\,b^8+1063004405760\,a^{21}\,b^9-472446402560\,a^{20}\,b^{10}+141733920768\,a^{19}\,b^{11}-25769803776\,a^{18}\,b^{12}+2147483648\,a^{17}\,b^{13}\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(471859200\,a^{22}\,b^2-3779592192\,a^{21}\,b^3+12354453504\,a^{20}\,b^4-18454413312\,a^{19}\,b^5+484835328\,a^{18}\,b^6+51536461824\,a^{17}\,b^7-108421447680\,a^{16}\,b^8+125505110016\,a^{15}\,b^9-94402510848\,a^{14}\,b^{10}+47520940032\,a^{13}\,b^{11}-15574892544\,a^{12}\,b^{12}+3024617472\,a^{11}\,b^{13}-265420800\,a^{10}\,b^{14}\right)\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}-\left(\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(201326592\,a^{14}\,b^{13}-2315255808\,a^{15}\,b^{12}+12079595520\,a^{16}\,b^{11}-37748736000\,a^{17}\,b^{10}+78517370880\,a^{18}\,b^9-114152177664\,a^{19}\,b^8+118380036096\,a^{20}\,b^7-87577067520\,a^{21}\,b^6+45298483200\,a^{22}\,b^5-15602810880\,a^{23}\,b^4+3221225472\,a^{24}\,b^3-301989888\,a^{25}\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,\left(2147483648\,a^{29}\,b-25769803776\,a^{28}\,b^2+141733920768\,a^{27}\,b^3-472446402560\,a^{26}\,b^4+1063004405760\,a^{25}\,b^5-1700807049216\,a^{24}\,b^6+1984274890752\,a^{23}\,b^7-1700807049216\,a^{22}\,b^8+1063004405760\,a^{21}\,b^9-472446402560\,a^{20}\,b^{10}+141733920768\,a^{19}\,b^{11}-25769803776\,a^{18}\,b^{12}+2147483648\,a^{17}\,b^{13}\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(471859200\,a^{22}\,b^2-3779592192\,a^{21}\,b^3+12354453504\,a^{20}\,b^4-18454413312\,a^{19}\,b^5+484835328\,a^{18}\,b^6+51536461824\,a^{17}\,b^7-108421447680\,a^{16}\,b^8+125505110016\,a^{15}\,b^9-94402510848\,a^{14}\,b^{10}+47520940032\,a^{13}\,b^{11}-15574892544\,a^{12}\,b^{12}+3024617472\,a^{11}\,b^{13}-265420800\,a^{10}\,b^{14}\right)\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}+186624000\,a^7\,b^{14}-2227875840\,a^8\,b^{13}+12162465792\,a^9\,b^{12}-40050892800\,a^{10}\,b^{11}+88332816384\,a^{11}\,b^{10}-136918204416\,a^{12}\,b^9+152103813120\,a^{13}\,b^8-121034760192\,a^{14}\,b^7+67571435520\,a^{15}\,b^6-25193631744\,a^{16}\,b^5+5643288576\,a^{17}\,b^4-575078400\,a^{18}\,b^3}\right)\,\sqrt{\frac{9\,\left(640\,a^4\,\sqrt{a^{13}\,b^3}+225\,b^4\,\sqrt{a^{13}\,b^3}+400\,a^{11}\,b+105\,a^7\,b^5-530\,a^8\,b^4+1085\,a^9\,b^3-1044\,a^{10}\,b^2+2085\,a^2\,b^2\,\sqrt{a^{13}\,b^3}-1094\,a\,b^3\,\sqrt{a^{13}\,b^3}-1840\,a^3\,b\,\sqrt{a^{13}\,b^3}\right)}{16384\,\left(-a^{18}+5\,a^{17}\,b-10\,a^{16}\,b^2+10\,a^{15}\,b^3-5\,a^{14}\,b^4+a^{13}\,b^5\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan((((-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2315255808*a^15*b^12 - 201326592*a^14*b^13 - 12079595520*a^16*b^11 + 37748736000*a^17*b^10 - 78517370880*a^18*b^9 + 114152177664*a^19*b^8 - 118380036096*a^20*b^7 + 87577067520*a^21*b^6 - 45298483200*a^22*b^5 + 15602810880*a^23*b^4 - 3221225472*a^24*b^3 + 301989888*a^25*b^2 + tan(c + d*x)*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2147483648*a^29*b + 2147483648*a^17*b^13 - 25769803776*a^18*b^12 + 141733920768*a^19*b^11 - 472446402560*a^20*b^10 + 1063004405760*a^21*b^9 - 1700807049216*a^22*b^8 + 1984274890752*a^23*b^7 - 1700807049216*a^24*b^6 + 1063004405760*a^25*b^5 - 472446402560*a^26*b^4 + 141733920768*a^27*b^3 - 25769803776*a^28*b^2)) + tan(c + d*x)*(3024617472*a^11*b^13 - 265420800*a^10*b^14 - 15574892544*a^12*b^12 + 47520940032*a^13*b^11 - 94402510848*a^14*b^10 + 125505110016*a^15*b^9 - 108421447680*a^16*b^8 + 51536461824*a^17*b^7 + 484835328*a^18*b^6 - 18454413312*a^19*b^5 + 12354453504*a^20*b^4 - 3779592192*a^21*b^3 + 471859200*a^22*b^2))*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*1i + ((-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(201326592*a^14*b^13 - 2315255808*a^15*b^12 + 12079595520*a^16*b^11 - 37748736000*a^17*b^10 + 78517370880*a^18*b^9 - 114152177664*a^19*b^8 + 118380036096*a^20*b^7 - 87577067520*a^21*b^6 + 45298483200*a^22*b^5 - 15602810880*a^23*b^4 + 3221225472*a^24*b^3 - 301989888*a^25*b^2 + tan(c + d*x)*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2147483648*a^29*b + 2147483648*a^17*b^13 - 25769803776*a^18*b^12 + 141733920768*a^19*b^11 - 472446402560*a^20*b^10 + 1063004405760*a^21*b^9 - 1700807049216*a^22*b^8 + 1984274890752*a^23*b^7 - 1700807049216*a^24*b^6 + 1063004405760*a^25*b^5 - 472446402560*a^26*b^4 + 141733920768*a^27*b^3 - 25769803776*a^28*b^2)) + tan(c + d*x)*(3024617472*a^11*b^13 - 265420800*a^10*b^14 - 15574892544*a^12*b^12 + 47520940032*a^13*b^11 - 94402510848*a^14*b^10 + 125505110016*a^15*b^9 - 108421447680*a^16*b^8 + 51536461824*a^17*b^7 + 484835328*a^18*b^6 - 18454413312*a^19*b^5 + 12354453504*a^20*b^4 - 3779592192*a^21*b^3 + 471859200*a^22*b^2))*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*1i)/(((-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2315255808*a^15*b^12 - 201326592*a^14*b^13 - 12079595520*a^16*b^11 + 37748736000*a^17*b^10 - 78517370880*a^18*b^9 + 114152177664*a^19*b^8 - 118380036096*a^20*b^7 + 87577067520*a^21*b^6 - 45298483200*a^22*b^5 + 15602810880*a^23*b^4 - 3221225472*a^24*b^3 + 301989888*a^25*b^2 + tan(c + d*x)*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2147483648*a^29*b + 2147483648*a^17*b^13 - 25769803776*a^18*b^12 + 141733920768*a^19*b^11 - 472446402560*a^20*b^10 + 1063004405760*a^21*b^9 - 1700807049216*a^22*b^8 + 1984274890752*a^23*b^7 - 1700807049216*a^24*b^6 + 1063004405760*a^25*b^5 - 472446402560*a^26*b^4 + 141733920768*a^27*b^3 - 25769803776*a^28*b^2)) + tan(c + d*x)*(3024617472*a^11*b^13 - 265420800*a^10*b^14 - 15574892544*a^12*b^12 + 47520940032*a^13*b^11 - 94402510848*a^14*b^10 + 125505110016*a^15*b^9 - 108421447680*a^16*b^8 + 51536461824*a^17*b^7 + 484835328*a^18*b^6 - 18454413312*a^19*b^5 + 12354453504*a^20*b^4 - 3779592192*a^21*b^3 + 471859200*a^22*b^2))*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2) - ((-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(201326592*a^14*b^13 - 2315255808*a^15*b^12 + 12079595520*a^16*b^11 - 37748736000*a^17*b^10 + 78517370880*a^18*b^9 - 114152177664*a^19*b^8 + 118380036096*a^20*b^7 - 87577067520*a^21*b^6 + 45298483200*a^22*b^5 - 15602810880*a^23*b^4 + 3221225472*a^24*b^3 - 301989888*a^25*b^2 + tan(c + d*x)*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2147483648*a^29*b + 2147483648*a^17*b^13 - 25769803776*a^18*b^12 + 141733920768*a^19*b^11 - 472446402560*a^20*b^10 + 1063004405760*a^21*b^9 - 1700807049216*a^22*b^8 + 1984274890752*a^23*b^7 - 1700807049216*a^24*b^6 + 1063004405760*a^25*b^5 - 472446402560*a^26*b^4 + 141733920768*a^27*b^3 - 25769803776*a^28*b^2)) + tan(c + d*x)*(3024617472*a^11*b^13 - 265420800*a^10*b^14 - 15574892544*a^12*b^12 + 47520940032*a^13*b^11 - 94402510848*a^14*b^10 + 125505110016*a^15*b^9 - 108421447680*a^16*b^8 + 51536461824*a^17*b^7 + 484835328*a^18*b^6 - 18454413312*a^19*b^5 + 12354453504*a^20*b^4 - 3779592192*a^21*b^3 + 471859200*a^22*b^2))*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2) + 186624000*a^7*b^14 - 2227875840*a^8*b^13 + 12162465792*a^9*b^12 - 40050892800*a^10*b^11 + 88332816384*a^11*b^10 - 136918204416*a^12*b^9 + 152103813120*a^13*b^8 - 121034760192*a^14*b^7 + 67571435520*a^15*b^6 - 25193631744*a^16*b^5 + 5643288576*a^17*b^4 - 575078400*a^18*b^3))*(-(9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) - 400*a^11*b - 105*a^7*b^5 + 530*a^8*b^4 - 1085*a^9*b^3 + 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*2i)/d - (1/a + (tan(c + d*x)^2*(64*a^2 - 119*a*b + 58*b^2))/(16*a*(a^2 - 2*a*b + b^2)) + (tan(c + d*x)^8*(111*a*b^2 - 78*a^2*b + 32*a^3 - 45*b^3))/(32*a^3*(a - b)) + (tan(c + d*x)^6*(190*a*b^2 - 165*a^2*b + 64*a^3 - 77*b^3))/(16*a^2*(a - b)^2) + (tan(c + d*x)^4*(307*a*b^2 - 394*a^2*b + 192*a^3 - 81*b^3))/(32*a^2*(a^2 - 2*a*b + b^2)))/(d*(tan(c + d*x)^9*(a^2 - 2*a*b + b^2) + a^2*tan(c + d*x) - tan(c + d*x)^5*(2*a*b - 6*a^2) - tan(c + d*x)^7*(4*a*b - 4*a^2) + 4*a^2*tan(c + d*x)^3)) + (atan(((((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2315255808*a^15*b^12 - 201326592*a^14*b^13 - 12079595520*a^16*b^11 + 37748736000*a^17*b^10 - 78517370880*a^18*b^9 + 114152177664*a^19*b^8 - 118380036096*a^20*b^7 + 87577067520*a^21*b^6 - 45298483200*a^22*b^5 + 15602810880*a^23*b^4 - 3221225472*a^24*b^3 + 301989888*a^25*b^2 + tan(c + d*x)*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2147483648*a^29*b + 2147483648*a^17*b^13 - 25769803776*a^18*b^12 + 141733920768*a^19*b^11 - 472446402560*a^20*b^10 + 1063004405760*a^21*b^9 - 1700807049216*a^22*b^8 + 1984274890752*a^23*b^7 - 1700807049216*a^24*b^6 + 1063004405760*a^25*b^5 - 472446402560*a^26*b^4 + 141733920768*a^27*b^3 - 25769803776*a^28*b^2)) + tan(c + d*x)*(3024617472*a^11*b^13 - 265420800*a^10*b^14 - 15574892544*a^12*b^12 + 47520940032*a^13*b^11 - 94402510848*a^14*b^10 + 125505110016*a^15*b^9 - 108421447680*a^16*b^8 + 51536461824*a^17*b^7 + 484835328*a^18*b^6 - 18454413312*a^19*b^5 + 12354453504*a^20*b^4 - 3779592192*a^21*b^3 + 471859200*a^22*b^2))*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*1i + (((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(201326592*a^14*b^13 - 2315255808*a^15*b^12 + 12079595520*a^16*b^11 - 37748736000*a^17*b^10 + 78517370880*a^18*b^9 - 114152177664*a^19*b^8 + 118380036096*a^20*b^7 - 87577067520*a^21*b^6 + 45298483200*a^22*b^5 - 15602810880*a^23*b^4 + 3221225472*a^24*b^3 - 301989888*a^25*b^2 + tan(c + d*x)*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2147483648*a^29*b + 2147483648*a^17*b^13 - 25769803776*a^18*b^12 + 141733920768*a^19*b^11 - 472446402560*a^20*b^10 + 1063004405760*a^21*b^9 - 1700807049216*a^22*b^8 + 1984274890752*a^23*b^7 - 1700807049216*a^24*b^6 + 1063004405760*a^25*b^5 - 472446402560*a^26*b^4 + 141733920768*a^27*b^3 - 25769803776*a^28*b^2)) + tan(c + d*x)*(3024617472*a^11*b^13 - 265420800*a^10*b^14 - 15574892544*a^12*b^12 + 47520940032*a^13*b^11 - 94402510848*a^14*b^10 + 125505110016*a^15*b^9 - 108421447680*a^16*b^8 + 51536461824*a^17*b^7 + 484835328*a^18*b^6 - 18454413312*a^19*b^5 + 12354453504*a^20*b^4 - 3779592192*a^21*b^3 + 471859200*a^22*b^2))*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*1i)/((((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2315255808*a^15*b^12 - 201326592*a^14*b^13 - 12079595520*a^16*b^11 + 37748736000*a^17*b^10 - 78517370880*a^18*b^9 + 114152177664*a^19*b^8 - 118380036096*a^20*b^7 + 87577067520*a^21*b^6 - 45298483200*a^22*b^5 + 15602810880*a^23*b^4 - 3221225472*a^24*b^3 + 301989888*a^25*b^2 + tan(c + d*x)*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2147483648*a^29*b + 2147483648*a^17*b^13 - 25769803776*a^18*b^12 + 141733920768*a^19*b^11 - 472446402560*a^20*b^10 + 1063004405760*a^21*b^9 - 1700807049216*a^22*b^8 + 1984274890752*a^23*b^7 - 1700807049216*a^24*b^6 + 1063004405760*a^25*b^5 - 472446402560*a^26*b^4 + 141733920768*a^27*b^3 - 25769803776*a^28*b^2)) + tan(c + d*x)*(3024617472*a^11*b^13 - 265420800*a^10*b^14 - 15574892544*a^12*b^12 + 47520940032*a^13*b^11 - 94402510848*a^14*b^10 + 125505110016*a^15*b^9 - 108421447680*a^16*b^8 + 51536461824*a^17*b^7 + 484835328*a^18*b^6 - 18454413312*a^19*b^5 + 12354453504*a^20*b^4 - 3779592192*a^21*b^3 + 471859200*a^22*b^2))*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2) - (((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(201326592*a^14*b^13 - 2315255808*a^15*b^12 + 12079595520*a^16*b^11 - 37748736000*a^17*b^10 + 78517370880*a^18*b^9 - 114152177664*a^19*b^8 + 118380036096*a^20*b^7 - 87577067520*a^21*b^6 + 45298483200*a^22*b^5 - 15602810880*a^23*b^4 + 3221225472*a^24*b^3 - 301989888*a^25*b^2 + tan(c + d*x)*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*(2147483648*a^29*b + 2147483648*a^17*b^13 - 25769803776*a^18*b^12 + 141733920768*a^19*b^11 - 472446402560*a^20*b^10 + 1063004405760*a^21*b^9 - 1700807049216*a^22*b^8 + 1984274890752*a^23*b^7 - 1700807049216*a^24*b^6 + 1063004405760*a^25*b^5 - 472446402560*a^26*b^4 + 141733920768*a^27*b^3 - 25769803776*a^28*b^2)) + tan(c + d*x)*(3024617472*a^11*b^13 - 265420800*a^10*b^14 - 15574892544*a^12*b^12 + 47520940032*a^13*b^11 - 94402510848*a^14*b^10 + 125505110016*a^15*b^9 - 108421447680*a^16*b^8 + 51536461824*a^17*b^7 + 484835328*a^18*b^6 - 18454413312*a^19*b^5 + 12354453504*a^20*b^4 - 3779592192*a^21*b^3 + 471859200*a^22*b^2))*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2) + 186624000*a^7*b^14 - 2227875840*a^8*b^13 + 12162465792*a^9*b^12 - 40050892800*a^10*b^11 + 88332816384*a^11*b^10 - 136918204416*a^12*b^9 + 152103813120*a^13*b^8 - 121034760192*a^14*b^7 + 67571435520*a^15*b^6 - 25193631744*a^16*b^5 + 5643288576*a^17*b^4 - 575078400*a^18*b^3))*((9*(640*a^4*(a^13*b^3)^(1/2) + 225*b^4*(a^13*b^3)^(1/2) + 400*a^11*b + 105*a^7*b^5 - 530*a^8*b^4 + 1085*a^9*b^3 - 1044*a^10*b^2 + 2085*a^2*b^2*(a^13*b^3)^(1/2) - 1094*a*b^3*(a^13*b^3)^(1/2) - 1840*a^3*b*(a^13*b^3)^(1/2)))/(16384*(5*a^17*b - a^18 + a^13*b^5 - 5*a^14*b^4 + 10*a^15*b^3 - 10*a^16*b^2)))^(1/2)*2i)/d","B"
236,1,17,25,14.340196,"\text{Not used}","int(-1/(sin(x)^4 - 1),x)","\frac{\mathrm{tan}\left(x\right)}{2}+\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\right)}{4}","Not used",1,"tan(x)/2 + (2^(1/2)*atan(2^(1/2)*tan(x)))/4","B"
237,1,407,487,15.177633,"\text{Not used}","int(1/(a + b*sin(x)^4),x)","\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{a^2-\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}}\,4{}\mathrm{i}+a^5\,\mathrm{tan}\left(x\right)\,{\left(-\frac{a^2-\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}\right)}^{3/2}\,64{}\mathrm{i}-a^2\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{a^2-\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}}\,4{}\mathrm{i}+a^4\,b\,\mathrm{tan}\left(x\right)\,{\left(-\frac{a^2-\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}\right)}^{3/2}\,64{}\mathrm{i}}{\sqrt{-a^3\,b}}\right)\,\sqrt{-\frac{a^2-\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{a^2+\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}}\,4{}\mathrm{i}+a^5\,\mathrm{tan}\left(x\right)\,{\left(-\frac{a^2+\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}\right)}^{3/2}\,64{}\mathrm{i}-a^2\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{a^2+\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}}\,4{}\mathrm{i}+a^4\,b\,\mathrm{tan}\left(x\right)\,{\left(-\frac{a^2+\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}\right)}^{3/2}\,64{}\mathrm{i}}{\sqrt{-a^3\,b}}\right)\,\sqrt{-\frac{a^2+\sqrt{-a^3\,b}}{16\,a^4+16\,b\,a^3}}\,2{}\mathrm{i}","Not used",1,"atan((a^3*tan(x)*(-(a^2 - (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(1/2)*4i + a^5*tan(x)*(-(a^2 - (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(3/2)*64i - a^2*b*tan(x)*(-(a^2 - (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(1/2)*4i + a^4*b*tan(x)*(-(a^2 - (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(3/2)*64i)/(-a^3*b)^(1/2))*(-(a^2 - (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(1/2)*2i - atan((a^3*tan(x)*(-(a^2 + (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(1/2)*4i + a^5*tan(x)*(-(a^2 + (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(3/2)*64i - a^2*b*tan(x)*(-(a^2 + (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(1/2)*4i + a^4*b*tan(x)*(-(a^2 + (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(3/2)*64i)/(-a^3*b)^(1/2))*(-(a^2 + (-a^3*b)^(1/2))/(16*a^3*b + 16*a^4))^(1/2)*2i","B"
238,1,236,309,14.351553,"\text{Not used}","int(1/(sin(x)^4 + 1),x)","\mathrm{atanh}\left(\frac{\mathrm{tan}\left(x\right)}{8\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}}-\frac{\mathrm{tan}\left(x\right)}{8\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{16\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{16\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}-2\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\right)+\mathrm{atanh}\left(\frac{\mathrm{tan}\left(x\right)}{8\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}}+\frac{\mathrm{tan}\left(x\right)}{8\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{16\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{16\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}+2\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\right)-\frac{\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)\,\left(\pi \,\left(2\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}-2\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\right)\,1{}\mathrm{i}+\pi \,\left(2\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}+2\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\right)\,1{}\mathrm{i}\right)}{\pi }","Not used",1,"atanh(tan(x)/(8*(- 2^(1/2)/64 - 1/64)^(1/2)) - tan(x)/(8*(2^(1/2)/64 - 1/64)^(1/2)) + (2^(1/2)*tan(x))/(16*(- 2^(1/2)/64 - 1/64)^(1/2)) + (2^(1/2)*tan(x))/(16*(2^(1/2)/64 - 1/64)^(1/2)))*(2*(- 2^(1/2)/64 - 1/64)^(1/2) - 2*(2^(1/2)/64 - 1/64)^(1/2)) + atanh(tan(x)/(8*(- 2^(1/2)/64 - 1/64)^(1/2)) + tan(x)/(8*(2^(1/2)/64 - 1/64)^(1/2)) + (2^(1/2)*tan(x))/(16*(- 2^(1/2)/64 - 1/64)^(1/2)) - (2^(1/2)*tan(x))/(16*(2^(1/2)/64 - 1/64)^(1/2)))*(2*(- 2^(1/2)/64 - 1/64)^(1/2) + 2*(2^(1/2)/64 - 1/64)^(1/2)) - ((x - atan(tan(x)))*(pi*(2*(- 2^(1/2)/64 - 1/64)^(1/2) - 2*(2^(1/2)/64 - 1/64)^(1/2))*1i + pi*(2*(- 2^(1/2)/64 - 1/64)^(1/2) + 2*(2^(1/2)/64 - 1/64)^(1/2))*1i))/pi","B"
239,0,-1,477,0.000000,"\text{Not used}","int(sin(c + d*x)*(a + b*sin(c + d*x)^4)^(1/2),x)","\int \sin\left(c+d\,x\right)\,\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a} \,d x","Not used",1,"int(sin(c + d*x)*(a + b*sin(c + d*x)^4)^(1/2), x)","F"
240,0,-1,521,0.000000,"\text{Not used}","int((a + b*sin(c + d*x)^4)^(1/2)/sin(c + d*x),x)","\int \frac{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*sin(c + d*x)^4)^(1/2)/sin(c + d*x), x)","F"
241,0,-1,484,0.000000,"\text{Not used}","int(sin(c + d*x)^5/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^5}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(sin(c + d*x)^5/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
242,0,-1,431,0.000000,"\text{Not used}","int(sin(c + d*x)^3/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^3}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(sin(c + d*x)^3/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
243,0,-1,171,0.000000,"\text{Not used}","int(sin(c + d*x)/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{\sin\left(c+d\,x\right)}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(sin(c + d*x)/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
244,0,-1,469,0.000000,"\text{Not used}","int(1/(sin(c + d*x)*(a + b*sin(c + d*x)^4)^(1/2)),x)","\int \frac{1}{\sin\left(c+d\,x\right)\,\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(1/(sin(c + d*x)*(a + b*sin(c + d*x)^4)^(1/2)), x)","F"
245,0,-1,776,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + b*sin(c + d*x)^4)^(1/2)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^3\,\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(1/(sin(c + d*x)^3*(a + b*sin(c + d*x)^4)^(1/2)), x)","F"
246,0,-1,499,0.000000,"\text{Not used}","int(sin(c + d*x)^2/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^2}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(sin(c + d*x)^2/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
247,0,-1,162,0.000000,"\text{Not used}","int(1/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{1}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(1/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
248,0,-1,493,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + b*sin(c + d*x)^4)^(1/2)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^2\,\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(1/(sin(c + d*x)^2*(a + b*sin(c + d*x)^4)^(1/2)), x)","F"
249,1,1515,384,19.752335,"\text{Not used}","int(1/(a + b*sin(x)^5),x)","\sum _{k=1}^{10}\ln\left(-a\,b^7\,\left(16\,\mathrm{tan}\left(\frac{x}{2}\right)+\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)\,a\,56+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^3\,a^3\,5425+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^5\,a^5\,196875+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^7\,3171875+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^9\,19140625+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^2\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,1560+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^4\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)\,57000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)\,925000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^8\,\mathrm{tan}\left(\frac{x}{2}\right)\,5625000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^4\,a^3\,b\,14000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^5\,b\,175000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^7\,b\,546875+\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,128+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^5\,b^2\,1000000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^7\,b^2\,18750000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^2\,a\,b\,320+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^3\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,6400+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^5\,a^4\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,100000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^6\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,500000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^8\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,390625+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^4\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,400000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^6\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,5000000\right)\,10995116277760\right)\,\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)","Not used",1,"symsum(log(-10995116277760*a*b^7*(16*tan(x/2) + 56*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)*a + 5425*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^3*a^3 + 196875*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^5*a^5 + 3171875*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^7 + 19140625*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^9 + 1560*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^2*a^2*tan(x/2) + 57000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^4*a^4*tan(x/2) + 925000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^6*tan(x/2) + 5625000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^8*tan(x/2) + 14000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^4*a^3*b + 175000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^5*b + 546875*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^7*b + 128*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)*b*tan(x/2) + 1000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^5*b^2 - 18750000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^7*b^2 + 320*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^2*a*b + 6400*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^3*a^2*b*tan(x/2) + 100000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^5*a^4*b*tan(x/2) + 500000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^6*b*tan(x/2) + 390625*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^8*b*tan(x/2) + 400000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^4*b^2*tan(x/2) - 5000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^6*b^2*tan(x/2)))*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k), k, 1, 10)","B"
250,1,513,171,15.705410,"\text{Not used}","int(1/(a + b*sin(x)^6),x)","\sum _{k=1}^6\ln\left(-\frac{b^3\,\left(a+b\right)\,\left(-\mathrm{cot}\left(x\right)+\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)\,a\,8+\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)\,b\,2+{\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^3\,a^3\,504+{\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^5\,a^5\,7776-{\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^3\,a^2\,b\,144+{\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^5\,a^4\,b\,7776-{\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^2\,a^2\,\mathrm{cot}\left(x\right)\,60-{\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^4\,a^4\,\mathrm{cot}\left(x\right)\,864-{\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^4\,a^3\,b\,\mathrm{cot}\left(x\right)\,864+{\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^2\,a\,b\,\mathrm{cot}\left(x\right)\,12\right)\,3}{\mathrm{cot}\left(x\right)}\right)\,\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)","Not used",1,"symsum(log(-(3*b^3*(a + b)*(8*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)*a - cot(x) + 2*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)*b + 504*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^3*a^3 + 7776*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^5*a^5 - 144*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^3*a^2*b + 7776*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^5*a^4*b - 60*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^2*a^2*cot(x) - 864*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^4*a^4*cot(x) - 864*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^4*a^3*b*cot(x) + 12*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^2*a*b*cot(x)))/cot(x))*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k), k, 1, 6)","B"
251,1,816,245,16.947519,"\text{Not used}","int(1/(a + b*sin(x)^8),x)","\sum _{k=1}^8\ln\left(-b^5\,\left(a+b\right)\,\left({\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^2\,a^2\,800+{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^4\,a^4\,43008+{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^6\,a^6\,786432+\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)\,b\,\mathrm{tan}\left(x\right)\,4-{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^4\,a^3\,b\,6144+{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^6\,a^5\,b\,786432-{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^3\,a^3\,\mathrm{tan}\left(x\right)\,9984-{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^5\,a^5\,\mathrm{tan}\left(x\right)\,557056-{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^7\,a^7\,\mathrm{tan}\left(x\right)\,10485760+{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^2\,a\,b\,32-\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)\,a\,\mathrm{tan}\left(x\right)\,60-{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^3\,a^2\,b\,\mathrm{tan}\left(x\right)\,768+{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^5\,a^4\,b\,\mathrm{tan}\left(x\right)\,98304-{\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^7\,a^6\,b\,\mathrm{tan}\left(x\right)\,10485760+5\right)\,2\right)\,\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)","Not used",1,"symsum(log(-2*b^5*(a + b)*(800*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^2*a^2 + 43008*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^4*a^4 + 786432*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^6*a^6 + 4*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)*b*tan(x) - 6144*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^4*a^3*b + 786432*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^6*a^5*b - 9984*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^3*a^3*tan(x) - 557056*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^5*a^5*tan(x) - 10485760*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^7*a^7*tan(x) + 32*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^2*a*b - 60*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)*a*tan(x) - 768*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^3*a^2*b*tan(x) + 98304*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^5*a^4*b*tan(x) - 10485760*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^7*a^6*b*tan(x) + 5))*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k), k, 1, 8)","B"
252,1,1515,379,20.140928,"\text{Not used}","int(1/(a - b*sin(x)^5),x)","\sum _{k=1}^{10}\ln\left(a\,b^7\,\left(16\,\mathrm{tan}\left(\frac{x}{2}\right)+\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)\,a\,56+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^3\,a^3\,5425+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^5\,a^5\,196875+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^7\,3171875+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^9\,19140625+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^2\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,1560+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^4\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)\,57000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)\,925000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^8\,\mathrm{tan}\left(\frac{x}{2}\right)\,5625000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^4\,a^3\,b\,14000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^5\,b\,175000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^7\,b\,546875-\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,128+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^5\,b^2\,1000000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^7\,b^2\,18750000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^2\,a\,b\,320-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^3\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,6400-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^5\,a^4\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,100000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^6\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,500000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^8\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,390625+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^4\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,400000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^6\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,5000000\right)\,10995116277760\right)\,\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)","Not used",1,"symsum(log(10995116277760*a*b^7*(16*tan(x/2) + 56*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)*a + 5425*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^3*a^3 + 196875*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^5*a^5 + 3171875*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^7 + 19140625*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^9 + 1560*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^2*a^2*tan(x/2) + 57000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^4*a^4*tan(x/2) + 925000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^6*tan(x/2) + 5625000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^8*tan(x/2) - 14000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^4*a^3*b - 175000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^5*b - 546875*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^7*b - 128*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)*b*tan(x/2) + 1000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^5*b^2 - 18750000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^7*b^2 - 320*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^2*a*b - 6400*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^3*a^2*b*tan(x/2) - 100000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^5*a^4*b*tan(x/2) - 500000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^6*b*tan(x/2) - 390625*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^8*b*tan(x/2) + 400000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^4*b^2*tan(x/2) - 5000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^6*b^2*tan(x/2)))*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k), k, 1, 10)","B"
253,1,513,175,16.068604,"\text{Not used}","int(1/(a - b*sin(x)^6),x)","\sum _{k=1}^6\ln\left(-\frac{b^3\,\left(a-b\right)\,\left(\mathrm{cot}\left(x\right)-\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)\,a\,8+\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)\,b\,2-{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^3\,a^3\,504-{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^5\,a^5\,7776-{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^3\,a^2\,b\,144+{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^5\,a^4\,b\,7776+{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^2\,a^2\,\mathrm{cot}\left(x\right)\,60+{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^4\,a^4\,\mathrm{cot}\left(x\right)\,864-{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^4\,a^3\,b\,\mathrm{cot}\left(x\right)\,864+{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^2\,a\,b\,\mathrm{cot}\left(x\right)\,12\right)\,3}{\mathrm{cot}\left(x\right)}\right)\,\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)","Not used",1,"symsum(log(-(3*b^3*(a - b)*(cot(x) - 8*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)*a + 2*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)*b - 504*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^3*a^3 - 7776*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^5*a^5 - 144*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^3*a^2*b + 7776*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^5*a^4*b + 60*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^2*a^2*cot(x) + 864*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^4*a^4*cot(x) - 864*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^4*a^3*b*cot(x) + 12*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^2*a*b*cot(x)))/cot(x))*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k), k, 1, 6)","B"
254,1,818,213,16.542055,"\text{Not used}","int(1/(a - b*sin(x)^8),x)","\sum _{k=1}^8\ln\left(-b^5\,\left(a-b\right)\,\left(-{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^2\,a^2\,800-{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^4\,a^4\,43008-{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^6\,a^6\,786432+\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)\,b\,\mathrm{tan}\left(x\right)\,4-{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^4\,a^3\,b\,6144+{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^6\,a^5\,b\,786432+{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^3\,a^3\,\mathrm{tan}\left(x\right)\,9984+{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^5\,a^5\,\mathrm{tan}\left(x\right)\,557056+{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^7\,a^7\,\mathrm{tan}\left(x\right)\,10485760+{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^2\,a\,b\,32+\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)\,a\,\mathrm{tan}\left(x\right)\,60-{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^3\,a^2\,b\,\mathrm{tan}\left(x\right)\,768+{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^5\,a^4\,b\,\mathrm{tan}\left(x\right)\,98304-{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^7\,a^6\,b\,\mathrm{tan}\left(x\right)\,10485760-5\right)\,2\right)\,\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)","Not used",1,"symsum(log(-2*b^5*(a - b)*(4*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)*b*tan(x) - 43008*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^4*a^4 - 786432*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^6*a^6 - 800*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^2*a^2 - 6144*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^4*a^3*b + 786432*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^6*a^5*b + 9984*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^3*a^3*tan(x) + 557056*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^5*a^5*tan(x) + 10485760*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^7*a^7*tan(x) + 32*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^2*a*b + 60*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)*a*tan(x) - 768*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^3*a^2*b*tan(x) + 98304*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^5*a^4*b*tan(x) - 10485760*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^7*a^6*b*tan(x) - 5))*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k), k, 1, 8)","B"
255,1,3513,195,15.253559,"\text{Not used}","int(1/(sin(x)^5 + 1),x)","2\,\mathrm{atanh}\left(\frac{989855744\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{2030043136\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{1627389952\,\sqrt{5}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{184549376\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{5083496448\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{553648128\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-2\,\mathrm{atanh}\left(\frac{2030043136\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{989855744\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{1627389952\,\sqrt{5}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{184549376\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{5083496448\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{553648128\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-\frac{2}{5\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}+2\,\mathrm{atanh}\left(\frac{989855744\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{2030043136\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{1627389952\,\sqrt{5}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{553648128\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{184549376\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{5083496448\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-2\,\mathrm{atanh}\left(\frac{2030043136\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{989855744\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{1627389952\,\sqrt{5}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{553648128\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{184549376\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{5083496448\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}","Not used",1,"2*atanh((989855744*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (2030043136*tan(x/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (1627389952*5^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*(- (2*5^(1/2))/5 - 1)^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (184549376*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (5083496448*5^(1/2)*tan(x/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (553648128*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)))*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2*atanh((2030043136*tan(x/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (989855744*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (1627389952*5^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*(- (2*5^(1/2))/5 - 1)^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (184549376*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (5083496448*5^(1/2)*tan(x/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (553648128*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)))*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2/(5*(tan(x/2) + 1)) + 2*atanh((989855744*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (2030043136*tan(x/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (1627389952*5^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (553648128*((2*5^(1/2))/5 - 1)^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (184549376*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (5083496448*5^(1/2)*tan(x/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)))*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2*atanh((2030043136*tan(x/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (989855744*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (1627389952*5^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (553648128*((2*5^(1/2))/5 - 1)^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (184549376*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (5083496448*5^(1/2)*tan(x/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)))*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2)","B"
256,1,98,103,14.226444,"\text{Not used}","int(1/(sin(x)^6 + 1),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\right)}{6}+\mathrm{atan}\left(\frac{\sqrt{3}\,\mathrm{tan}\left(x\right)}{2}+\frac{\mathrm{tan}\left(x\right)\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{3}}{6}-\frac{1}{6}{}\mathrm{i}\right)-\mathrm{atan}\left(-\frac{\sqrt{3}\,\mathrm{tan}\left(x\right)}{2}+\frac{\mathrm{tan}\left(x\right)\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{3}}{6}+\frac{1}{6}{}\mathrm{i}\right)+\frac{\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)\,\left(\frac{\pi \,\sqrt{2}}{6}+\pi \,\left(\frac{\sqrt{3}}{6}-\frac{1}{6}{}\mathrm{i}\right)+\pi \,\left(\frac{\sqrt{3}}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)}{\pi }","Not used",1,"atan((tan(x)*1i)/2 + (3^(1/2)*tan(x))/2)*(3^(1/2)/6 - 1i/6) - atan((tan(x)*1i)/2 - (3^(1/2)*tan(x))/2)*(3^(1/2)/6 + 1i/6) + (2^(1/2)*atan(2^(1/2)*tan(x)))/6 + ((x - atan(tan(x)))*((2^(1/2)*pi)/6 + pi*(3^(1/2)/6 - 1i/6) + pi*(3^(1/2)/6 + 1i/6)))/pi","B"
257,1,945,218,14.918935,"\text{Not used}","int(1/(sin(x)^8 + 1),x)","-\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,1{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2048}-\frac{\sqrt{-2\,\sqrt{2}-3}}{512}\right)}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,1{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2048}-\frac{\sqrt{-2\,\sqrt{2}-3}}{512}\right)}+\frac{\mathrm{tan}\left(x\right)\,\sqrt{-2\,\sqrt{2}-3}\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,7{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2048}-\frac{\sqrt{-2\,\sqrt{2}-3}}{512}\right)}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-2\,\sqrt{2}-3}\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,5{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2048}-\frac{\sqrt{-2\,\sqrt{2}-3}}{512}\right)}\right)\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,1{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2048}-\frac{\sqrt{-2\,\sqrt{2}-3}}{512}\right)}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,1{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2048}-\frac{\sqrt{-2\,\sqrt{2}-3}}{512}\right)}-\frac{\mathrm{tan}\left(x\right)\,\sqrt{-2\,\sqrt{2}-3}\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,7{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2048}-\frac{\sqrt{-2\,\sqrt{2}-3}}{512}\right)}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-2\,\sqrt{2}-3}\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,5{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2048}-\frac{\sqrt{-2\,\sqrt{2}-3}}{512}\right)}\right)\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,1{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2048}+\frac{\sqrt{2\,\sqrt{2}-3}}{512}\right)}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,1{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2048}+\frac{\sqrt{2\,\sqrt{2}-3}}{512}\right)}+\frac{\mathrm{tan}\left(x\right)\,\sqrt{2\,\sqrt{2}-3}\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,7{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2048}+\frac{\sqrt{2\,\sqrt{2}-3}}{512}\right)}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{2\,\sqrt{2}-3}\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,5{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2048}+\frac{\sqrt{2\,\sqrt{2}-3}}{512}\right)}\right)\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,1{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2048}+\frac{\sqrt{2\,\sqrt{2}-3}}{512}\right)}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,1{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2048}+\frac{\sqrt{2\,\sqrt{2}-3}}{512}\right)}-\frac{\mathrm{tan}\left(x\right)\,\sqrt{2\,\sqrt{2}-3}\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,7{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2048}+\frac{\sqrt{2\,\sqrt{2}-3}}{512}\right)}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{2\,\sqrt{2}-3}\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,5{}\mathrm{i}}{256\,\left(\frac{3\,\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2048}+\frac{\sqrt{2\,\sqrt{2}-3}}{512}\right)}\right)\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,2{}\mathrm{i}","Not used",1,"atan((tan(x)*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*1i)/(256*((3*2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2048 - (- 2*2^(1/2) - 3)^(1/2)/512)) - (2^(1/2)*tan(x)*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*1i)/(256*((3*2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2048 - (- 2*2^(1/2) - 3)^(1/2)/512)) - (tan(x)*(- 2*2^(1/2) - 3)^(1/2)*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*7i)/(256*((3*2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2048 - (- 2*2^(1/2) - 3)^(1/2)/512)) + (2^(1/2)*tan(x)*(- 2*2^(1/2) - 3)^(1/2)*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*5i)/(256*((3*2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2048 - (- 2*2^(1/2) - 3)^(1/2)/512)))*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*2i - atan((tan(x)*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*1i)/(256*((3*2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2048 - (- 2*2^(1/2) - 3)^(1/2)/512)) - (2^(1/2)*tan(x)*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*1i)/(256*((3*2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2048 - (- 2*2^(1/2) - 3)^(1/2)/512)) + (tan(x)*(- 2*2^(1/2) - 3)^(1/2)*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*7i)/(256*((3*2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2048 - (- 2*2^(1/2) - 3)^(1/2)/512)) - (2^(1/2)*tan(x)*(- 2*2^(1/2) - 3)^(1/2)*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*5i)/(256*((3*2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2048 - (- 2*2^(1/2) - 3)^(1/2)/512)))*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*2i + atan((tan(x)*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*1i)/(256*((3*2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2048 + (2*2^(1/2) - 3)^(1/2)/512)) + (2^(1/2)*tan(x)*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*1i)/(256*((3*2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2048 + (2*2^(1/2) - 3)^(1/2)/512)) + (tan(x)*(2*2^(1/2) - 3)^(1/2)*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*7i)/(256*((3*2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2048 + (2*2^(1/2) - 3)^(1/2)/512)) + (2^(1/2)*tan(x)*(2*2^(1/2) - 3)^(1/2)*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*5i)/(256*((3*2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2048 + (2*2^(1/2) - 3)^(1/2)/512)))*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*2i - atan((tan(x)*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*1i)/(256*((3*2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2048 + (2*2^(1/2) - 3)^(1/2)/512)) + (2^(1/2)*tan(x)*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*1i)/(256*((3*2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2048 + (2*2^(1/2) - 3)^(1/2)/512)) - (tan(x)*(2*2^(1/2) - 3)^(1/2)*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*7i)/(256*((3*2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2048 + (2*2^(1/2) - 3)^(1/2)/512)) - (2^(1/2)*tan(x)*(2*2^(1/2) - 3)^(1/2)*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*5i)/(256*((3*2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2048 + (2*2^(1/2) - 3)^(1/2)/512)))*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*2i","B"
258,1,3513,187,14.440372,"\text{Not used}","int(-1/(sin(x)^5 - 1),x)","2\,\mathrm{atanh}\left(\frac{989855744\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{2030043136\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{1627389952\,\sqrt{5}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{184549376\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{5083496448\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{553648128\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}-\frac{553648128\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-2\,\mathrm{atanh}\left(\frac{989855744\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{2030043136\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{1627389952\,\sqrt{5}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{553648128\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{184549376\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{5083496448\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}-\frac{553648128\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+\frac{452984832\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{184549376}{25}\right)}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-\frac{2}{5\,\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}-2\,\mathrm{atanh}\left(\frac{1627389952\,\sqrt{5}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}-\frac{2030043136\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}-\frac{989855744\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}-\frac{184549376\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{5083496448\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{553648128\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}-\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}-16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}+2\,\mathrm{atanh}\left(\frac{989855744\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{2030043136\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}-\frac{1627389952\,\sqrt{5}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}-\frac{184549376\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}-\frac{5083496448\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{25\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{553648128\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}+\frac{553648128\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\left(\frac{301989888\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}-\frac{2382364672\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)}{125}+\frac{1308622848\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{452984832\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}+\frac{16777216\,\sqrt{5}}{5}+16777216\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-\frac{436207616\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{25}-\frac{184549376}{25}\right)}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}","Not used",1,"2*atanh((989855744*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (2030043136*tan(x/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (1627389952*5^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (553648128*(- (2*5^(1/2))/5 - 1)^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (184549376*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (5083496448*5^(1/2)*tan(x/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (553648128*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) - (553648128*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 + (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)))*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2*atanh((989855744*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (2382364672*5^(1/2)*tan(x/2))/125 - (301989888*tan(x/2))/5 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (2030043136*tan(x/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (2382364672*5^(1/2)*tan(x/2))/125 - (301989888*tan(x/2))/5 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (1627389952*5^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (2382364672*5^(1/2)*tan(x/2))/125 - (301989888*tan(x/2))/5 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (553648128*(- (2*5^(1/2))/5 - 1)^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (2382364672*5^(1/2)*tan(x/2))/125 - (301989888*tan(x/2))/5 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (184549376*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (2382364672*5^(1/2)*tan(x/2))/125 - (301989888*tan(x/2))/5 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (5083496448*5^(1/2)*tan(x/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (2382364672*5^(1/2)*tan(x/2))/125 - (301989888*tan(x/2))/5 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) - (553648128*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (2382364672*5^(1/2)*tan(x/2))/125 - (301989888*tan(x/2))/5 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)) + (553648128*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((1308622848*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 - (2382364672*5^(1/2)*tan(x/2))/125 - (301989888*tan(x/2))/5 + (452984832*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*(- (2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/25 + 184549376/25)))*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2/(5*(tan(x/2) - 1)) - 2*atanh((1627389952*5^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) - (2030043136*tan(x/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) - (989855744*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (553648128*((2*5^(1/2))/5 - 1)^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) - (184549376*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (5083496448*5^(1/2)*tan(x/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (553648128*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (553648128*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 - (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 - 16777216*((2*5^(1/2))/5 - 1)^(1/2) + (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)))*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) + 2*atanh((989855744*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (2030043136*tan(x/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) - (1627389952*5^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (553648128*((2*5^(1/2))/5 - 1)^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) - (184549376*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) - (5083496448*5^(1/2)*tan(x/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(25*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (553648128*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)) + (553648128*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*((301989888*tan(x/2))/5 - (2382364672*5^(1/2)*tan(x/2))/125 + (1308622848*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - (452984832*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 + (16777216*5^(1/2))/5 + 16777216*((2*5^(1/2))/5 - 1)^(1/2) - (436207616*5^(1/2)*tan(x/2)*((2*5^(1/2))/5 - 1)^(1/2))/25 - 184549376/25)))*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2)","B"
259,1,99,71,14.207738,"\text{Not used}","int(-1/(sin(x)^6 - 1),x)","\frac{\mathrm{tan}\left(x\right)}{3}-\frac{\sqrt{6}\,\mathrm{atan}\left(3^{1/4}\,\sqrt{6}\,\mathrm{tan}\left(x\right)\,\left(\frac{1}{4}-\frac{1}{4}{}\mathrm{i}\right)+3^{3/4}\,\sqrt{6}\,\mathrm{tan}\left(x\right)\,\left(\frac{1}{12}+\frac{1}{12}{}\mathrm{i}\right)\right)\,\left(3^{1/4}\,\left(1+1{}\mathrm{i}\right)+3^{3/4}\,\left(-1+1{}\mathrm{i}\right)\right)\,1{}\mathrm{i}}{36}+\frac{\sqrt{6}\,\mathrm{atan}\left(3^{1/4}\,\sqrt{6}\,\mathrm{tan}\left(x\right)\,\left(\frac{1}{4}+\frac{1}{4}{}\mathrm{i}\right)+3^{3/4}\,\sqrt{6}\,\mathrm{tan}\left(x\right)\,\left(\frac{1}{12}-\frac{1}{12}{}\mathrm{i}\right)\right)\,\left(3^{1/4}\,\left(1-\mathrm{i}\right)+3^{3/4}\,\left(-1-\mathrm{i}\right)\right)\,1{}\mathrm{i}}{36}","Not used",1,"tan(x)/3 - (6^(1/2)*atan(3^(1/4)*6^(1/2)*tan(x)*(1/4 - 1i/4) + 3^(3/4)*6^(1/2)*tan(x)*(1/12 + 1i/12))*(3^(1/4)*(1 + 1i) - 3^(3/4)*(1 - 1i))*1i)/36 + (6^(1/2)*atan(3^(1/4)*6^(1/2)*tan(x)*(1/4 + 1i/4) + 3^(3/4)*6^(1/2)*tan(x)*(1/12 - 1i/12))*(3^(1/4)*(1 - 1i) - 3^(3/4)*(1 + 1i))*1i)/36","B"
260,1,141,89,14.038238,"\text{Not used}","int(-1/(sin(x)^8 - 1),x)","\frac{\mathrm{tan}\left(x\right)}{4}+\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}\,8{}\mathrm{i}-\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,8{}\mathrm{i}\right)\,\left(\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}\,2{}\mathrm{i}+\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,2{}\mathrm{i}\right)+\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}\,8{}\mathrm{i}+\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,8{}\mathrm{i}\right)\,\left(\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}\,2{}\mathrm{i}-\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,2{}\mathrm{i}\right)+\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\right)}{8}","Not used",1,"tan(x)/4 + atan(2^(1/2)*tan(x)*(- 2^(1/2)/256 - 1/256)^(1/2)*8i - 2^(1/2)*tan(x)*(2^(1/2)/256 - 1/256)^(1/2)*8i)*((- 2^(1/2)/256 - 1/256)^(1/2)*2i + (2^(1/2)/256 - 1/256)^(1/2)*2i) + atan(2^(1/2)*tan(x)*(- 2^(1/2)/256 - 1/256)^(1/2)*8i + 2^(1/2)*tan(x)*(2^(1/2)/256 - 1/256)^(1/2)*8i)*((- 2^(1/2)/256 - 1/256)^(1/2)*2i - (2^(1/2)/256 - 1/256)^(1/2)*2i) + (2^(1/2)*atan(2^(1/2)*tan(x)))/8","B"
261,1,34,38,0.097477,"\text{Not used}","int(cos(x)^9/(a - a*sin(x)^2),x)","\frac{\sin\left(x\right)}{a}-\frac{{\sin\left(x\right)}^3}{a}+\frac{3\,{\sin\left(x\right)}^5}{5\,a}-\frac{{\sin\left(x\right)}^7}{7\,a}","Not used",1,"sin(x)/a - sin(x)^3/a + (3*sin(x)^5)/(5*a) - sin(x)^7/(7*a)","B"
262,1,19,29,0.075665,"\text{Not used}","int(cos(x)^7/(a - a*sin(x)^2),x)","\frac{\frac{{\sin\left(x\right)}^5}{5}-\frac{2\,{\sin\left(x\right)}^3}{3}+\sin\left(x\right)}{a}","Not used",1,"(sin(x) - (2*sin(x)^3)/3 + sin(x)^5/5)/a","B"
263,1,16,18,0.059366,"\text{Not used}","int(cos(x)^5/(a - a*sin(x)^2),x)","\frac{3\,\sin\left(x\right)-{\sin\left(x\right)}^3}{3\,a}","Not used",1,"(3*sin(x) - sin(x)^3)/(3*a)","B"
264,1,6,6,13.756710,"\text{Not used}","int(cos(x)^3/(a - a*sin(x)^2),x)","\frac{\sin\left(x\right)}{a}","Not used",1,"sin(x)/a","B"
265,1,7,7,13.598361,"\text{Not used}","int(cos(x)/(a - a*sin(x)^2),x)","\frac{\mathrm{atanh}\left(\sin\left(x\right)\right)}{a}","Not used",1,"atanh(sin(x))/a","B"
266,1,31,35,13.879112,"\text{Not used}","int(1/(cos(x)^3*(a - a*sin(x)^2)),x)","\frac{3\,\mathrm{atanh}\left(\sin\left(x\right)\right)}{8\,a}+\frac{3\,\sin\left(x\right)}{8\,a\,{\cos\left(x\right)}^2}+\frac{\sin\left(x\right)}{4\,a\,{\cos\left(x\right)}^4}","Not used",1,"(3*atanh(sin(x)))/(8*a) + (3*sin(x))/(8*a*cos(x)^2) + sin(x)/(4*a*cos(x)^4)","B"
267,1,25,33,13.614061,"\text{Not used}","int(cos(x)^6/(a - a*sin(x)^2),x)","\frac{\sin\left(2\,x\right)}{4\,a}+\frac{\sin\left(4\,x\right)}{32\,a}+\frac{3\,x}{8\,a}","Not used",1,"sin(2*x)/(4*a) + sin(4*x)/(32*a) + (3*x)/(8*a)","B"
268,1,13,20,13.813021,"\text{Not used}","int(cos(x)^4/(a - a*sin(x)^2),x)","\frac{2\,x+\sin\left(2\,x\right)}{4\,a}","Not used",1,"(2*x + sin(2*x))/(4*a)","B"
269,1,5,5,13.811189,"\text{Not used}","int(cos(x)^2/(a - a*sin(x)^2),x)","\frac{x}{a}","Not used",1,"x/a","B"
270,1,25,22,13.872710,"\text{Not used}","int(1/(cos(x)*(a - a*sin(x)^2)),x)","\frac{\mathrm{atanh}\left(\sin\left(x\right)\right)}{2\,a}+\frac{\sin\left(x\right)}{2\,\left(a-a\,{\sin\left(x\right)}^2\right)}","Not used",1,"atanh(sin(x))/(2*a) + sin(x)/(2*(a - a*sin(x)^2))","B"
271,1,13,18,13.867743,"\text{Not used}","int(1/(cos(x)^2*(a - a*sin(x)^2)),x)","\frac{\mathrm{tan}\left(x\right)\,\left({\mathrm{tan}\left(x\right)}^2+3\right)}{3\,a}","Not used",1,"(tan(x)*(tan(x)^2 + 3))/(3*a)","B"
272,1,21,29,13.921739,"\text{Not used}","int(1/(cos(x)^4*(a - a*sin(x)^2)),x)","\frac{\mathrm{tan}\left(x\right)\,\left(3\,{\mathrm{tan}\left(x\right)}^4+10\,{\mathrm{tan}\left(x\right)}^2+15\right)}{15\,a}","Not used",1,"(tan(x)*(10*tan(x)^2 + 3*tan(x)^4 + 15))/(15*a)","B"
273,1,19,29,14.000277,"\text{Not used}","int(cos(x)^9/(a - a*sin(x)^2)^2,x)","\frac{\frac{{\sin\left(x\right)}^5}{5}-\frac{2\,{\sin\left(x\right)}^3}{3}+\sin\left(x\right)}{a^2}","Not used",1,"(sin(x) - (2*sin(x)^3)/3 + sin(x)^5/5)/a^2","B"
274,1,16,18,0.035918,"\text{Not used}","int(cos(x)^7/(a - a*sin(x)^2)^2,x)","\frac{3\,\sin\left(x\right)-{\sin\left(x\right)}^3}{3\,a^2}","Not used",1,"(3*sin(x) - sin(x)^3)/(3*a^2)","B"
275,1,6,6,0.024549,"\text{Not used}","int(cos(x)^5/(a - a*sin(x)^2)^2,x)","\frac{\sin\left(x\right)}{a^2}","Not used",1,"sin(x)/a^2","B"
276,1,7,7,0.056074,"\text{Not used}","int(cos(x)^3/(a - a*sin(x)^2)^2,x)","\frac{\mathrm{atanh}\left(\sin\left(x\right)\right)}{a^2}","Not used",1,"atanh(sin(x))/a^2","B"
277,1,30,22,0.076188,"\text{Not used}","int(cos(x)/(a - a*sin(x)^2)^2,x)","\frac{\mathrm{atanh}\left(\sin\left(x\right)\right)}{2\,a^2}-\frac{\sin\left(x\right)}{2\,\left(a^2\,{\sin\left(x\right)}^2-a^2\right)}","Not used",1,"atanh(sin(x))/(2*a^2) - sin(x)/(2*(a^2*sin(x)^2 - a^2))","B"
278,1,31,35,13.984703,"\text{Not used}","int(1/(cos(x)*(a - a*sin(x)^2)^2),x)","\frac{3\,\mathrm{atanh}\left(\sin\left(x\right)\right)}{8\,a^2}+\frac{3\,\sin\left(x\right)}{8\,a^2\,{\cos\left(x\right)}^2}+\frac{\sin\left(x\right)}{4\,a^2\,{\cos\left(x\right)}^4}","Not used",1,"(3*atanh(sin(x)))/(8*a^2) + (3*sin(x))/(8*a^2*cos(x)^2) + sin(x)/(4*a^2*cos(x)^4)","B"
279,1,29,33,13.821141,"\text{Not used}","int(cos(x)^8/(a - a*sin(x)^2)^2,x)","\frac{3\,x}{8\,a^2}+\frac{3\,\cos\left(x\right)\,{\sin\left(x\right)}^3}{8\,a^2}+\frac{5\,{\cos\left(x\right)}^3\,\sin\left(x\right)}{8\,a^2}","Not used",1,"(3*x)/(8*a^2) + (3*cos(x)*sin(x)^3)/(8*a^2) + (5*cos(x)^3*sin(x))/(8*a^2)","B"
280,1,13,20,13.925524,"\text{Not used}","int(cos(x)^6/(a - a*sin(x)^2)^2,x)","\frac{2\,x+\sin\left(2\,x\right)}{4\,a^2}","Not used",1,"(2*x + sin(2*x))/(4*a^2)","B"
281,1,5,5,13.943169,"\text{Not used}","int(cos(x)^4/(a - a*sin(x)^2)^2,x)","\frac{x}{a^2}","Not used",1,"x/a^2","B"
282,1,6,6,13.779530,"\text{Not used}","int(cos(x)^2/(a - a*sin(x)^2)^2,x)","\frac{\mathrm{tan}\left(x\right)}{a^2}","Not used",1,"tan(x)/a^2","B"
283,1,21,29,13.799485,"\text{Not used}","int(1/(cos(x)^2*(a - a*sin(x)^2)^2),x)","\frac{\mathrm{tan}\left(x\right)\,\left(3\,{\mathrm{tan}\left(x\right)}^4+10\,{\mathrm{tan}\left(x\right)}^2+15\right)}{15\,a^2}","Not used",1,"(tan(x)*(10*tan(x)^2 + 3*tan(x)^4 + 15))/(15*a^2)","B"
284,1,33,37,13.837286,"\text{Not used}","int(1/(cos(x)^4*(a - a*sin(x)^2)^2),x)","\frac{\mathrm{tan}\left(x\right)}{a^2}+\frac{{\mathrm{tan}\left(x\right)}^3}{a^2}+\frac{3\,{\mathrm{tan}\left(x\right)}^5}{5\,a^2}+\frac{{\mathrm{tan}\left(x\right)}^7}{7\,a^2}","Not used",1,"tan(x)/a^2 + tan(x)^3/a^2 + (3*tan(x)^5)/(5*a^2) + tan(x)^7/(7*a^2)","B"
285,1,119,109,15.222483,"\text{Not used}","int(cos(e + f*x)^6*(a + b*sin(e + f*x)^2),x)","x\,\left(\frac{5\,a}{16}+\frac{5\,b}{128}\right)+\frac{\left(\frac{5\,a}{16}+\frac{5\,b}{128}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^7+\left(\frac{55\,a}{48}+\frac{55\,b}{384}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^5+\left(\frac{73\,a}{48}+\frac{73\,b}{384}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^3+\left(\frac{11\,a}{16}-\frac{5\,b}{128}\right)\,\mathrm{tan}\left(e+f\,x\right)}{f\,\left({\mathrm{tan}\left(e+f\,x\right)}^8+4\,{\mathrm{tan}\left(e+f\,x\right)}^6+6\,{\mathrm{tan}\left(e+f\,x\right)}^4+4\,{\mathrm{tan}\left(e+f\,x\right)}^2+1\right)}","Not used",1,"x*((5*a)/16 + (5*b)/128) + (tan(e + f*x)^7*((5*a)/16 + (5*b)/128) + tan(e + f*x)^5*((55*a)/48 + (55*b)/384) + tan(e + f*x)^3*((73*a)/48 + (73*b)/384) + tan(e + f*x)*((11*a)/16 - (5*b)/128))/(f*(4*tan(e + f*x)^2 + 6*tan(e + f*x)^4 + 4*tan(e + f*x)^6 + tan(e + f*x)^8 + 1))","B"
286,1,91,83,14.203063,"\text{Not used}","int(cos(e + f*x)^4*(a + b*sin(e + f*x)^2),x)","x\,\left(\frac{3\,a}{8}+\frac{b}{16}\right)+\frac{\left(\frac{3\,a}{8}+\frac{b}{16}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^5+\left(a+\frac{b}{6}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^3+\left(\frac{5\,a}{8}-\frac{b}{16}\right)\,\mathrm{tan}\left(e+f\,x\right)}{f\,\left({\mathrm{tan}\left(e+f\,x\right)}^6+3\,{\mathrm{tan}\left(e+f\,x\right)}^4+3\,{\mathrm{tan}\left(e+f\,x\right)}^2+1\right)}","Not used",1,"x*((3*a)/8 + b/16) + (tan(e + f*x)^5*((3*a)/8 + b/16) + tan(e + f*x)*((5*a)/8 - b/16) + tan(e + f*x)^3*(a + b/6))/(f*(3*tan(e + f*x)^2 + 3*tan(e + f*x)^4 + tan(e + f*x)^6 + 1))","B"
287,1,67,57,13.655458,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x)^2),x)","x\,\left(\frac{a}{2}+\frac{b}{8}\right)+\frac{\left(\frac{a}{2}+\frac{b}{8}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^3+\left(\frac{a}{2}-\frac{b}{8}\right)\,\mathrm{tan}\left(e+f\,x\right)}{f\,\left({\mathrm{tan}\left(e+f\,x\right)}^4+2\,{\mathrm{tan}\left(e+f\,x\right)}^2+1\right)}","Not used",1,"x*(a/2 + b/8) + (tan(e + f*x)^3*(a/2 + b/8) + tan(e + f*x)*(a/2 - b/8))/(f*(2*tan(e + f*x)^2 + tan(e + f*x)^4 + 1))","B"
288,1,27,30,13.645663,"\text{Not used}","int(a + b*sin(e + f*x)^2,x)","-\frac{\frac{b\,\sin\left(2\,e+2\,f\,x\right)}{4}-f\,x\,\left(a+\frac{b}{2}\right)}{f}","Not used",1,"-((b*sin(2*e + 2*f*x))/4 - f*x*(a + b/2))/f","B"
289,1,26,18,13.643368,"\text{Not used}","int((a + b*sin(e + f*x)^2)/cos(e + f*x)^2,x)","\frac{a\,\mathrm{tan}\left(e+f\,x\right)+b\,\mathrm{tan}\left(e+f\,x\right)-b\,f\,x}{f}","Not used",1,"(a*tan(e + f*x) + b*tan(e + f*x) - b*f*x)/f","B"
290,1,31,30,14.161708,"\text{Not used}","int((a + b*sin(e + f*x)^2)/cos(e + f*x)^4,x)","\frac{{\mathrm{tan}\left(e+f\,x\right)}^3\,\left(\frac{a}{3}+\frac{b}{3}\right)}{f}+\frac{a\,\mathrm{tan}\left(e+f\,x\right)}{f}","Not used",1,"(tan(e + f*x)^3*(a/3 + b/3))/f + (a*tan(e + f*x))/f","B"
291,1,45,50,13.895456,"\text{Not used}","int((a + b*sin(e + f*x)^2)/cos(e + f*x)^6,x)","\frac{\left(\frac{a}{5}+\frac{b}{5}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^5+\left(\frac{2\,a}{3}+\frac{b}{3}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^3+a\,\mathrm{tan}\left(e+f\,x\right)}{f}","Not used",1,"(tan(e + f*x)^3*((2*a)/3 + b/3) + tan(e + f*x)^5*(a/5 + b/5) + a*tan(e + f*x))/f","B"
292,1,59,72,13.844291,"\text{Not used}","int((a + b*sin(e + f*x)^2)/cos(e + f*x)^8,x)","\frac{\left(\frac{a}{7}+\frac{b}{7}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^7+\left(\frac{3\,a}{5}+\frac{2\,b}{5}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^5+\left(a+\frac{b}{3}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^3+a\,\mathrm{tan}\left(e+f\,x\right)}{f}","Not used",1,"(tan(e + f*x)^5*((3*a)/5 + (2*b)/5) + tan(e + f*x)^7*(a/7 + b/7) + a*tan(e + f*x) + tan(e + f*x)^3*(a + b/3))/f","B"
293,1,160,156,15.489763,"\text{Not used}","int(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^2,x)","x\,\left(\frac{3\,a^2}{8}+\frac{a\,b}{8}+\frac{3\,b^2}{128}\right)+\frac{\left(\frac{3\,a^2}{8}+\frac{a\,b}{8}+\frac{3\,b^2}{128}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^7+\left(\frac{11\,a^2}{8}+\frac{11\,a\,b}{24}+\frac{11\,b^2}{128}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^5+\left(\frac{13\,a^2}{8}+\frac{5\,a\,b}{24}-\frac{11\,b^2}{128}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^3+\left(\frac{5\,a^2}{8}-\frac{a\,b}{8}-\frac{3\,b^2}{128}\right)\,\mathrm{tan}\left(e+f\,x\right)}{f\,\left({\mathrm{tan}\left(e+f\,x\right)}^8+4\,{\mathrm{tan}\left(e+f\,x\right)}^6+6\,{\mathrm{tan}\left(e+f\,x\right)}^4+4\,{\mathrm{tan}\left(e+f\,x\right)}^2+1\right)}","Not used",1,"x*((a*b)/8 + (3*a^2)/8 + (3*b^2)/128) + (tan(e + f*x)^7*((a*b)/8 + (3*a^2)/8 + (3*b^2)/128) - tan(e + f*x)*((a*b)/8 - (5*a^2)/8 + (3*b^2)/128) + tan(e + f*x)^3*((5*a*b)/24 + (13*a^2)/8 - (11*b^2)/128) + tan(e + f*x)^5*((11*a*b)/24 + (11*a^2)/8 + (11*b^2)/128))/(f*(4*tan(e + f*x)^2 + 6*tan(e + f*x)^4 + 4*tan(e + f*x)^6 + tan(e + f*x)^8 + 1))","B"
294,1,120,116,14.733143,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^2,x)","x\,\left(\frac{a^2}{2}+\frac{a\,b}{4}+\frac{b^2}{16}\right)+\frac{\left(\frac{a^2}{2}+\frac{a\,b}{4}+\frac{b^2}{16}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^5+\left(a^2-\frac{b^2}{6}\right)\,{\mathrm{tan}\left(e+f\,x\right)}^3+\left(\frac{a^2}{2}-\frac{a\,b}{4}-\frac{b^2}{16}\right)\,\mathrm{tan}\left(e+f\,x\right)}{f\,\left({\mathrm{tan}\left(e+f\,x\right)}^6+3\,{\mathrm{tan}\left(e+f\,x\right)}^4+3\,{\mathrm{tan}\left(e+f\,x\right)}^2+1\right)}","Not used",1,"x*((a*b)/4 + a^2/2 + b^2/16) + (tan(e + f*x)^3*(a^2 - b^2/6) - tan(e + f*x)*((a*b)/4 - a^2/2 + b^2/16) + tan(e + f*x)^5*((a*b)/4 + a^2/2 + b^2/16))/(f*(3*tan(e + f*x)^2 + 3*tan(e + f*x)^4 + tan(e + f*x)^6 + 1))","B"
295,1,77,72,14.486707,"\text{Not used}","int((a + b*sin(e + f*x)^2)^2,x)","x\,\left(a^2+a\,b+\frac{3\,b^2}{8}\right)-\frac{\left(\frac{5\,b^2}{8}+a\,b\right)\,{\mathrm{tan}\left(e+f\,x\right)}^3+\left(\frac{3\,b^2}{8}+a\,b\right)\,\mathrm{tan}\left(e+f\,x\right)}{f\,\left({\mathrm{tan}\left(e+f\,x\right)}^4+2\,{\mathrm{tan}\left(e+f\,x\right)}^2+1\right)}","Not used",1,"x*(a*b + a^2 + (3*b^2)/8) - (tan(e + f*x)*(a*b + (3*b^2)/8) + tan(e + f*x)^3*(a*b + (5*b^2)/8))/(f*(2*tan(e + f*x)^2 + tan(e + f*x)^4 + 1))","B"
296,1,74,51,14.087845,"\text{Not used}","int((a + b*sin(e + f*x)^2)^2/cos(e + f*x)^2,x)","\frac{\mathrm{tan}\left(e+f\,x\right)\,{\left(a+b\right)}^2}{f}+\frac{b^2\,\sin\left(2\,e+2\,f\,x\right)}{4\,f}-\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(e+f\,x\right)\,\left(4\,a+3\,b\right)}{2\,\left(\frac{3\,b^2}{2}+2\,a\,b\right)}\right)\,\left(4\,a+3\,b\right)}{2\,f}","Not used",1,"(tan(e + f*x)*(a + b)^2)/f + (b^2*sin(2*e + 2*f*x))/(4*f) - (b*atan((b*tan(e + f*x)*(4*a + 3*b))/(2*(2*a*b + (3*b^2)/2)))*(4*a + 3*b))/(2*f)","B"
297,1,46,45,13.759143,"\text{Not used}","int((a + b*sin(e + f*x)^2)^2/cos(e + f*x)^4,x)","\frac{\frac{{\mathrm{tan}\left(e+f\,x\right)}^3\,{\left(a+b\right)}^2}{3}-\mathrm{tan}\left(e+f\,x\right)\,\left({\left(a+b\right)}^2-2\,a\,\left(a+b\right)\right)+b^2\,f\,x}{f}","Not used",1,"((tan(e + f*x)^3*(a + b)^2)/3 - tan(e + f*x)*((a + b)^2 - 2*a*(a + b)) + b^2*f*x)/f","B"
298,1,44,53,15.833079,"\text{Not used}","int((a + b*sin(e + f*x)^2)^2/cos(e + f*x)^6,x)","\frac{a^2\,\mathrm{tan}\left(e+f\,x\right)+\frac{{\mathrm{tan}\left(e+f\,x\right)}^5\,{\left(a+b\right)}^2}{5}+\frac{2\,a\,{\mathrm{tan}\left(e+f\,x\right)}^3\,\left(a+b\right)}{3}}{f}","Not used",1,"(a^2*tan(e + f*x) + (tan(e + f*x)^5*(a + b)^2)/5 + (2*a*tan(e + f*x)^3*(a + b))/3)/f","B"
299,1,72,80,15.137318,"\text{Not used}","int((a + b*sin(e + f*x)^2)^2/cos(e + f*x)^8,x)","\frac{a^2\,\mathrm{tan}\left(e+f\,x\right)+\frac{{\mathrm{tan}\left(e+f\,x\right)}^7\,{\left(a+b\right)}^2}{7}+{\mathrm{tan}\left(e+f\,x\right)}^5\,\left(\frac{3\,a^2}{5}+\frac{4\,a\,b}{5}+\frac{b^2}{5}\right)+\frac{a\,{\mathrm{tan}\left(e+f\,x\right)}^3\,\left(3\,a+2\,b\right)}{3}}{f}","Not used",1,"(a^2*tan(e + f*x) + (tan(e + f*x)^7*(a + b)^2)/7 + tan(e + f*x)^5*((4*a*b)/5 + (3*a^2)/5 + b^2/5) + (a*tan(e + f*x)^3*(3*a + 2*b))/3)/f","B"
300,1,94,106,14.217660,"\text{Not used}","int((a + b*sin(e + f*x)^2)^2/cos(e + f*x)^10,x)","\frac{a^2\,\mathrm{tan}\left(e+f\,x\right)+\frac{{\mathrm{tan}\left(e+f\,x\right)}^9\,{\left(a+b\right)}^2}{9}+{\mathrm{tan}\left(e+f\,x\right)}^5\,\left(\frac{6\,a^2}{5}+\frac{6\,a\,b}{5}+\frac{b^2}{5}\right)+{\mathrm{tan}\left(e+f\,x\right)}^7\,\left(\frac{4\,a^2}{7}+\frac{6\,a\,b}{7}+\frac{2\,b^2}{7}\right)+\frac{2\,a\,{\mathrm{tan}\left(e+f\,x\right)}^3\,\left(2\,a+b\right)}{3}}{f}","Not used",1,"(a^2*tan(e + f*x) + (tan(e + f*x)^9*(a + b)^2)/9 + tan(e + f*x)^5*((6*a*b)/5 + (6*a^2)/5 + b^2/5) + tan(e + f*x)^7*((6*a*b)/7 + (4*a^2)/7 + (2*b^2)/7) + (2*a*tan(e + f*x)^3*(2*a + b))/3)/f","B"
301,1,99,78,0.115171,"\text{Not used}","int(cos(x)^7/(a + b*sin(x)^2),x)","{\sin\left(x\right)}^3\,\left(\frac{a}{3\,b^2}+\frac{1}{b}\right)-\sin\left(x\right)\,\left(\frac{3}{b}+\frac{a\,\left(\frac{a}{b^2}+\frac{3}{b}\right)}{b}\right)-\frac{{\sin\left(x\right)}^5}{5\,b}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sin\left(x\right)\,{\left(a+b\right)}^3}{\sqrt{a}\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}\right)\,{\left(a+b\right)}^3}{\sqrt{a}\,b^{7/2}}","Not used",1,"sin(x)^3*(a/(3*b^2) + 1/b) - sin(x)*(3/b + (a*(a/b^2 + 3/b))/b) - sin(x)^5/(5*b) + (atan((b^(1/2)*sin(x)*(a + b)^3)/(a^(1/2)*(3*a*b^2 + 3*a^2*b + a^3 + b^3)))*(a + b)^3)/(a^(1/2)*b^(7/2))","B"
302,1,1804,87,15.451319,"\text{Not used}","int(cos(x)^6/(a + b*sin(x)^2),x)","-\frac{\frac{{\mathrm{tan}\left(x\right)}^3\,\left(4\,a+7\,b\right)}{8\,b^2}+\frac{\mathrm{tan}\left(x\right)\,\left(4\,a+9\,b\right)}{8\,b^2}}{{\mathrm{tan}\left(x\right)}^4+2\,{\mathrm{tan}\left(x\right)}^2+1}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7+960\,a^6\,b+3136\,a^5\,b^2+5784\,a^4\,b^3+6505\,a^3\,b^4+4459\,a^2\,b^5+1723\,a\,b^6+289\,b^7\right)}{32\,b^4}-\frac{\left(\frac{2\,a^4\,b^6+\frac{17\,a^3\,b^7}{2}+15\,a^2\,b^8+\frac{25\,a\,b^9}{2}+4\,b^{10}}{b^6}-\frac{\mathrm{tan}\left(x\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{512\,b^7}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)}{16\,b^3}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^3}+\frac{\left(\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7+960\,a^6\,b+3136\,a^5\,b^2+5784\,a^4\,b^3+6505\,a^3\,b^4+4459\,a^2\,b^5+1723\,a\,b^6+289\,b^7\right)}{32\,b^4}+\frac{\left(\frac{2\,a^4\,b^6+\frac{17\,a^3\,b^7}{2}+15\,a^2\,b^8+\frac{25\,a\,b^9}{2}+4\,b^{10}}{b^6}+\frac{\mathrm{tan}\left(x\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{512\,b^7}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)}{16\,b^3}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,b^3}}{\frac{a^8+\frac{37\,a^7\,b}{4}+\frac{75\,a^6\,b^2}{2}+\frac{2785\,a^5\,b^3}{32}+\frac{4045\,a^4\,b^4}{32}+\frac{1881\,a^3\,b^5}{16}+\frac{1093\,a^2\,b^6}{16}+\frac{725\,a\,b^7}{32}+\frac{105\,b^8}{32}}{b^6}-\frac{\left(\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7+960\,a^6\,b+3136\,a^5\,b^2+5784\,a^4\,b^3+6505\,a^3\,b^4+4459\,a^2\,b^5+1723\,a\,b^6+289\,b^7\right)}{32\,b^4}-\frac{\left(\frac{2\,a^4\,b^6+\frac{17\,a^3\,b^7}{2}+15\,a^2\,b^8+\frac{25\,a\,b^9}{2}+4\,b^{10}}{b^6}-\frac{\mathrm{tan}\left(x\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{512\,b^7}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)}{16\,b^3}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)}{16\,b^3}+\frac{\left(\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7+960\,a^6\,b+3136\,a^5\,b^2+5784\,a^4\,b^3+6505\,a^3\,b^4+4459\,a^2\,b^5+1723\,a\,b^6+289\,b^7\right)}{32\,b^4}+\frac{\left(\frac{2\,a^4\,b^6+\frac{17\,a^3\,b^7}{2}+15\,a^2\,b^8+\frac{25\,a\,b^9}{2}+4\,b^{10}}{b^6}+\frac{\mathrm{tan}\left(x\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{512\,b^7}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)}{16\,b^3}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)}{16\,b^3}}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^3}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7+960\,a^6\,b+3136\,a^5\,b^2+5784\,a^4\,b^3+6505\,a^3\,b^4+4459\,a^2\,b^5+1723\,a\,b^6+289\,b^7\right)}{64\,b^4}-\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{2\,a^4\,b^6+\frac{17\,a^3\,b^7}{2}+15\,a^2\,b^8+\frac{25\,a\,b^9}{2}+4\,b^{10}}{2\,b^6}-\frac{\mathrm{tan}\left(x\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{128\,a\,b^7}\right)}{2\,a\,b^3}\right)\,1{}\mathrm{i}}{a\,b^3}+\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7+960\,a^6\,b+3136\,a^5\,b^2+5784\,a^4\,b^3+6505\,a^3\,b^4+4459\,a^2\,b^5+1723\,a\,b^6+289\,b^7\right)}{64\,b^4}+\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{2\,a^4\,b^6+\frac{17\,a^3\,b^7}{2}+15\,a^2\,b^8+\frac{25\,a\,b^9}{2}+4\,b^{10}}{2\,b^6}+\frac{\mathrm{tan}\left(x\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{128\,a\,b^7}\right)}{2\,a\,b^3}\right)\,1{}\mathrm{i}}{a\,b^3}}{\frac{a^8+\frac{37\,a^7\,b}{4}+\frac{75\,a^6\,b^2}{2}+\frac{2785\,a^5\,b^3}{32}+\frac{4045\,a^4\,b^4}{32}+\frac{1881\,a^3\,b^5}{16}+\frac{1093\,a^2\,b^6}{16}+\frac{725\,a\,b^7}{32}+\frac{105\,b^8}{32}}{b^6}-\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7+960\,a^6\,b+3136\,a^5\,b^2+5784\,a^4\,b^3+6505\,a^3\,b^4+4459\,a^2\,b^5+1723\,a\,b^6+289\,b^7\right)}{64\,b^4}-\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{2\,a^4\,b^6+\frac{17\,a^3\,b^7}{2}+15\,a^2\,b^8+\frac{25\,a\,b^9}{2}+4\,b^{10}}{2\,b^6}-\frac{\mathrm{tan}\left(x\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{128\,a\,b^7}\right)}{2\,a\,b^3}\right)}{a\,b^3}+\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7+960\,a^6\,b+3136\,a^5\,b^2+5784\,a^4\,b^3+6505\,a^3\,b^4+4459\,a^2\,b^5+1723\,a\,b^6+289\,b^7\right)}{64\,b^4}+\frac{\sqrt{-a\,{\left(a+b\right)}^5}\,\left(\frac{2\,a^4\,b^6+\frac{17\,a^3\,b^7}{2}+15\,a^2\,b^8+\frac{25\,a\,b^9}{2}+4\,b^{10}}{2\,b^6}+\frac{\mathrm{tan}\left(x\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,\left(512\,a^3\,b^6+1280\,a^2\,b^7+1024\,a\,b^8+256\,b^9\right)}{128\,a\,b^7}\right)}{2\,a\,b^3}\right)}{a\,b^3}}\right)\,\sqrt{-a\,{\left(a+b\right)}^5}\,1{}\mathrm{i}}{a\,b^3}","Not used",1,"(atan(((((tan(x)*(1723*a*b^6 + 960*a^6*b + 128*a^7 + 289*b^7 + 4459*a^2*b^5 + 6505*a^3*b^4 + 5784*a^4*b^3 + 3136*a^5*b^2))/(32*b^4) - ((((25*a*b^9)/2 + 4*b^10 + 15*a^2*b^8 + (17*a^3*b^7)/2 + 2*a^4*b^6)/b^6 - (tan(x)*(a*b*20i + a^2*8i + b^2*15i)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(512*b^7))*(a*b*20i + a^2*8i + b^2*15i))/(16*b^3))*(a*b*20i + a^2*8i + b^2*15i)*1i)/(16*b^3) + (((tan(x)*(1723*a*b^6 + 960*a^6*b + 128*a^7 + 289*b^7 + 4459*a^2*b^5 + 6505*a^3*b^4 + 5784*a^4*b^3 + 3136*a^5*b^2))/(32*b^4) + ((((25*a*b^9)/2 + 4*b^10 + 15*a^2*b^8 + (17*a^3*b^7)/2 + 2*a^4*b^6)/b^6 + (tan(x)*(a*b*20i + a^2*8i + b^2*15i)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(512*b^7))*(a*b*20i + a^2*8i + b^2*15i))/(16*b^3))*(a*b*20i + a^2*8i + b^2*15i)*1i)/(16*b^3))/(((725*a*b^7)/32 + (37*a^7*b)/4 + a^8 + (105*b^8)/32 + (1093*a^2*b^6)/16 + (1881*a^3*b^5)/16 + (4045*a^4*b^4)/32 + (2785*a^5*b^3)/32 + (75*a^6*b^2)/2)/b^6 - (((tan(x)*(1723*a*b^6 + 960*a^6*b + 128*a^7 + 289*b^7 + 4459*a^2*b^5 + 6505*a^3*b^4 + 5784*a^4*b^3 + 3136*a^5*b^2))/(32*b^4) - ((((25*a*b^9)/2 + 4*b^10 + 15*a^2*b^8 + (17*a^3*b^7)/2 + 2*a^4*b^6)/b^6 - (tan(x)*(a*b*20i + a^2*8i + b^2*15i)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(512*b^7))*(a*b*20i + a^2*8i + b^2*15i))/(16*b^3))*(a*b*20i + a^2*8i + b^2*15i))/(16*b^3) + (((tan(x)*(1723*a*b^6 + 960*a^6*b + 128*a^7 + 289*b^7 + 4459*a^2*b^5 + 6505*a^3*b^4 + 5784*a^4*b^3 + 3136*a^5*b^2))/(32*b^4) + ((((25*a*b^9)/2 + 4*b^10 + 15*a^2*b^8 + (17*a^3*b^7)/2 + 2*a^4*b^6)/b^6 + (tan(x)*(a*b*20i + a^2*8i + b^2*15i)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(512*b^7))*(a*b*20i + a^2*8i + b^2*15i))/(16*b^3))*(a*b*20i + a^2*8i + b^2*15i))/(16*b^3)))*(a*b*20i + a^2*8i + b^2*15i)*1i)/(8*b^3) - ((tan(x)^3*(4*a + 7*b))/(8*b^2) + (tan(x)*(4*a + 9*b))/(8*b^2))/(2*tan(x)^2 + tan(x)^4 + 1) + (atan((((-a*(a + b)^5)^(1/2)*((tan(x)*(1723*a*b^6 + 960*a^6*b + 128*a^7 + 289*b^7 + 4459*a^2*b^5 + 6505*a^3*b^4 + 5784*a^4*b^3 + 3136*a^5*b^2))/(64*b^4) - ((-a*(a + b)^5)^(1/2)*(((25*a*b^9)/2 + 4*b^10 + 15*a^2*b^8 + (17*a^3*b^7)/2 + 2*a^4*b^6)/(2*b^6) - (tan(x)*(-a*(a + b)^5)^(1/2)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(128*a*b^7)))/(2*a*b^3))*1i)/(a*b^3) + ((-a*(a + b)^5)^(1/2)*((tan(x)*(1723*a*b^6 + 960*a^6*b + 128*a^7 + 289*b^7 + 4459*a^2*b^5 + 6505*a^3*b^4 + 5784*a^4*b^3 + 3136*a^5*b^2))/(64*b^4) + ((-a*(a + b)^5)^(1/2)*(((25*a*b^9)/2 + 4*b^10 + 15*a^2*b^8 + (17*a^3*b^7)/2 + 2*a^4*b^6)/(2*b^6) + (tan(x)*(-a*(a + b)^5)^(1/2)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(128*a*b^7)))/(2*a*b^3))*1i)/(a*b^3))/(((725*a*b^7)/32 + (37*a^7*b)/4 + a^8 + (105*b^8)/32 + (1093*a^2*b^6)/16 + (1881*a^3*b^5)/16 + (4045*a^4*b^4)/32 + (2785*a^5*b^3)/32 + (75*a^6*b^2)/2)/b^6 - ((-a*(a + b)^5)^(1/2)*((tan(x)*(1723*a*b^6 + 960*a^6*b + 128*a^7 + 289*b^7 + 4459*a^2*b^5 + 6505*a^3*b^4 + 5784*a^4*b^3 + 3136*a^5*b^2))/(64*b^4) - ((-a*(a + b)^5)^(1/2)*(((25*a*b^9)/2 + 4*b^10 + 15*a^2*b^8 + (17*a^3*b^7)/2 + 2*a^4*b^6)/(2*b^6) - (tan(x)*(-a*(a + b)^5)^(1/2)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(128*a*b^7)))/(2*a*b^3)))/(a*b^3) + ((-a*(a + b)^5)^(1/2)*((tan(x)*(1723*a*b^6 + 960*a^6*b + 128*a^7 + 289*b^7 + 4459*a^2*b^5 + 6505*a^3*b^4 + 5784*a^4*b^3 + 3136*a^5*b^2))/(64*b^4) + ((-a*(a + b)^5)^(1/2)*(((25*a*b^9)/2 + 4*b^10 + 15*a^2*b^8 + (17*a^3*b^7)/2 + 2*a^4*b^6)/(2*b^6) + (tan(x)*(-a*(a + b)^5)^(1/2)*(1024*a*b^8 + 256*b^9 + 1280*a^2*b^7 + 512*a^3*b^6))/(128*a*b^7)))/(2*a*b^3)))/(a*b^3)))*(-a*(a + b)^5)^(1/2)*1i)/(a*b^3)","B"
303,1,65,54,14.300526,"\text{Not used}","int(cos(x)^5/(a + b*sin(x)^2),x)","\frac{{\sin\left(x\right)}^3}{3\,b}-\sin\left(x\right)\,\left(\frac{a}{b^2}+\frac{2}{b}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sin\left(x\right)\,{\left(a+b\right)}^2}{\sqrt{a}\,\left(a^2+2\,a\,b+b^2\right)}\right)\,{\left(a+b\right)}^2}{\sqrt{a}\,b^{5/2}}","Not used",1,"sin(x)^3/(3*b) - sin(x)*(a/b^2 + 2/b) + (atan((b^(1/2)*sin(x)*(a + b)^2)/(a^(1/2)*(2*a*b + a^2 + b^2)))*(a + b)^2)/(a^(1/2)*b^(5/2))","B"
304,1,119,59,14.665544,"\text{Not used}","int(cos(x)^4/(a + b*sin(x)^2),x)","-\frac{3\,\mathrm{atan}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)}{2\,b}-\frac{a\,\mathrm{atan}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)}{b^2}-\frac{\cos\left(x\right)\,\sin\left(x\right)}{2\,b}-\frac{\mathrm{atanh}\left(\frac{\sin\left(x\right)\,\sqrt{-a^4-3\,a^3\,b-3\,a^2\,b^2-a\,b^3}}{\cos\left(x\right)\,a^2+b\,\cos\left(x\right)\,a}\right)\,\sqrt{-a^4-3\,a^3\,b-3\,a^2\,b^2-a\,b^3}}{a\,b^2}","Not used",1,"- (3*atan(sin(x)/cos(x)))/(2*b) - (a*atan(sin(x)/cos(x)))/b^2 - (cos(x)*sin(x))/(2*b) - (atanh((sin(x)*(- a*b^3 - 3*a^3*b - a^4 - 3*a^2*b^2)^(1/2))/(a^2*cos(x) + a*b*cos(x)))*(- a*b^3 - 3*a^3*b - a^4 - 3*a^2*b^2)^(1/2))/(a*b^2)","B"
305,1,28,36,0.094634,"\text{Not used}","int(cos(x)^3/(a + b*sin(x)^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sin\left(x\right)}{\sqrt{a}}\right)\,\left(a+b\right)}{\sqrt{a}\,b^{3/2}}-\frac{\sin\left(x\right)}{b}","Not used",1,"(atan((b^(1/2)*sin(x))/a^(1/2))*(a + b))/(a^(1/2)*b^(3/2)) - sin(x)/b","B"
306,1,272,39,14.713382,"\text{Not used}","int(cos(x)^2/(a + b*sin(x)^2),x)","-\frac{\mathrm{atan}\left(\frac{2\,a^2\,\mathrm{tan}\left(x\right)}{2\,a^2+4\,a\,b+2\,b^2}+\frac{2\,b^2\,\mathrm{tan}\left(x\right)}{2\,a^2+4\,a\,b+2\,b^2}+\frac{4\,a\,b\,\mathrm{tan}\left(x\right)}{2\,a^2+4\,a\,b+2\,b^2}\right)}{b}-\frac{\mathrm{atanh}\left(\frac{6\,b^2\,\mathrm{tan}\left(x\right)\,\sqrt{-a^2-b\,a}}{2\,a^3+6\,a^2\,b+6\,a\,b^2+2\,b^3}+\frac{2\,a\,\mathrm{tan}\left(x\right)\,\sqrt{-a^2-b\,a}}{6\,a\,b+2\,a^2+6\,b^2+\frac{2\,b^3}{a}}+\frac{6\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-a^2-b\,a}}{6\,a\,b+2\,a^2+6\,b^2+\frac{2\,b^3}{a}}+\frac{2\,b^3\,\mathrm{tan}\left(x\right)\,\sqrt{-a^2-b\,a}}{2\,a^4+6\,a^3\,b+6\,a^2\,b^2+2\,a\,b^3}\right)\,\sqrt{-a\,\left(a+b\right)}}{a\,b}","Not used",1,"- atan((2*a^2*tan(x))/(4*a*b + 2*a^2 + 2*b^2) + (2*b^2*tan(x))/(4*a*b + 2*a^2 + 2*b^2) + (4*a*b*tan(x))/(4*a*b + 2*a^2 + 2*b^2))/b - (atanh((6*b^2*tan(x)*(- a*b - a^2)^(1/2))/(6*a*b^2 + 6*a^2*b + 2*a^3 + 2*b^3) + (2*a*tan(x)*(- a*b - a^2)^(1/2))/(6*a*b + 2*a^2 + 6*b^2 + (2*b^3)/a) + (6*b*tan(x)*(- a*b - a^2)^(1/2))/(6*a*b + 2*a^2 + 6*b^2 + (2*b^3)/a) + (2*b^3*tan(x)*(- a*b - a^2)^(1/2))/(2*a*b^3 + 6*a^3*b + 2*a^4 + 6*a^2*b^2))*(-a*(a + b))^(1/2))/(a*b)","B"
307,1,17,25,14.635620,"\text{Not used}","int(cos(x)/(a + b*sin(x)^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sin\left(x\right)}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}}","Not used",1,"atan((b^(1/2)*sin(x))/a^(1/2))/(a^(1/2)*b^(1/2))","B"
308,1,856,40,14.694964,"\text{Not used}","int(1/(cos(x)*(a + b*sin(x)^2)),x)","-\frac{\mathrm{atan}\left(\frac{\frac{\left(4\,b^3\,\sin\left(x\right)+\frac{8\,a\,b^3+4\,b^4+4\,a^2\,b^2-\frac{\sin\left(x\right)\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}\right)\,1{}\mathrm{i}}{2\,\left(a+b\right)}+\frac{\left(4\,b^3\,\sin\left(x\right)-\frac{8\,a\,b^3+4\,b^4+4\,a^2\,b^2+\frac{\sin\left(x\right)\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}\right)\,1{}\mathrm{i}}{2\,\left(a+b\right)}}{\frac{4\,b^3\,\sin\left(x\right)+\frac{8\,a\,b^3+4\,b^4+4\,a^2\,b^2-\frac{\sin\left(x\right)\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}-\frac{4\,b^3\,\sin\left(x\right)-\frac{8\,a\,b^3+4\,b^4+4\,a^2\,b^2+\frac{\sin\left(x\right)\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}}\right)\,1{}\mathrm{i}}{a+b}-\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,b^3\,\sin\left(x\right)+\frac{\sqrt{-a\,b}\,\left(4\,a\,b^3+2\,b^4+2\,a^2\,b^2-\frac{\sin\left(x\right)\,\sqrt{-a\,b}\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{4\,\left(a^2+b\,a\right)}\right)}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{-a\,b}\,1{}\mathrm{i}}{a^2+b\,a}+\frac{\left(2\,b^3\,\sin\left(x\right)-\frac{\sqrt{-a\,b}\,\left(4\,a\,b^3+2\,b^4+2\,a^2\,b^2+\frac{\sin\left(x\right)\,\sqrt{-a\,b}\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{4\,\left(a^2+b\,a\right)}\right)}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{-a\,b}\,1{}\mathrm{i}}{a^2+b\,a}}{\frac{\left(2\,b^3\,\sin\left(x\right)+\frac{\sqrt{-a\,b}\,\left(4\,a\,b^3+2\,b^4+2\,a^2\,b^2-\frac{\sin\left(x\right)\,\sqrt{-a\,b}\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{4\,\left(a^2+b\,a\right)}\right)}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{-a\,b}}{a^2+b\,a}-\frac{\left(2\,b^3\,\sin\left(x\right)-\frac{\sqrt{-a\,b}\,\left(4\,a\,b^3+2\,b^4+2\,a^2\,b^2+\frac{\sin\left(x\right)\,\sqrt{-a\,b}\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{4\,\left(a^2+b\,a\right)}\right)}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{-a\,b}}{a^2+b\,a}}\right)\,\sqrt{-a\,b}\,1{}\mathrm{i}}{a\,\left(a+b\right)}","Not used",1,"- (atan((((4*b^3*sin(x) + (8*a*b^3 + 4*b^4 + 4*a^2*b^2 - (sin(x)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(2*(a + b)))/(2*(a + b)))*1i)/(2*(a + b)) + ((4*b^3*sin(x) - (8*a*b^3 + 4*b^4 + 4*a^2*b^2 + (sin(x)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(2*(a + b)))/(2*(a + b)))*1i)/(2*(a + b)))/((4*b^3*sin(x) + (8*a*b^3 + 4*b^4 + 4*a^2*b^2 - (sin(x)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(2*(a + b)))/(2*(a + b)))/(2*(a + b)) - (4*b^3*sin(x) - (8*a*b^3 + 4*b^4 + 4*a^2*b^2 + (sin(x)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(2*(a + b)))/(2*(a + b)))/(2*(a + b))))*1i)/(a + b) - (atan((((2*b^3*sin(x) + ((-a*b)^(1/2)*(4*a*b^3 + 2*b^4 + 2*a^2*b^2 - (sin(x)*(-a*b)^(1/2)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(4*(a*b + a^2))))/(2*(a*b + a^2)))*(-a*b)^(1/2)*1i)/(a*b + a^2) + ((2*b^3*sin(x) - ((-a*b)^(1/2)*(4*a*b^3 + 2*b^4 + 2*a^2*b^2 + (sin(x)*(-a*b)^(1/2)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(4*(a*b + a^2))))/(2*(a*b + a^2)))*(-a*b)^(1/2)*1i)/(a*b + a^2))/(((2*b^3*sin(x) + ((-a*b)^(1/2)*(4*a*b^3 + 2*b^4 + 2*a^2*b^2 - (sin(x)*(-a*b)^(1/2)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(4*(a*b + a^2))))/(2*(a*b + a^2)))*(-a*b)^(1/2))/(a*b + a^2) - ((2*b^3*sin(x) - ((-a*b)^(1/2)*(4*a*b^3 + 2*b^4 + 2*a^2*b^2 + (sin(x)*(-a*b)^(1/2)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(4*(a*b + a^2))))/(2*(a*b + a^2)))*(-a*b)^(1/2))/(a*b + a^2)))*(-a*b)^(1/2)*1i)/(a*(a + b))","B"
309,1,39,39,14.655622,"\text{Not used}","int(1/(cos(x)^2*(a + b*sin(x)^2)),x)","\frac{\mathrm{tan}\left(x\right)}{a+b}+\frac{b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\left(2\,a+2\,b\right)}{2\,\sqrt{a}\,\sqrt{a+b}}\right)}{\sqrt{a}\,{\left(a+b\right)}^{3/2}}","Not used",1,"tan(x)/(a + b) + (b*atan((tan(x)*(2*a + 2*b))/(2*a^(1/2)*(a + b)^(1/2))))/(a^(1/2)*(a + b)^(3/2))","B"
310,1,1139,61,15.356761,"\text{Not used}","int(1/(cos(x)^3*(a + b*sin(x)^2)),x)","\frac{\sin\left(x\right)}{2\,{\cos\left(x\right)}^2\,\left(a+b\right)}-\ln\left(\sin\left(x\right)-1\right)\,\left(\frac{b}{2\,{\left(a+b\right)}^2}+\frac{1}{4\,\left(a+b\right)}\right)+\frac{\ln\left(\sin\left(x\right)+1\right)\,\left(a+3\,b\right)}{4\,{\left(a+b\right)}^2}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b^3}\,\left(\frac{\sin\left(x\right)\,\left(a^2\,b^3+6\,a\,b^4+13\,b^5\right)}{4\,\left(a^2+2\,a\,b+b^2\right)}+\frac{\left(\frac{2\,a^5\,b^2+12\,a^4\,b^3+28\,a^3\,b^4+32\,a^2\,b^5+18\,a\,b^6+4\,b^7}{2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}-\frac{\sin\left(x\right)\,\sqrt{-a\,b^3}\,\left(-16\,a^5\,b^2-48\,a^4\,b^3-32\,a^3\,b^4+32\,a^2\,b^5+48\,a\,b^6+16\,b^7\right)}{8\,\left(a^2+2\,a\,b+b^2\right)\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,1{}\mathrm{i}}{a^3+2\,a^2\,b+a\,b^2}+\frac{\sqrt{-a\,b^3}\,\left(\frac{\sin\left(x\right)\,\left(a^2\,b^3+6\,a\,b^4+13\,b^5\right)}{4\,\left(a^2+2\,a\,b+b^2\right)}-\frac{\left(\frac{2\,a^5\,b^2+12\,a^4\,b^3+28\,a^3\,b^4+32\,a^2\,b^5+18\,a\,b^6+4\,b^7}{2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}+\frac{\sin\left(x\right)\,\sqrt{-a\,b^3}\,\left(-16\,a^5\,b^2-48\,a^4\,b^3-32\,a^3\,b^4+32\,a^2\,b^5+48\,a\,b^6+16\,b^7\right)}{8\,\left(a^2+2\,a\,b+b^2\right)\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,1{}\mathrm{i}}{a^3+2\,a^2\,b+a\,b^2}}{\frac{\frac{3\,b^5}{2}+\frac{a\,b^4}{2}}{a^3+3\,a^2\,b+3\,a\,b^2+b^3}-\frac{\sqrt{-a\,b^3}\,\left(\frac{\sin\left(x\right)\,\left(a^2\,b^3+6\,a\,b^4+13\,b^5\right)}{4\,\left(a^2+2\,a\,b+b^2\right)}+\frac{\left(\frac{2\,a^5\,b^2+12\,a^4\,b^3+28\,a^3\,b^4+32\,a^2\,b^5+18\,a\,b^6+4\,b^7}{2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}-\frac{\sin\left(x\right)\,\sqrt{-a\,b^3}\,\left(-16\,a^5\,b^2-48\,a^4\,b^3-32\,a^3\,b^4+32\,a^2\,b^5+48\,a\,b^6+16\,b^7\right)}{8\,\left(a^2+2\,a\,b+b^2\right)\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)}{a^3+2\,a^2\,b+a\,b^2}+\frac{\sqrt{-a\,b^3}\,\left(\frac{\sin\left(x\right)\,\left(a^2\,b^3+6\,a\,b^4+13\,b^5\right)}{4\,\left(a^2+2\,a\,b+b^2\right)}-\frac{\left(\frac{2\,a^5\,b^2+12\,a^4\,b^3+28\,a^3\,b^4+32\,a^2\,b^5+18\,a\,b^6+4\,b^7}{2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}+\frac{\sin\left(x\right)\,\sqrt{-a\,b^3}\,\left(-16\,a^5\,b^2-48\,a^4\,b^3-32\,a^3\,b^4+32\,a^2\,b^5+48\,a\,b^6+16\,b^7\right)}{8\,\left(a^2+2\,a\,b+b^2\right)\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)}{a^3+2\,a^2\,b+a\,b^2}}\right)\,\sqrt{-a\,b^3}\,1{}\mathrm{i}}{a^3+2\,a^2\,b+a\,b^2}","Not used",1,"sin(x)/(2*cos(x)^2*(a + b)) - log(sin(x) - 1)*(b/(2*(a + b)^2) + 1/(4*(a + b))) + (log(sin(x) + 1)*(a + 3*b))/(4*(a + b)^2) + (atan((((-a*b^3)^(1/2)*((sin(x)*(6*a*b^4 + 13*b^5 + a^2*b^3))/(4*(2*a*b + a^2 + b^2)) + (((18*a*b^6 + 4*b^7 + 32*a^2*b^5 + 28*a^3*b^4 + 12*a^4*b^3 + 2*a^5*b^2)/(2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) - (sin(x)*(-a*b^3)^(1/2)*(48*a*b^6 + 16*b^7 + 32*a^2*b^5 - 32*a^3*b^4 - 48*a^4*b^3 - 16*a^5*b^2))/(8*(2*a*b + a^2 + b^2)*(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2))/(2*(a*b^2 + 2*a^2*b + a^3)))*1i)/(a*b^2 + 2*a^2*b + a^3) + ((-a*b^3)^(1/2)*((sin(x)*(6*a*b^4 + 13*b^5 + a^2*b^3))/(4*(2*a*b + a^2 + b^2)) - (((18*a*b^6 + 4*b^7 + 32*a^2*b^5 + 28*a^3*b^4 + 12*a^4*b^3 + 2*a^5*b^2)/(2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) + (sin(x)*(-a*b^3)^(1/2)*(48*a*b^6 + 16*b^7 + 32*a^2*b^5 - 32*a^3*b^4 - 48*a^4*b^3 - 16*a^5*b^2))/(8*(2*a*b + a^2 + b^2)*(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2))/(2*(a*b^2 + 2*a^2*b + a^3)))*1i)/(a*b^2 + 2*a^2*b + a^3))/(((a*b^4)/2 + (3*b^5)/2)/(3*a*b^2 + 3*a^2*b + a^3 + b^3) - ((-a*b^3)^(1/2)*((sin(x)*(6*a*b^4 + 13*b^5 + a^2*b^3))/(4*(2*a*b + a^2 + b^2)) + (((18*a*b^6 + 4*b^7 + 32*a^2*b^5 + 28*a^3*b^4 + 12*a^4*b^3 + 2*a^5*b^2)/(2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) - (sin(x)*(-a*b^3)^(1/2)*(48*a*b^6 + 16*b^7 + 32*a^2*b^5 - 32*a^3*b^4 - 48*a^4*b^3 - 16*a^5*b^2))/(8*(2*a*b + a^2 + b^2)*(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2))/(2*(a*b^2 + 2*a^2*b + a^3))))/(a*b^2 + 2*a^2*b + a^3) + ((-a*b^3)^(1/2)*((sin(x)*(6*a*b^4 + 13*b^5 + a^2*b^3))/(4*(2*a*b + a^2 + b^2)) - (((18*a*b^6 + 4*b^7 + 32*a^2*b^5 + 28*a^3*b^4 + 12*a^4*b^3 + 2*a^5*b^2)/(2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) + (sin(x)*(-a*b^3)^(1/2)*(48*a*b^6 + 16*b^7 + 32*a^2*b^5 - 32*a^3*b^4 - 48*a^4*b^3 - 16*a^5*b^2))/(8*(2*a*b + a^2 + b^2)*(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2))/(2*(a*b^2 + 2*a^2*b + a^3))))/(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2)*1i)/(a*b^2 + 2*a^2*b + a^3)","B"
311,1,77,59,15.024826,"\text{Not used}","int(1/(cos(x)^4*(a + b*sin(x)^2)),x)","\frac{{\mathrm{tan}\left(x\right)}^3}{3\,\left(a+b\right)}-\mathrm{tan}\left(x\right)\,\left(\frac{a}{{\left(a+b\right)}^2}-\frac{2}{a+b}\right)+\frac{b^2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\left(2\,a+2\,b\right)\,\left(a^2+2\,a\,b+b^2\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{5/2}}\right)}{\sqrt{a}\,{\left(a+b\right)}^{5/2}}","Not used",1,"tan(x)^3/(3*(a + b)) - tan(x)*(a/(a + b)^2 - 2/(a + b)) + (b^2*atan((tan(x)*(2*a + 2*b)*(2*a*b + a^2 + b^2))/(2*a^(1/2)*(a + b)^(5/2))))/(a^(1/2)*(a + b)^(5/2))","B"
312,1,832,93,17.449533,"\text{Not used}","int(1/(cos(x)^5*(a + b*sin(x)^2)),x)","\frac{5\,a^3\,\sin\left(x\right)-3\,a^3\,{\sin\left(x\right)}^3+3\,a^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)+9\,a\,b^2\,\sin\left(x\right)+14\,a^2\,b\,\sin\left(x\right)-6\,a^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+3\,a^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^4-7\,a\,b^2\,{\sin\left(x\right)}^3-10\,a^2\,b\,{\sin\left(x\right)}^3+15\,a\,b^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)+10\,a^2\,b\,\mathrm{atanh}\left(\sin\left(x\right)\right)-30\,a\,b^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2-20\,a^2\,b\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+15\,a\,b^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^4+10\,a^2\,b\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^4+\mathrm{atan}\left(\frac{a\,\sin\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\sin\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}+a^6\,b\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,289{}\mathrm{i}+a^3\,b^4\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,300{}\mathrm{i}+a^4\,b^3\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,190{}\mathrm{i}+a^5\,b^2\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,60{}\mathrm{i}}{9\,a^7\,b^3+60\,a^6\,b^4+190\,a^5\,b^5+300\,a^4\,b^6+225\,a^3\,b^7+64\,a^2\,b^8}\right)\,\sqrt{-a\,b^5}\,8{}\mathrm{i}-\mathrm{atan}\left(\frac{a\,\sin\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\sin\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}+a^6\,b\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,289{}\mathrm{i}+a^3\,b^4\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,300{}\mathrm{i}+a^4\,b^3\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,190{}\mathrm{i}+a^5\,b^2\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,60{}\mathrm{i}}{9\,a^7\,b^3+60\,a^6\,b^4+190\,a^5\,b^5+300\,a^4\,b^6+225\,a^3\,b^7+64\,a^2\,b^8}\right)\,{\sin\left(x\right)}^2\,\sqrt{-a\,b^5}\,16{}\mathrm{i}+\mathrm{atan}\left(\frac{a\,\sin\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\sin\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}+a^6\,b\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,289{}\mathrm{i}+a^3\,b^4\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,300{}\mathrm{i}+a^4\,b^3\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,190{}\mathrm{i}+a^5\,b^2\,\sin\left(x\right)\,\sqrt{-a\,b^5}\,60{}\mathrm{i}}{9\,a^7\,b^3+60\,a^6\,b^4+190\,a^5\,b^5+300\,a^4\,b^6+225\,a^3\,b^7+64\,a^2\,b^8}\right)\,{\sin\left(x\right)}^4\,\sqrt{-a\,b^5}\,8{}\mathrm{i}}{8\,a^4\,{\sin\left(x\right)}^4-16\,a^4\,{\sin\left(x\right)}^2+8\,a^4+24\,a^3\,b\,{\sin\left(x\right)}^4-48\,a^3\,b\,{\sin\left(x\right)}^2+24\,a^3\,b+24\,a^2\,b^2\,{\sin\left(x\right)}^4-48\,a^2\,b^2\,{\sin\left(x\right)}^2+24\,a^2\,b^2+8\,a\,b^3\,{\sin\left(x\right)}^4-16\,a\,b^3\,{\sin\left(x\right)}^2+8\,a\,b^3}","Not used",1,"(5*a^3*sin(x) - 3*a^3*sin(x)^3 + 3*a^3*atanh(sin(x)) + atan((a*sin(x)*(-a*b^5)^(3/2)*64i - b*sin(x)*(-a*b^5)^(3/2)*64i + a^6*b*sin(x)*(-a*b^5)^(1/2)*9i + a^2*b^5*sin(x)*(-a*b^5)^(1/2)*289i + a^3*b^4*sin(x)*(-a*b^5)^(1/2)*300i + a^4*b^3*sin(x)*(-a*b^5)^(1/2)*190i + a^5*b^2*sin(x)*(-a*b^5)^(1/2)*60i)/(64*a^2*b^8 + 225*a^3*b^7 + 300*a^4*b^6 + 190*a^5*b^5 + 60*a^6*b^4 + 9*a^7*b^3))*(-a*b^5)^(1/2)*8i + 9*a*b^2*sin(x) + 14*a^2*b*sin(x) - 6*a^3*atanh(sin(x))*sin(x)^2 + 3*a^3*atanh(sin(x))*sin(x)^4 - 7*a*b^2*sin(x)^3 - 10*a^2*b*sin(x)^3 + 15*a*b^2*atanh(sin(x)) + 10*a^2*b*atanh(sin(x)) - atan((a*sin(x)*(-a*b^5)^(3/2)*64i - b*sin(x)*(-a*b^5)^(3/2)*64i + a^6*b*sin(x)*(-a*b^5)^(1/2)*9i + a^2*b^5*sin(x)*(-a*b^5)^(1/2)*289i + a^3*b^4*sin(x)*(-a*b^5)^(1/2)*300i + a^4*b^3*sin(x)*(-a*b^5)^(1/2)*190i + a^5*b^2*sin(x)*(-a*b^5)^(1/2)*60i)/(64*a^2*b^8 + 225*a^3*b^7 + 300*a^4*b^6 + 190*a^5*b^5 + 60*a^6*b^4 + 9*a^7*b^3))*sin(x)^2*(-a*b^5)^(1/2)*16i + atan((a*sin(x)*(-a*b^5)^(3/2)*64i - b*sin(x)*(-a*b^5)^(3/2)*64i + a^6*b*sin(x)*(-a*b^5)^(1/2)*9i + a^2*b^5*sin(x)*(-a*b^5)^(1/2)*289i + a^3*b^4*sin(x)*(-a*b^5)^(1/2)*300i + a^4*b^3*sin(x)*(-a*b^5)^(1/2)*190i + a^5*b^2*sin(x)*(-a*b^5)^(1/2)*60i)/(64*a^2*b^8 + 225*a^3*b^7 + 300*a^4*b^6 + 190*a^5*b^5 + 60*a^6*b^4 + 9*a^7*b^3))*sin(x)^4*(-a*b^5)^(1/2)*8i - 30*a*b^2*atanh(sin(x))*sin(x)^2 - 20*a^2*b*atanh(sin(x))*sin(x)^2 + 15*a*b^2*atanh(sin(x))*sin(x)^4 + 10*a^2*b*atanh(sin(x))*sin(x)^4)/(8*a^4*sin(x)^4 - 16*a^4*sin(x)^2 + 8*a*b^3 + 24*a^3*b + 8*a^4 + 24*a^2*b^2 - 48*a^2*b^2*sin(x)^2 + 24*a^2*b^2*sin(x)^4 - 16*a*b^3*sin(x)^2 - 48*a^3*b*sin(x)^2 + 8*a*b^3*sin(x)^4 + 24*a^3*b*sin(x)^4)","B"
313,1,121,87,13.989734,"\text{Not used}","int(1/(cos(x)^6*(a + b*sin(x)^2)),x)","\frac{{\mathrm{tan}\left(x\right)}^5}{5\,\left(a+b\right)}-{\mathrm{tan}\left(x\right)}^3\,\left(\frac{a}{3\,{\left(a+b\right)}^2}-\frac{1}{a+b}\right)+\mathrm{tan}\left(x\right)\,\left(\frac{3}{a+b}+\frac{a\,\left(\frac{a}{{\left(a+b\right)}^2}-\frac{3}{a+b}\right)}{a+b}\right)+\frac{b^3\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\left(2\,a+2\,b\right)\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{7/2}}\right)}{\sqrt{a}\,{\left(a+b\right)}^{7/2}}","Not used",1,"tan(x)^5/(5*(a + b)) - tan(x)^3*(a/(3*(a + b)^2) - 1/(a + b)) + tan(x)*(3/(a + b) + (a*(a/(a + b)^2 - 3/(a + b)))/(a + b)) + (b^3*atan((tan(x)*(2*a + 2*b)*(3*a*b^2 + 3*a^2*b + a^3 + b^3))/(2*a^(1/2)*(a + b)^(7/2))))/(a^(1/2)*(a + b)^(7/2))","B"
314,1,463,113,14.697397,"\text{Not used}","int(cos(x)^6/(a + b*sin(x)^2)^2,x)","\frac{\frac{\mathrm{tan}\left(x\right)\,\left(2\,a^2+2\,a\,b+b^2\right)}{2\,a\,b^2}+\frac{{\mathrm{tan}\left(x\right)}^3\,\left(a+b\right)\,\left(2\,a+b\right)}{2\,a\,b^2}}{\left(a+b\right)\,{\mathrm{tan}\left(x\right)}^4+\left(2\,a+b\right)\,{\mathrm{tan}\left(x\right)}^2+a}-\frac{\ln\left(a^2\,b-\mathrm{tan}\left(x\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}+a^3\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}\,\left(4\,a-b\right)}{4\,a^3\,b^3}+\frac{\ln\left(\mathrm{tan}\left(x\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}+a^2\,b+a^3\right)\,\left(a-\frac{b}{4}\right)\,\sqrt{-a^3\,{\left(a+b\right)}^3}}{a^3\,b^3}-\frac{\mathrm{atan}\left(\frac{41\,\mathrm{tan}\left(x\right)}{2\,\left(\frac{131\,a}{4\,b}+\frac{11\,b}{4\,a}-\frac{5\,b^2}{4\,a^2}+\frac{85\,a^2}{4\,b^2}+\frac{5\,a^3}{b^3}+\frac{41}{2}\right)}+\frac{11\,\mathrm{tan}\left(x\right)}{4\,\left(\frac{41\,a}{2\,b}-\frac{5\,b}{4\,a}+\frac{131\,a^2}{4\,b^2}+\frac{85\,a^3}{4\,b^3}+\frac{5\,a^4}{b^4}+\frac{11}{4}\right)}+\frac{131\,a\,\mathrm{tan}\left(x\right)}{4\,\left(\frac{131\,a}{4}+\frac{41\,b}{2}+\frac{11\,b^2}{4\,a}+\frac{85\,a^2}{4\,b}-\frac{5\,b^3}{4\,a^2}+\frac{5\,a^3}{b^2}\right)}-\frac{5\,b\,\mathrm{tan}\left(x\right)}{4\,\left(\frac{11\,a}{4}-\frac{5\,b}{4}+\frac{41\,a^2}{2\,b}+\frac{131\,a^3}{4\,b^2}+\frac{85\,a^4}{4\,b^3}+\frac{5\,a^5}{b^4}\right)}+\frac{85\,a^2\,\mathrm{tan}\left(x\right)}{4\,\left(\frac{131\,a\,b}{4}+\frac{85\,a^2}{4}+\frac{41\,b^2}{2}+\frac{11\,b^3}{4\,a}+\frac{5\,a^3}{b}-\frac{5\,b^4}{4\,a^2}\right)}+\frac{5\,a^3\,\mathrm{tan}\left(x\right)}{\frac{131\,a\,b^2}{4}+\frac{85\,a^2\,b}{4}+5\,a^3+\frac{41\,b^3}{2}+\frac{11\,b^4}{4\,a}-\frac{5\,b^5}{4\,a^2}}\right)\,\left(a\,1{}\mathrm{i}+\frac{b\,5{}\mathrm{i}}{4}\right)\,2{}\mathrm{i}}{b^3}","Not used",1,"((tan(x)*(2*a*b + 2*a^2 + b^2))/(2*a*b^2) + (tan(x)^3*(a + b)*(2*a + b))/(2*a*b^2))/(a + tan(x)^2*(2*a + b) + tan(x)^4*(a + b)) - (atan((41*tan(x))/(2*((131*a)/(4*b) + (11*b)/(4*a) - (5*b^2)/(4*a^2) + (85*a^2)/(4*b^2) + (5*a^3)/b^3 + 41/2)) + (11*tan(x))/(4*((41*a)/(2*b) - (5*b)/(4*a) + (131*a^2)/(4*b^2) + (85*a^3)/(4*b^3) + (5*a^4)/b^4 + 11/4)) + (131*a*tan(x))/(4*((131*a)/4 + (41*b)/2 + (11*b^2)/(4*a) + (85*a^2)/(4*b) - (5*b^3)/(4*a^2) + (5*a^3)/b^2)) - (5*b*tan(x))/(4*((11*a)/4 - (5*b)/4 + (41*a^2)/(2*b) + (131*a^3)/(4*b^2) + (85*a^4)/(4*b^3) + (5*a^5)/b^4)) + (85*a^2*tan(x))/(4*((131*a*b)/4 + (85*a^2)/4 + (41*b^2)/2 + (11*b^3)/(4*a) + (5*a^3)/b - (5*b^4)/(4*a^2))) + (5*a^3*tan(x))/((131*a*b^2)/4 + (85*a^2*b)/4 + 5*a^3 + (41*b^3)/2 + (11*b^4)/(4*a) - (5*b^5)/(4*a^2)))*(a*1i + (b*5i)/4)*2i)/b^3 - (log(a^2*b - tan(x)*(-a^3*(a + b)^3)^(1/2) + a^3)*(-a^3*(a + b)^3)^(1/2)*(4*a - b))/(4*a^3*b^3) + (log(tan(x)*(-a^3*(a + b)^3)^(1/2) + a^2*b + a^3)*(a - b/4)*(-a^3*(a + b)^3)^(1/2))/(a^3*b^3)","B"
315,1,96,72,14.402429,"\text{Not used}","int(cos(x)^5/(a + b*sin(x)^2)^2,x)","\frac{\sin\left(x\right)}{b^2}+\frac{\sin\left(x\right)\,\left(a^2+2\,a\,b+b^2\right)}{2\,a\,\left(b^3\,{\sin\left(x\right)}^2+a\,b^2\right)}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sin\left(x\right)\,\left(a+b\right)\,\left(3\,a-b\right)}{\sqrt{a}\,\left(3\,a^2+2\,a\,b-b^2\right)}\right)\,\left(a+b\right)\,\left(3\,a-b\right)}{2\,a^{3/2}\,b^{5/2}}","Not used",1,"sin(x)/b^2 + (sin(x)*(2*a*b + a^2 + b^2))/(2*a*(b^3*sin(x)^2 + a*b^2)) - (atan((b^(1/2)*sin(x)*(a + b)*(3*a - b))/(a^(1/2)*(2*a*b + 3*a^2 - b^2)))*(a + b)*(3*a - b))/(2*a^(3/2)*b^(5/2))","B"
316,1,533,75,14.326566,"\text{Not used}","int(cos(x)^4/(a + b*sin(x)^2)^2,x)","\frac{\mathrm{atan}\left(\frac{5\,\mathrm{tan}\left(x\right)}{2\,\left(\frac{3\,a}{2\,b}+\frac{b}{2\,a}-\frac{b^2}{2\,a^2}+\frac{5}{2}\right)}+\frac{\mathrm{tan}\left(x\right)}{2\,\left(\frac{5\,a}{2\,b}-\frac{b}{2\,a}+\frac{3\,a^2}{2\,b^2}+\frac{1}{2}\right)}+\frac{3\,a\,\mathrm{tan}\left(x\right)}{2\,\left(\frac{3\,a}{2}+\frac{5\,b}{2}+\frac{b^2}{2\,a}-\frac{b^3}{2\,a^2}\right)}-\frac{b\,\mathrm{tan}\left(x\right)}{2\,\left(\frac{a}{2}-\frac{b}{2}+\frac{5\,a^2}{2\,b}+\frac{3\,a^3}{2\,b^2}\right)}\right)}{b^2}+\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{-a^4-b\,a^3}}{a^2-\frac{3\,a\,b}{2}-\frac{b^2}{2}+\frac{b^3}{4\,a}+\frac{13\,a^3}{4\,b}+\frac{3\,a^4}{2\,b^2}}+\frac{3\,\mathrm{tan}\left(x\right)\,\sqrt{-a^4-b\,a^3}}{2\,\left(\frac{13\,a\,b}{4}+\frac{3\,a^2}{2}+b^2-\frac{3\,b^3}{2\,a}-\frac{b^4}{2\,a^2}+\frac{b^5}{4\,a^3}\right)}+\frac{13\,\mathrm{tan}\left(x\right)\,\sqrt{-a^4-b\,a^3}}{4\,\left(a\,b+\frac{13\,a^2}{4}-\frac{3\,b^2}{2}-\frac{b^3}{2\,a}+\frac{3\,a^3}{2\,b}+\frac{b^4}{4\,a^2}\right)}-\frac{3\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-a^4-b\,a^3}}{2\,\left(a^3-\frac{3\,a^2\,b}{2}-\frac{a\,b^2}{2}+\frac{b^3}{4}+\frac{13\,a^4}{4\,b}+\frac{3\,a^5}{2\,b^2}\right)}-\frac{b^2\,\mathrm{tan}\left(x\right)\,\sqrt{-a^4-b\,a^3}}{2\,\left(\frac{a\,b^3}{4}-\frac{3\,a^3\,b}{2}+a^4-\frac{a^2\,b^2}{2}+\frac{13\,a^5}{4\,b}+\frac{3\,a^6}{2\,b^2}\right)}+\frac{b^3\,\mathrm{tan}\left(x\right)\,\sqrt{-a^4-b\,a^3}}{4\,\left(a^5-\frac{3\,a^4\,b}{2}+\frac{a^2\,b^3}{4}-\frac{a^3\,b^2}{2}+\frac{13\,a^6}{4\,b}+\frac{3\,a^7}{2\,b^2}\right)}\right)\,\sqrt{-a^3\,\left(a+b\right)}\,\left(2\,a-b\right)}{2\,a^3\,b^2}+\frac{\mathrm{tan}\left(x\right)\,\left(a+b\right)}{2\,a\,b\,\left(\left(a+b\right)\,{\mathrm{tan}\left(x\right)}^2+a\right)}","Not used",1,"atan((5*tan(x))/(2*((3*a)/(2*b) + b/(2*a) - b^2/(2*a^2) + 5/2)) + tan(x)/(2*((5*a)/(2*b) - b/(2*a) + (3*a^2)/(2*b^2) + 1/2)) + (3*a*tan(x))/(2*((3*a)/2 + (5*b)/2 + b^2/(2*a) - b^3/(2*a^2))) - (b*tan(x))/(2*(a/2 - b/2 + (5*a^2)/(2*b) + (3*a^3)/(2*b^2))))/b^2 + (atanh((tan(x)*(- a^3*b - a^4)^(1/2))/(a^2 - (3*a*b)/2 - b^2/2 + b^3/(4*a) + (13*a^3)/(4*b) + (3*a^4)/(2*b^2)) + (3*tan(x)*(- a^3*b - a^4)^(1/2))/(2*((13*a*b)/4 + (3*a^2)/2 + b^2 - (3*b^3)/(2*a) - b^4/(2*a^2) + b^5/(4*a^3))) + (13*tan(x)*(- a^3*b - a^4)^(1/2))/(4*(a*b + (13*a^2)/4 - (3*b^2)/2 - b^3/(2*a) + (3*a^3)/(2*b) + b^4/(4*a^2))) - (3*b*tan(x)*(- a^3*b - a^4)^(1/2))/(2*(a^3 - (3*a^2*b)/2 - (a*b^2)/2 + b^3/4 + (13*a^4)/(4*b) + (3*a^5)/(2*b^2))) - (b^2*tan(x)*(- a^3*b - a^4)^(1/2))/(2*((a*b^3)/4 - (3*a^3*b)/2 + a^4 - (a^2*b^2)/2 + (13*a^5)/(4*b) + (3*a^6)/(2*b^2))) + (b^3*tan(x)*(- a^3*b - a^4)^(1/2))/(4*(a^5 - (3*a^4*b)/2 + (a^2*b^3)/4 - (a^3*b^2)/2 + (13*a^6)/(4*b) + (3*a^7)/(2*b^2))))*(-a^3*(a + b))^(1/2)*(2*a - b))/(2*a^3*b^2) + (tan(x)*(a + b))/(2*a*b*(a + tan(x)^2*(a + b)))","B"
317,1,47,59,0.136282,"\text{Not used}","int(cos(x)^3/(a + b*sin(x)^2)^2,x)","\frac{\sin\left(x\right)\,\left(a+b\right)}{2\,a\,b\,\left(b\,{\sin\left(x\right)}^2+a\right)}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sin\left(x\right)}{\sqrt{a}}\right)\,\left(a-b\right)}{2\,a^{3/2}\,b^{3/2}}","Not used",1,"(sin(x)*(a + b))/(2*a*b*(a + b*sin(x)^2)) - (atan((b^(1/2)*sin(x))/a^(1/2))*(a - b))/(2*a^(3/2)*b^(3/2))","B"
318,1,50,54,14.305369,"\text{Not used}","int(cos(x)^2/(a + b*sin(x)^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\left(2\,a+2\,b\right)}{2\,\sqrt{a}\,\sqrt{a+b}}\right)}{2\,a^{3/2}\,\sqrt{a+b}}+\frac{\mathrm{tan}\left(x\right)}{2\,a\,\left(\left(a+b\right)\,{\mathrm{tan}\left(x\right)}^2+a\right)}","Not used",1,"atan((tan(x)*(2*a + 2*b))/(2*a^(1/2)*(a + b)^(1/2)))/(2*a^(3/2)*(a + b)^(1/2)) + tan(x)/(2*a*(a + tan(x)^2*(a + b)))","B"
319,1,36,48,15.377385,"\text{Not used}","int(cos(x)/(a + b*sin(x)^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sin\left(x\right)}{\sqrt{a}}\right)}{2\,a^{3/2}\,\sqrt{b}}+\frac{\sin\left(x\right)}{2\,a\,\left(b\,{\sin\left(x\right)}^2+a\right)}","Not used",1,"atan((b^(1/2)*sin(x))/a^(1/2))/(2*a^(3/2)*b^(1/2)) + sin(x)/(2*a*(a + b*sin(x)^2))","B"
320,1,2213,73,15.835396,"\text{Not used}","int(1/(cos(x)*(a + b*sin(x)^2)^2),x)","\frac{b\,\sin\left(x\right)}{2\,a\,\left(a+b\right)\,\left(b\,{\sin\left(x\right)}^2+a\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{\left(\frac{4\,a^6\,b^2+18\,a^5\,b^3+32\,a^4\,b^4+28\,a^3\,b^5+12\,a^2\,b^6+2\,a\,b^7}{2\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}-\frac{\sin\left(x\right)\,\left(-16\,a^7\,b^2-48\,a^6\,b^3-32\,a^5\,b^4+32\,a^4\,b^5+48\,a^3\,b^6+16\,a^2\,b^7\right)}{8\,{\left(a+b\right)}^2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}\right)\,1{}\mathrm{i}}{2\,{\left(a+b\right)}^2}+\frac{\sin\left(x\right)\,\left(13\,a^2\,b^3+6\,a\,b^4+b^5\right)\,1{}\mathrm{i}}{4\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{{\left(a+b\right)}^2}-\frac{\frac{\left(\frac{4\,a^6\,b^2+18\,a^5\,b^3+32\,a^4\,b^4+28\,a^3\,b^5+12\,a^2\,b^6+2\,a\,b^7}{2\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}+\frac{\sin\left(x\right)\,\left(-16\,a^7\,b^2-48\,a^6\,b^3-32\,a^5\,b^4+32\,a^4\,b^5+48\,a^3\,b^6+16\,a^2\,b^7\right)}{8\,{\left(a+b\right)}^2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}\right)\,1{}\mathrm{i}}{2\,{\left(a+b\right)}^2}-\frac{\sin\left(x\right)\,\left(13\,a^2\,b^3+6\,a\,b^4+b^5\right)\,1{}\mathrm{i}}{4\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{{\left(a+b\right)}^2}}{\frac{\frac{b^4}{2}+\frac{3\,a\,b^3}{2}}{a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3}+\frac{\frac{\frac{4\,a^6\,b^2+18\,a^5\,b^3+32\,a^4\,b^4+28\,a^3\,b^5+12\,a^2\,b^6+2\,a\,b^7}{2\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}-\frac{\sin\left(x\right)\,\left(-16\,a^7\,b^2-48\,a^6\,b^3-32\,a^5\,b^4+32\,a^4\,b^5+48\,a^3\,b^6+16\,a^2\,b^7\right)}{8\,{\left(a+b\right)}^2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{2\,{\left(a+b\right)}^2}+\frac{\sin\left(x\right)\,\left(13\,a^2\,b^3+6\,a\,b^4+b^5\right)}{4\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{{\left(a+b\right)}^2}+\frac{\frac{\frac{4\,a^6\,b^2+18\,a^5\,b^3+32\,a^4\,b^4+28\,a^3\,b^5+12\,a^2\,b^6+2\,a\,b^7}{2\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}+\frac{\sin\left(x\right)\,\left(-16\,a^7\,b^2-48\,a^6\,b^3-32\,a^5\,b^4+32\,a^4\,b^5+48\,a^3\,b^6+16\,a^2\,b^7\right)}{8\,{\left(a+b\right)}^2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{2\,{\left(a+b\right)}^2}-\frac{\sin\left(x\right)\,\left(13\,a^2\,b^3+6\,a\,b^4+b^5\right)}{4\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{{\left(a+b\right)}^2}}\right)\,1{}\mathrm{i}}{{\left(a+b\right)}^2}-\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(\frac{\sin\left(x\right)\,\left(13\,a^2\,b^3+6\,a\,b^4+b^5\right)}{2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}+\frac{\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(\frac{4\,a^6\,b^2+18\,a^5\,b^3+32\,a^4\,b^4+28\,a^3\,b^5+12\,a^2\,b^6+2\,a\,b^7}{a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3}-\frac{\sin\left(x\right)\,\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(-16\,a^7\,b^2-48\,a^6\,b^3-32\,a^5\,b^4+32\,a^4\,b^5+48\,a^3\,b^6+16\,a^2\,b^7\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}\right)}{4\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}+\frac{\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(\frac{\sin\left(x\right)\,\left(13\,a^2\,b^3+6\,a\,b^4+b^5\right)}{2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}-\frac{\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(\frac{4\,a^6\,b^2+18\,a^5\,b^3+32\,a^4\,b^4+28\,a^3\,b^5+12\,a^2\,b^6+2\,a\,b^7}{a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3}+\frac{\sin\left(x\right)\,\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(-16\,a^7\,b^2-48\,a^6\,b^3-32\,a^5\,b^4+32\,a^4\,b^5+48\,a^3\,b^6+16\,a^2\,b^7\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}\right)}{4\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}}{\frac{\frac{b^4}{2}+\frac{3\,a\,b^3}{2}}{a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3}+\frac{\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(\frac{\sin\left(x\right)\,\left(13\,a^2\,b^3+6\,a\,b^4+b^5\right)}{2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}+\frac{\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(\frac{4\,a^6\,b^2+18\,a^5\,b^3+32\,a^4\,b^4+28\,a^3\,b^5+12\,a^2\,b^6+2\,a\,b^7}{a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3}-\frac{\sin\left(x\right)\,\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(-16\,a^7\,b^2-48\,a^6\,b^3-32\,a^5\,b^4+32\,a^4\,b^5+48\,a^3\,b^6+16\,a^2\,b^7\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}\right)}{4\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}\right)}{4\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}-\frac{\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(\frac{\sin\left(x\right)\,\left(13\,a^2\,b^3+6\,a\,b^4+b^5\right)}{2\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}-\frac{\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(\frac{4\,a^6\,b^2+18\,a^5\,b^3+32\,a^4\,b^4+28\,a^3\,b^5+12\,a^2\,b^6+2\,a\,b^7}{a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3}+\frac{\sin\left(x\right)\,\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,\left(-16\,a^7\,b^2-48\,a^6\,b^3-32\,a^5\,b^4+32\,a^4\,b^5+48\,a^3\,b^6+16\,a^2\,b^7\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}\right)}{4\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}\right)}{4\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}}\right)\,\left(3\,a+b\right)\,\sqrt{-a^3\,b}\,1{}\mathrm{i}}{2\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}","Not used",1,"(b*sin(x))/(2*a*(a + b)*(a + b*sin(x)^2)) - (atan((((3*a + b)*(-a^3*b)^(1/2)*((sin(x)*(6*a*b^4 + b^5 + 13*a^2*b^3))/(2*(2*a^3*b + a^4 + a^2*b^2)) + ((3*a + b)*(-a^3*b)^(1/2)*((2*a*b^7 + 12*a^2*b^6 + 28*a^3*b^5 + 32*a^4*b^4 + 18*a^5*b^3 + 4*a^6*b^2)/(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2) - (sin(x)*(3*a + b)*(-a^3*b)^(1/2)*(16*a^2*b^7 + 48*a^3*b^6 + 32*a^4*b^5 - 32*a^5*b^4 - 48*a^6*b^3 - 16*a^7*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)*(2*a^4*b + a^5 + a^3*b^2))))/(4*(2*a^4*b + a^5 + a^3*b^2)))*1i)/(4*(2*a^4*b + a^5 + a^3*b^2)) + ((3*a + b)*(-a^3*b)^(1/2)*((sin(x)*(6*a*b^4 + b^5 + 13*a^2*b^3))/(2*(2*a^3*b + a^4 + a^2*b^2)) - ((3*a + b)*(-a^3*b)^(1/2)*((2*a*b^7 + 12*a^2*b^6 + 28*a^3*b^5 + 32*a^4*b^4 + 18*a^5*b^3 + 4*a^6*b^2)/(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2) + (sin(x)*(3*a + b)*(-a^3*b)^(1/2)*(16*a^2*b^7 + 48*a^3*b^6 + 32*a^4*b^5 - 32*a^5*b^4 - 48*a^6*b^3 - 16*a^7*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)*(2*a^4*b + a^5 + a^3*b^2))))/(4*(2*a^4*b + a^5 + a^3*b^2)))*1i)/(4*(2*a^4*b + a^5 + a^3*b^2)))/(((3*a*b^3)/2 + b^4/2)/(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2) + ((3*a + b)*(-a^3*b)^(1/2)*((sin(x)*(6*a*b^4 + b^5 + 13*a^2*b^3))/(2*(2*a^3*b + a^4 + a^2*b^2)) + ((3*a + b)*(-a^3*b)^(1/2)*((2*a*b^7 + 12*a^2*b^6 + 28*a^3*b^5 + 32*a^4*b^4 + 18*a^5*b^3 + 4*a^6*b^2)/(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2) - (sin(x)*(3*a + b)*(-a^3*b)^(1/2)*(16*a^2*b^7 + 48*a^3*b^6 + 32*a^4*b^5 - 32*a^5*b^4 - 48*a^6*b^3 - 16*a^7*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)*(2*a^4*b + a^5 + a^3*b^2))))/(4*(2*a^4*b + a^5 + a^3*b^2))))/(4*(2*a^4*b + a^5 + a^3*b^2)) - ((3*a + b)*(-a^3*b)^(1/2)*((sin(x)*(6*a*b^4 + b^5 + 13*a^2*b^3))/(2*(2*a^3*b + a^4 + a^2*b^2)) - ((3*a + b)*(-a^3*b)^(1/2)*((2*a*b^7 + 12*a^2*b^6 + 28*a^3*b^5 + 32*a^4*b^4 + 18*a^5*b^3 + 4*a^6*b^2)/(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2) + (sin(x)*(3*a + b)*(-a^3*b)^(1/2)*(16*a^2*b^7 + 48*a^3*b^6 + 32*a^4*b^5 - 32*a^5*b^4 - 48*a^6*b^3 - 16*a^7*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)*(2*a^4*b + a^5 + a^3*b^2))))/(4*(2*a^4*b + a^5 + a^3*b^2))))/(4*(2*a^4*b + a^5 + a^3*b^2))))*(3*a + b)*(-a^3*b)^(1/2)*1i)/(2*(2*a^4*b + a^5 + a^3*b^2)) - (atan((((((2*a*b^7 + 12*a^2*b^6 + 28*a^3*b^5 + 32*a^4*b^4 + 18*a^5*b^3 + 4*a^6*b^2)/(2*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) - (sin(x)*(16*a^2*b^7 + 48*a^3*b^6 + 32*a^4*b^5 - 32*a^5*b^4 - 48*a^6*b^3 - 16*a^7*b^2))/(8*(a + b)^2*(2*a^3*b + a^4 + a^2*b^2)))*1i)/(2*(a + b)^2) + (sin(x)*(6*a*b^4 + b^5 + 13*a^2*b^3)*1i)/(4*(2*a^3*b + a^4 + a^2*b^2)))/(a + b)^2 - ((((2*a*b^7 + 12*a^2*b^6 + 28*a^3*b^5 + 32*a^4*b^4 + 18*a^5*b^3 + 4*a^6*b^2)/(2*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) + (sin(x)*(16*a^2*b^7 + 48*a^3*b^6 + 32*a^4*b^5 - 32*a^5*b^4 - 48*a^6*b^3 - 16*a^7*b^2))/(8*(a + b)^2*(2*a^3*b + a^4 + a^2*b^2)))*1i)/(2*(a + b)^2) - (sin(x)*(6*a*b^4 + b^5 + 13*a^2*b^3)*1i)/(4*(2*a^3*b + a^4 + a^2*b^2)))/(a + b)^2)/(((3*a*b^3)/2 + b^4/2)/(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2) + (((2*a*b^7 + 12*a^2*b^6 + 28*a^3*b^5 + 32*a^4*b^4 + 18*a^5*b^3 + 4*a^6*b^2)/(2*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) - (sin(x)*(16*a^2*b^7 + 48*a^3*b^6 + 32*a^4*b^5 - 32*a^5*b^4 - 48*a^6*b^3 - 16*a^7*b^2))/(8*(a + b)^2*(2*a^3*b + a^4 + a^2*b^2)))/(2*(a + b)^2) + (sin(x)*(6*a*b^4 + b^5 + 13*a^2*b^3))/(4*(2*a^3*b + a^4 + a^2*b^2)))/(a + b)^2 + (((2*a*b^7 + 12*a^2*b^6 + 28*a^3*b^5 + 32*a^4*b^4 + 18*a^5*b^3 + 4*a^6*b^2)/(2*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) + (sin(x)*(16*a^2*b^7 + 48*a^3*b^6 + 32*a^4*b^5 - 32*a^5*b^4 - 48*a^6*b^3 - 16*a^7*b^2))/(8*(a + b)^2*(2*a^3*b + a^4 + a^2*b^2)))/(2*(a + b)^2) - (sin(x)*(6*a*b^4 + b^5 + 13*a^2*b^3))/(4*(2*a^3*b + a^4 + a^2*b^2)))/(a + b)^2))*1i)/(a + b)^2","B"
321,1,123,76,14.776742,"\text{Not used}","int(1/(cos(x)^2*(a + b*sin(x)^2)^2),x)","\frac{\mathrm{tan}\left(x\right)}{{\left(a+b\right)}^2}+\frac{b^2\,\mathrm{tan}\left(x\right)}{2\,a\,\left(a\,b^2+2\,a^2\,b+{\mathrm{tan}\left(x\right)}^2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)+a^3\right)}+\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(x\right)\,\left(4\,a+b\right)\,\left(2\,a+2\,b\right)\,\left(a^2+2\,a\,b+b^2\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{5/2}\,\left(b^2+4\,a\,b\right)}\right)\,\left(4\,a+b\right)}{2\,a^{3/2}\,{\left(a+b\right)}^{5/2}}","Not used",1,"tan(x)/(a + b)^2 + (b^2*tan(x))/(2*a*(a*b^2 + 2*a^2*b + tan(x)^2*(3*a*b^2 + 3*a^2*b + a^3 + b^3) + a^3)) + (b*atan((b*tan(x)*(4*a + b)*(2*a + 2*b)*(2*a*b + a^2 + b^2))/(2*a^(1/2)*(a + b)^(5/2)*(4*a*b + b^2)))*(4*a + b))/(2*a^(3/2)*(a + b)^(5/2))","B"
322,1,2009,109,15.057775,"\text{Not used}","int(1/(cos(x)^3*(a + b*sin(x)^2)^2),x)","\frac{\ln\left(\sin\left(x\right)+1\right)\,\left(a+5\,b\right)}{4\,{\left(a+b\right)}^3}-\ln\left(\sin\left(x\right)-1\right)\,\left(\frac{b}{{\left(a+b\right)}^3}+\frac{1}{4\,{\left(a+b\right)}^2}\right)-\frac{\frac{\sin\left(x\right)\,\left(a^2+b^2\right)}{2\,a\,\left(a^2+2\,a\,b+b^2\right)}+\frac{b\,{\sin\left(x\right)}^3\,\left(a-b\right)}{2\,a\,\left(a^2+2\,a\,b+b^2\right)}}{b\,{\sin\left(x\right)}^4+\left(a-b\right)\,{\sin\left(x\right)}^2-a}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sin\left(x\right)\,\left(a^4\,b^3+10\,a^3\,b^4+50\,a^2\,b^5+10\,a\,b^6+b^7\right)}{2\,\left(a^6+4\,a^5\,b+6\,a^4\,b^2+4\,a^3\,b^3+a^2\,b^4\right)}+\frac{\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,\left(\frac{2\,a^9\,b^2+20\,a^8\,b^3+80\,a^7\,b^4+172\,a^6\,b^5+220\,a^5\,b^6+172\,a^4\,b^7+80\,a^3\,b^8+20\,a^2\,b^9+2\,a\,b^{10}}{a^8+6\,a^7\,b+15\,a^6\,b^2+20\,a^5\,b^3+15\,a^4\,b^4+6\,a^3\,b^5+a^2\,b^6}-\frac{\sin\left(x\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,\left(-16\,a^9\,b^2-80\,a^8\,b^3-144\,a^7\,b^4-80\,a^6\,b^5+80\,a^5\,b^6+144\,a^4\,b^7+80\,a^3\,b^8+16\,a^2\,b^9\right)}{8\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)\,\left(a^6+4\,a^5\,b+6\,a^4\,b^2+4\,a^3\,b^3+a^2\,b^4\right)}\right)}{4\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{4\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}+\frac{\left(\frac{\sin\left(x\right)\,\left(a^4\,b^3+10\,a^3\,b^4+50\,a^2\,b^5+10\,a\,b^6+b^7\right)}{2\,\left(a^6+4\,a^5\,b+6\,a^4\,b^2+4\,a^3\,b^3+a^2\,b^4\right)}-\frac{\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,\left(\frac{2\,a^9\,b^2+20\,a^8\,b^3+80\,a^7\,b^4+172\,a^6\,b^5+220\,a^5\,b^6+172\,a^4\,b^7+80\,a^3\,b^8+20\,a^2\,b^9+2\,a\,b^{10}}{a^8+6\,a^7\,b+15\,a^6\,b^2+20\,a^5\,b^3+15\,a^4\,b^4+6\,a^3\,b^5+a^2\,b^6}+\frac{\sin\left(x\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,\left(-16\,a^9\,b^2-80\,a^8\,b^3-144\,a^7\,b^4-80\,a^6\,b^5+80\,a^5\,b^6+144\,a^4\,b^7+80\,a^3\,b^8+16\,a^2\,b^9\right)}{8\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)\,\left(a^6+4\,a^5\,b+6\,a^4\,b^2+4\,a^3\,b^3+a^2\,b^4\right)}\right)}{4\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{4\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}}{\frac{-\frac{5\,a^3\,b^4}{4}-\frac{21\,a^2\,b^5}{4}+\frac{21\,a\,b^6}{4}+\frac{5\,b^7}{4}}{a^8+6\,a^7\,b+15\,a^6\,b^2+20\,a^5\,b^3+15\,a^4\,b^4+6\,a^3\,b^5+a^2\,b^6}+\frac{\left(\frac{\sin\left(x\right)\,\left(a^4\,b^3+10\,a^3\,b^4+50\,a^2\,b^5+10\,a\,b^6+b^7\right)}{2\,\left(a^6+4\,a^5\,b+6\,a^4\,b^2+4\,a^3\,b^3+a^2\,b^4\right)}+\frac{\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,\left(\frac{2\,a^9\,b^2+20\,a^8\,b^3+80\,a^7\,b^4+172\,a^6\,b^5+220\,a^5\,b^6+172\,a^4\,b^7+80\,a^3\,b^8+20\,a^2\,b^9+2\,a\,b^{10}}{a^8+6\,a^7\,b+15\,a^6\,b^2+20\,a^5\,b^3+15\,a^4\,b^4+6\,a^3\,b^5+a^2\,b^6}-\frac{\sin\left(x\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,\left(-16\,a^9\,b^2-80\,a^8\,b^3-144\,a^7\,b^4-80\,a^6\,b^5+80\,a^5\,b^6+144\,a^4\,b^7+80\,a^3\,b^8+16\,a^2\,b^9\right)}{8\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)\,\left(a^6+4\,a^5\,b+6\,a^4\,b^2+4\,a^3\,b^3+a^2\,b^4\right)}\right)}{4\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}-\frac{\left(\frac{\sin\left(x\right)\,\left(a^4\,b^3+10\,a^3\,b^4+50\,a^2\,b^5+10\,a\,b^6+b^7\right)}{2\,\left(a^6+4\,a^5\,b+6\,a^4\,b^2+4\,a^3\,b^3+a^2\,b^4\right)}-\frac{\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,\left(\frac{2\,a^9\,b^2+20\,a^8\,b^3+80\,a^7\,b^4+172\,a^6\,b^5+220\,a^5\,b^6+172\,a^4\,b^7+80\,a^3\,b^8+20\,a^2\,b^9+2\,a\,b^{10}}{a^8+6\,a^7\,b+15\,a^6\,b^2+20\,a^5\,b^3+15\,a^4\,b^4+6\,a^3\,b^5+a^2\,b^6}+\frac{\sin\left(x\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,\left(-16\,a^9\,b^2-80\,a^8\,b^3-144\,a^7\,b^4-80\,a^6\,b^5+80\,a^5\,b^6+144\,a^4\,b^7+80\,a^3\,b^8+16\,a^2\,b^9\right)}{8\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)\,\left(a^6+4\,a^5\,b+6\,a^4\,b^2+4\,a^3\,b^3+a^2\,b^4\right)}\right)}{4\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}}\right)\,\left(5\,a+b\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{2\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}","Not used",1,"(log(sin(x) + 1)*(a + 5*b))/(4*(a + b)^3) - log(sin(x) - 1)*(b/(a + b)^3 + 1/(4*(a + b)^2)) - ((sin(x)*(a^2 + b^2))/(2*a*(2*a*b + a^2 + b^2)) + (b*sin(x)^3*(a - b))/(2*a*(2*a*b + a^2 + b^2)))/(b*sin(x)^4 - a + sin(x)^2*(a - b)) - (atan(((((sin(x)*(10*a*b^6 + b^7 + 50*a^2*b^5 + 10*a^3*b^4 + a^4*b^3))/(2*(4*a^5*b + a^6 + a^2*b^4 + 4*a^3*b^3 + 6*a^4*b^2)) + ((5*a + b)*(-a^3*b^3)^(1/2)*((2*a*b^10 + 20*a^2*b^9 + 80*a^3*b^8 + 172*a^4*b^7 + 220*a^5*b^6 + 172*a^6*b^5 + 80*a^7*b^4 + 20*a^8*b^3 + 2*a^9*b^2)/(6*a^7*b + a^8 + a^2*b^6 + 6*a^3*b^5 + 15*a^4*b^4 + 20*a^5*b^3 + 15*a^6*b^2) - (sin(x)*(5*a + b)*(-a^3*b^3)^(1/2)*(16*a^2*b^9 + 80*a^3*b^8 + 144*a^4*b^7 + 80*a^5*b^6 - 80*a^6*b^5 - 144*a^7*b^4 - 80*a^8*b^3 - 16*a^9*b^2))/(8*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)*(4*a^5*b + a^6 + a^2*b^4 + 4*a^3*b^3 + 6*a^4*b^2))))/(4*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*(5*a + b)*(-a^3*b^3)^(1/2)*1i)/(4*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)) + (((sin(x)*(10*a*b^6 + b^7 + 50*a^2*b^5 + 10*a^3*b^4 + a^4*b^3))/(2*(4*a^5*b + a^6 + a^2*b^4 + 4*a^3*b^3 + 6*a^4*b^2)) - ((5*a + b)*(-a^3*b^3)^(1/2)*((2*a*b^10 + 20*a^2*b^9 + 80*a^3*b^8 + 172*a^4*b^7 + 220*a^5*b^6 + 172*a^6*b^5 + 80*a^7*b^4 + 20*a^8*b^3 + 2*a^9*b^2)/(6*a^7*b + a^8 + a^2*b^6 + 6*a^3*b^5 + 15*a^4*b^4 + 20*a^5*b^3 + 15*a^6*b^2) + (sin(x)*(5*a + b)*(-a^3*b^3)^(1/2)*(16*a^2*b^9 + 80*a^3*b^8 + 144*a^4*b^7 + 80*a^5*b^6 - 80*a^6*b^5 - 144*a^7*b^4 - 80*a^8*b^3 - 16*a^9*b^2))/(8*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)*(4*a^5*b + a^6 + a^2*b^4 + 4*a^3*b^3 + 6*a^4*b^2))))/(4*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*(5*a + b)*(-a^3*b^3)^(1/2)*1i)/(4*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))/(((21*a*b^6)/4 + (5*b^7)/4 - (21*a^2*b^5)/4 - (5*a^3*b^4)/4)/(6*a^7*b + a^8 + a^2*b^6 + 6*a^3*b^5 + 15*a^4*b^4 + 20*a^5*b^3 + 15*a^6*b^2) + (((sin(x)*(10*a*b^6 + b^7 + 50*a^2*b^5 + 10*a^3*b^4 + a^4*b^3))/(2*(4*a^5*b + a^6 + a^2*b^4 + 4*a^3*b^3 + 6*a^4*b^2)) + ((5*a + b)*(-a^3*b^3)^(1/2)*((2*a*b^10 + 20*a^2*b^9 + 80*a^3*b^8 + 172*a^4*b^7 + 220*a^5*b^6 + 172*a^6*b^5 + 80*a^7*b^4 + 20*a^8*b^3 + 2*a^9*b^2)/(6*a^7*b + a^8 + a^2*b^6 + 6*a^3*b^5 + 15*a^4*b^4 + 20*a^5*b^3 + 15*a^6*b^2) - (sin(x)*(5*a + b)*(-a^3*b^3)^(1/2)*(16*a^2*b^9 + 80*a^3*b^8 + 144*a^4*b^7 + 80*a^5*b^6 - 80*a^6*b^5 - 144*a^7*b^4 - 80*a^8*b^3 - 16*a^9*b^2))/(8*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)*(4*a^5*b + a^6 + a^2*b^4 + 4*a^3*b^3 + 6*a^4*b^2))))/(4*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*(5*a + b)*(-a^3*b^3)^(1/2))/(4*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)) - (((sin(x)*(10*a*b^6 + b^7 + 50*a^2*b^5 + 10*a^3*b^4 + a^4*b^3))/(2*(4*a^5*b + a^6 + a^2*b^4 + 4*a^3*b^3 + 6*a^4*b^2)) - ((5*a + b)*(-a^3*b^3)^(1/2)*((2*a*b^10 + 20*a^2*b^9 + 80*a^3*b^8 + 172*a^4*b^7 + 220*a^5*b^6 + 172*a^6*b^5 + 80*a^7*b^4 + 20*a^8*b^3 + 2*a^9*b^2)/(6*a^7*b + a^8 + a^2*b^6 + 6*a^3*b^5 + 15*a^4*b^4 + 20*a^5*b^3 + 15*a^6*b^2) + (sin(x)*(5*a + b)*(-a^3*b^3)^(1/2)*(16*a^2*b^9 + 80*a^3*b^8 + 144*a^4*b^7 + 80*a^5*b^6 - 80*a^6*b^5 - 144*a^7*b^4 - 80*a^8*b^3 - 16*a^9*b^2))/(8*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)*(4*a^5*b + a^6 + a^2*b^4 + 4*a^3*b^3 + 6*a^4*b^2))))/(4*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))*(5*a + b)*(-a^3*b^3)^(1/2))/(4*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2))))*(5*a + b)*(-a^3*b^3)^(1/2)*1i)/(2*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2))","B"
323,1,176,96,14.296908,"\text{Not used}","int(1/(cos(x)^4*(a + b*sin(x)^2)^2),x)","\frac{{\mathrm{tan}\left(x\right)}^3}{3\,{\left(a+b\right)}^2}-\mathrm{tan}\left(x\right)\,\left(\frac{2\,a}{{\left(a+b\right)}^3}-\frac{3}{{\left(a+b\right)}^2}\right)+\frac{b^3\,\mathrm{tan}\left(x\right)}{2\,a\,\left({\mathrm{tan}\left(x\right)}^2\,\left(a^4+4\,a^3\,b+6\,a^2\,b^2+4\,a\,b^3+b^4\right)+a\,b^3+3\,a^3\,b+a^4+3\,a^2\,b^2\right)}+\frac{b^2\,\mathrm{atan}\left(\frac{b^2\,\mathrm{tan}\left(x\right)\,\left(6\,a+b\right)\,\left(2\,a+2\,b\right)\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{7/2}\,\left(b^3+6\,a\,b^2\right)}\right)\,\left(6\,a+b\right)}{2\,a^{3/2}\,{\left(a+b\right)}^{7/2}}","Not used",1,"tan(x)^3/(3*(a + b)^2) - tan(x)*((2*a)/(a + b)^3 - 3/(a + b)^2) + (b^3*tan(x))/(2*a*(tan(x)^2*(4*a*b^3 + 4*a^3*b + a^4 + b^4 + 6*a^2*b^2) + a*b^3 + 3*a^3*b + a^4 + 3*a^2*b^2)) + (b^2*atan((b^2*tan(x)*(6*a + b)*(2*a + 2*b)*(3*a*b^2 + 3*a^2*b + a^3 + b^3))/(2*a^(1/2)*(a + b)^(7/2)*(6*a*b^2 + b^3)))*(6*a + b))/(2*a^(3/2)*(a + b)^(7/2))","B"
324,0,-1,117,0.000000,"\text{Not used}","int(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\cos\left(e+f\,x\right)}^3\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
325,1,61,72,14.477452,"\text{Not used}","int(cos(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2),x)","\frac{\sin\left(e+f\,x\right)\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{2\,f}+\frac{a\,\ln\left(\sqrt{b}\,\sin\left(e+f\,x\right)+\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}\right)}{2\,\sqrt{b}\,f}","Not used",1,"(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2))/(2*f) + (a*log(b^(1/2)*sin(e + f*x) + (a + b*sin(e + f*x)^2)^(1/2)))/(2*b^(1/2)*f)","B"
326,0,-1,82,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x),x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{\cos\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x), x)","F"
327,0,-1,82,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x)^3,x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{{\cos\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x)^3, x)","F"
328,0,-1,143,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x)^5,x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{{\cos\left(e+f\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x)^5, x)","F"
329,0,-1,220,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\cos\left(e+f\,x\right)}^4\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
330,0,-1,159,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\cos\left(e+f\,x\right)}^2\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
331,0,-1,51,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2),x)","\left\{\begin{array}{cl} \frac{\sqrt{a}\,\mathrm{E}\left(e+f\,x\middle|-\frac{b}{a}\right)}{f} & \text{\ if\ \ }0<a\\ \int \sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x & \text{\ if\ \ }\neg 0<a \end{array}\right.","Not used",1,"piecewise(0 < a, (a^(1/2)*ellipticE(e + f*x, -b/a))/f, ~0 < a, int((a + b*sin(e + f*x)^2)^(1/2), x))","F"
332,0,-1,131,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x)^2,x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{{\cos\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x)^2, x)","F"
333,0,-1,196,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x)^4,x)","\int \frac{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}}{{\cos\left(e+f\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(1/2)/cos(e + f*x)^4, x)","F"
334,0,-1,157,0.000000,"\text{Not used}","int(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\cos\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
335,1,60,104,14.538639,"\text{Not used}","int(cos(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2),x)","\frac{\sin\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,{\sin\left(e+f\,x\right)}^2}{a}\right)}{f\,{\left(\frac{b\,{\sin\left(e+f\,x\right)}^2}{a}+1\right)}^{3/2}}","Not used",1,"(sin(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2)*hypergeom([-3/2, 1/2], 3/2, -(b*sin(e + f*x)^2)/a))/(f*((b*sin(e + f*x)^2)/a + 1)^(3/2))","B"
336,0,-1,121,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x),x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{\cos\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x), x)","F"
337,0,-1,127,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^3,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\cos\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^3, x)","F"
338,0,-1,122,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^5,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\cos\left(e+f\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^5, x)","F"
339,0,-1,195,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^7,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\cos\left(e+f\,x\right)}^7} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^7, x)","F"
340,0,-1,321,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\cos\left(e+f\,x\right)}^4\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
341,0,-1,259,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
342,0,-1,154,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2),x)","\int {\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2), x)","F"
343,0,-1,182,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^2,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\cos\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^2, x)","F"
344,0,-1,236,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^4,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}}{{\cos\left(e+f\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2)/cos(e + f*x)^4, x)","F"
345,0,-1,79,0.000000,"\text{Not used}","int(cos(e + f*x)^3/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^3}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(cos(e + f*x)^3/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
346,1,33,38,14.741238,"\text{Not used}","int(cos(e + f*x)/(a + b*sin(e + f*x)^2)^(1/2),x)","\frac{\ln\left(\sqrt{b}\,\sin\left(e+f\,x\right)+\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}\right)}{\sqrt{b}\,f}","Not used",1,"log(b^(1/2)*sin(e + f*x) + (a + b*sin(e + f*x)^2)^(1/2))/(b^(1/2)*f)","B"
347,0,-1,42,0.000000,"\text{Not used}","int(1/(cos(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2)),x)","\int \frac{1}{\cos\left(e+f\,x\right)\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(cos(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2)), x)","F"
348,0,-1,91,0.000000,"\text{Not used}","int(1/(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2)),x)","\int \frac{1}{{\cos\left(e+f\,x\right)}^3\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2)), x)","F"
349,0,-1,168,0.000000,"\text{Not used}","int(cos(e + f*x)^4/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^4}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(cos(e + f*x)^4/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
350,0,-1,114,0.000000,"\text{Not used}","int(cos(e + f*x)^2/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(cos(e + f*x)^2/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
351,0,-1,51,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{1}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
352,0,-1,140,0.000000,"\text{Not used}","int(1/(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2)),x)","\int \frac{1}{{\cos\left(e+f\,x\right)}^2\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2)), x)","F"
353,0,-1,212,0.000000,"\text{Not used}","int(1/(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2)),x)","\int \frac{1}{{\cos\left(e+f\,x\right)}^4\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2)), x)","F"
354,0,-1,75,0.000000,"\text{Not used}","int(cos(e + f*x)^3/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^3}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cos(e + f*x)^3/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
355,1,117,29,15.612954,"\text{Not used}","int(cos(e + f*x)/(a + b*sin(e + f*x)^2)^(3/2),x)","\frac{\sqrt{2}\,\sqrt{2\,a+b-b\,\cos\left(2\,e+2\,f\,x\right)}\,\left(4\,a\,\sin\left(e+f\,x\right)+3\,b\,\sin\left(e+f\,x\right)-b\,\sin\left(3\,e+3\,f\,x\right)\right)}{a\,f\,\left(8\,a\,b+8\,a^2+3\,b^2-4\,b^2\,\cos\left(2\,e+2\,f\,x\right)+b^2\,\cos\left(4\,e+4\,f\,x\right)-8\,a\,b\,\cos\left(2\,e+2\,f\,x\right)\right)}","Not used",1,"(2^(1/2)*(2*a + b - b*cos(2*e + 2*f*x))^(1/2)*(4*a*sin(e + f*x) + 3*b*sin(e + f*x) - b*sin(3*e + 3*f*x)))/(a*f*(8*a*b + 8*a^2 + 3*b^2 - 4*b^2*cos(2*e + 2*f*x) + b^2*cos(4*e + 4*f*x) - 8*a*b*cos(2*e + 2*f*x)))","B"
356,0,-1,78,0.000000,"\text{Not used}","int(1/(cos(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2)),x)","\int \frac{1}{\cos\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2)), x)","F"
357,0,-1,134,0.000000,"\text{Not used}","int(1/(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2)),x)","\int \frac{1}{{\cos\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2)), x)","F"
358,0,-1,274,0.000000,"\text{Not used}","int(cos(e + f*x)^6/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^6}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cos(e + f*x)^6/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
359,0,-1,202,0.000000,"\text{Not used}","int(cos(e + f*x)^4/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^4}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cos(e + f*x)^4/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
360,0,-1,188,0.000000,"\text{Not used}","int(cos(e + f*x)^2/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cos(e + f*x)^2/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
361,0,-1,101,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{1}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
362,0,-1,240,0.000000,"\text{Not used}","int(1/(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2)),x)","\int \frac{1}{{\cos\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2)), x)","F"
363,0,-1,130,0.000000,"\text{Not used}","int(cos(e + f*x)^5/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^5}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cos(e + f*x)^5/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
364,1,183,73,23.810059,"\text{Not used}","int(cos(e + f*x)^3/(a + b*sin(e + f*x)^2)^(5/2),x)","-\frac{2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)\,\sqrt{a+b\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,\left(a\,1{}\mathrm{i}-b\,2{}\mathrm{i}+a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,10{}\mathrm{i}+a\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}+b\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}-b\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,2{}\mathrm{i}\right)}{3\,a^2\,f\,{\left(b-4\,a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-2\,b\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+b\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\right)}^2}","Not used",1,"-(2*exp(e*1i + f*x*1i)*(exp(e*2i + f*x*2i) - 1)*(a + b*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*(a*1i - b*2i + a*exp(e*2i + f*x*2i)*10i + a*exp(e*4i + f*x*4i)*1i + b*exp(e*2i + f*x*2i)*4i - b*exp(e*4i + f*x*4i)*2i))/(3*a^2*f*(b - 4*a*exp(e*2i + f*x*2i) - 2*b*exp(e*2i + f*x*2i) + b*exp(e*4i + f*x*4i))^2)","B"
365,1,164,65,21.838787,"\text{Not used}","int(cos(e + f*x)/(a + b*sin(e + f*x)^2)^(5/2),x)","\frac{4\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)\,\sqrt{a+b\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,\left(b\,1{}\mathrm{i}-a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,6{}\mathrm{i}-b\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,2{}\mathrm{i}+b\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}\right)}{3\,a^2\,f\,{\left(b-4\,a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-2\,b\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+b\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\right)}^2}","Not used",1,"(4*exp(e*1i + f*x*1i)*(exp(e*2i + f*x*2i) - 1)*(a + b*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*(b*1i - a*exp(e*2i + f*x*2i)*6i - b*exp(e*2i + f*x*2i)*2i + b*exp(e*4i + f*x*4i)*1i))/(3*a^2*f*(b - 4*a*exp(e*2i + f*x*2i) - 2*b*exp(e*2i + f*x*2i) + b*exp(e*4i + f*x*4i))^2)","B"
366,0,-1,126,0.000000,"\text{Not used}","int(1/(cos(e + f*x)*(a + b*sin(e + f*x)^2)^(5/2)),x)","\int \frac{1}{\cos\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(e + f*x)*(a + b*sin(e + f*x)^2)^(5/2)), x)","F"
367,0,-1,243,0.000000,"\text{Not used}","int(cos(e + f*x)^6/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^6}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cos(e + f*x)^6/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
368,0,-1,223,0.000000,"\text{Not used}","int(cos(e + f*x)^4/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^4}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cos(e + f*x)^4/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
369,0,-1,217,0.000000,"\text{Not used}","int(cos(e + f*x)^2/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\cos\left(e+f\,x\right)}^2}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cos(e + f*x)^2/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
370,0,-1,223,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{1}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
371,0,-1,288,0.000000,"\text{Not used}","int(1/(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(5/2)),x)","\int \frac{1}{{\cos\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^(5/2)), x)","F"
372,0,-1,115,0.000000,"\text{Not used}","int((d*cos(e + f*x))^m*(a + b*sin(e + f*x)^2)^p,x)","\int {\left(d\,\cos\left(e+f\,x\right)\right)}^m\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int((d*cos(e + f*x))^m*(a + b*sin(e + f*x)^2)^p, x)","F"
373,0,-1,214,0.000000,"\text{Not used}","int(cos(e + f*x)^5*(a + b*sin(e + f*x)^2)^p,x)","\int {\cos\left(e+f\,x\right)}^5\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(cos(e + f*x)^5*(a + b*sin(e + f*x)^2)^p, x)","F"
374,0,-1,124,0.000000,"\text{Not used}","int(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^p,x)","\int {\cos\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(cos(e + f*x)^3*(a + b*sin(e + f*x)^2)^p, x)","F"
375,1,64,67,15.216545,"\text{Not used}","int(cos(e + f*x)*(a + b*sin(e + f*x)^2)^p,x)","\frac{\sin\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},-p;\ \frac{3}{2};\ -\frac{b\,{\sin\left(e+f\,x\right)}^2}{a}\right)}{f\,{\left(\frac{b\,{\sin\left(e+f\,x\right)}^2}{a}+1\right)}^p}","Not used",1,"(sin(e + f*x)*(a + b*sin(e + f*x)^2)^p*hypergeom([1/2, -p], 3/2, -(b*sin(e + f*x)^2)/a))/(f*((b*sin(e + f*x)^2)/a + 1)^p)","B"
376,0,-1,76,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/cos(e + f*x),x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{\cos\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/cos(e + f*x), x)","F"
377,0,-1,76,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/cos(e + f*x)^3,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{{\cos\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/cos(e + f*x)^3, x)","F"
378,0,-1,90,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^p,x)","\int {\cos\left(e+f\,x\right)}^4\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(cos(e + f*x)^4*(a + b*sin(e + f*x)^2)^p, x)","F"
379,0,-1,90,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^p,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(cos(e + f*x)^2*(a + b*sin(e + f*x)^2)^p, x)","F"
380,0,-1,90,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p,x)","\int {\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p, x)","F"
381,0,-1,90,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/cos(e + f*x)^2,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{{\cos\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/cos(e + f*x)^2, x)","F"
382,0,-1,90,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^p/cos(e + f*x)^4,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p}{{\cos\left(e+f\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^p/cos(e + f*x)^4, x)","F"
383,1,229,219,15.019274,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x)^3),x)","\frac{\left(\sum _{k=1}^3\ln\left(3\,a+\mathrm{root}\left(27\,a^2\,b^5\,d^3+54\,a^2\,b^4\,d^2+27\,a^2\,b^3\,d+2\,a^2\,b^2-b^4-a^4,d,k\right)\,\left(12\,a\,b+3\,b^2\,\sin\left(c+d\,x\right)+\mathrm{root}\left(27\,a^2\,b^5\,d^3+54\,a^2\,b^4\,d^2+27\,a^2\,b^3\,d+2\,a^2\,b^2-b^4-a^4,d,k\right)\,a\,b^2\,9\right)+\frac{\sin\left(c+d\,x\right)\,\left(a^2+2\,b^2\right)}{b}\right)\,\mathrm{root}\left(27\,a^2\,b^5\,d^3+54\,a^2\,b^4\,d^2+27\,a^2\,b^3\,d+2\,a^2\,b^2-b^4-a^4,d,k\right)\right)+\frac{{\sin\left(c+d\,x\right)}^2}{2\,b}}{d}","Not used",1,"(symsum(log(3*a + root(27*a^2*b^5*d^3 + 54*a^2*b^4*d^2 + 27*a^2*b^3*d + 2*a^2*b^2 - b^4 - a^4, d, k)*(12*a*b + 3*b^2*sin(c + d*x) + 9*root(27*a^2*b^5*d^3 + 54*a^2*b^4*d^2 + 27*a^2*b^3*d + 2*a^2*b^2 - b^4 - a^4, d, k)*a*b^2) + (sin(c + d*x)*(a^2 + 2*b^2))/b)*root(27*a^2*b^5*d^3 + 54*a^2*b^4*d^2 + 27*a^2*b^3*d + 2*a^2*b^2 - b^4 - a^4, d, k), k, 1, 3) + sin(c + d*x)^2/(2*b))/d","B"
384,1,153,167,15.024767,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^3\ln\left(\left(\mathrm{root}\left(27\,a^2\,b^3\,d^3+27\,a^2\,b^2\,d^2+9\,a^2\,b\,d-b^2+a^2,d,k\right)\,b\,3+1\right)\,\left(a+b\,\sin\left(c+d\,x\right)+\mathrm{root}\left(27\,a^2\,b^3\,d^3+27\,a^2\,b^2\,d^2+9\,a^2\,b\,d-b^2+a^2,d,k\right)\,a\,b\,3\right)\right)\,\mathrm{root}\left(27\,a^2\,b^3\,d^3+27\,a^2\,b^2\,d^2+9\,a^2\,b\,d-b^2+a^2,d,k\right)}{d}","Not used",1,"symsum(log((3*root(27*a^2*b^3*d^3 + 27*a^2*b^2*d^2 + 9*a^2*b*d - b^2 + a^2, d, k)*b + 1)*(a + b*sin(c + d*x) + 3*root(27*a^2*b^3*d^3 + 27*a^2*b^2*d^2 + 9*a^2*b*d - b^2 + a^2, d, k)*a*b))*root(27*a^2*b^3*d^3 + 27*a^2*b^2*d^2 + 9*a^2*b*d - b^2 + a^2, d, k), k, 1, 3)/d","B"
385,1,123,144,0.282004,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x)^3),x)","\frac{\ln\left(b^{1/3}\,\sin\left(c+d\,x\right)+a^{1/3}\right)}{3\,a^{2/3}\,b^{1/3}\,d}+\frac{\ln\left(3\,b^2\,\sin\left(c+d\,x\right)+\frac{3\,a^{1/3}\,b^{5/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{6\,a^{2/3}\,b^{1/3}\,d}-\frac{\ln\left(3\,b^2\,\sin\left(c+d\,x\right)-\frac{3\,a^{1/3}\,b^{5/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{6\,a^{2/3}\,b^{1/3}\,d}","Not used",1,"log(b^(1/3)*sin(c + d*x) + a^(1/3))/(3*a^(2/3)*b^(1/3)*d) + (log(3*b^2*sin(c + d*x) + (3*a^(1/3)*b^(5/3)*(3^(1/2)*1i - 1))/2)*(3^(1/2)*1i - 1))/(6*a^(2/3)*b^(1/3)*d) - (log(3*b^2*sin(c + d*x) - (3*a^(1/3)*b^(5/3)*(3^(1/2)*1i + 1))/2)*(3^(1/2)*1i + 1))/(6*a^(2/3)*b^(1/3)*d)","B"
386,1,600,290,0.269523,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x)^3)),x)","\frac{\left(\sum _{k=1}^3\ln\left(-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^2\,a\,b^4\,13-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^3\,a\,b^5\,36-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^4\,a\,b^6\,36-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^2\,b^5\,\sin\left(c+d\,x\right)\,16-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^3\,b^6\,\sin\left(c+d\,x\right)\,12-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^3\,a^3\,b^3\,27-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^4\,a^3\,b^4\,180-\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)\,b^4\,\sin\left(c+d\,x\right)\,5-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^3\,a^2\,b^4\,\sin\left(c+d\,x\right)\,69-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^4\,a^2\,b^5\,\sin\left(c+d\,x\right)\,162-{\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)}^4\,a^4\,b^3\,\sin\left(c+d\,x\right)\,54\right)\,\mathrm{root}\left(27\,a^2\,b^2\,z^3-27\,a^4\,z^3-27\,a^2\,b\,z^2-b,z,k\right)\right)-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)}{2\,a+2\,b}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{2\,a-2\,b}}{d}","Not used",1,"(symsum(log(- 13*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^2*a*b^4 - 36*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^3*a*b^5 - 36*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^4*a*b^6 - 16*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^2*b^5*sin(c + d*x) - 12*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^3*b^6*sin(c + d*x) - 27*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^3*a^3*b^3 - 180*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^4*a^3*b^4 - 5*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)*b^4*sin(c + d*x) - 69*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^3*a^2*b^4*sin(c + d*x) - 162*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^4*a^2*b^5*sin(c + d*x) - 54*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k)^4*a^4*b^3*sin(c + d*x))*root(27*a^2*b^2*z^3 - 27*a^4*z^3 - 27*a^2*b*z^2 - b, z, k), k, 1, 3) - log(sin(c + d*x) - 1)/(2*a + 2*b) + log(sin(c + d*x) + 1)/(2*a - 2*b))/d","B"
387,1,898,385,15.265351,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x)^3)),x)","\frac{\left(\sum _{k=1}^3\ln\left(-\mathrm{root}\left(54\,a^4\,b^2\,z^3-27\,a^2\,b^4\,z^3-27\,a^6\,z^3+54\,a^2\,b^3\,z^2+27\,a^4\,b\,z^2-9\,a^2\,b^2\,z+b^3,z,k\right)\,\left(-\frac{28\,a\,b^7-6\,a^3\,b^5}{a^4-2\,a^2\,b^2+b^4}+\mathrm{root}\left(54\,a^4\,b^2\,z^3-27\,a^2\,b^4\,z^3-27\,a^6\,z^3+54\,a^2\,b^3\,z^2+27\,a^4\,b\,z^2-9\,a^2\,b^2\,z+b^3,z,k\right)\,\left(-\frac{18\,a^5\,b^4-\frac{219\,a^3\,b^6}{4}+12\,a\,b^8}{a^4-2\,a^2\,b^2+b^4}+\mathrm{root}\left(54\,a^4\,b^2\,z^3-27\,a^2\,b^4\,z^3-27\,a^6\,z^3+54\,a^2\,b^3\,z^2+27\,a^4\,b\,z^2-9\,a^2\,b^2\,z+b^3,z,k\right)\,\left(\frac{\frac{27\,a^7\,b^3}{2}-87\,a^5\,b^5+\frac{51\,a^3\,b^7}{2}+48\,a\,b^9}{a^4-2\,a^2\,b^2+b^4}+\mathrm{root}\left(54\,a^4\,b^2\,z^3-27\,a^2\,b^4\,z^3-27\,a^6\,z^3+54\,a^2\,b^3\,z^2+27\,a^4\,b\,z^2-9\,a^2\,b^2\,z+b^3,z,k\right)\,\left(\frac{180\,a^7\,b^4-324\,a^5\,b^6+108\,a^3\,b^8+36\,a\,b^{10}}{a^4-2\,a^2\,b^2+b^4}+\frac{\sin\left(c+d\,x\right)\,\left(216\,a^8\,b^3+216\,a^6\,b^5-1080\,a^4\,b^7+648\,a^2\,b^9\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}\right)+\frac{\sin\left(c+d\,x\right)\,\left(-600\,a^4\,b^6+552\,a^2\,b^8+48\,b^{10}\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}\right)+\frac{\sin\left(c+d\,x\right)\,\left(-171\,a^4\,b^5+120\,a^2\,b^7+96\,b^9\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}\right)+\frac{\sin\left(c+d\,x\right)\,\left(61\,a^2\,b^6+40\,b^8\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}\right)+\frac{a\,b^6}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,b^7\,\sin\left(c+d\,x\right)}{a^4-2\,a^2\,b^2+b^4}\right)\,\mathrm{root}\left(54\,a^4\,b^2\,z^3-27\,a^2\,b^4\,z^3-27\,a^6\,z^3+54\,a^2\,b^3\,z^2+27\,a^4\,b\,z^2-9\,a^2\,b^2\,z+b^3,z,k\right)\right)+\frac{\frac{b}{2\,\left(a^2-b^2\right)}-\frac{a\,\sin\left(c+d\,x\right)}{2\,\left(a^2-b^2\right)}}{{\sin\left(c+d\,x\right)}^2-1}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(a+4\,b\right)}{4\,a^2+8\,a\,b+4\,b^2}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-4\,b\right)}{4\,a^2-8\,a\,b+4\,b^2}}{d}","Not used",1,"(symsum(log((a*b^6)/(2*(a^4 + b^4 - 2*a^2*b^2)) - root(54*a^4*b^2*z^3 - 27*a^2*b^4*z^3 - 27*a^6*z^3 + 54*a^2*b^3*z^2 + 27*a^4*b*z^2 - 9*a^2*b^2*z + b^3, z, k)*(root(54*a^4*b^2*z^3 - 27*a^2*b^4*z^3 - 27*a^6*z^3 + 54*a^2*b^3*z^2 + 27*a^4*b*z^2 - 9*a^2*b^2*z + b^3, z, k)*(root(54*a^4*b^2*z^3 - 27*a^2*b^4*z^3 - 27*a^6*z^3 + 54*a^2*b^3*z^2 + 27*a^4*b*z^2 - 9*a^2*b^2*z + b^3, z, k)*((48*a*b^9 + (51*a^3*b^7)/2 - 87*a^5*b^5 + (27*a^7*b^3)/2)/(a^4 + b^4 - 2*a^2*b^2) + root(54*a^4*b^2*z^3 - 27*a^2*b^4*z^3 - 27*a^6*z^3 + 54*a^2*b^3*z^2 + 27*a^4*b*z^2 - 9*a^2*b^2*z + b^3, z, k)*((36*a*b^10 + 108*a^3*b^8 - 324*a^5*b^6 + 180*a^7*b^4)/(a^4 + b^4 - 2*a^2*b^2) + (sin(c + d*x)*(648*a^2*b^9 - 1080*a^4*b^7 + 216*a^6*b^5 + 216*a^8*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2))) + (sin(c + d*x)*(48*b^10 + 552*a^2*b^8 - 600*a^4*b^6))/(4*(a^4 + b^4 - 2*a^2*b^2))) - (12*a*b^8 - (219*a^3*b^6)/4 + 18*a^5*b^4)/(a^4 + b^4 - 2*a^2*b^2) + (sin(c + d*x)*(96*b^9 + 120*a^2*b^7 - 171*a^4*b^5))/(4*(a^4 + b^4 - 2*a^2*b^2))) - (28*a*b^7 - 6*a^3*b^5)/(a^4 + b^4 - 2*a^2*b^2) + (sin(c + d*x)*(40*b^8 + 61*a^2*b^6))/(4*(a^4 + b^4 - 2*a^2*b^2))) + (2*b^7*sin(c + d*x))/(a^4 + b^4 - 2*a^2*b^2))*root(54*a^4*b^2*z^3 - 27*a^2*b^4*z^3 - 27*a^6*z^3 + 54*a^2*b^3*z^2 + 27*a^4*b*z^2 - 9*a^2*b^2*z + b^3, z, k), k, 1, 3) + (b/(2*(a^2 - b^2)) - (a*sin(c + d*x))/(2*(a^2 - b^2)))/(sin(c + d*x)^2 - 1) - (log(sin(c + d*x) - 1)*(a + 4*b))/(8*a*b + 4*a^2 + 4*b^2) + (log(sin(c + d*x) + 1)*(a - 4*b))/(4*a^2 - 8*a*b + 4*b^2))/d","B"
388,1,2338,764,18.040976,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(-81920\,a^2\,b^{11}+172032\,a^4\,b^9-98304\,a^6\,b^7+8192\,a^8\,b^5-\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)\,a^2\,b^{12}\,319488-\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)\,a^4\,b^{10}\,688128+\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)\,a^6\,b^8\,344064-98304\,a\,b^{12}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^2\,a^2\,b^{13}\,294912-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^2\,a^4\,b^{11}\,1400832+{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^2\,a^6\,b^9\,1695744+{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^3\,a^4\,b^{12}\,5750784-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^3\,a^6\,b^{10}\,3760128+{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^4\,a^4\,b^{13}\,3317760-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^4\,a^6\,b^{11}\,3317760-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^5\,a^4\,b^{14}\,7962624+{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^5\,a^6\,b^{12}\,5971968+196608\,a^3\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-98304\,a^5\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)\,a^3\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1277952+\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)\,a^5\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,712704+\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)\,a^7\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,98304+{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^2\,a^3\,b^{12}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,589824-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^2\,a^5\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294912-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^2\,a^7\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294912+{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^3\,a^3\,b^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5308416-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^3\,a^5\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3538944+{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^3\,a^7\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,221184-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^4\,a^3\,b^{14}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5308416+{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^4\,a^5\,b^{12}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5308416-{\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}^5\,a^5\,b^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1990656-\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)\,a\,b^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,196608\right)\,\mathrm{root}\left(729\,a^4\,b^8\,d^6-729\,a^4\,b^6\,d^4+162\,a^4\,b^4\,d^2+81\,a^2\,b^6\,d^2-3\,a^4\,b^2+3\,a^2\,b^4+a^6-b^6,d,k\right)}{d}-\frac{2}{d\,\left(b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\right)}","Not used",1,"symsum(log(172032*a^4*b^9 - 81920*a^2*b^11 - 98304*a^6*b^7 + 8192*a^8*b^5 - 319488*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)*a^2*b^12 - 688128*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)*a^4*b^10 + 344064*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)*a^6*b^8 - 98304*a*b^12*tan(c/2 + (d*x)/2) - 294912*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^2*a^2*b^13 - 1400832*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^2*a^4*b^11 + 1695744*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^2*a^6*b^9 + 5750784*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^3*a^4*b^12 - 3760128*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^3*a^6*b^10 + 3317760*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^4*a^4*b^13 - 3317760*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^4*a^6*b^11 - 7962624*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^5*a^4*b^14 + 5971968*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^5*a^6*b^12 + 196608*a^3*b^10*tan(c/2 + (d*x)/2) - 98304*a^5*b^8*tan(c/2 + (d*x)/2) - 1277952*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)*a^3*b^11*tan(c/2 + (d*x)/2) + 712704*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)*a^5*b^9*tan(c/2 + (d*x)/2) + 98304*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)*a^7*b^7*tan(c/2 + (d*x)/2) + 589824*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^2*a^3*b^12*tan(c/2 + (d*x)/2) - 294912*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^2*a^5*b^10*tan(c/2 + (d*x)/2) - 294912*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^2*a^7*b^8*tan(c/2 + (d*x)/2) + 5308416*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^3*a^3*b^13*tan(c/2 + (d*x)/2) - 3538944*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^3*a^5*b^11*tan(c/2 + (d*x)/2) + 221184*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^3*a^7*b^9*tan(c/2 + (d*x)/2) - 5308416*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^4*a^3*b^14*tan(c/2 + (d*x)/2) + 5308416*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^4*a^5*b^12*tan(c/2 + (d*x)/2) - 1990656*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)^5*a^5*b^13*tan(c/2 + (d*x)/2) - 196608*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k)*a*b^13*tan(c/2 + (d*x)/2))*root(729*a^4*b^8*d^6 - 729*a^4*b^6*d^4 + 162*a^4*b^4*d^2 + 81*a^2*b^6*d^2 - 3*a^4*b^2 + 3*a^2*b^4 + a^6 - b^6, d, k), k, 1, 6)/d - 2/(d*(b + b*tan(c/2 + (d*x)/2)^2))","B"
389,1,951,484,17.400688,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(24576\,a^4-24576\,a^2\,b^2-\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)\,a^2\,b^3\,122880-\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24576-32768\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+32768\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^2\,a^2\,b^4\,294912+{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^2\,a^4\,b^2\,294912+{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^4\,a^4\,b^4\,663552-{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^4\,a^6\,b^2\,663552-{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^5\,a^4\,b^5\,7962624+{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^5\,a^6\,b^3\,5971968+\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)\,a^4\,b\,49152+\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,147456+{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^2\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294912-{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^2\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294912+{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^3\,a^3\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1769472-{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^3\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1769472-{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^4\,a^3\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5308416+{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^4\,a^5\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5308416-{\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}^5\,a^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1990656-\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,196608\right)\,\mathrm{root}\left(729\,a^4\,b^4\,d^6+27\,a^2\,b^2\,d^2+a^2-b^2,d,k\right)}{d}","Not used",1,"symsum(log(24576*a^4 - 24576*a^2*b^2 - 122880*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)*a^2*b^3 - 24576*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)*a^5*tan(c/2 + (d*x)/2) - 32768*a*b^3*tan(c/2 + (d*x)/2) + 32768*a^3*b*tan(c/2 + (d*x)/2) - 294912*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^2*a^2*b^4 + 294912*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^2*a^4*b^2 + 663552*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^4*a^4*b^4 - 663552*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^4*a^6*b^2 - 7962624*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^5*a^4*b^5 + 5971968*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^5*a^6*b^3 + 49152*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)*a^4*b + 147456*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)*a^3*b^2*tan(c/2 + (d*x)/2) + 294912*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^2*a^5*b*tan(c/2 + (d*x)/2) - 294912*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^2*a^3*b^3*tan(c/2 + (d*x)/2) + 1769472*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^3*a^3*b^4*tan(c/2 + (d*x)/2) - 1769472*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^3*a^5*b^2*tan(c/2 + (d*x)/2) - 5308416*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^4*a^3*b^5*tan(c/2 + (d*x)/2) + 5308416*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^4*a^5*b^3*tan(c/2 + (d*x)/2) - 1990656*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)^5*a^5*b^4*tan(c/2 + (d*x)/2) - 196608*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k)*a*b^4*tan(c/2 + (d*x)/2))*root(729*a^4*b^4*d^6 + 27*a^2*b^2*d^2 + a^2 - b^2, d, k), k, 1, 6)/d","B"
390,1,609,245,16.713925,"\text{Not used}","int(1/(a + b*sin(c + d*x)^3),x)","\frac{\sum _{k=1}^6\ln\left(-\frac{8192\,a\,b^3\,\left(-729\,a^5+243\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b-324\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)+972\,a^3\,b^2+a^3\,b\,\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)\,243-162\,a^3\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^2+648\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2\,\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)+216\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^2-72\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^3+36\,a\,b\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^3-9\,a\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^4+24\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^4-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^5\right)}{{\mathrm{root}\left(d^6+27\,a^2\,d^4+243\,a^4\,d^2+729\,a^4\,\left(a^2-b^2\right),d,k\right)}^5}\right)\,\mathrm{root}\left(729\,a^4\,b^2\,d^6-729\,a^6\,d^6-243\,a^4\,d^4-27\,a^2\,d^2-1,d,k\right)}{d}","Not used",1,"symsum(log(-(8192*a*b^3*(972*a^3*b^2 - 729*a^5 - 9*a*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^4 - 162*a^3*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^2 - 4*tan(c/2 + (d*x)/2)*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^5 + 243*a^4*b*tan(c/2 + (d*x)/2) - 324*tan(c/2 + (d*x)/2)*a^4*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k) + 24*b*tan(c/2 + (d*x)/2)*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^4 - 72*a^2*tan(c/2 + (d*x)/2)*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^3 + 36*a*b*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^3 + 243*b*a^3*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k) + 648*tan(c/2 + (d*x)/2)*a^2*b^2*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k) + 216*a^2*b*tan(c/2 + (d*x)/2)*root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^2))/root(d^6 + 27*a^2*d^4 + 243*a^4*d^2 + 729*a^4*(a^2 - b^2), d, k)^5)*root(729*a^4*b^2*d^6 - 729*a^6*d^6 - 243*a^4*d^4 - 27*a^2*d^2 - 1, d, k), k, 1, 6)/d","B"
391,1,19737,299,18.524030,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x)^3)),x)","\frac{a^2\,\left(\sum _{k=1}^6\ln\left(\frac{\left(-12\,a\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-7\,a^4\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+21\,a^6\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-35\,a^8\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+35\,a^{10}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-21\,a^{12}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7\,a^{14}\,b^8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a^{16}\,b^6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+84\,a^3\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-252\,a^5\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+420\,a^7\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-420\,a^9\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+252\,a^{11}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{13}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+12\,a^{15}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^3\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^5\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,714-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^7\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1470+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^9\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1890-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{11}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1554+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{13}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,798-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{15}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,234+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{17}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^2\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^4\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,369+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^6\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1575-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^8\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3717+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{10}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5355-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{12}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4851+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{14}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2709-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{16}\,b^8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,855+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{18}\,b^6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,117-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^4\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1188+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^6\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7803-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^8\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,21357+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{10}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30807-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{12}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,23625+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{14}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,6993+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{16}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2457-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{18}\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2403+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{20}\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,513+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^4\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,567-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^6\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^8\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,14580-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{10}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27216+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{12}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30618-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{14}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,20412+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{16}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,6804-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{20}\,b^6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{22}\,b^4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^4\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,972-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^6\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,9477+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^8\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,41553-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{10}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,107892+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{12}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,183708-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{14}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,214326+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{16}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,173502-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{18}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96228+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{20}\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,34992-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{22}\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7533+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{24}\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^3\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,396+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^5\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2736-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^7\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,8064+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^9\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,13104-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{11}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,12600+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{13}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7056-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{15}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2016+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{17}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,144+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{19}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^3\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,648-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^5\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3456+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^7\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,6021+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^9\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,189-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{11}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,15687+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{13}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25137-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{15}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,19089+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{17}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7479-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{19}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1269+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{21}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^3\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,648-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^5\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4860+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^7\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,15552-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^9\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27216+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{11}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27216-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{13}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,13608+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{17}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3888-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{19}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1944+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{21}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,324+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^5\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^7\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2187+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^9\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,8748-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{11}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,20412+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{13}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30618-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{15}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30618+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{17}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,20412-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{19}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,8748+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{21}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2187-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{23}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^2\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,33+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^4\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,231-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^6\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,693+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^8\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1155-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{10}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1155+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{12}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,693-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{14}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,231+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{16}\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,33\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\right)}{d\,\left(a^2-b^2\right)}-\frac{b^2\,\left(\sum _{k=1}^6\ln\left(\frac{\left(-12\,a\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-7\,a^4\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+21\,a^6\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-35\,a^8\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+35\,a^{10}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-21\,a^{12}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7\,a^{14}\,b^8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a^{16}\,b^6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+84\,a^3\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-252\,a^5\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+420\,a^7\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-420\,a^9\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+252\,a^{11}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{13}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+12\,a^{15}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^3\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^5\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,714-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^7\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1470+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^9\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1890-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{11}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1554+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{13}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,798-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{15}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,234+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{17}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^2\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^4\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,369+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^6\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1575-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^8\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3717+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{10}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5355-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{12}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4851+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{14}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2709-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{16}\,b^8\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,855+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{18}\,b^6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,117-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^4\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1188+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^6\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7803-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^8\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,21357+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{10}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30807-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{12}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,23625+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{14}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,6993+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{16}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2457-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{18}\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2403+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{20}\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,513+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^4\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,567-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^6\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^8\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,14580-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{10}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27216+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{12}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30618-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{14}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,20412+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{16}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,6804-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{20}\,b^6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{22}\,b^4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^4\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,972-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^6\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,9477+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^8\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,41553-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{10}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,107892+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{12}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,183708-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{14}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,214326+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{16}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,173502-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{18}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96228+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{20}\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,34992-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{22}\,b^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7533+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{24}\,b^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^3\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,396+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^5\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2736-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^7\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,8064+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^9\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,13104-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{11}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,12600+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{13}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7056-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{15}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2016+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{17}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,144+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^2\,a^{19}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^3\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,648-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^5\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3456+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^7\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,6021+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^9\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,189-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{11}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,15687+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{13}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25137-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{15}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,19089+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{17}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7479-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{19}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1269+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^3\,a^{21}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^3\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,648-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^5\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4860+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^7\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,15552-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^9\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27216+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{11}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,27216-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{13}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,13608+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{17}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3888-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{19}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1944+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^4\,a^{21}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,324+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^5\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^7\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2187+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^9\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,8748-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{11}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,20412+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{13}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30618-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{15}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,30618+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{17}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,20412-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{19}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,8748+{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{21}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2187-{\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)}^5\,a^{23}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^2\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,33+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^4\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,231-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^6\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,693+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^8\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1155-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{10}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1155+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{12}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,693-\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{14}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,231+\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\,a^{16}\,b^7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,33\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(2187\,a^8\,b^2\,d^6-2187\,a^6\,b^4\,d^6+729\,a^4\,b^6\,d^6-729\,a^{10}\,d^6-1458\,a^4\,b^4\,d^4-729\,a^6\,b^2\,d^4-81\,a^2\,b^4\,d^2-b^4,d,k\right)\right)}{d\,\left(a^2-b^2\right)}-\frac{b}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)}+\frac{a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)}","Not used",1,"(a^2*symsum(log((8192*(a^2*b^20*cos(c/2 + (d*x)/2) - 12*a*b^21*sin(c/2 + (d*x)/2) - 7*a^4*b^18*cos(c/2 + (d*x)/2) + 21*a^6*b^16*cos(c/2 + (d*x)/2) - 35*a^8*b^14*cos(c/2 + (d*x)/2) + 35*a^10*b^12*cos(c/2 + (d*x)/2) - 21*a^12*b^10*cos(c/2 + (d*x)/2) + 7*a^14*b^8*cos(c/2 + (d*x)/2) - a^16*b^6*cos(c/2 + (d*x)/2) + 84*a^3*b^19*sin(c/2 + (d*x)/2) - 252*a^5*b^17*sin(c/2 + (d*x)/2) + 420*a^7*b^15*sin(c/2 + (d*x)/2) - 420*a^9*b^13*sin(c/2 + (d*x)/2) + 252*a^11*b^11*sin(c/2 + (d*x)/2) - 84*a^13*b^9*sin(c/2 + (d*x)/2) + 12*a^15*b^7*sin(c/2 + (d*x)/2) - 198*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^3*b^20*sin(c/2 + (d*x)/2) + 714*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^5*b^18*sin(c/2 + (d*x)/2) - 1470*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^7*b^16*sin(c/2 + (d*x)/2) + 1890*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^9*b^14*sin(c/2 + (d*x)/2) - 1554*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^11*b^12*sin(c/2 + (d*x)/2) + 798*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^13*b^10*sin(c/2 + (d*x)/2) - 234*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^15*b^8*sin(c/2 + (d*x)/2) + 30*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^17*b^6*sin(c/2 + (d*x)/2) + 36*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^2*b^22*cos(c/2 + (d*x)/2) - 369*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^4*b^20*cos(c/2 + (d*x)/2) + 1575*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^6*b^18*cos(c/2 + (d*x)/2) - 3717*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^8*b^16*cos(c/2 + (d*x)/2) + 5355*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^10*b^14*cos(c/2 + (d*x)/2) - 4851*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^12*b^12*cos(c/2 + (d*x)/2) + 2709*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^14*b^10*cos(c/2 + (d*x)/2) - 855*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^16*b^8*cos(c/2 + (d*x)/2) + 117*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^18*b^6*cos(c/2 + (d*x)/2) - 1188*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^4*b^21*cos(c/2 + (d*x)/2) + 7803*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^6*b^19*cos(c/2 + (d*x)/2) - 21357*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^8*b^17*cos(c/2 + (d*x)/2) + 30807*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^10*b^15*cos(c/2 + (d*x)/2) - 23625*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^12*b^13*cos(c/2 + (d*x)/2) + 6993*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^14*b^11*cos(c/2 + (d*x)/2) + 2457*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^16*b^9*cos(c/2 + (d*x)/2) - 2403*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^18*b^7*cos(c/2 + (d*x)/2) + 513*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^20*b^5*cos(c/2 + (d*x)/2) + 567*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^4*b^22*cos(c/2 + (d*x)/2) - 4374*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^6*b^20*cos(c/2 + (d*x)/2) + 14580*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^8*b^18*cos(c/2 + (d*x)/2) - 27216*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^10*b^16*cos(c/2 + (d*x)/2) + 30618*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^12*b^14*cos(c/2 + (d*x)/2) - 20412*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^14*b^12*cos(c/2 + (d*x)/2) + 6804*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^16*b^10*cos(c/2 + (d*x)/2) - 729*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^20*b^6*cos(c/2 + (d*x)/2) + 162*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^22*b^4*cos(c/2 + (d*x)/2) + 972*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^4*b^23*cos(c/2 + (d*x)/2) - 9477*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^6*b^21*cos(c/2 + (d*x)/2) + 41553*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^8*b^19*cos(c/2 + (d*x)/2) - 107892*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^10*b^17*cos(c/2 + (d*x)/2) + 183708*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^12*b^15*cos(c/2 + (d*x)/2) - 214326*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^14*b^13*cos(c/2 + (d*x)/2) + 173502*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^16*b^11*cos(c/2 + (d*x)/2) - 96228*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^18*b^9*cos(c/2 + (d*x)/2) + 34992*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^20*b^7*cos(c/2 + (d*x)/2) - 7533*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^22*b^5*cos(c/2 + (d*x)/2) + 729*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^24*b^3*cos(c/2 + (d*x)/2) - 396*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^3*b^21*sin(c/2 + (d*x)/2) + 2736*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^5*b^19*sin(c/2 + (d*x)/2) - 8064*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^7*b^17*sin(c/2 + (d*x)/2) + 13104*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^9*b^15*sin(c/2 + (d*x)/2) - 12600*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^11*b^13*sin(c/2 + (d*x)/2) + 7056*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^13*b^11*sin(c/2 + (d*x)/2) - 2016*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^15*b^9*sin(c/2 + (d*x)/2) + 144*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^17*b^7*sin(c/2 + (d*x)/2) + 36*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^19*b^5*sin(c/2 + (d*x)/2) + 648*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^3*b^22*sin(c/2 + (d*x)/2) - 3456*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^5*b^20*sin(c/2 + (d*x)/2) + 6021*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^7*b^18*sin(c/2 + (d*x)/2) + 189*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^9*b^16*sin(c/2 + (d*x)/2) - 15687*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^11*b^14*sin(c/2 + (d*x)/2) + 25137*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^13*b^12*sin(c/2 + (d*x)/2) - 19089*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^15*b^10*sin(c/2 + (d*x)/2) + 7479*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^17*b^8*sin(c/2 + (d*x)/2) - 1269*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^19*b^6*sin(c/2 + (d*x)/2) + 27*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^21*b^4*sin(c/2 + (d*x)/2) + 648*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^3*b^23*sin(c/2 + (d*x)/2) - 4860*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^5*b^21*sin(c/2 + (d*x)/2) + 15552*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^7*b^19*sin(c/2 + (d*x)/2) - 27216*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^9*b^17*sin(c/2 + (d*x)/2) + 27216*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^11*b^15*sin(c/2 + (d*x)/2) - 13608*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^13*b^13*sin(c/2 + (d*x)/2) + 3888*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^17*b^9*sin(c/2 + (d*x)/2) - 1944*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^19*b^7*sin(c/2 + (d*x)/2) + 324*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^21*b^5*sin(c/2 + (d*x)/2) + 243*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^5*b^22*sin(c/2 + (d*x)/2) - 2187*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^7*b^20*sin(c/2 + (d*x)/2) + 8748*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^9*b^18*sin(c/2 + (d*x)/2) - 20412*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^11*b^16*sin(c/2 + (d*x)/2) + 30618*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^13*b^14*sin(c/2 + (d*x)/2) - 30618*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^15*b^12*sin(c/2 + (d*x)/2) + 20412*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^17*b^10*sin(c/2 + (d*x)/2) - 8748*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^19*b^8*sin(c/2 + (d*x)/2) + 2187*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^21*b^6*sin(c/2 + (d*x)/2) - 243*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^23*b^4*sin(c/2 + (d*x)/2) + 24*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a*b^22*sin(c/2 + (d*x)/2) - 33*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^2*b^21*cos(c/2 + (d*x)/2) + 231*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^4*b^19*cos(c/2 + (d*x)/2) - 693*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^6*b^17*cos(c/2 + (d*x)/2) + 1155*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^8*b^15*cos(c/2 + (d*x)/2) - 1155*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^10*b^13*cos(c/2 + (d*x)/2) + 693*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^12*b^11*cos(c/2 + (d*x)/2) - 231*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^14*b^9*cos(c/2 + (d*x)/2) + 33*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^16*b^7*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k), k, 1, 6))/(d*(a^2 - b^2)) - (b^2*symsum(log((8192*(a^2*b^20*cos(c/2 + (d*x)/2) - 12*a*b^21*sin(c/2 + (d*x)/2) - 7*a^4*b^18*cos(c/2 + (d*x)/2) + 21*a^6*b^16*cos(c/2 + (d*x)/2) - 35*a^8*b^14*cos(c/2 + (d*x)/2) + 35*a^10*b^12*cos(c/2 + (d*x)/2) - 21*a^12*b^10*cos(c/2 + (d*x)/2) + 7*a^14*b^8*cos(c/2 + (d*x)/2) - a^16*b^6*cos(c/2 + (d*x)/2) + 84*a^3*b^19*sin(c/2 + (d*x)/2) - 252*a^5*b^17*sin(c/2 + (d*x)/2) + 420*a^7*b^15*sin(c/2 + (d*x)/2) - 420*a^9*b^13*sin(c/2 + (d*x)/2) + 252*a^11*b^11*sin(c/2 + (d*x)/2) - 84*a^13*b^9*sin(c/2 + (d*x)/2) + 12*a^15*b^7*sin(c/2 + (d*x)/2) - 198*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^3*b^20*sin(c/2 + (d*x)/2) + 714*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^5*b^18*sin(c/2 + (d*x)/2) - 1470*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^7*b^16*sin(c/2 + (d*x)/2) + 1890*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^9*b^14*sin(c/2 + (d*x)/2) - 1554*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^11*b^12*sin(c/2 + (d*x)/2) + 798*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^13*b^10*sin(c/2 + (d*x)/2) - 234*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^15*b^8*sin(c/2 + (d*x)/2) + 30*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^17*b^6*sin(c/2 + (d*x)/2) + 36*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^2*b^22*cos(c/2 + (d*x)/2) - 369*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^4*b^20*cos(c/2 + (d*x)/2) + 1575*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^6*b^18*cos(c/2 + (d*x)/2) - 3717*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^8*b^16*cos(c/2 + (d*x)/2) + 5355*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^10*b^14*cos(c/2 + (d*x)/2) - 4851*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^12*b^12*cos(c/2 + (d*x)/2) + 2709*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^14*b^10*cos(c/2 + (d*x)/2) - 855*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^16*b^8*cos(c/2 + (d*x)/2) + 117*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^18*b^6*cos(c/2 + (d*x)/2) - 1188*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^4*b^21*cos(c/2 + (d*x)/2) + 7803*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^6*b^19*cos(c/2 + (d*x)/2) - 21357*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^8*b^17*cos(c/2 + (d*x)/2) + 30807*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^10*b^15*cos(c/2 + (d*x)/2) - 23625*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^12*b^13*cos(c/2 + (d*x)/2) + 6993*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^14*b^11*cos(c/2 + (d*x)/2) + 2457*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^16*b^9*cos(c/2 + (d*x)/2) - 2403*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^18*b^7*cos(c/2 + (d*x)/2) + 513*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^20*b^5*cos(c/2 + (d*x)/2) + 567*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^4*b^22*cos(c/2 + (d*x)/2) - 4374*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^6*b^20*cos(c/2 + (d*x)/2) + 14580*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^8*b^18*cos(c/2 + (d*x)/2) - 27216*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^10*b^16*cos(c/2 + (d*x)/2) + 30618*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^12*b^14*cos(c/2 + (d*x)/2) - 20412*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^14*b^12*cos(c/2 + (d*x)/2) + 6804*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^16*b^10*cos(c/2 + (d*x)/2) - 729*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^20*b^6*cos(c/2 + (d*x)/2) + 162*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^22*b^4*cos(c/2 + (d*x)/2) + 972*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^4*b^23*cos(c/2 + (d*x)/2) - 9477*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^6*b^21*cos(c/2 + (d*x)/2) + 41553*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^8*b^19*cos(c/2 + (d*x)/2) - 107892*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^10*b^17*cos(c/2 + (d*x)/2) + 183708*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^12*b^15*cos(c/2 + (d*x)/2) - 214326*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^14*b^13*cos(c/2 + (d*x)/2) + 173502*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^16*b^11*cos(c/2 + (d*x)/2) - 96228*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^18*b^9*cos(c/2 + (d*x)/2) + 34992*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^20*b^7*cos(c/2 + (d*x)/2) - 7533*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^22*b^5*cos(c/2 + (d*x)/2) + 729*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^24*b^3*cos(c/2 + (d*x)/2) - 396*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^3*b^21*sin(c/2 + (d*x)/2) + 2736*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^5*b^19*sin(c/2 + (d*x)/2) - 8064*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^7*b^17*sin(c/2 + (d*x)/2) + 13104*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^9*b^15*sin(c/2 + (d*x)/2) - 12600*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^11*b^13*sin(c/2 + (d*x)/2) + 7056*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^13*b^11*sin(c/2 + (d*x)/2) - 2016*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^15*b^9*sin(c/2 + (d*x)/2) + 144*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^17*b^7*sin(c/2 + (d*x)/2) + 36*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^2*a^19*b^5*sin(c/2 + (d*x)/2) + 648*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^3*b^22*sin(c/2 + (d*x)/2) - 3456*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^5*b^20*sin(c/2 + (d*x)/2) + 6021*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^7*b^18*sin(c/2 + (d*x)/2) + 189*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^9*b^16*sin(c/2 + (d*x)/2) - 15687*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^11*b^14*sin(c/2 + (d*x)/2) + 25137*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^13*b^12*sin(c/2 + (d*x)/2) - 19089*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^15*b^10*sin(c/2 + (d*x)/2) + 7479*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^17*b^8*sin(c/2 + (d*x)/2) - 1269*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^19*b^6*sin(c/2 + (d*x)/2) + 27*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^3*a^21*b^4*sin(c/2 + (d*x)/2) + 648*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^3*b^23*sin(c/2 + (d*x)/2) - 4860*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^5*b^21*sin(c/2 + (d*x)/2) + 15552*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^7*b^19*sin(c/2 + (d*x)/2) - 27216*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^9*b^17*sin(c/2 + (d*x)/2) + 27216*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^11*b^15*sin(c/2 + (d*x)/2) - 13608*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^13*b^13*sin(c/2 + (d*x)/2) + 3888*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^17*b^9*sin(c/2 + (d*x)/2) - 1944*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^19*b^7*sin(c/2 + (d*x)/2) + 324*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^4*a^21*b^5*sin(c/2 + (d*x)/2) + 243*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^5*b^22*sin(c/2 + (d*x)/2) - 2187*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^7*b^20*sin(c/2 + (d*x)/2) + 8748*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^9*b^18*sin(c/2 + (d*x)/2) - 20412*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^11*b^16*sin(c/2 + (d*x)/2) + 30618*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^13*b^14*sin(c/2 + (d*x)/2) - 30618*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^15*b^12*sin(c/2 + (d*x)/2) + 20412*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^17*b^10*sin(c/2 + (d*x)/2) - 8748*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^19*b^8*sin(c/2 + (d*x)/2) + 2187*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^21*b^6*sin(c/2 + (d*x)/2) - 243*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)^5*a^23*b^4*sin(c/2 + (d*x)/2) + 24*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a*b^22*sin(c/2 + (d*x)/2) - 33*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^2*b^21*cos(c/2 + (d*x)/2) + 231*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^4*b^19*cos(c/2 + (d*x)/2) - 693*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^6*b^17*cos(c/2 + (d*x)/2) + 1155*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^8*b^15*cos(c/2 + (d*x)/2) - 1155*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^10*b^13*cos(c/2 + (d*x)/2) + 693*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^12*b^11*cos(c/2 + (d*x)/2) - 231*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^14*b^9*cos(c/2 + (d*x)/2) + 33*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k)*a^16*b^7*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(2187*a^8*b^2*d^6 - 2187*a^6*b^4*d^6 + 729*a^4*b^6*d^6 - 729*a^10*d^6 - 1458*a^4*b^4*d^4 - 729*a^6*b^2*d^4 - 81*a^2*b^4*d^2 - b^4, d, k), k, 1, 6))/(d*(a^2 - b^2)) - b/(d*cos(c + d*x)*(a^2 - b^2)) + (a*sin(c + d*x))/(d*cos(c + d*x)*(a^2 - b^2))","B"
392,1,323390,1093,25.850001,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x)^3)),x)","\frac{14\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3\,\left(d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}-\frac{4\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,\left(d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}+\frac{6\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{8\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{4\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3\,\left(d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}+\frac{2\,a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{2\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{11}\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{13}\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{15}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{17}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{19}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{21}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{23}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11814660+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{25}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{27}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{29}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{31}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{33}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{35}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{37}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{39}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{3\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{11}\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{13}\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{15}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{17}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{19}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{21}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{23}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11814660+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{25}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{27}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{29}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{31}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{33}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{35}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{37}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{39}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{3\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{11}\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{13}\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{15}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{17}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{19}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{21}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{23}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11814660+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{25}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{27}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{29}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{31}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{33}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{35}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{37}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{39}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{3\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{11}\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{13}\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{15}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{17}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{19}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{21}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{23}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11814660+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{25}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{27}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{29}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{31}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{33}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{35}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{37}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{39}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{3\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{8\,a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{8\,a\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{40\,a\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,\left(d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}-\frac{4\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{2\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{2\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{11}\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{13}\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{15}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{17}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{19}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{21}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{23}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11814660+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{25}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{27}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{29}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{31}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{33}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{35}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{37}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{39}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{6\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{11}\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{13}\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{15}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{17}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{19}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{21}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{23}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11814660+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{25}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{27}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{29}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{31}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{33}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{35}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{37}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{39}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}+\frac{6\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\sum _{k=1}^6\ln\left(-\frac{\left(-20\,a\,b^{39}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^4\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^6\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^8\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{10}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{12}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{14}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20592\,a^{16}\,b^{24}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+18018\,a^{18}\,b^{22}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12012\,a^{20}\,b^{20}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6006\,a^{22}\,b^{18}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2184\,a^{24}\,b^{16}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+546\,a^{26}\,b^{14}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-84\,a^{28}\,b^{12}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^{30}\,b^{10}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^3\,b^{37}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^5\,b^{35}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^7\,b^{33}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^9\,b^{31}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{11}\,b^{29}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{13}\,b^{27}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+68640\,a^{15}\,b^{25}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60060\,a^{17}\,b^{23}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40040\,a^{19}\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20020\,a^{21}\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7280\,a^{23}\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1820\,a^{25}\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+280\,a^{27}\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,a^{29}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^3\,b^{38}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,588+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^5\,b^{36}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5715-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^7\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,31710+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^9\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,116025-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{11}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,301392+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{13}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,579579-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{15}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,845130+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{17}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,945945-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{19}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,815100+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{21}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,537537-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{23}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,266994+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{25}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,96915-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{27}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24360+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{29}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3825-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{31}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,294+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{33}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^2\,b^{40}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,36-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^4\,b^{38}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1143+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^6\,b^{36}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11853-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^8\,b^{34}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,66087+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{10}\,b^{32}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,235053-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{12}\,b^{30}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,577395+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{14}\,b^{28}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1018017-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^2\,a^{16}\,b^{26}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1303731+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4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}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{11}\,b^{34}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{13}\,b^{32}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{15}\,b^{30}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{17}\,b^{28}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{19}\,b^{26}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{21}\,b^{24}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{23}\,b^{22}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,11814660+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{25}\,b^{20}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,10633194-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{27}\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,7733232+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{29}\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4511052-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{31}\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2082024+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{33}\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,743580-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{35}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,198288+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{37}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,37179-{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{39}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4374+{\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)}^5\,a^{41}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,243+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a\,b^{40}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,24-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^2\,b^{39}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,57+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^4\,b^{37}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,846-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^6\,b^{35}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5859+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^8\,b^{33}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,25116-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{10}\,b^{31}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,74529+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{12}\,b^{29}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,162162-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{14}\,b^{27}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,267267+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{16}\,b^{25}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,339768-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{18}\,b^{23}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,335907+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{20}\,b^{21}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,258258-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{22}\,b^{19}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,153153+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{24}\,b^{17}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,68796-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{26}\,b^{15}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,22659+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{28}\,b^{13}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5166-\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{30}\,b^{11}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,729+\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\,a^{32}\,b^9\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,48\right)\,8192}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\mathrm{root}\left(7290\,a^{10}\,b^4\,d^6-7290\,a^8\,b^6\,d^6-3645\,a^{12}\,b^2\,d^6+3645\,a^6\,b^8\,d^6-729\,a^4\,b^{10}\,d^6+729\,a^{14}\,d^6+12393\,a^6\,b^6\,d^4+3645\,a^8\,b^4\,d^4+3645\,a^4\,b^8\,d^4-135\,a^4\,b^6\,d^2+135\,a^2\,b^8\,d^2+b^8,d,k\right)\right)}{d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,a^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,d\,a^2\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,d\,a^2\,b^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,d\,b^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-d\,b^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"(14*b^3*cos(c/2 + (d*x)/2)^6)/(3*(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)) - (4*a^3*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^3)/(3*(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)) + (6*b^3*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4)/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (8*b^3*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (4*a^2*b*cos(c/2 + (d*x)/2)^6)/(3*(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)) + (2*a^3*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^5)/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (2*a^3*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (a^4*cos(c/2 + (d*x)/2)^6*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (b^4*cos(c/2 + (d*x)/2)^6*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (a^4*sin(c/2 + (d*x)/2)^6*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (b^4*sin(c/2 + (d*x)/2)^6*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (3*a^4*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (3*a^4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (3*b^4*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (3*b^4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (8*a*b^2*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^5)/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (8*a*b^2*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (40*a*b^2*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^3)/(3*(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)) - (4*a^2*b*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (2*a^2*b^2*cos(c/2 + (d*x)/2)^6*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (2*a^2*b^2*sin(c/2 + (d*x)/2)^6*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) - (6*a^2*b^2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2) + (6*a^2*b^2*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2*symsum(log(-(8192*(6*a^2*b^38*cos(c/2 + (d*x)/2) - 20*a*b^39*sin(c/2 + (d*x)/2) - 84*a^4*b^36*cos(c/2 + (d*x)/2) + 546*a^6*b^34*cos(c/2 + (d*x)/2) - 2184*a^8*b^32*cos(c/2 + (d*x)/2) + 6006*a^10*b^30*cos(c/2 + (d*x)/2) - 12012*a^12*b^28*cos(c/2 + (d*x)/2) + 18018*a^14*b^26*cos(c/2 + (d*x)/2) - 20592*a^16*b^24*cos(c/2 + (d*x)/2) + 18018*a^18*b^22*cos(c/2 + (d*x)/2) - 12012*a^20*b^20*cos(c/2 + (d*x)/2) + 6006*a^22*b^18*cos(c/2 + (d*x)/2) - 2184*a^24*b^16*cos(c/2 + (d*x)/2) + 546*a^26*b^14*cos(c/2 + (d*x)/2) - 84*a^28*b^12*cos(c/2 + (d*x)/2) + 6*a^30*b^10*cos(c/2 + (d*x)/2) + 280*a^3*b^37*sin(c/2 + (d*x)/2) - 1820*a^5*b^35*sin(c/2 + (d*x)/2) + 7280*a^7*b^33*sin(c/2 + (d*x)/2) - 20020*a^9*b^31*sin(c/2 + (d*x)/2) + 40040*a^11*b^29*sin(c/2 + (d*x)/2) - 60060*a^13*b^27*sin(c/2 + (d*x)/2) + 68640*a^15*b^25*sin(c/2 + (d*x)/2) - 60060*a^17*b^23*sin(c/2 + (d*x)/2) + 40040*a^19*b^21*sin(c/2 + (d*x)/2) - 20020*a^21*b^19*sin(c/2 + (d*x)/2) + 7280*a^23*b^17*sin(c/2 + (d*x)/2) - 1820*a^25*b^15*sin(c/2 + (d*x)/2) + 280*a^27*b^13*sin(c/2 + (d*x)/2) - 20*a^29*b^11*sin(c/2 + (d*x)/2) - 588*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^3*b^38*sin(c/2 + (d*x)/2) + 5715*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^5*b^36*sin(c/2 + (d*x)/2) - 31710*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^7*b^34*sin(c/2 + (d*x)/2) + 116025*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^9*b^32*sin(c/2 + (d*x)/2) - 301392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^11*b^30*sin(c/2 + (d*x)/2) + 579579*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^13*b^28*sin(c/2 + (d*x)/2) - 845130*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^15*b^26*sin(c/2 + (d*x)/2) + 945945*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^17*b^24*sin(c/2 + (d*x)/2) - 815100*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^19*b^22*sin(c/2 + (d*x)/2) + 537537*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^21*b^20*sin(c/2 + (d*x)/2) - 266994*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^23*b^18*sin(c/2 + (d*x)/2) + 96915*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^25*b^16*sin(c/2 + (d*x)/2) - 24360*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^27*b^14*sin(c/2 + (d*x)/2) + 3825*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^29*b^12*sin(c/2 + (d*x)/2) - 294*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^31*b^10*sin(c/2 + (d*x)/2) + 3*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^33*b^8*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^2*b^40*cos(c/2 + (d*x)/2) - 1143*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^4*b^38*cos(c/2 + (d*x)/2) + 11853*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^6*b^36*cos(c/2 + (d*x)/2) - 66087*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^8*b^34*cos(c/2 + (d*x)/2) + 235053*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^10*b^32*cos(c/2 + (d*x)/2) - 577395*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^12*b^30*cos(c/2 + (d*x)/2) + 1018017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^14*b^28*cos(c/2 + (d*x)/2) - 1303731*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^16*b^26*cos(c/2 + (d*x)/2) + 1193049*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^18*b^24*cos(c/2 + (d*x)/2) - 724581*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^20*b^22*cos(c/2 + (d*x)/2) + 207207*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^22*b^20*cos(c/2 + (d*x)/2) + 85995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^24*b^18*cos(c/2 + (d*x)/2) - 133497*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^26*b^16*cos(c/2 + (d*x)/2) + 75663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^28*b^14*cos(c/2 + (d*x)/2) - 24597*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^30*b^12*cos(c/2 + (d*x)/2) + 4527*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^32*b^10*cos(c/2 + (d*x)/2) - 369*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^34*b^8*cos(c/2 + (d*x)/2) - 3078*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^4*b^39*cos(c/2 + (d*x)/2) + 33453*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^6*b^37*cos(c/2 + (d*x)/2) - 147744*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^8*b^35*cos(c/2 + (d*x)/2) + 279531*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^10*b^33*cos(c/2 + (d*x)/2) + 191646*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^12*b^31*cos(c/2 + (d*x)/2) - 2542995*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^14*b^29*cos(c/2 + (d*x)/2) + 7459452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^16*b^27*cos(c/2 + (d*x)/2) - 13193037*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^18*b^25*cos(c/2 + (d*x)/2) + 16054038*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^20*b^23*cos(c/2 + (d*x)/2) - 13888017*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^22*b^21*cos(c/2 + (d*x)/2) + 8432424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^24*b^19*cos(c/2 + (d*x)/2) - 3339063*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^26*b^17*cos(c/2 + (d*x)/2) + 633906*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^28*b^15*cos(c/2 + (d*x)/2) + 109431*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^30*b^13*cos(c/2 + (d*x)/2) - 104004*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^32*b^11*cos(c/2 + (d*x)/2) + 26649*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^34*b^9*cos(c/2 + (d*x)/2) - 2592*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^36*b^7*cos(c/2 + (d*x)/2) + 891*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^4*b^40*cos(c/2 + (d*x)/2) - 12879*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^6*b^38*cos(c/2 + (d*x)/2) + 84807*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^8*b^36*cos(c/2 + (d*x)/2) - 332424*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^10*b^34*cos(c/2 + (d*x)/2) + 840780*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^12*b^32*cos(c/2 + (d*x)/2) - 1340388*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^14*b^30*cos(c/2 + (d*x)/2) + 972972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^16*b^28*cos(c/2 + (d*x)/2) + 1187784*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^18*b^26*cos(c/2 + (d*x)/2) - 4934358*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^20*b^24*cos(c/2 + (d*x)/2) + 8455590*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^22*b^22*cos(c/2 + (d*x)/2) - 9660222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^24*b^20*cos(c/2 + (d*x)/2) + 8061768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^26*b^18*cos(c/2 + (d*x)/2) - 5041764*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^28*b^16*cos(c/2 + (d*x)/2) + 2360988*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^30*b^14*cos(c/2 + (d*x)/2) - 811620*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^32*b^12*cos(c/2 + (d*x)/2) + 196344*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^34*b^10*cos(c/2 + (d*x)/2) - 30861*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^36*b^8*cos(c/2 + (d*x)/2) + 2673*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^38*b^6*cos(c/2 + (d*x)/2) - 81*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^40*b^4*cos(c/2 + (d*x)/2) + 972*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^4*b^41*cos(c/2 + (d*x)/2) - 18225*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^6*b^39*cos(c/2 + (d*x)/2) + 161838*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^8*b^37*cos(c/2 + (d*x)/2) - 904689*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^10*b^35*cos(c/2 + (d*x)/2) + 3569184*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^12*b^33*cos(c/2 + (d*x)/2) - 10558836*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^14*b^31*cos(c/2 + (d*x)/2) + 24290280*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^16*b^29*cos(c/2 + (d*x)/2) - 44466084*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^18*b^27*cos(c/2 + (d*x)/2) + 65732472*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^20*b^25*cos(c/2 + (d*x)/2) - 79158222*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^22*b^23*cos(c/2 + (d*x)/2) + 77976756*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^24*b^21*cos(c/2 + (d*x)/2) - 62832510*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^26*b^19*cos(c/2 + (d*x)/2) + 41243904*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^28*b^17*cos(c/2 + (d*x)/2) - 21861252*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^30*b^15*cos(c/2 + (d*x)/2) + 9220392*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^32*b^13*cos(c/2 + (d*x)/2) - 3023892*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^34*b^11*cos(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^36*b^9*cos(c/2 + (d*x)/2) - 129033*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^38*b^7*cos(c/2 + (d*x)/2) + 14094*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^40*b^5*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^42*b^3*cos(c/2 + (d*x)/2) - 936*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^3*b^39*sin(c/2 + (d*x)/2) + 13032*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^5*b^37*sin(c/2 + (d*x)/2) - 84132*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^7*b^35*sin(c/2 + (d*x)/2) + 333648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^9*b^33*sin(c/2 + (d*x)/2) - 907452*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^11*b^31*sin(c/2 + (d*x)/2) + 1788696*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^13*b^29*sin(c/2 + (d*x)/2) - 2630628*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^15*b^27*sin(c/2 + (d*x)/2) + 2924064*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^17*b^25*sin(c/2 + (d*x)/2) - 2455596*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^19*b^23*sin(c/2 + (d*x)/2) + 1534104*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^21*b^21*sin(c/2 + (d*x)/2) - 684684*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^23*b^19*sin(c/2 + (d*x)/2) + 196560*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^25*b^17*sin(c/2 + (d*x)/2) - 22932*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^27*b^15*sin(c/2 + (d*x)/2) - 6552*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^29*b^13*sin(c/2 + (d*x)/2) + 3348*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^31*b^11*sin(c/2 + (d*x)/2) - 576*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^33*b^9*sin(c/2 + (d*x)/2) + 36*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^2*a^35*b^7*sin(c/2 + (d*x)/2) + 1080*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^3*b^40*sin(c/2 + (d*x)/2) - 6048*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^5*b^38*sin(c/2 + (d*x)/2) - 23625*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^7*b^36*sin(c/2 + (d*x)/2) + 361044*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^9*b^34*sin(c/2 + (d*x)/2) - 1757511*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^11*b^32*sin(c/2 + (d*x)/2) + 5066334*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^13*b^30*sin(c/2 + (d*x)/2) - 9830457*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^15*b^28*sin(c/2 + (d*x)/2) + 13374504*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^17*b^26*sin(c/2 + (d*x)/2) - 12675663*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^19*b^24*sin(c/2 + (d*x)/2) + 7729722*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^21*b^22*sin(c/2 + (d*x)/2) - 1942083*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^23*b^20*sin(c/2 + (d*x)/2) - 1366092*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^25*b^18*sin(c/2 + (d*x)/2) + 1796067*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^27*b^16*sin(c/2 + (d*x)/2) - 993006*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^29*b^14*sin(c/2 + (d*x)/2) + 318789*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^31*b^12*sin(c/2 + (d*x)/2) - 57456*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^33*b^10*sin(c/2 + (d*x)/2) + 4347*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^35*b^8*sin(c/2 + (d*x)/2) + 54*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^3*a^37*b^6*sin(c/2 + (d*x)/2) + 648*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^3*b^41*sin(c/2 + (d*x)/2) - 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^5*b^39*sin(c/2 + (d*x)/2) + 35964*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^7*b^37*sin(c/2 + (d*x)/2) - 46656*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^9*b^35*sin(c/2 + (d*x)/2) - 311040*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^11*b^33*sin(c/2 + (d*x)/2) + 2068416*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^13*b^31*sin(c/2 + (d*x)/2) - 6722352*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^15*b^29*sin(c/2 + (d*x)/2) + 14758848*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^17*b^27*sin(c/2 + (d*x)/2) - 23907312*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^19*b^25*sin(c/2 + (d*x)/2) + 29652480*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^21*b^23*sin(c/2 + (d*x)/2) - 28633176*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^23*b^21*sin(c/2 + (d*x)/2) + 21632832*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^25*b^19*sin(c/2 + (d*x)/2) - 12737088*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^27*b^17*sin(c/2 + (d*x)/2) + 5769792*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^29*b^15*sin(c/2 + (d*x)/2) - 1963440*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^31*b^13*sin(c/2 + (d*x)/2) + 482112*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^33*b^11*sin(c/2 + (d*x)/2) - 79704*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^35*b^9*sin(c/2 + (d*x)/2) + 7776*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^37*b^7*sin(c/2 + (d*x)/2) - 324*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^4*a^39*b^5*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^5*b^40*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^7*b^38*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^9*b^36*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^11*b^34*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^13*b^32*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^15*b^30*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^17*b^28*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^19*b^26*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^21*b^24*sin(c/2 + (d*x)/2) - 11814660*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^23*b^22*sin(c/2 + (d*x)/2) + 10633194*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^25*b^20*sin(c/2 + (d*x)/2) - 7733232*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^27*b^18*sin(c/2 + (d*x)/2) + 4511052*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^29*b^16*sin(c/2 + (d*x)/2) - 2082024*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^31*b^14*sin(c/2 + (d*x)/2) + 743580*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^33*b^12*sin(c/2 + (d*x)/2) - 198288*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^35*b^10*sin(c/2 + (d*x)/2) + 37179*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^37*b^8*sin(c/2 + (d*x)/2) - 4374*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^39*b^6*sin(c/2 + (d*x)/2) + 243*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)^5*a^41*b^4*sin(c/2 + (d*x)/2) + 24*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a*b^40*sin(c/2 + (d*x)/2) - 57*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^2*b^39*cos(c/2 + (d*x)/2) + 846*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^4*b^37*cos(c/2 + (d*x)/2) - 5859*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^6*b^35*cos(c/2 + (d*x)/2) + 25116*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^8*b^33*cos(c/2 + (d*x)/2) - 74529*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^10*b^31*cos(c/2 + (d*x)/2) + 162162*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^12*b^29*cos(c/2 + (d*x)/2) - 267267*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^14*b^27*cos(c/2 + (d*x)/2) + 339768*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^16*b^25*cos(c/2 + (d*x)/2) - 335907*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^18*b^23*cos(c/2 + (d*x)/2) + 258258*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^20*b^21*cos(c/2 + (d*x)/2) - 153153*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^22*b^19*cos(c/2 + (d*x)/2) + 68796*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^24*b^17*cos(c/2 + (d*x)/2) - 22659*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^26*b^15*cos(c/2 + (d*x)/2) + 5166*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^28*b^13*cos(c/2 + (d*x)/2) - 729*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^30*b^11*cos(c/2 + (d*x)/2) + 48*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k)*a^32*b^9*cos(c/2 + (d*x)/2)))/cos(c/2 + (d*x)/2))*root(7290*a^10*b^4*d^6 - 7290*a^8*b^6*d^6 - 3645*a^12*b^2*d^6 + 3645*a^6*b^8*d^6 - 729*a^4*b^10*d^6 + 729*a^14*d^6 + 12393*a^6*b^6*d^4 + 3645*a^8*b^4*d^4 + 3645*a^4*b^8*d^4 - 135*a^4*b^6*d^2 + 135*a^2*b^8*d^2 + b^8, d, k), k, 1, 6))/(a^4*d*cos(c/2 + (d*x)/2)^6 + b^4*d*cos(c/2 + (d*x)/2)^6 - a^4*d*sin(c/2 + (d*x)/2)^6 - b^4*d*sin(c/2 + (d*x)/2)^6 - 2*a^2*b^2*d*cos(c/2 + (d*x)/2)^6 + 2*a^2*b^2*d*sin(c/2 + (d*x)/2)^6 + 3*a^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*a^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 + 3*b^4*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 - 3*b^4*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2 - 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^4 + 6*a^2*b^2*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^2)","B"
393,1,384,288,0.424337,"\text{Not used}","int(cos(c + d*x)^7/(a + b*sin(c + d*x)^3)^2,x)","\frac{\sum _{k=1}^3\ln\left(\frac{8\,a^2+4\,b^2+{\mathrm{root}\left(729\,a^5\,b^7\,d^3+648\,a^5\,b^3\,d+324\,a^3\,b^5\,d+120\,a^4\,b^2-48\,a^2\,b^4-8\,b^6-64\,a^6,d,k\right)}^2\,a^2\,b^4\,27+12\,a\,b\,\sin\left(c+d\,x\right)+\mathrm{root}\left(729\,a^5\,b^7\,d^3+648\,a^5\,b^3\,d+324\,a^3\,b^5\,d+120\,a^4\,b^2-48\,a^2\,b^4-8\,b^6-64\,a^6,d,k\right)\,b^4\,\sin\left(c+d\,x\right)\,6+\mathrm{root}\left(729\,a^5\,b^7\,d^3+648\,a^5\,b^3\,d+324\,a^3\,b^5\,d+120\,a^4\,b^2-48\,a^2\,b^4-8\,b^6-64\,a^6,d,k\right)\,a^2\,b^2\,\sin\left(c+d\,x\right)\,12}{a\,b^2\,3}\right)\,\mathrm{root}\left(729\,a^5\,b^7\,d^3+648\,a^5\,b^3\,d+324\,a^3\,b^5\,d+120\,a^4\,b^2-48\,a^2\,b^4-8\,b^6-64\,a^6,d,k\right)}{d}-\frac{\sin\left(c+d\,x\right)}{b^2\,d}-\frac{b\,{\sin\left(c+d\,x\right)}^2-b+\frac{\sin\left(c+d\,x\right)\,\left(a^2-b^2\right)}{3\,a}}{d\,\left(b^3\,{\sin\left(c+d\,x\right)}^3+a\,b^2\right)}","Not used",1,"symsum(log((8*a^2 + 4*b^2 + 27*root(729*a^5*b^7*d^3 + 648*a^5*b^3*d + 324*a^3*b^5*d + 120*a^4*b^2 - 48*a^2*b^4 - 8*b^6 - 64*a^6, d, k)^2*a^2*b^4 + 12*a*b*sin(c + d*x) + 6*root(729*a^5*b^7*d^3 + 648*a^5*b^3*d + 324*a^3*b^5*d + 120*a^4*b^2 - 48*a^2*b^4 - 8*b^6 - 64*a^6, d, k)*b^4*sin(c + d*x) + 12*root(729*a^5*b^7*d^3 + 648*a^5*b^3*d + 324*a^3*b^5*d + 120*a^4*b^2 - 48*a^2*b^4 - 8*b^6 - 64*a^6, d, k)*a^2*b^2*sin(c + d*x))/(3*a*b^2))*root(729*a^5*b^7*d^3 + 648*a^5*b^3*d + 324*a^3*b^5*d + 120*a^4*b^2 - 48*a^2*b^4 - 8*b^6 - 64*a^6, d, k), k, 1, 3)/d - sin(c + d*x)/(b^2*d) - (b*sin(c + d*x)^2 - b + (sin(c + d*x)*(a^2 - b^2))/(3*a))/(d*(a*b^2 + b^3*sin(c + d*x)^3))","B"
394,1,203,238,14.982202,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x)^3)^2,x)","\frac{\sum _{k=1}^3\ln\left(\frac{4\,b+4\,a\,\sin\left(c+d\,x\right)+{\mathrm{root}\left(729\,a^5\,b^5\,d^3+108\,a^3\,b^3\,d-8\,b^4+8\,a^4,d,k\right)}^2\,a^2\,b^3\,81+\mathrm{root}\left(729\,a^5\,b^5\,d^3+108\,a^3\,b^3\,d-8\,b^4+8\,a^4,d,k\right)\,b^3\,\sin\left(c+d\,x\right)\,18}{a\,b\,9}\right)\,\mathrm{root}\left(729\,a^5\,b^5\,d^3+108\,a^3\,b^3\,d-8\,b^4+8\,a^4,d,k\right)}{d}+\frac{\frac{\sin\left(c+d\,x\right)}{3\,a}+\frac{2}{3\,b}-\frac{{\sin\left(c+d\,x\right)}^2}{3\,b}}{d\,\left(b\,{\sin\left(c+d\,x\right)}^3+a\right)}","Not used",1,"symsum(log((4*b + 4*a*sin(c + d*x) + 81*root(729*a^5*b^5*d^3 + 108*a^3*b^3*d - 8*b^4 + 8*a^4, d, k)^2*a^2*b^3 + 18*root(729*a^5*b^5*d^3 + 108*a^3*b^3*d - 8*b^4 + 8*a^4, d, k)*b^3*sin(c + d*x))/(9*a*b))*root(729*a^5*b^5*d^3 + 108*a^3*b^3*d - 8*b^4 + 8*a^4, d, k), k, 1, 3)/d + (sin(c + d*x)/(3*a) + 2/(3*b) - sin(c + d*x)^2/(3*b))/(d*(a + b*sin(c + d*x)^3))","B"
395,1,172,183,0.380444,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x)^3)^2,x)","\frac{\frac{\sin\left(c+d\,x\right)}{3\,a}+\frac{1}{3\,b}}{d\,\left(b\,{\sin\left(c+d\,x\right)}^3+a\right)}+\frac{2\,\ln\left(\frac{2\,b^{5/3}}{a^{2/3}}+\frac{2\,b^2\,\sin\left(c+d\,x\right)}{a}\right)}{9\,a^{5/3}\,b^{1/3}\,d}+\frac{\ln\left(\frac{2\,b^2\,\sin\left(c+d\,x\right)}{a}+\frac{b^{5/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{a^{2/3}}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{9\,a^{5/3}\,b^{1/3}\,d}-\frac{\ln\left(\frac{2\,b^2\,\sin\left(c+d\,x\right)}{a}-\frac{b^{5/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{a^{2/3}}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{9\,a^{5/3}\,b^{1/3}\,d}","Not used",1,"(sin(c + d*x)/(3*a) + 1/(3*b))/(d*(a + b*sin(c + d*x)^3)) + (2*log((2*b^(5/3))/a^(2/3) + (2*b^2*sin(c + d*x))/a))/(9*a^(5/3)*b^(1/3)*d) + (log((2*b^2*sin(c + d*x))/a + (b^(5/3)*(3^(1/2)*1i - 1))/a^(2/3))*(3^(1/2)*1i - 1))/(9*a^(5/3)*b^(1/3)*d) - (log((2*b^2*sin(c + d*x))/a - (b^(5/3)*(3^(1/2)*1i + 1))/a^(2/3))*(3^(1/2)*1i + 1))/(9*a^(5/3)*b^(1/3)*d)","B"
396,1,165,176,15.004115,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x)^3)^2,x)","\frac{\sin\left(c+d\,x\right)}{3\,a\,d\,\left(b\,{\sin\left(c+d\,x\right)}^3+a\right)}+\frac{2\,\ln\left(\frac{2\,b^{5/3}}{a^{2/3}}+\frac{2\,b^2\,\sin\left(c+d\,x\right)}{a}\right)}{9\,a^{5/3}\,b^{1/3}\,d}+\frac{\ln\left(\frac{2\,b^2\,\sin\left(c+d\,x\right)}{a}+\frac{b^{5/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{a^{2/3}}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{9\,a^{5/3}\,b^{1/3}\,d}-\frac{\ln\left(\frac{2\,b^2\,\sin\left(c+d\,x\right)}{a}-\frac{b^{5/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{a^{2/3}}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{9\,a^{5/3}\,b^{1/3}\,d}","Not used",1,"sin(c + d*x)/(3*a*d*(a + b*sin(c + d*x)^3)) + (2*log((2*b^(5/3))/a^(2/3) + (2*b^2*sin(c + d*x))/a))/(9*a^(5/3)*b^(1/3)*d) + (log((2*b^2*sin(c + d*x))/a + (b^(5/3)*(3^(1/2)*1i - 1))/a^(2/3))*(3^(1/2)*1i - 1))/(9*a^(5/3)*b^(1/3)*d) - (log((2*b^2*sin(c + d*x))/a - (b^(5/3)*(3^(1/2)*1i + 1))/a^(2/3))*(3^(1/2)*1i + 1))/(9*a^(5/3)*b^(1/3)*d)","B"
397,1,980,587,15.172536,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x)^3)^2),x)","\frac{\sum _{k=1}^3\ln\left(\frac{\frac{8\,b^6}{27}-\frac{16\,a^2\,b^4}{27}}{a^7-2\,a^5\,b^2+a^3\,b^4}+\mathrm{root}\left(1458\,a^7\,b^2\,z^3-729\,a^5\,b^4\,z^3-729\,a^9\,z^3-1458\,a^6\,b\,z^2-108\,a^3\,b^2\,z-64\,a^2\,b+8\,b^3,z,k\right)\,\left(\frac{\frac{128\,a^3\,b^5}{27}+\frac{32\,a\,b^7}{27}}{a^7-2\,a^5\,b^2+a^3\,b^4}-\mathrm{root}\left(1458\,a^7\,b^2\,z^3-729\,a^5\,b^4\,z^3-729\,a^9\,z^3-1458\,a^6\,b\,z^2-108\,a^3\,b^2\,z-64\,a^2\,b+8\,b^3,z,k\right)\,\left(\mathrm{root}\left(1458\,a^7\,b^2\,z^3-729\,a^5\,b^4\,z^3-729\,a^9\,z^3-1458\,a^6\,b\,z^2-108\,a^3\,b^2\,z-64\,a^2\,b+8\,b^3,z,k\right)\,\left(\frac{27\,a^9\,b^3+34\,a^7\,b^5-77\,a^5\,b^7+16\,a^3\,b^9}{a^7-2\,a^5\,b^2+a^3\,b^4}+\mathrm{root}\left(1458\,a^7\,b^2\,z^3-729\,a^5\,b^4\,z^3-729\,a^9\,z^3-1458\,a^6\,b\,z^2-108\,a^3\,b^2\,z-64\,a^2\,b+8\,b^3,z,k\right)\,\left(\frac{180\,a^{10}\,b^4-324\,a^8\,b^6+108\,a^6\,b^8+36\,a^4\,b^{10}}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{\sin\left(c+d\,x\right)\,\left(1458\,a^{11}\,b^3+1458\,a^9\,b^5-7290\,a^7\,b^7+4374\,a^5\,b^9\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)+\frac{\sin\left(c+d\,x\right)\,\left(2484\,a^8\,b^4-1836\,a^6\,b^6-864\,a^4\,b^8+216\,a^2\,b^{10}\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)+\frac{\frac{388\,a^6\,b^4}{9}-\frac{353\,a^4\,b^6}{9}+\frac{64\,a^2\,b^8}{9}}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{\sin\left(c+d\,x\right)\,\left(447\,a^5\,b^5-408\,a^3\,b^7+96\,a\,b^9\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)+\frac{\sin\left(c+d\,x\right)\,\left(-236\,a^4\,b^4+134\,a^2\,b^6+16\,b^8\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)+\frac{8\,a\,b^5\,\sin\left(c+d\,x\right)}{9\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)\,\mathrm{root}\left(1458\,a^7\,b^2\,z^3-729\,a^5\,b^4\,z^3-729\,a^9\,z^3-1458\,a^6\,b\,z^2-108\,a^3\,b^2\,z-64\,a^2\,b+8\,b^3,z,k\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)}{d\,\left(2\,a^2+4\,a\,b+2\,b^2\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{d\,\left(2\,a^2-4\,a\,b+2\,b^2\right)}+\frac{\frac{b}{3\,\left(a^2-b^2\right)}+\frac{b\,{\sin\left(c+d\,x\right)}^2}{3\,\left(a^2-b^2\right)}-\frac{b^2\,\sin\left(c+d\,x\right)}{3\,a\,\left(a^2-b^2\right)}}{d\,\left(b\,{\sin\left(c+d\,x\right)}^3+a\right)}","Not used",1,"symsum(log(((8*b^6)/27 - (16*a^2*b^4)/27)/(a^7 + a^3*b^4 - 2*a^5*b^2) + root(1458*a^7*b^2*z^3 - 729*a^5*b^4*z^3 - 729*a^9*z^3 - 1458*a^6*b*z^2 - 108*a^3*b^2*z - 64*a^2*b + 8*b^3, z, k)*(((32*a*b^7)/27 + (128*a^3*b^5)/27)/(a^7 + a^3*b^4 - 2*a^5*b^2) - root(1458*a^7*b^2*z^3 - 729*a^5*b^4*z^3 - 729*a^9*z^3 - 1458*a^6*b*z^2 - 108*a^3*b^2*z - 64*a^2*b + 8*b^3, z, k)*(root(1458*a^7*b^2*z^3 - 729*a^5*b^4*z^3 - 729*a^9*z^3 - 1458*a^6*b*z^2 - 108*a^3*b^2*z - 64*a^2*b + 8*b^3, z, k)*((16*a^3*b^9 - 77*a^5*b^7 + 34*a^7*b^5 + 27*a^9*b^3)/(a^7 + a^3*b^4 - 2*a^5*b^2) + root(1458*a^7*b^2*z^3 - 729*a^5*b^4*z^3 - 729*a^9*z^3 - 1458*a^6*b*z^2 - 108*a^3*b^2*z - 64*a^2*b + 8*b^3, z, k)*((36*a^4*b^10 + 108*a^6*b^8 - 324*a^8*b^6 + 180*a^10*b^4)/(a^7 + a^3*b^4 - 2*a^5*b^2) + (sin(c + d*x)*(4374*a^5*b^9 - 7290*a^7*b^7 + 1458*a^9*b^5 + 1458*a^11*b^3))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) + (sin(c + d*x)*(216*a^2*b^10 - 864*a^4*b^8 - 1836*a^6*b^6 + 2484*a^8*b^4))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) + ((64*a^2*b^8)/9 - (353*a^4*b^6)/9 + (388*a^6*b^4)/9)/(a^7 + a^3*b^4 - 2*a^5*b^2) + (sin(c + d*x)*(96*a*b^9 - 408*a^3*b^7 + 447*a^5*b^5))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) + (sin(c + d*x)*(16*b^8 + 134*a^2*b^6 - 236*a^4*b^4))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) + (8*a*b^5*sin(c + d*x))/(9*(a^7 + a^3*b^4 - 2*a^5*b^2)))*root(1458*a^7*b^2*z^3 - 729*a^5*b^4*z^3 - 729*a^9*z^3 - 1458*a^6*b*z^2 - 108*a^3*b^2*z - 64*a^2*b + 8*b^3, z, k), k, 1, 3)/d - log(sin(c + d*x) - 1)/(d*(4*a*b + 2*a^2 + 2*b^2)) + log(sin(c + d*x) + 1)/(d*(2*a^2 - 4*a*b + 2*b^2)) + (b/(3*(a^2 - b^2)) + (b*sin(c + d*x)^2)/(3*(a^2 - b^2)) - (b^2*sin(c + d*x))/(3*a*(a^2 - b^2)))/(d*(a + b*sin(c + d*x)^3))","B"
398,1,1605,747,15.752203,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x)^3)^2),x)","\frac{\sum _{k=1}^3\ln\left(\mathrm{root}\left(2187\,a^9\,b^2\,z^3-2187\,a^7\,b^4\,z^3+729\,a^5\,b^6\,z^3-729\,a^{11}\,z^3+7290\,a^6\,b^3\,z^2+1458\,a^8\,b\,z^2-972\,a^5\,b^2\,z+324\,a^3\,b^4\,z+216\,a^2\,b^3-8\,b^5,z,k\right)\,\left(-\mathrm{root}\left(2187\,a^9\,b^2\,z^3-2187\,a^7\,b^4\,z^3+729\,a^5\,b^6\,z^3-729\,a^{11}\,z^3+7290\,a^6\,b^3\,z^2+1458\,a^8\,b\,z^2-972\,a^5\,b^2\,z+324\,a^3\,b^4\,z+216\,a^2\,b^3-8\,b^5,z,k\right)\,\left(\frac{-\frac{63\,a^{10}\,b^4}{2}+\frac{4153\,a^8\,b^6}{12}+325\,a^6\,b^8-\frac{1017\,a^4\,b^{10}}{4}+\frac{32\,a^2\,b^{12}}{3}}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}+\mathrm{root}\left(2187\,a^9\,b^2\,z^3-2187\,a^7\,b^4\,z^3+729\,a^5\,b^6\,z^3-729\,a^{11}\,z^3+7290\,a^6\,b^3\,z^2+1458\,a^8\,b\,z^2-972\,a^5\,b^2\,z+324\,a^3\,b^4\,z+216\,a^2\,b^3-8\,b^5,z,k\right)\,\left(\frac{\frac{27\,a^{13}\,b^3}{2}-239\,a^{11}\,b^5+188\,a^9\,b^7+303\,a^7\,b^9-\frac{563\,a^5\,b^{11}}{2}+16\,a^3\,b^{13}}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}+\mathrm{root}\left(2187\,a^9\,b^2\,z^3-2187\,a^7\,b^4\,z^3+729\,a^5\,b^6\,z^3-729\,a^{11}\,z^3+7290\,a^6\,b^3\,z^2+1458\,a^8\,b\,z^2-972\,a^5\,b^2\,z+324\,a^3\,b^4\,z+216\,a^2\,b^3-8\,b^5,z,k\right)\,\left(\frac{180\,a^{14}\,b^4-684\,a^{12}\,b^6+936\,a^{10}\,b^8-504\,a^8\,b^{10}+36\,a^6\,b^{12}+36\,a^4\,b^{14}}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}+\frac{\sin\left(c+d\,x\right)\,\left(5832\,a^{15}\,b^3-5832\,a^{13}\,b^5-34992\,a^{11}\,b^7+81648\,a^9\,b^9-64152\,a^7\,b^{11}+17496\,a^5\,b^{13}\right)}{108\,\left(a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8\right)}\right)-\frac{\sin\left(c+d\,x\right)\,\left(2916\,a^{12}\,b^4+50004\,a^{10}\,b^6-96660\,a^8\,b^8+30780\,a^6\,b^{10}+13824\,a^4\,b^{12}-864\,a^2\,b^{14}\right)}{108\,\left(a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8\right)}\right)-\frac{\sin\left(c+d\,x\right)\,\left(10449\,a^9\,b^5+31542\,a^7\,b^7-68247\,a^5\,b^9+7200\,a^3\,b^{11}-384\,a\,b^{13}\right)}{108\,\left(a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8\right)}\right)+\frac{-20\,a^7\,b^5+\frac{847\,a^5\,b^7}{3}+\frac{2173\,a^3\,b^9}{27}+\frac{32\,a\,b^{11}}{27}}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}+\frac{\sin\left(c+d\,x\right)\,\left(-9234\,a^6\,b^6-29860\,a^4\,b^8+4758\,a^2\,b^{10}+64\,b^{12}\right)}{108\,\left(a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8\right)}\right)+\frac{\frac{10\,a^4\,b^6}{3}+\frac{122\,a^2\,b^8}{27}+\frac{28\,b^{10}}{27}}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}+\frac{\sin\left(c+d\,x\right)\,\left(2568\,a^3\,b^7+1080\,a\,b^9\right)}{108\,\left(a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8\right)}\right)\,\mathrm{root}\left(2187\,a^9\,b^2\,z^3-2187\,a^7\,b^4\,z^3+729\,a^5\,b^6\,z^3-729\,a^{11}\,z^3+7290\,a^6\,b^3\,z^2+1458\,a^8\,b\,z^2-972\,a^5\,b^2\,z+324\,a^3\,b^4\,z+216\,a^2\,b^3-8\,b^5,z,k\right)}{d}+\frac{\frac{b\,{\sin\left(c+d\,x\right)}^2}{3\,\left(a^2-b^2\right)}+\frac{{\sin\left(c+d\,x\right)}^4\,\left(\frac{a^2\,b}{2}+\frac{3\,b^3}{2}\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,b\,\left(2\,a^2+b^2\right)}{3\,{\left(a^2-b^2\right)}^2}+\frac{\sin\left(c+d\,x\right)\,\left(3\,a^4+7\,a^2\,b^2+2\,b^4\right)}{6\,a\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{5\,a^2\,b^2}{3}+\frac{b^4}{3}\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(-b\,{\sin\left(c+d\,x\right)}^5+b\,{\sin\left(c+d\,x\right)}^3-a\,{\sin\left(c+d\,x\right)}^2+a\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(a+7\,b\right)}{d\,\left(4\,a^3+12\,a^2\,b+12\,a\,b^2+4\,b^3\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-7\,b\right)}{d\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)}","Not used",1,"symsum(log(root(2187*a^9*b^2*z^3 - 2187*a^7*b^4*z^3 + 729*a^5*b^6*z^3 - 729*a^11*z^3 + 7290*a^6*b^3*z^2 + 1458*a^8*b*z^2 - 972*a^5*b^2*z + 324*a^3*b^4*z + 216*a^2*b^3 - 8*b^5, z, k)*(((32*a*b^11)/27 + (2173*a^3*b^9)/27 + (847*a^5*b^7)/3 - 20*a^7*b^5)/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) - root(2187*a^9*b^2*z^3 - 2187*a^7*b^4*z^3 + 729*a^5*b^6*z^3 - 729*a^11*z^3 + 7290*a^6*b^3*z^2 + 1458*a^8*b*z^2 - 972*a^5*b^2*z + 324*a^3*b^4*z + 216*a^2*b^3 - 8*b^5, z, k)*(((32*a^2*b^12)/3 - (1017*a^4*b^10)/4 + 325*a^6*b^8 + (4153*a^8*b^6)/12 - (63*a^10*b^4)/2)/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) + root(2187*a^9*b^2*z^3 - 2187*a^7*b^4*z^3 + 729*a^5*b^6*z^3 - 729*a^11*z^3 + 7290*a^6*b^3*z^2 + 1458*a^8*b*z^2 - 972*a^5*b^2*z + 324*a^3*b^4*z + 216*a^2*b^3 - 8*b^5, z, k)*((16*a^3*b^13 - (563*a^5*b^11)/2 + 303*a^7*b^9 + 188*a^9*b^7 - 239*a^11*b^5 + (27*a^13*b^3)/2)/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) + root(2187*a^9*b^2*z^3 - 2187*a^7*b^4*z^3 + 729*a^5*b^6*z^3 - 729*a^11*z^3 + 7290*a^6*b^3*z^2 + 1458*a^8*b*z^2 - 972*a^5*b^2*z + 324*a^3*b^4*z + 216*a^2*b^3 - 8*b^5, z, k)*((36*a^4*b^14 + 36*a^6*b^12 - 504*a^8*b^10 + 936*a^10*b^8 - 684*a^12*b^6 + 180*a^14*b^4)/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) + (sin(c + d*x)*(17496*a^5*b^13 - 64152*a^7*b^11 + 81648*a^9*b^9 - 34992*a^11*b^7 - 5832*a^13*b^5 + 5832*a^15*b^3))/(108*(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2))) - (sin(c + d*x)*(13824*a^4*b^12 - 864*a^2*b^14 + 30780*a^6*b^10 - 96660*a^8*b^8 + 50004*a^10*b^6 + 2916*a^12*b^4))/(108*(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2))) - (sin(c + d*x)*(7200*a^3*b^11 - 384*a*b^13 - 68247*a^5*b^9 + 31542*a^7*b^7 + 10449*a^9*b^5))/(108*(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2))) + (sin(c + d*x)*(64*b^12 + 4758*a^2*b^10 - 29860*a^4*b^8 - 9234*a^6*b^6))/(108*(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2))) + ((28*b^10)/27 + (122*a^2*b^8)/27 + (10*a^4*b^6)/3)/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) + (sin(c + d*x)*(1080*a*b^9 + 2568*a^3*b^7))/(108*(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2)))*root(2187*a^9*b^2*z^3 - 2187*a^7*b^4*z^3 + 729*a^5*b^6*z^3 - 729*a^11*z^3 + 7290*a^6*b^3*z^2 + 1458*a^8*b*z^2 - 972*a^5*b^2*z + 324*a^3*b^4*z + 216*a^2*b^3 - 8*b^5, z, k), k, 1, 3)/d + ((b*sin(c + d*x)^2)/(3*(a^2 - b^2)) + (sin(c + d*x)^4*((a^2*b)/2 + (3*b^3)/2))/(a^4 + b^4 - 2*a^2*b^2) - (2*b*(2*a^2 + b^2))/(3*(a^2 - b^2)^2) + (sin(c + d*x)*(3*a^4 + 2*b^4 + 7*a^2*b^2))/(6*a*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^3*(b^4/3 + (5*a^2*b^2)/3))/(a*(a^4 + b^4 - 2*a^2*b^2)))/(d*(a - a*sin(c + d*x)^2 + b*sin(c + d*x)^3 - b*sin(c + d*x)^5)) - (log(sin(c + d*x) - 1)*(a + 7*b))/(d*(12*a*b^2 + 12*a^2*b + 4*a^3 + 4*b^3)) + (log(sin(c + d*x) + 1)*(a - 7*b))/(d*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3))","B"
399,1,2431,26,15.994528,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x)^3)^2,x)","\frac{2}{3\,d\,\left(8\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\,b\right)}+\frac{\sum _{k=1}^6\ln\left(\frac{-8192\,a^6-655360\,b^6+638976\,a^2\,b^4+24576\,a^4\,b^2-\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)\,a^3\,b^5\,2949120+\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)\,a^5\,b^3\,2138112-\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,9437184-786432\,a\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+98304\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^2\,a^2\,b^8\,21233664+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^2\,a^4\,b^6\,18579456+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^2\,a^6\,b^4\,2654208-{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^3\,a^5\,b^7\,167215104+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^3\,a^7\,b^5\,113467392-{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^4\,a^6\,b^8\,107495424+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^4\,a^8\,b^6\,107495424-{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^5\,a^7\,b^9\,1934917632+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^5\,a^9\,b^7\,1451188224+688128\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)\,a\,b^7\,1179648+\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)\,a^2\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,12976128-\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)\,a^4\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,6266880+\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)\,a^6\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,737280-{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^2\,a^3\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,53084160+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^2\,a^5\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,50429952+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^2\,a^7\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2654208-{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^3\,a^6\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,59719680+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^3\,a^8\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5971968-{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^4\,a^5\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,859963392+{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^4\,a^7\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,859963392-{\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}^5\,a^8\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,483729408}{a^3\,b^4}\right)\,\mathrm{root}\left(531441\,a^{10}\,b^8\,d^6+59049\,a^8\,b^6\,d^4+2187\,a^6\,b^4\,d^2+48\,a^2\,b^4+15\,a^4\,b^2+a^6-64\,b^6,d,k\right)}{d}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2+8\,b\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3\,d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2+8\,b\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3\,d\,\left(8\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\,b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3\,d\,\left(8\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\,b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2+8\,b\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",0,"2/(3*d*(a*b + 8*b^2*tan(c/2 + (d*x)/2)^3 + 3*a*b*tan(c/2 + (d*x)/2)^2 + 3*a*b*tan(c/2 + (d*x)/2)^4 + a*b*tan(c/2 + (d*x)/2)^6)) + symsum(log((638976*a^2*b^4 - 655360*b^6 - 8192*a^6 + 24576*a^4*b^2 - 2949120*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)*a^3*b^5 + 2138112*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)*a^5*b^3 - 9437184*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)*b^8*tan(c/2 + (d*x)/2) - 786432*a*b^5*tan(c/2 + (d*x)/2) + 98304*a^5*b*tan(c/2 + (d*x)/2) - 21233664*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^2*a^2*b^8 + 18579456*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^2*a^4*b^6 + 2654208*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^2*a^6*b^4 - 167215104*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^3*a^5*b^7 + 113467392*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^3*a^7*b^5 - 107495424*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^4*a^6*b^8 + 107495424*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^4*a^8*b^6 - 1934917632*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^5*a^7*b^9 + 1451188224*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^5*a^9*b^7 + 688128*a^3*b^3*tan(c/2 + (d*x)/2) - 1179648*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)*a*b^7 + 12976128*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)*a^2*b^6*tan(c/2 + (d*x)/2) - 6266880*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)*a^4*b^4*tan(c/2 + (d*x)/2) + 737280*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)*a^6*b^2*tan(c/2 + (d*x)/2) - 53084160*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^2*a^3*b^7*tan(c/2 + (d*x)/2) + 50429952*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^2*a^5*b^5*tan(c/2 + (d*x)/2) + 2654208*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^2*a^7*b^3*tan(c/2 + (d*x)/2) - 59719680*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^3*a^6*b^6*tan(c/2 + (d*x)/2) + 5971968*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^3*a^8*b^4*tan(c/2 + (d*x)/2) - 859963392*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^4*a^5*b^9*tan(c/2 + (d*x)/2) + 859963392*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^4*a^7*b^7*tan(c/2 + (d*x)/2) - 483729408*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k)^5*a^8*b^8*tan(c/2 + (d*x)/2))/(a^3*b^4))*root(531441*a^10*b^8*d^6 + 59049*a^8*b^6*d^4 + 2187*a^6*b^4*d^2 + 48*a^2*b^4 + 15*a^4*b^2 + a^6 - 64*b^6, d, k), k, 1, 6)/d + (8*tan(c/2 + (d*x)/2)^3)/(3*d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2 + 8*a*b*tan(c/2 + (d*x)/2)^3)) - (2*tan(c/2 + (d*x)/2)^5)/(3*d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2 + 8*a*b*tan(c/2 + (d*x)/2)^3)) + (4*tan(c/2 + (d*x)/2)^2)/(3*d*(a*b + 8*b^2*tan(c/2 + (d*x)/2)^3 + 3*a*b*tan(c/2 + (d*x)/2)^2 + 3*a*b*tan(c/2 + (d*x)/2)^4 + a*b*tan(c/2 + (d*x)/2)^6)) + (2*tan(c/2 + (d*x)/2)^4)/(3*d*(a*b + 8*b^2*tan(c/2 + (d*x)/2)^3 + 3*a*b*tan(c/2 + (d*x)/2)^2 + 3*a*b*tan(c/2 + (d*x)/2)^4 + a*b*tan(c/2 + (d*x)/2)^6)) + (2*tan(c/2 + (d*x)/2))/(3*d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2 + 8*a*b*tan(c/2 + (d*x)/2)^3))","B"
400,1,1648,26,15.745760,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x)^3)^2,x)","\frac{\sum _{k=1}^6\ln\left(-\frac{-\frac{16384\,a^2}{243}+\frac{131072\,b^2}{243}+\frac{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,8192}{27}+\frac{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1048576}{27}+\frac{{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^2\,a^2\,b^4\,262144}{3}-\frac{{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^2\,a^4\,b^2\,131072}{3}-{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^3\,a^5\,b^3\,98304+{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^4\,a^6\,b^4\,442368+{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^4\,a^8\,b^2\,221184+{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^5\,a^7\,b^5\,7962624-{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^5\,a^9\,b^3\,5971968+\frac{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)\,a\,b^3\,131072}{27}-\frac{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)\,a^3\,b\,65536}{27}-\frac{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,131072}{9}-\frac{{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^2\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,32768}{3}-\frac{{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^2\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,131072}{3}+{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^3\,a^6\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,245760+{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^4\,a^5\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3538944-{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^4\,a^7\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2654208+{\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}^5\,a^8\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1990656}{a^3}\right)\,\mathrm{root}\left(531441\,a^{12}\,b^4\,d^6-531441\,a^{10}\,b^6\,d^6+19683\,a^8\,b^4\,d^4+729\,a^6\,b^2\,d^2-16\,a^2\,b^2+a^4+64\,b^4,d,k\right)}{d}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3\,d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2+8\,b\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2+8\,b\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",0,"symsum(log(-((131072*b^2)/243 - (16384*a^2)/243 + (8192*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)*a^4*tan(c/2 + (d*x)/2))/27 + (1048576*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)*b^4*tan(c/2 + (d*x)/2))/27 + (262144*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^2*a^2*b^4)/3 - (131072*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^2*a^4*b^2)/3 - 98304*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^3*a^5*b^3 + 442368*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^4*a^6*b^4 + 221184*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^4*a^8*b^2 + 7962624*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^5*a^7*b^5 - 5971968*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^5*a^9*b^3 + (131072*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)*a*b^3)/27 - (65536*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)*a^3*b)/27 - (131072*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)*a^2*b^2*tan(c/2 + (d*x)/2))/9 - (32768*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^2*a^5*b*tan(c/2 + (d*x)/2))/3 - (131072*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^2*a^3*b^3*tan(c/2 + (d*x)/2))/3 + 245760*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^3*a^6*b^2*tan(c/2 + (d*x)/2) + 3538944*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^4*a^5*b^5*tan(c/2 + (d*x)/2) - 2654208*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^4*a^7*b^3*tan(c/2 + (d*x)/2) + 1990656*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k)^5*a^8*b^4*tan(c/2 + (d*x)/2))/a^3)*root(531441*a^12*b^4*d^6 - 531441*a^10*b^6*d^6 + 19683*a^8*b^4*d^4 + 729*a^6*b^2*d^2 - 16*a^2*b^2 + a^4 + 64*b^4, d, k), k, 1, 6)/d - (2*tan(c/2 + (d*x)/2)^5)/(3*d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2 + 8*a*b*tan(c/2 + (d*x)/2)^3)) + (2*tan(c/2 + (d*x)/2))/(3*d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2 + 8*a*b*tan(c/2 + (d*x)/2)^3))","B"
401,1,1567,17,17.892985,"\text{Not used}","int(1/(a + b*sin(c + d*x)^3)^2,x)","\frac{\sum _{k=1}^6\ln\left(-\frac{8192\,\left(80\,b^6-270\,a^2\,b^4\right)}{243\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}-\mathrm{root}\left(1594323\,a^{14}\,b^2\,d^6-1594323\,a^{12}\,b^4\,d^6+531441\,a^{10}\,b^6\,d^6-531441\,a^{16}\,d^6-59049\,a^{10}\,b^2\,d^4+59049\,a^8\,b^4\,d^4-177147\,a^{12}\,d^4+8019\,a^6\,b^2\,d^2-19683\,a^8\,d^2+432\,a^2\,b^2-64\,b^4-729\,a^4,d,k\right)\,\left(\frac{8192\,\left(-2187\,a^5\,b^3+648\,a^3\,b^5+144\,a\,b^7\right)}{243\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}-\mathrm{root}\left(1594323\,a^{14}\,b^2\,d^6-1594323\,a^{12}\,b^4\,d^6+531441\,a^{10}\,b^6\,d^6-531441\,a^{16}\,d^6-59049\,a^{10}\,b^2\,d^4+59049\,a^8\,b^4\,d^4-177147\,a^{12}\,d^4+8019\,a^6\,b^2\,d^2-19683\,a^8\,d^2+432\,a^2\,b^2-64\,b^4-729\,a^4,d,k\right)\,\left(\mathrm{root}\left(1594323\,a^{14}\,b^2\,d^6-1594323\,a^{12}\,b^4\,d^6+531441\,a^{10}\,b^6\,d^6-531441\,a^{16}\,d^6-59049\,a^{10}\,b^2\,d^4+59049\,a^8\,b^4\,d^4-177147\,a^{12}\,d^4+8019\,a^6\,b^2\,d^2-19683\,a^8\,d^2+432\,a^2\,b^2-64\,b^4-729\,a^4,d,k\right)\,\left(-\mathrm{root}\left(1594323\,a^{14}\,b^2\,d^6-1594323\,a^{12}\,b^4\,d^6+531441\,a^{10}\,b^6\,d^6-531441\,a^{16}\,d^6-59049\,a^{10}\,b^2\,d^4+59049\,a^8\,b^4\,d^4-177147\,a^{12}\,d^4+8019\,a^6\,b^2\,d^2-19683\,a^8\,d^2+432\,a^2\,b^2-64\,b^4-729\,a^4,d,k\right)\,\left(\mathrm{root}\left(1594323\,a^{14}\,b^2\,d^6-1594323\,a^{12}\,b^4\,d^6+531441\,a^{10}\,b^6\,d^6-531441\,a^{16}\,d^6-59049\,a^{10}\,b^2\,d^4+59049\,a^8\,b^4\,d^4-177147\,a^{12}\,d^4+8019\,a^6\,b^2\,d^2-19683\,a^8\,d^2+432\,a^2\,b^2-64\,b^4-729\,a^4,d,k\right)\,\left(\frac{8192\,\left(-177147\,a^{13}\,b^3+590490\,a^{11}\,b^5-649539\,a^9\,b^7+236196\,a^7\,b^9\right)}{243\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6561\,a^{12}\,b^4-13122\,a^{10}\,b^6+6561\,a^8\,b^8\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)+\frac{8192\,\left(72171\,a^{10}\,b^4-85293\,a^8\,b^6+13122\,a^6\,b^8\right)}{243\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8748\,a^{11}\,b^3+37908\,a^9\,b^5-40824\,a^7\,b^7+11664\,a^5\,b^9\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)+\frac{8192\,\left(39366\,a^9\,b^3+26973\,a^7\,b^5-20412\,a^5\,b^7\right)}{243\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3078\,a^6\,b^6-8181\,a^8\,b^4\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)-\frac{8192\,\left(11664\,a^6\,b^4-11340\,a^4\,b^6+2592\,a^2\,b^8\right)}{243\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1944\,a^7\,b^3+1260\,a^5\,b^5-720\,a^3\,b^7\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1053\,a^4\,b^4-688\,a^2\,b^6+128\,b^8\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a\,b^5-108\,a^3\,b^3\right)}{27\,\left(a^7-2\,a^5\,b^2+a^3\,b^4\right)}\right)\,\mathrm{root}\left(1594323\,a^{14}\,b^2\,d^6-1594323\,a^{12}\,b^4\,d^6+531441\,a^{10}\,b^6\,d^6-531441\,a^{16}\,d^6-59049\,a^{10}\,b^2\,d^4+59049\,a^8\,b^4\,d^4-177147\,a^{12}\,d^4+8019\,a^6\,b^2\,d^2-19683\,a^8\,d^2+432\,a^2\,b^2-64\,b^4-729\,a^4,d,k\right)}{d}+\frac{\frac{2\,b}{3\,\left(a^2-b^2\right)}+\frac{8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3\,\left(a^2-b^2\right)}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3\,\left(a^2-b^2\right)}-\frac{2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3\,a\,\left(a^2-b^2\right)}+\frac{8\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,a\,\left(a^2-b^2\right)}+\frac{2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3\,a\,\left(a^2-b^2\right)}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",0,"symsum(log(- (8192*(80*b^6 - 270*a^2*b^4))/(243*(a^7 + a^3*b^4 - 2*a^5*b^2)) - root(1594323*a^14*b^2*d^6 - 1594323*a^12*b^4*d^6 + 531441*a^10*b^6*d^6 - 531441*a^16*d^6 - 59049*a^10*b^2*d^4 + 59049*a^8*b^4*d^4 - 177147*a^12*d^4 + 8019*a^6*b^2*d^2 - 19683*a^8*d^2 + 432*a^2*b^2 - 64*b^4 - 729*a^4, d, k)*((8192*(144*a*b^7 + 648*a^3*b^5 - 2187*a^5*b^3))/(243*(a^7 + a^3*b^4 - 2*a^5*b^2)) - root(1594323*a^14*b^2*d^6 - 1594323*a^12*b^4*d^6 + 531441*a^10*b^6*d^6 - 531441*a^16*d^6 - 59049*a^10*b^2*d^4 + 59049*a^8*b^4*d^4 - 177147*a^12*d^4 + 8019*a^6*b^2*d^2 - 19683*a^8*d^2 + 432*a^2*b^2 - 64*b^4 - 729*a^4, d, k)*(root(1594323*a^14*b^2*d^6 - 1594323*a^12*b^4*d^6 + 531441*a^10*b^6*d^6 - 531441*a^16*d^6 - 59049*a^10*b^2*d^4 + 59049*a^8*b^4*d^4 - 177147*a^12*d^4 + 8019*a^6*b^2*d^2 - 19683*a^8*d^2 + 432*a^2*b^2 - 64*b^4 - 729*a^4, d, k)*((8192*(26973*a^7*b^5 - 20412*a^5*b^7 + 39366*a^9*b^3))/(243*(a^7 + a^3*b^4 - 2*a^5*b^2)) - root(1594323*a^14*b^2*d^6 - 1594323*a^12*b^4*d^6 + 531441*a^10*b^6*d^6 - 531441*a^16*d^6 - 59049*a^10*b^2*d^4 + 59049*a^8*b^4*d^4 - 177147*a^12*d^4 + 8019*a^6*b^2*d^2 - 19683*a^8*d^2 + 432*a^2*b^2 - 64*b^4 - 729*a^4, d, k)*(root(1594323*a^14*b^2*d^6 - 1594323*a^12*b^4*d^6 + 531441*a^10*b^6*d^6 - 531441*a^16*d^6 - 59049*a^10*b^2*d^4 + 59049*a^8*b^4*d^4 - 177147*a^12*d^4 + 8019*a^6*b^2*d^2 - 19683*a^8*d^2 + 432*a^2*b^2 - 64*b^4 - 729*a^4, d, k)*((8192*(236196*a^7*b^9 - 649539*a^9*b^7 + 590490*a^11*b^5 - 177147*a^13*b^3))/(243*(a^7 + a^3*b^4 - 2*a^5*b^2)) + (8192*tan(c/2 + (d*x)/2)*(6561*a^8*b^8 - 13122*a^10*b^6 + 6561*a^12*b^4))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) + (8192*(13122*a^6*b^8 - 85293*a^8*b^6 + 72171*a^10*b^4))/(243*(a^7 + a^3*b^4 - 2*a^5*b^2)) + (8192*tan(c/2 + (d*x)/2)*(11664*a^5*b^9 - 40824*a^7*b^7 + 37908*a^9*b^5 - 8748*a^11*b^3))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) + (8192*tan(c/2 + (d*x)/2)*(3078*a^6*b^6 - 8181*a^8*b^4))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) - (8192*(2592*a^2*b^8 - 11340*a^4*b^6 + 11664*a^6*b^4))/(243*(a^7 + a^3*b^4 - 2*a^5*b^2)) + (8192*tan(c/2 + (d*x)/2)*(1260*a^5*b^5 - 720*a^3*b^7 + 1944*a^7*b^3))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) + (8192*tan(c/2 + (d*x)/2)*(128*b^8 - 688*a^2*b^6 + 1053*a^4*b^4))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2))) - (8192*tan(c/2 + (d*x)/2)*(32*a*b^5 - 108*a^3*b^3))/(27*(a^7 + a^3*b^4 - 2*a^5*b^2)))*root(1594323*a^14*b^2*d^6 - 1594323*a^12*b^4*d^6 + 531441*a^10*b^6*d^6 - 531441*a^16*d^6 - 59049*a^10*b^2*d^4 + 59049*a^8*b^4*d^4 - 177147*a^12*d^4 + 8019*a^6*b^2*d^2 - 19683*a^8*d^2 + 432*a^2*b^2 - 64*b^4 - 729*a^4, d, k), k, 1, 6)/d + ((2*b)/(3*(a^2 - b^2)) + (8*b*tan(c/2 + (d*x)/2)^2)/(3*(a^2 - b^2)) - (2*b*tan(c/2 + (d*x)/2)^4)/(3*(a^2 - b^2)) - (2*b^2*tan(c/2 + (d*x)/2))/(3*a*(a^2 - b^2)) + (8*b^2*tan(c/2 + (d*x)/2)^3)/(3*a*(a^2 - b^2)) + (2*b^2*tan(c/2 + (d*x)/2)^5)/(3*a*(a^2 - b^2)))/(d*(a + 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 + a*tan(c/2 + (d*x)/2)^6 + 8*b*tan(c/2 + (d*x)/2)^3))","B"
402,1,3148,26,21.207206,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x)^3)^2),x)","\frac{\sum _{k=1}^6\ln\left(5479612416\,a^8\,b^{36}-180486144\,a^6\,b^{38}-\mathrm{root}\left(5314410\,a^{16}\,b^4\,d^6-5314410\,a^{14}\,b^6\,d^6-2657205\,a^{18}\,b^2\,d^6+2657205\,a^{12}\,b^8\,d^6-531441\,a^{10}\,b^{10}\,d^6+531441\,a^{20}\,d^6+11514555\,a^{12}\,b^4\,d^4+2066715\,a^{14}\,b^2\,d^4+1062882\,a^{10}\,b^6\,d^4-295245\,a^8\,b^8\,d^4+984150\,a^8\,b^4\,d^2-98415\,a^6\,b^6\,d^2+15625\,a^4\,b^4-2000\,a^2\,b^6+64\,b^8,d,k\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-41803776000\,a^{40}\,b^6+713536708608\,a^{38}\,b^8-5617221156864\,a^{36}\,b^{10}+27130620764160\,a^{34}\,b^{12}-90108039168000\,a^{32}\,b^{14}+218398602240000\,a^{30}\,b^{16}-399760062234624\,a^{28}\,b^{18}+563713761042432\,a^{26}\,b^{20}-618699706859520\,a^{24}\,b^{22}+529923028377600\,a^{22}\,b^{24}-352655758540800\,a^{20}\,b^{26}+180165872001024\,a^{18}\,b^{28}-69150635753472\,a^{16}\,b^{30}+19250011791360\,a^{14}\,b^{32}-3672461721600\,a^{12}\,b^{34}+437297356800\,a^{10}\,b^{36}-27805483008\,a^8\,b^{38}+764411904\,a^6\,b^{40}\right)-\mathrm{root}\left(5314410\,a^{16}\,b^4\,d^6-5314410\,a^{14}\,b^6\,d^6-2657205\,a^{18}\,b^2\,d^6+2657205\,a^{12}\,b^8\,d^6-531441\,a^{10}\,b^{10}\,d^6+531441\,a^{20}\,d^6+11514555\,a^{12}\,b^4\,d^4+2066715\,a^{14}\,b^2\,d^4+1062882\,a^{10}\,b^6\,d^4-295245\,a^8\,b^8\,d^4+984150\,a^8\,b^4\,d^2-98415\,a^6\,b^6\,d^2+15625\,a^4\,b^4-2000\,a^2\,b^6+64\,b^8,d,k\right)\,\left(\mathrm{root}\left(5314410\,a^{16}\,b^4\,d^6-5314410\,a^{14}\,b^6\,d^6-2657205\,a^{18}\,b^2\,d^6+2657205\,a^{12}\,b^8\,d^6-531441\,a^{10}\,b^{10}\,d^6+531441\,a^{20}\,d^6+11514555\,a^{12}\,b^4\,d^4+2066715\,a^{14}\,b^2\,d^4+1062882\,a^{10}\,b^6\,d^4-295245\,a^8\,b^8\,d^4+984150\,a^8\,b^4\,d^2-98415\,a^6\,b^6\,d^2+15625\,a^4\,b^4-2000\,a^2\,b^6+64\,b^8,d,k\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12093235200\,a^{46}\,b^4-976165945344\,a^{44}\,b^6+10565134000128\,a^{42}\,b^8-52028967665664\,a^{40}\,b^{10}+136937506922496\,a^{38}\,b^{12}-150898421366784\,a^{36}\,b^{14}-238981192998912\,a^{34}\,b^{16}+1359808836452352\,a^{32}\,b^{18}-3009938035433472\,a^{30}\,b^{20}+4311710468702208\,a^{28}\,b^{22}-4413464400863232\,a^{26}\,b^{24}+3327952874029056\,a^{24}\,b^{26}-1854140141887488\,a^{22}\,b^{28}+750889290203136\,a^{20}\,b^{30}-212750482120704\,a^{18}\,b^{32}+39183049506816\,a^{16}\,b^{34}-4039140556800\,a^{14}\,b^{36}+157695787008\,a^{12}\,b^{38}\right)-\mathrm{root}\left(5314410\,a^{16}\,b^4\,d^6-5314410\,a^{14}\,b^6\,d^6-2657205\,a^{18}\,b^2\,d^6+2657205\,a^{12}\,b^8\,d^6-531441\,a^{10}\,b^{10}\,d^6+531441\,a^{20}\,d^6+11514555\,a^{12}\,b^4\,d^4+2066715\,a^{14}\,b^2\,d^4+1062882\,a^{10}\,b^6\,d^4-295245\,a^8\,b^8\,d^4+984150\,a^8\,b^4\,d^2-98415\,a^6\,b^6\,d^2+15625\,a^4\,b^4-2000\,a^2\,b^6+64\,b^8,d,k\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-34828517376\,a^{47}\,b^5+52242776064\,a^{45}\,b^7+3970450980864\,a^{43}\,b^9-42212163059712\,a^{41}\,b^{11}+227778503639040\,a^{39}\,b^{13}-806001549115392\,a^{37}\,b^{15}+2053768012627968\,a^{35}\,b^{17}-3949971812646912\,a^{33}\,b^{19}+5886924977995776\,a^{31}\,b^{21}-6897962008903680\,a^{29}\,b^{23}+6394933732442112\,a^{27}\,b^{25}-4688893637296128\,a^{25}\,b^{27}+2700324609196032\,a^{23}\,b^{29}-1203882531618816\,a^{21}\,b^{31}+405403942256640\,a^{19}\,b^{33}-99052303417344\,a^{17}\,b^{35}+16404231684096\,a^{15}\,b^{37}-1619526057984\,a^{13}\,b^{39}+69657034752\,a^{11}\,b^{41}\right)+8707129344\,a^{12}\,b^{40}-470184984576\,a^{14}\,b^{38}+6308315209728\,a^{16}\,b^{36}-44092902998016\,a^{18}\,b^{34}+197477693521920\,a^{20}\,b^{32}-623151832891392\,a^{22}\,b^{30}+1459506434899968\,a^{24}\,b^{28}-2616109254180864\,a^{26}\,b^{26}+3653180601827328\,a^{28}\,b^{24}-4009284777738240\,a^{30}\,b^{22}+3462677318909952\,a^{32}\,b^{20}-2339013569937408\,a^{34}\,b^{18}+1217047711186944\,a^{36}\,b^{16}-473946464452608\,a^{38}\,b^{14}+130868154040320\,a^{40}\,b^{12}-22777850363904\,a^{42}\,b^{10}+1645647446016\,a^{44}\,b^8+156728328192\,a^{46}\,b^6-30474952704\,a^{48}\,b^4+\mathrm{root}\left(5314410\,a^{16}\,b^4\,d^6-5314410\,a^{14}\,b^6\,d^6-2657205\,a^{18}\,b^2\,d^6+2657205\,a^{12}\,b^8\,d^6-531441\,a^{10}\,b^{10}\,d^6+531441\,a^{20}\,d^6+11514555\,a^{12}\,b^4\,d^4+2066715\,a^{14}\,b^2\,d^4+1062882\,a^{10}\,b^6\,d^4-295245\,a^8\,b^8\,d^4+984150\,a^8\,b^4\,d^2-98415\,a^6\,b^6\,d^2+15625\,a^4\,b^4-2000\,a^2\,b^6+64\,b^8,d,k\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(39182082048\,a^{50}\,b^4-705277476864\,a^{48}\,b^6+5994858553344\,a^{46}\,b^8-31972578951168\,a^{44}\,b^{10}+119897171066880\,a^{42}\,b^{12}-335712078987264\,a^{40}\,b^{14}+727376171139072\,a^{38}\,b^{16}-1246930579095552\,a^{36}\,b^{18}+1714529546256384\,a^{34}\,b^{20}-1905032829173760\,a^{32}\,b^{22}+1714529546256384\,a^{30}\,b^{24}-1246930579095552\,a^{28}\,b^{26}+727376171139072\,a^{26}\,b^{28}-335712078987264\,a^{24}\,b^{30}+119897171066880\,a^{22}\,b^{32}-31972578951168\,a^{20}\,b^{34}+5994858553344\,a^{18}\,b^{36}-705277476864\,a^{16}\,b^{38}+39182082048\,a^{14}\,b^{40}\right)+156728328192\,a^{13}\,b^{41}-2938656153600\,a^{15}\,b^{39}+26095266643968\,a^{17}\,b^{37}-145874891464704\,a^{19}\,b^{35}+575506421121024\,a^{21}\,b^{33}-1702539829149696\,a^{23}\,b^{31}+3916640921518080\,a^{25}\,b^{29}-7169850829799424\,a^{27}\,b^{27}+10598909922312192\,a^{29}\,b^{25}-12763719955464192\,a^{31}\,b^{23}+12573216672546816\,a^{33}\,b^{21}-10131310955151360\,a^{35}\,b^{19}+6650296421842944\,a^{37}\,b^{17}-3524976829366272\,a^{39}\,b^{15}+1486724921229312\,a^{41}\,b^{13}-487581829005312\,a^{43}\,b^{11}+119897171066880\,a^{45}\,b^9-20805685567488\,a^{47}\,b^7+2272560758784\,a^{49}\,b^5-117546246144\,a^{51}\,b^3\right)\right)-59982446592\,a^{11}\,b^{39}+1080651497472\,a^{13}\,b^{37}-6860250464256\,a^{15}\,b^{35}+16482112118784\,a^{17}\,b^{33}+27170113388544\,a^{19}\,b^{31}-327284061511680\,a^{21}\,b^{29}+1194949984370688\,a^{23}\,b^{27}-2698934854606848\,a^{25}\,b^{25}+4276847122808832\,a^{27}\,b^{23}-4968511002943488\,a^{29}\,b^{21}+4288329891495936\,a^{31}\,b^{19}-2730918075604992\,a^{33}\,b^{17}+1245220111908864\,a^{35}\,b^{15}-377418744815616\,a^{37}\,b^{13}+60571629010944\,a^{39}\,b^{11}+1483598094336\,a^{41}\,b^9-2465085063168\,a^{43}\,b^7+316842762240\,a^{45}\,b^5\right)-1719926784\,a^8\,b^{40}+52457766912\,a^{10}\,b^{38}-657657004032\,a^{12}\,b^{36}+4778655326208\,a^{14}\,b^{34}-23130112868352\,a^{16}\,b^{32}+80237540597760\,a^{18}\,b^{30}-208280123670528\,a^{20}\,b^{28}+415493301510144\,a^{22}\,b^{26}-647354535100416\,a^{24}\,b^{24}+794486155567104\,a^{26}\,b^{22}-769729798176768\,a^{28}\,b^{20}+586362545233920\,a^{30}\,b^{18}-347391134318592\,a^{32}\,b^{16}+156884680286208\,a^{34}\,b^{14}-52204937674752\,a^{36}\,b^{12}+12071252385792\,a^{38}\,b^{10}-1732933730304\,a^{40}\,b^8+116363796480\,a^{42}\,b^6-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-26873856000\,a^{43}\,b^5-345490292736\,a^{41}\,b^7+7499310759936\,a^{39}\,b^9-53644731383808\,a^{37}\,b^{11}+221032950792192\,a^{35}\,b^{13}-608856446435328\,a^{33}\,b^{15}+1197522672353280\,a^{31}\,b^{17}-1736372938899456\,a^{29}\,b^{19}+1878255074082816\,a^{27}\,b^{21}-1507393926365184\,a^{25}\,b^{23}+871706622099456\,a^{23}\,b^{25}-334332052733952\,a^{21}\,b^{27}+61196714901504\,a^{19}\,b^{29}+12486453460992\,a^{17}\,b^{31}-11619395371008\,a^{15}\,b^{33}+3308494159872\,a^{13}\,b^{35}-436216430592\,a^{11}\,b^{37}+19779158016\,a^9\,b^{39}\right)\right)+95551488\,a^7\,b^{39}+6640828416\,a^9\,b^{37}-187507851264\,a^{11}\,b^{35}+1874314100736\,a^{13}\,b^{33}-10498349481984\,a^{15}\,b^{31}+38554452099072\,a^{17}\,b^{29}-100273965023232\,a^{19}\,b^{27}+192807351779328\,a^{21}\,b^{25}-280858991542272\,a^{23}\,b^{23}+313783776903168\,a^{25}\,b^{21}-269640960196608\,a^{27}\,b^{19}+177127448150016\,a^{29}\,b^{17}-87483347288064\,a^{31}\,b^{15}+31483928641536\,a^{33}\,b^{13}-7801408733184\,a^{35}\,b^{11}+1191025410048\,a^{37}\,b^9-84503347200\,a^{39}\,b^7\right)-59837128704\,a^{10}\,b^{34}+363432738816\,a^{12}\,b^{32}-1444185759744\,a^{14}\,b^{30}+4071882866688\,a^{16}\,b^{28}-8529191903232\,a^{18}\,b^{26}+13638053265408\,a^{20}\,b^{24}-16903052255232\,a^{22}\,b^{22}+16345206079488\,a^{24}\,b^{20}-12319205842944\,a^{26}\,b^{18}+7172803362816\,a^{28}\,b^{16}-3166919368704\,a^{30}\,b^{14}+1026022588416\,a^{32}\,b^{12}-230217375744\,a^{34}\,b^{10}+31983206400\,a^{36}\,b^8-2073600000\,a^{38}\,b^6-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-29859840000\,a^{37}\,b^7+419948789760\,a^{35}\,b^9-2743999856640\,a^{33}\,b^{11}+11042885468160\,a^{31}\,b^{13}-30585314672640\,a^{29}\,b^{15}+61692340469760\,a^{27}\,b^{17}-93494981099520\,a^{25}\,b^{19}+108217793249280\,a^{23}\,b^{21}-96227753656320\,a^{21}\,b^{23}+65518222049280\,a^{19}\,b^{25}-33715581419520\,a^{17}\,b^{27}+12781922549760\,a^{15}\,b^{29}-3412860272640\,a^{13}\,b^{31}+591941468160\,a^{11}\,b^{33}-56614256640\,a^9\,b^{35}+1911029760\,a^7\,b^{37}\right)\right)\,\mathrm{root}\left(5314410\,a^{16}\,b^4\,d^6-5314410\,a^{14}\,b^6\,d^6-2657205\,a^{18}\,b^2\,d^6+2657205\,a^{12}\,b^8\,d^6-531441\,a^{10}\,b^{10}\,d^6+531441\,a^{20}\,d^6+11514555\,a^{12}\,b^4\,d^4+2066715\,a^{14}\,b^2\,d^4+1062882\,a^{10}\,b^6\,d^4-295245\,a^8\,b^8\,d^4+984150\,a^8\,b^4\,d^2-98415\,a^6\,b^6\,d^2+15625\,a^4\,b^4-2000\,a^2\,b^6+64\,b^8,d,k\right)}{d}-\frac{\frac{2\,\left(7\,a^2\,b+2\,b^3\right)}{3\,{\left(a^2-b^2\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5\,a^2\,b+4\,b^3\right)}{3\,{\left(a^2-b^2\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(19\,a^2\,b+8\,b^3\right)}{3\,{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(7\,a^2\,b+38\,b^3\right)}{3\,{\left(a^2-b^2\right)}^2}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-a^4+5\,a^2\,b^2+b^4\right)}{a\,{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,a^4+11\,a^2\,b^2+7\,b^4\right)}{3\,a\,{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(3\,a^4+5\,a^2\,b^2+b^4\right)}{3\,a\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^4+5\,a^2\,b^2+b^4\right)}{3\,a\,{\left(a^2-b^2\right)}^2}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",0,"symsum(log(5479612416*a^8*b^36 - 180486144*a^6*b^38 - root(5314410*a^16*b^4*d^6 - 5314410*a^14*b^6*d^6 - 2657205*a^18*b^2*d^6 + 2657205*a^12*b^8*d^6 - 531441*a^10*b^10*d^6 + 531441*a^20*d^6 + 11514555*a^12*b^4*d^4 + 2066715*a^14*b^2*d^4 + 1062882*a^10*b^6*d^4 - 295245*a^8*b^8*d^4 + 984150*a^8*b^4*d^2 - 98415*a^6*b^6*d^2 + 15625*a^4*b^4 - 2000*a^2*b^6 + 64*b^8, d, k)*(tan(c/2 + (d*x)/2)*(764411904*a^6*b^40 - 27805483008*a^8*b^38 + 437297356800*a^10*b^36 - 3672461721600*a^12*b^34 + 19250011791360*a^14*b^32 - 69150635753472*a^16*b^30 + 180165872001024*a^18*b^28 - 352655758540800*a^20*b^26 + 529923028377600*a^22*b^24 - 618699706859520*a^24*b^22 + 563713761042432*a^26*b^20 - 399760062234624*a^28*b^18 + 218398602240000*a^30*b^16 - 90108039168000*a^32*b^14 + 27130620764160*a^34*b^12 - 5617221156864*a^36*b^10 + 713536708608*a^38*b^8 - 41803776000*a^40*b^6) - root(5314410*a^16*b^4*d^6 - 5314410*a^14*b^6*d^6 - 2657205*a^18*b^2*d^6 + 2657205*a^12*b^8*d^6 - 531441*a^10*b^10*d^6 + 531441*a^20*d^6 + 11514555*a^12*b^4*d^4 + 2066715*a^14*b^2*d^4 + 1062882*a^10*b^6*d^4 - 295245*a^8*b^8*d^4 + 984150*a^8*b^4*d^2 - 98415*a^6*b^6*d^2 + 15625*a^4*b^4 - 2000*a^2*b^6 + 64*b^8, d, k)*(root(5314410*a^16*b^4*d^6 - 5314410*a^14*b^6*d^6 - 2657205*a^18*b^2*d^6 + 2657205*a^12*b^8*d^6 - 531441*a^10*b^10*d^6 + 531441*a^20*d^6 + 11514555*a^12*b^4*d^4 + 2066715*a^14*b^2*d^4 + 1062882*a^10*b^6*d^4 - 295245*a^8*b^8*d^4 + 984150*a^8*b^4*d^2 - 98415*a^6*b^6*d^2 + 15625*a^4*b^4 - 2000*a^2*b^6 + 64*b^8, d, k)*(tan(c/2 + (d*x)/2)*(157695787008*a^12*b^38 - 4039140556800*a^14*b^36 + 39183049506816*a^16*b^34 - 212750482120704*a^18*b^32 + 750889290203136*a^20*b^30 - 1854140141887488*a^22*b^28 + 3327952874029056*a^24*b^26 - 4413464400863232*a^26*b^24 + 4311710468702208*a^28*b^22 - 3009938035433472*a^30*b^20 + 1359808836452352*a^32*b^18 - 238981192998912*a^34*b^16 - 150898421366784*a^36*b^14 + 136937506922496*a^38*b^12 - 52028967665664*a^40*b^10 + 10565134000128*a^42*b^8 - 976165945344*a^44*b^6 + 12093235200*a^46*b^4) - root(5314410*a^16*b^4*d^6 - 5314410*a^14*b^6*d^6 - 2657205*a^18*b^2*d^6 + 2657205*a^12*b^8*d^6 - 531441*a^10*b^10*d^6 + 531441*a^20*d^6 + 11514555*a^12*b^4*d^4 + 2066715*a^14*b^2*d^4 + 1062882*a^10*b^6*d^4 - 295245*a^8*b^8*d^4 + 984150*a^8*b^4*d^2 - 98415*a^6*b^6*d^2 + 15625*a^4*b^4 - 2000*a^2*b^6 + 64*b^8, d, k)*(tan(c/2 + (d*x)/2)*(69657034752*a^11*b^41 - 1619526057984*a^13*b^39 + 16404231684096*a^15*b^37 - 99052303417344*a^17*b^35 + 405403942256640*a^19*b^33 - 1203882531618816*a^21*b^31 + 2700324609196032*a^23*b^29 - 4688893637296128*a^25*b^27 + 6394933732442112*a^27*b^25 - 6897962008903680*a^29*b^23 + 5886924977995776*a^31*b^21 - 3949971812646912*a^33*b^19 + 2053768012627968*a^35*b^17 - 806001549115392*a^37*b^15 + 227778503639040*a^39*b^13 - 42212163059712*a^41*b^11 + 3970450980864*a^43*b^9 + 52242776064*a^45*b^7 - 34828517376*a^47*b^5) + 8707129344*a^12*b^40 - 470184984576*a^14*b^38 + 6308315209728*a^16*b^36 - 44092902998016*a^18*b^34 + 197477693521920*a^20*b^32 - 623151832891392*a^22*b^30 + 1459506434899968*a^24*b^28 - 2616109254180864*a^26*b^26 + 3653180601827328*a^28*b^24 - 4009284777738240*a^30*b^22 + 3462677318909952*a^32*b^20 - 2339013569937408*a^34*b^18 + 1217047711186944*a^36*b^16 - 473946464452608*a^38*b^14 + 130868154040320*a^40*b^12 - 22777850363904*a^42*b^10 + 1645647446016*a^44*b^8 + 156728328192*a^46*b^6 - 30474952704*a^48*b^4 + root(5314410*a^16*b^4*d^6 - 5314410*a^14*b^6*d^6 - 2657205*a^18*b^2*d^6 + 2657205*a^12*b^8*d^6 - 531441*a^10*b^10*d^6 + 531441*a^20*d^6 + 11514555*a^12*b^4*d^4 + 2066715*a^14*b^2*d^4 + 1062882*a^10*b^6*d^4 - 295245*a^8*b^8*d^4 + 984150*a^8*b^4*d^2 - 98415*a^6*b^6*d^2 + 15625*a^4*b^4 - 2000*a^2*b^6 + 64*b^8, d, k)*(tan(c/2 + (d*x)/2)*(39182082048*a^14*b^40 - 705277476864*a^16*b^38 + 5994858553344*a^18*b^36 - 31972578951168*a^20*b^34 + 119897171066880*a^22*b^32 - 335712078987264*a^24*b^30 + 727376171139072*a^26*b^28 - 1246930579095552*a^28*b^26 + 1714529546256384*a^30*b^24 - 1905032829173760*a^32*b^22 + 1714529546256384*a^34*b^20 - 1246930579095552*a^36*b^18 + 727376171139072*a^38*b^16 - 335712078987264*a^40*b^14 + 119897171066880*a^42*b^12 - 31972578951168*a^44*b^10 + 5994858553344*a^46*b^8 - 705277476864*a^48*b^6 + 39182082048*a^50*b^4) + 156728328192*a^13*b^41 - 2938656153600*a^15*b^39 + 26095266643968*a^17*b^37 - 145874891464704*a^19*b^35 + 575506421121024*a^21*b^33 - 1702539829149696*a^23*b^31 + 3916640921518080*a^25*b^29 - 7169850829799424*a^27*b^27 + 10598909922312192*a^29*b^25 - 12763719955464192*a^31*b^23 + 12573216672546816*a^33*b^21 - 10131310955151360*a^35*b^19 + 6650296421842944*a^37*b^17 - 3524976829366272*a^39*b^15 + 1486724921229312*a^41*b^13 - 487581829005312*a^43*b^11 + 119897171066880*a^45*b^9 - 20805685567488*a^47*b^7 + 2272560758784*a^49*b^5 - 117546246144*a^51*b^3)) - 59982446592*a^11*b^39 + 1080651497472*a^13*b^37 - 6860250464256*a^15*b^35 + 16482112118784*a^17*b^33 + 27170113388544*a^19*b^31 - 327284061511680*a^21*b^29 + 1194949984370688*a^23*b^27 - 2698934854606848*a^25*b^25 + 4276847122808832*a^27*b^23 - 4968511002943488*a^29*b^21 + 4288329891495936*a^31*b^19 - 2730918075604992*a^33*b^17 + 1245220111908864*a^35*b^15 - 377418744815616*a^37*b^13 + 60571629010944*a^39*b^11 + 1483598094336*a^41*b^9 - 2465085063168*a^43*b^7 + 316842762240*a^45*b^5) - 1719926784*a^8*b^40 + 52457766912*a^10*b^38 - 657657004032*a^12*b^36 + 4778655326208*a^14*b^34 - 23130112868352*a^16*b^32 + 80237540597760*a^18*b^30 - 208280123670528*a^20*b^28 + 415493301510144*a^22*b^26 - 647354535100416*a^24*b^24 + 794486155567104*a^26*b^22 - 769729798176768*a^28*b^20 + 586362545233920*a^30*b^18 - 347391134318592*a^32*b^16 + 156884680286208*a^34*b^14 - 52204937674752*a^36*b^12 + 12071252385792*a^38*b^10 - 1732933730304*a^40*b^8 + 116363796480*a^42*b^6 - tan(c/2 + (d*x)/2)*(19779158016*a^9*b^39 - 436216430592*a^11*b^37 + 3308494159872*a^13*b^35 - 11619395371008*a^15*b^33 + 12486453460992*a^17*b^31 + 61196714901504*a^19*b^29 - 334332052733952*a^21*b^27 + 871706622099456*a^23*b^25 - 1507393926365184*a^25*b^23 + 1878255074082816*a^27*b^21 - 1736372938899456*a^29*b^19 + 1197522672353280*a^31*b^17 - 608856446435328*a^33*b^15 + 221032950792192*a^35*b^13 - 53644731383808*a^37*b^11 + 7499310759936*a^39*b^9 - 345490292736*a^41*b^7 - 26873856000*a^43*b^5)) + 95551488*a^7*b^39 + 6640828416*a^9*b^37 - 187507851264*a^11*b^35 + 1874314100736*a^13*b^33 - 10498349481984*a^15*b^31 + 38554452099072*a^17*b^29 - 100273965023232*a^19*b^27 + 192807351779328*a^21*b^25 - 280858991542272*a^23*b^23 + 313783776903168*a^25*b^21 - 269640960196608*a^27*b^19 + 177127448150016*a^29*b^17 - 87483347288064*a^31*b^15 + 31483928641536*a^33*b^13 - 7801408733184*a^35*b^11 + 1191025410048*a^37*b^9 - 84503347200*a^39*b^7) - 59837128704*a^10*b^34 + 363432738816*a^12*b^32 - 1444185759744*a^14*b^30 + 4071882866688*a^16*b^28 - 8529191903232*a^18*b^26 + 13638053265408*a^20*b^24 - 16903052255232*a^22*b^22 + 16345206079488*a^24*b^20 - 12319205842944*a^26*b^18 + 7172803362816*a^28*b^16 - 3166919368704*a^30*b^14 + 1026022588416*a^32*b^12 - 230217375744*a^34*b^10 + 31983206400*a^36*b^8 - 2073600000*a^38*b^6 - tan(c/2 + (d*x)/2)*(1911029760*a^7*b^37 - 56614256640*a^9*b^35 + 591941468160*a^11*b^33 - 3412860272640*a^13*b^31 + 12781922549760*a^15*b^29 - 33715581419520*a^17*b^27 + 65518222049280*a^19*b^25 - 96227753656320*a^21*b^23 + 108217793249280*a^23*b^21 - 93494981099520*a^25*b^19 + 61692340469760*a^27*b^17 - 30585314672640*a^29*b^15 + 11042885468160*a^31*b^13 - 2743999856640*a^33*b^11 + 419948789760*a^35*b^9 - 29859840000*a^37*b^7))*root(5314410*a^16*b^4*d^6 - 5314410*a^14*b^6*d^6 - 2657205*a^18*b^2*d^6 + 2657205*a^12*b^8*d^6 - 531441*a^10*b^10*d^6 + 531441*a^20*d^6 + 11514555*a^12*b^4*d^4 + 2066715*a^14*b^2*d^4 + 1062882*a^10*b^6*d^4 - 295245*a^8*b^8*d^4 + 984150*a^8*b^4*d^2 - 98415*a^6*b^6*d^2 + 15625*a^4*b^4 - 2000*a^2*b^6 + 64*b^8, d, k), k, 1, 6)/d - ((2*(7*a^2*b + 2*b^3))/(3*(a^2 - b^2)^2) + (2*tan(c/2 + (d*x)/2)^6*(5*a^2*b + 4*b^3))/(3*(a^2 - b^2)^2) + (2*tan(c/2 + (d*x)/2)^2*(19*a^2*b + 8*b^3))/(3*(a^2 - b^2)^2) - (2*tan(c/2 + (d*x)/2)^4*(7*a^2*b + 38*b^3))/(3*(a^2 - b^2)^2) + (6*tan(c/2 + (d*x)/2)^3*(b^4 - a^4 + 5*a^2*b^2))/(a*(a^2 - b^2)^2) - (2*tan(c/2 + (d*x)/2)^5*(9*a^4 + 7*b^4 + 11*a^2*b^2))/(3*a*(a^2 - b^2)^2) - (2*tan(c/2 + (d*x)/2)^7*(3*a^4 + b^4 + 5*a^2*b^2))/(3*a*(a^4 + b^4 - 2*a^2*b^2)) - (2*tan(c/2 + (d*x)/2)*(3*a^4 + b^4 + 5*a^2*b^2))/(3*a*(a^2 - b^2)^2))/(d*(a + 2*a*tan(c/2 + (d*x)/2)^2 - 2*a*tan(c/2 + (d*x)/2)^6 - a*tan(c/2 + (d*x)/2)^8 + 8*b*tan(c/2 + (d*x)/2)^3 - 8*b*tan(c/2 + (d*x)/2)^5))","B"
403,1,4657,26,25.436751,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x)^3)^2),x)","\frac{\sum _{k=1}^6\ln\left(26838024192\,a^8\,b^{54}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(341397504000\,a^{51}\,b^{11}-7177310208000\,a^{49}\,b^{13}+71860690944000\,a^{47}\,b^{15}-455730831360000\,a^{45}\,b^{17}+2053854351360000\,a^{43}\,b^{19}-6994754113536000\,a^{41}\,b^{21}+18687625592832000\,a^{39}\,b^{23}-40129785593856000\,a^{37}\,b^{25}+70396872007680000\,a^{35}\,b^{27}-101967282708480000\,a^{33}\,b^{29}+122756816093184000\,a^{31}\,b^{31}-123224906907648000\,a^{29}\,b^{33}+103155513237504000\,a^{27}\,b^{35}-71811432161280000\,a^{25}\,b^{37}+41318016122880000\,a^{23}\,b^{39}-19451488075776000\,a^{21}\,b^{41}+7379181637632000\,a^{19}\,b^{43}-2205295497216000\,a^{17}\,b^{45}+501714984960000\,a^{15}\,b^{47}-82283765760000\,a^{13}\,b^{49}+8841498624000\,a^{11}\,b^{51}-508612608000\,a^9\,b^{53}+7962624000\,a^7\,b^{55}\right)-392822784\,a^6\,b^{56}-\mathrm{root}\left(18600435\,a^{18}\,b^6\,d^6-18600435\,a^{16}\,b^8\,d^6-11160261\,a^{20}\,b^4\,d^6+11160261\,a^{14}\,b^{10}\,d^6+3720087\,a^{22}\,b^2\,d^6-3720087\,a^{12}\,b^{12}\,d^6+531441\,a^{10}\,b^{14}\,d^6-531441\,a^{24}\,d^6-173879622\,a^{14}\,b^6\,d^4-155830311\,a^{12}\,b^8\,d^4-23225940\,a^{16}\,b^4\,d^4-6475707\,a^{10}\,b^{10}\,d^4+688905\,a^8\,b^{12}\,d^4-11565585\,a^8\,b^8\,d^2+3750705\,a^{10}\,b^6\,d^2+433755\,a^6\,b^{10}\,d^2-117649\,a^4\,b^8+5488\,a^2\,b^{10}-64\,b^{12},d,k\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-14338695168\,a^{56}\,b^8+2463538323456\,a^{54}\,b^{10}-49418889191424\,a^{52}\,b^{12}+494158536400896\,a^{50}\,b^{14}-3172130021597184\,a^{48}\,b^{16}+14569217952178176\,a^{46}\,b^{18}-50807786761396224\,a^{44}\,b^{20}+139566181489975296\,a^{42}\,b^{22}-309384400894377984\,a^{40}\,b^{24}+562635592701198336\,a^{38}\,b^{26}-848821864657895424\,a^{36}\,b^{28}+1070100496146087936\,a^{34}\,b^{30}-1132028278205497344\,a^{32}\,b^{32}+1006348379003928576\,a^{30}\,b^{34}-750973819695611904\,a^{28}\,b^{36}+468678655511248896\,a^{26}\,b^{38}-243004699498881024\,a^{24}\,b^{40}+103613766013034496\,a^{22}\,b^{42}-35797302942326784\,a^{20}\,b^{44}+9810082122817536\,a^{18}\,b^{46}-2067381036048384\,a^{16}\,b^{48}+319697763065856\,a^{14}\,b^{50}-33643637121024\,a^{12}\,b^{52}+2110475575296\,a^{10}\,b^{54}-61439606784\,a^8\,b^{56}+764411904\,a^6\,b^{58}\right)+95551488\,a^7\,b^{57}+35879583744\,a^9\,b^{55}-1812522147840\,a^{11}\,b^{53}+29896430247936\,a^{13}\,b^{51}-273690491977728\,a^{15}\,b^{49}+1665068560662528\,a^{17}\,b^{47}-7358934856605696\,a^{19}\,b^{45}+24887080515133440\,a^{21}\,b^{43}-66575487905316864\,a^{23}\,b^{41}+144045035942510592\,a^{25}\,b^{39}-255939373888192512\,a^{27}\,b^{37}+377317716543258624\,a^{29}\,b^{35}-464589495171809280\,a^{31}\,b^{33}+479470084160126976\,a^{33}\,b^{31}-415092174607761408\,a^{35}\,b^{29}+300910589340991488\,a^{37}\,b^{27}-181823043267035136\,a^{39}\,b^{25}+90863416678809600\,a^{41}\,b^{23}-37111903240495104\,a^{43}\,b^{21}+12175612162301952\,a^{45}\,b^{19}-3127996467412992\,a^{47}\,b^{17}+605418993598464\,a^{49}\,b^{15}-82897275985920\,a^{51}\,b^{13}+7145262637056\,a^{53}\,b^{11}-290870673408\,a^{55}\,b^9+\mathrm{root}\left(18600435\,a^{18}\,b^6\,d^6-18600435\,a^{16}\,b^8\,d^6-11160261\,a^{20}\,b^4\,d^6+11160261\,a^{14}\,b^{10}\,d^6+3720087\,a^{22}\,b^2\,d^6-3720087\,a^{12}\,b^{12}\,d^6+531441\,a^{10}\,b^{14}\,d^6-531441\,a^{24}\,d^6-173879622\,a^{14}\,b^6\,d^4-155830311\,a^{12}\,b^8\,d^4-23225940\,a^{16}\,b^4\,d^4-6475707\,a^{10}\,b^{10}\,d^4+688905\,a^8\,b^{12}\,d^4-11565585\,a^8\,b^8\,d^2+3750705\,a^{10}\,b^6\,d^2+433755\,a^6\,b^{10}\,d^2-117649\,a^4\,b^8+5488\,a^2\,b^{10}-64\,b^{12},d,k\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-73741860864\,a^{59}\,b^7+2461645209600\,a^{57}\,b^9-25165538721792\,a^{55}\,b^{11}+91463986446336\,a^{53}\,b^{13}+316457498640384\,a^{51}\,b^{15}-5445156193763328\,a^{49}\,b^{17}+32863270985072640\,a^{47}\,b^{19}-128854679612424192\,a^{45}\,b^{21}+372789943915216896\,a^{43}\,b^{23}-839694861496221696\,a^{41}\,b^{25}+1515332894269243392\,a^{39}\,b^{27}-2227622993351147520\,a^{37}\,b^{29}+2692902186903011328\,a^{35}\,b^{31}-2688523449382600704\,a^{33}\,b^{33}+2216700870917750784\,a^{31}\,b^{35}-1502808604998893568\,a^{29}\,b^{37}+829818883454238720\,a^{27}\,b^{39}-367050326151462912\,a^{25}\,b^{41}+126404118900965376\,a^{23}\,b^{43}-32144913894998016\,a^{21}\,b^{45}+5337288405614592\,a^{19}\,b^{47}-330769869373440\,a^{17}\,b^{49}-78629462802432\,a^{15}\,b^{51}+21725255172096\,a^{13}\,b^{53}-1988020371456\,a^{11}\,b^{55}+45578059776\,a^9\,b^{57}\right)+\mathrm{root}\left(18600435\,a^{18}\,b^6\,d^6-18600435\,a^{16}\,b^8\,d^6-11160261\,a^{20}\,b^4\,d^6+11160261\,a^{14}\,b^{10}\,d^6+3720087\,a^{22}\,b^2\,d^6-3720087\,a^{12}\,b^{12}\,d^6+531441\,a^{10}\,b^{14}\,d^6-531441\,a^{24}\,d^6-173879622\,a^{14}\,b^6\,d^4-155830311\,a^{12}\,b^8\,d^4-23225940\,a^{16}\,b^4\,d^4-6475707\,a^{10}\,b^{10}\,d^4+688905\,a^8\,b^{12}\,d^4-11565585\,a^8\,b^8\,d^2+3750705\,a^{10}\,b^6\,d^2+433755\,a^6\,b^{10}\,d^2-117649\,a^4\,b^8+548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\frac{d\,x}{2}\right)}^9\,\left(-7\,a^6+24\,a^4\,b^2+19\,a^2\,b^4+9\,b^6\right)}{3\,a\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(3\,a^6+26\,a^4\,b^2+179\,a^2\,b^4+17\,b^6\right)}{3\,a\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(7\,a^6+8\,a^4\,b^2+285\,a^2\,b^4+15\,b^6\right)}{3\,a\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-3\,a^6+22\,a^4\,b^2+277\,a^2\,b^4+19\,b^6\right)}{3\,a\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3\,a^6+28\,a^4\,b^2+19\,a^2\,b^4+b^6\right)}{3\,a\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-24\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+a\right)}","Not used",0,"symsum(log(26838024192*a^8*b^54 - tan(c/2 + (d*x)/2)*(7962624000*a^7*b^55 - 508612608000*a^9*b^53 + 8841498624000*a^11*b^51 - 82283765760000*a^13*b^49 + 501714984960000*a^15*b^47 - 2205295497216000*a^17*b^45 + 7379181637632000*a^19*b^43 - 19451488075776000*a^21*b^41 + 41318016122880000*a^23*b^39 - 71811432161280000*a^25*b^37 + 103155513237504000*a^27*b^35 - 123224906907648000*a^29*b^33 + 122756816093184000*a^31*b^31 - 101967282708480000*a^33*b^29 + 70396872007680000*a^35*b^27 - 40129785593856000*a^37*b^25 + 18687625592832000*a^39*b^23 - 6994754113536000*a^41*b^21 + 2053854351360000*a^43*b^19 - 455730831360000*a^45*b^17 + 71860690944000*a^47*b^15 - 7177310208000*a^49*b^13 + 341397504000*a^51*b^11) - 392822784*a^6*b^56 - root(18600435*a^18*b^6*d^6 - 18600435*a^16*b^8*d^6 - 11160261*a^20*b^4*d^6 + 11160261*a^14*b^10*d^6 + 3720087*a^22*b^2*d^6 - 3720087*a^12*b^12*d^6 + 531441*a^10*b^14*d^6 - 531441*a^24*d^6 - 173879622*a^14*b^6*d^4 - 155830311*a^12*b^8*d^4 - 23225940*a^16*b^4*d^4 - 6475707*a^10*b^10*d^4 + 688905*a^8*b^12*d^4 - 11565585*a^8*b^8*d^2 + 3750705*a^10*b^6*d^2 + 433755*a^6*b^10*d^2 - 117649*a^4*b^8 + 5488*a^2*b^10 - 64*b^12, d, k)*(tan(c/2 + (d*x)/2)*(764411904*a^6*b^58 - 61439606784*a^8*b^56 + 2110475575296*a^10*b^54 - 33643637121024*a^12*b^52 + 319697763065856*a^14*b^50 - 2067381036048384*a^16*b^48 + 9810082122817536*a^18*b^46 - 35797302942326784*a^20*b^44 + 103613766013034496*a^22*b^42 - 243004699498881024*a^24*b^40 + 468678655511248896*a^26*b^38 - 750973819695611904*a^28*b^36 + 1006348379003928576*a^30*b^34 - 1132028278205497344*a^32*b^32 + 1070100496146087936*a^34*b^30 - 848821864657895424*a^36*b^28 + 562635592701198336*a^38*b^26 - 309384400894377984*a^40*b^24 + 139566181489975296*a^42*b^22 - 50807786761396224*a^44*b^20 + 14569217952178176*a^46*b^18 - 3172130021597184*a^48*b^16 + 494158536400896*a^50*b^14 - 49418889191424*a^52*b^12 + 2463538323456*a^54*b^10 - 14338695168*a^56*b^8) + 95551488*a^7*b^57 + 35879583744*a^9*b^55 - 1812522147840*a^11*b^53 + 29896430247936*a^13*b^51 - 273690491977728*a^15*b^49 + 1665068560662528*a^17*b^47 - 7358934856605696*a^19*b^45 + 24887080515133440*a^21*b^43 - 66575487905316864*a^23*b^41 + 144045035942510592*a^25*b^39 - 255939373888192512*a^27*b^37 + 377317716543258624*a^29*b^35 - 464589495171809280*a^31*b^33 + 479470084160126976*a^33*b^31 - 415092174607761408*a^35*b^29 + 300910589340991488*a^37*b^27 - 181823043267035136*a^39*b^25 + 90863416678809600*a^41*b^23 - 37111903240495104*a^43*b^21 + 12175612162301952*a^45*b^19 - 3127996467412992*a^47*b^17 + 605418993598464*a^49*b^15 - 82897275985920*a^51*b^13 + 7145262637056*a^53*b^11 - 290870673408*a^55*b^9 + root(18600435*a^18*b^6*d^6 - 18600435*a^16*b^8*d^6 - 11160261*a^20*b^4*d^6 + 11160261*a^14*b^10*d^6 + 3720087*a^22*b^2*d^6 - 3720087*a^12*b^12*d^6 + 531441*a^10*b^14*d^6 - 531441*a^24*d^6 - 173879622*a^14*b^6*d^4 - 155830311*a^12*b^8*d^4 - 23225940*a^16*b^4*d^4 - 6475707*a^10*b^10*d^4 + 688905*a^8*b^12*d^4 - 11565585*a^8*b^8*d^2 + 3750705*a^10*b^6*d^2 + 433755*a^6*b^10*d^2 - 117649*a^4*b^8 + 5488*a^2*b^10 - 64*b^12, d, k)*(tan(c/2 + (d*x)/2)*(45578059776*a^9*b^57 - 1988020371456*a^11*b^55 + 21725255172096*a^13*b^53 - 78629462802432*a^15*b^51 - 330769869373440*a^17*b^49 + 5337288405614592*a^19*b^47 - 32144913894998016*a^21*b^45 + 126404118900965376*a^23*b^43 - 367050326151462912*a^25*b^41 + 829818883454238720*a^27*b^39 - 1502808604998893568*a^29*b^37 + 2216700870917750784*a^31*b^35 - 2688523449382600704*a^33*b^33 + 2692902186903011328*a^35*b^31 - 2227622993351147520*a^37*b^29 + 1515332894269243392*a^39*b^27 - 839694861496221696*a^41*b^25 + 372789943915216896*a^43*b^23 - 128854679612424192*a^45*b^21 + 32863270985072640*a^47*b^19 - 5445156193763328*a^49*b^17 + 316457498640384*a^51*b^15 + 91463986446336*a^53*b^13 - 25165538721792*a^55*b^11 + 2461645209600*a^57*b^9 - 73741860864*a^59*b^7) + root(18600435*a^18*b^6*d^6 - 18600435*a^16*b^8*d^6 - 11160261*a^20*b^4*d^6 + 11160261*a^14*b^10*d^6 + 3720087*a^22*b^2*d^6 - 3720087*a^12*b^12*d^6 + 531441*a^10*b^14*d^6 - 531441*a^24*d^6 - 173879622*a^14*b^6*d^4 - 155830311*a^12*b^8*d^4 - 23225940*a^16*b^4*d^4 - 6475707*a^10*b^10*d^4 + 688905*a^8*b^12*d^4 - 11565585*a^8*b^8*d^2 + 3750705*a^10*b^6*d^2 + 433755*a^6*b^10*d^2 - 117649*a^4*b^8 + 5488*a^2*b^10 - 64*b^12, d, k)*(root(18600435*a^18*b^6*d^6 - 18600435*a^16*b^8*d^6 - 11160261*a^20*b^4*d^6 + 11160261*a^14*b^10*d^6 + 3720087*a^22*b^2*d^6 - 3720087*a^12*b^12*d^6 + 531441*a^10*b^14*d^6 - 531441*a^24*d^6 - 173879622*a^14*b^6*d^4 - 155830311*a^12*b^8*d^4 - 23225940*a^16*b^4*d^4 - 6475707*a^10*b^10*d^4 + 688905*a^8*b^12*d^4 - 11565585*a^8*b^8*d^2 + 3750705*a^10*b^6*d^2 + 433755*a^6*b^10*d^2 - 117649*a^4*b^8 + 5488*a^2*b^10 - 64*b^12, d, k)*(tan(c/2 + (d*x)/2)*(69657034752*a^11*b^59 - 2855938424832*a^13*b^57 + 46200028299264*a^15*b^55 - 432918470983680*a^17*b^53 + 2732993758494720*a^19*b^51 - 12560556506480640*a^21*b^49 + 43925900257198080*a^23*b^47 - 119837962587340800*a^25*b^45 + 257651619562782720*a^27*b^43 - 433619569038458880*a^29*b^41 + 549558392034263040*a^31*b^39 - 452796847276032000*a^33*b^37 + 36223747782082560*a^35*b^35 + 641677817854033920*a^37*b^33 - 1337691257381191680*a^39*b^31 + 1759439177986867200*a^41*b^29 - 1756851767431004160*a^43*b^27 + 1404659530591764480*a^45*b^25 - 917046791277281280*a^47*b^23 + 491599995054981120*a^49*b^21 - 215796448806174720*a^51*b^19 + 76837281894236160*a^53*b^17 - 21824767985909760*a^55*b^15 + 4817480523448320*a^57*b^13 - 793393625825280*a^59*b^11 + 91181058490368*a^61*b^9 - 6460689973248*a^63*b^7 + 208971104256*a^65*b^5) + root(18600435*a^18*b^6*d^6 - 18600435*a^16*b^8*d^6 - 11160261*a^20*b^4*d^6 + 11160261*a^14*b^10*d^6 + 3720087*a^22*b^2*d^6 - 3720087*a^12*b^12*d^6 + 531441*a^10*b^14*d^6 - 531441*a^24*d^6 - 173879622*a^14*b^6*d^4 - 155830311*a^12*b^8*d^4 - 23225940*a^16*b^4*d^4 - 6475707*a^10*b^10*d^4 + 688905*a^8*b^12*d^4 - 11565585*a^8*b^8*d^2 + 3750705*a^10*b^6*d^2 + 433755*a^6*b^10*d^2 - 117649*a^4*b^8 + 5488*a^2*b^10 - 64*b^12, d, k)*(tan(c/2 + (d*x)/2)*(39182082048*a^14*b^58 - 1057916215296*a^16*b^56 + 13752910798848*a^18*b^54 - 114607589990400*a^20*b^52 + 687645539942400*a^22*b^50 - 3163169483735040*a^24*b^48 + 11598288107028480*a^26*b^46 - 34794864321085440*a^28*b^44 + 86987160802713600*a^30*b^42 - 183639561694617600*a^32*b^40 + 330551211050311680*a^34*b^38 - 510851871623208960*a^36*b^36 + 681135828830945280*a^38*b^34 - 785925956343398400*a^40*b^32 + 785925956343398400*a^42*b^30 - 681135828830945280*a^44*b^28 + 510851871623208960*a^46*b^26 - 330551211050311680*a^48*b^24 + 183639561694617600*a^50*b^22 - 86987160802713600*a^52*b^20 + 34794864321085440*a^54*b^18 - 11598288107028480*a^56*b^16 + 3163169483735040*a^58*b^14 - 687645539942400*a^60*b^12 + 114607589990400*a^62*b^10 - 13752910798848*a^64*b^8 + 1057916215296*a^66*b^6 - 39182082048*a^68*b^4) + 156728328192*a^13*b^59 - 4349211107328*a^15*b^57 + 58185391841280*a^17*b^55 - 499689092358144*a^19*b^53 + 3094404929740800*a^21*b^51 - 14715614554767360*a^23*b^49 + 55882660879319040*a^25*b^47 - 173974321605427200*a^27*b^45 + 452333236174110720*a^29*b^43 - 995519729186611200*a^31*b^41 + 1873123529285099520*a^33*b^39 - 3035061119643770880*a^35*b^37 + 4257098930193408000*a^37*b^35 - 5187111311866429440*a^39*b^33 + 5501481694403788800*a^41*b^31 - 5082321184353976320*a^43*b^29 + 4086814972985671680*a^45*b^27 - 2854760459070873600*a^47*b^25 + 1726211879929405440*a^49*b^23 - 898867328294707200*a^51*b^21 + 400140939692482560*a^53*b^19 - 150777745391370240*a^55*b^17 + 47447542256025600*a^57*b^15 - 12240090610974720*a^59*b^13 + 2521366979788800*a^61*b^11 - 398834413166592*a^63*b^9 + 45490397257728*a^65*b^7 - 3330476974080*a^67*b^5 + 117546246144*a^69*b^3) + 8707129344*a^12*b^58 - 1332190789632*a^14*b^56 + 28681284059136*a^16*b^54 - 311301641871360*a^18*b^52 + 2177740120227840*a^20*b^50 - 10922397191700480*a^22*b^48 + 41634880384204800*a^24*b^46 - 125003771820195840*a^26*b^44 + 302447666790973440*a^28*b^42 - 598319665965711360*a^30*b^40 + 975644030336532480*a^32*b^38 - 1314242849218682880*a^34*b^36 + 1455418437672960000*a^36*b^34 - 1304054920154972160*a^38*b^32 + 908181105107927040*a^40*b^30 - 436625531301888000*a^42*b^28 + 66949248132956160*a^44*b^26 + 118659409094983680*a^46*b^24 - 149422959601090560*a^48*b^22 + 105921118310768640*a^50*b^20 - 54125344499466240*a^52*b^18 + 21015701527265280*a^54*b^16 - 6236220178759680*a^56*b^14 + 1388221166960640*a^58*b^12 - 222162405212160*a^60*b^10 + 23587613392896*a^62*b^8 - 1410554953728*a^64*b^6 + 30474952704*a^66*b^4) - tan(c/2 + (d*x)/2)*(505980960768*a^12*b^56 - 28050984640512*a^14*b^54 + 435764251090944*a^16*b^52 - 3575718109347840*a^18*b^50 + 18730264859099136*a^20*b^48 - 67896173119315968*a^22*b^46 + 175151109969174528*a^24*b^44 - 313178493592682496*a^26*b^42 + 322543721316925440*a^28*b^40 + 87817901724942336*a^30*b^38 - 1141107740572336128*a^32*b^36 + 2683287241504063488*a^34*b^34 - 4099946394045874176*a^36*b^32 + 4680202272693534720*a^38*b^30 - 4159807137221197824*a^40*b^28 + 2907691359083200512*a^42*b^26 - 1583635567837888512*a^44*b^24 + 650291463103832064*a^46*b^22 - 184497987902054400*a^48*b^20 + 25459845498372096*a^50*b^18 + 4948055537467392*a^52*b^16 - 3746991697108992*a^54*b^14 + 988831432433664*a^56*b^12 - 136164991057920*a^58*b^10 + 8069573984256*a^60*b^8 + 13544423424*a^62*b^6) + 137379151872*a^11*b^57 - 4254400143360*a^13*b^55 + 29689859874816*a^15*b^53 + 87020018122752*a^17*b^51 - 2614627107274752*a^19*b^49 + 20133104812498944*a^21*b^47 - 94005764925972480*a^23*b^45 + 309275227789295616*a^25*b^43 - 759972938071523328*a^27*b^41 + 1428994663615807488*a^29*b^39 - 2057877923764617216*a^31*b^37 + 2199908326418841600*a^33*b^35 - 1543980376177311744*a^35*b^33 + 260078196862697472*a^37*b^31 + 1033592707257090048*a^39*b^29 - 1728050263069556736*a^41*b^27 + 1665648670228807680*a^43*b^25 - 1148576443783962624*a^45*b^23 + 593098899751084032*a^47*b^21 - 228687912023703552*a^49*b^19 + 63216104157609984*a^51*b^17 - 11132817065533440*a^53*b^15 + 707704347303936*a^55*b^13 + 175924646019072*a^57*b^11 - 46657636319232*a^59*b^9 + 3600881713152*a^61*b^7) + 1719926784*a^8*b^58 - 109860323328*a^10*b^56 + 2586984873984*a^12*b^54 - 35812476739584*a^14*b^52 + 329722810195968*a^16*b^50 - 2157051013447680*a^18*b^48 + 10507597396918272*a^20*b^46 - 39457190948069376*a^22*b^44 + 117177686419562496*a^24*b^42 - 280405445559386112*a^26*b^40 + 547971334969098240*a^28*b^38 - 882457306853326848*a^30*b^36 + 1177391139070132224*a^32*b^34 - 1303949437690281984*a^34*b^32 + 1196629258750230528*a^36*b^30 - 904425852978708480*a^38*b^28 + 556165530870792192*a^40*b^26 - 272082763494752256*a^42*b^24 + 101333478214434816*a^44*b^22 - 25813305663086592*a^46*b^20 + 2756171653079040*a^48*b^18 + 957737252339712*a^50*b^16 - 557094927384576*a^52*b^14 + 135955536224256*a^54*b^12 - 17862568353792*a^56*b^10 + 1032386052096*a^58*b^8)) - 547736297472*a^10*b^52 + 5998567809024*a^12*b^50 - 42798845214720*a^14*b^48 + 218837397897216*a^16*b^46 - 847734439845888*a^18*b^44 + 2578107250925568*a^20*b^42 - 6304715180015616*a^22*b^40 + 12605115522908160*a^24*b^38 - 20839646107090944*a^26*b^36 + 28704537977536512*a^28*b^34 - 33083332509007872*a^30*b^32 + 31955047610056704*a^32*b^30 - 25837736359772160*a^34*b^28 + 17420116682981376*a^36*b^26 - 9723722502832128*a^38*b^24 + 4443893749628928*a^40*b^22 - 1635506216902656*a^42*b^20 + 472961442078720*a^44*b^18 - 103502089764864*a^46*b^16 + 16115525517312*a^48*b^14 - 1591065649152*a^50*b^12 + 74879852544*a^52*b^10)*root(18600435*a^18*b^6*d^6 - 18600435*a^16*b^8*d^6 - 11160261*a^20*b^4*d^6 + 11160261*a^14*b^10*d^6 + 3720087*a^22*b^2*d^6 - 3720087*a^12*b^12*d^6 + 531441*a^10*b^14*d^6 - 531441*a^24*d^6 - 173879622*a^14*b^6*d^4 - 155830311*a^12*b^8*d^4 - 23225940*a^16*b^4*d^4 - 6475707*a^10*b^10*d^4 + 688905*a^8*b^12*d^4 - 11565585*a^8*b^8*d^2 + 3750705*a^10*b^6*d^2 + 433755*a^6*b^10*d^2 - 117649*a^4*b^8 + 5488*a^2*b^10 - 64*b^12, d, k), k, 1, 6)/d + ((2*(4*a^4*b + 3*b^5 + 38*a^2*b^3))/(3*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (2*tan(c/2 + (d*x)/2)^8*(47*b^5 - 4*a^4*b + 62*a^2*b^3))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (4*tan(c/2 + (d*x)/2)^6*(119*b^5 - 24*a^4*b + 220*a^2*b^3))/(3*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (6*tan(c/2 + (d*x)/2)^2*(b^5 + 4*a^2*b^3))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (100*tan(c/2 + (d*x)/2)^4*(b^5 + 2*a^2*b^3))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (6*tan(c/2 + (d*x)/2)^10*(b^5 + 4*a^2*b^3))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (2*tan(c/2 + (d*x)/2)^11*(b^6 - 3*a^6 + 19*a^2*b^4 + 28*a^4*b^2))/(3*a*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (2*tan(c/2 + (d*x)/2)^9*(9*b^6 - 7*a^6 + 19*a^2*b^4 + 24*a^4*b^2))/(3*a*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (4*tan(c/2 + (d*x)/2)^7*(3*a^6 + 17*b^6 + 179*a^2*b^4 + 26*a^4*b^2))/(3*a*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (2*tan(c/2 + (d*x)/2)^3*(7*a^6 + 15*b^6 + 285*a^2*b^4 + 8*a^4*b^2))/(3*a*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (4*tan(c/2 + (d*x)/2)^5*(19*b^6 - 3*a^6 + 277*a^2*b^4 + 22*a^4*b^2))/(3*a*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (2*tan(c/2 + (d*x)/2)*(b^6 - 3*a^6 + 19*a^2*b^4 + 28*a^4*b^2))/(3*a*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)))/(d*(a - 3*a*tan(c/2 + (d*x)/2)^4 + 3*a*tan(c/2 + (d*x)/2)^8 - a*tan(c/2 + (d*x)/2)^12 + 8*b*tan(c/2 + (d*x)/2)^3 - 24*b*tan(c/2 + (d*x)/2)^5 + 24*b*tan(c/2 + (d*x)/2)^7 - 8*b*tan(c/2 + (d*x)/2)^9))","B"
404,1,1931,131,0.774317,"\text{Not used}","int(cos(c + d*x)^7/(a - b*sin(c + d*x)^4),x)","\frac{{\sin\left(c+d\,x\right)}^3}{3\,b\,d}-\frac{3\,\sin\left(c+d\,x\right)}{b\,d}+\frac{\mathrm{atan}\left(\frac{a^3\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}}{16\,b^7}-\frac{3\,a}{8\,b^3}-\frac{5}{4\,b^2}-\frac{3}{8\,a\,b}-\frac{15\,\sqrt{a^3\,b^7}}{16\,a\,b^6}-\frac{15\,\sqrt{a^3\,b^7}}{16\,a^2\,b^5}-\frac{\sqrt{a^3\,b^7}}{16\,a^3\,b^4}}\,8{}\mathrm{i}}{92\,a\,b+\frac{120\,\sqrt{a^3\,b^7}}{b^3}+120\,a^2+6\,b^2+\frac{36\,a^3}{b}+\frac{2\,a^4}{b^2}+\frac{36\,\sqrt{a^3\,b^7}}{a\,b^2}+\frac{2\,\sqrt{a^3\,b^7}}{a^2\,b}+\frac{6\,a^2\,\sqrt{a^3\,b^7}}{b^5}+\frac{92\,a\,\sqrt{a^3\,b^7}}{b^4}}+\frac{b^3\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}}{16\,b^7}-\frac{3\,a}{8\,b^3}-\frac{5}{4\,b^2}-\frac{3}{8\,a\,b}-\frac{15\,\sqrt{a^3\,b^7}}{16\,a\,b^6}-\frac{15\,\sqrt{a^3\,b^7}}{16\,a^2\,b^5}-\frac{\sqrt{a^3\,b^7}}{16\,a^3\,b^4}}\,8{}\mathrm{i}}{92\,a\,b+\frac{120\,\sqrt{a^3\,b^7}}{b^3}+120\,a^2+6\,b^2+\frac{36\,a^3}{b}+\frac{2\,a^4}{b^2}+\frac{36\,\sqrt{a^3\,b^7}}{a\,b^2}+\frac{2\,\sqrt{a^3\,b^7}}{a^2\,b}+\frac{6\,a^2\,\sqrt{a^3\,b^7}}{b^5}+\frac{92\,a\,\sqrt{a^3\,b^7}}{b^4}}+\frac{a\,b^2\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}}{16\,b^7}-\frac{3\,a}{8\,b^3}-\frac{5}{4\,b^2}-\frac{3}{8\,a\,b}-\frac{15\,\sqrt{a^3\,b^7}}{16\,a\,b^6}-\frac{15\,\sqrt{a^3\,b^7}}{16\,a^2\,b^5}-\frac{\sqrt{a^3\,b^7}}{16\,a^3\,b^4}}\,120{}\mathrm{i}}{92\,a\,b+\frac{120\,\sqrt{a^3\,b^7}}{b^3}+120\,a^2+6\,b^2+\frac{36\,a^3}{b}+\frac{2\,a^4}{b^2}+\frac{36\,\sqrt{a^3\,b^7}}{a\,b^2}+\frac{2\,\sqrt{a^3\,b^7}}{a^2\,b}+\frac{6\,a^2\,\sqrt{a^3\,b^7}}{b^5}+\frac{92\,a\,\sqrt{a^3\,b^7}}{b^4}}+\frac{a^2\,b\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{\sqrt{a^3\,b^7}}{16\,b^7}-\frac{3\,a}{8\,b^3}-\frac{5}{4\,b^2}-\frac{3}{8\,a\,b}-\frac{15\,\sqrt{a^3\,b^7}}{16\,a\,b^6}-\frac{15\,\sqrt{a^3\,b^7}}{16\,a^2\,b^5}-\frac{\sqrt{a^3\,b^7}}{16\,a^3\,b^4}}\,120{}\mathrm{i}}{92\,a\,b+\frac{120\,\sqrt{a^3\,b^7}}{b^3}+120\,a^2+6\,b^2+\frac{36\,a^3}{b}+\frac{2\,a^4}{b^2}+\frac{36\,\sqrt{a^3\,b^7}}{a\,b^2}+\frac{2\,\sqrt{a^3\,b^7}}{a^2\,b}+\frac{6\,a^2\,\sqrt{a^3\,b^7}}{b^5}+\frac{92\,a\,\sqrt{a^3\,b^7}}{b^4}}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+6\,a^2\,b^6+20\,a^3\,b^5+6\,a^4\,b^4+15\,a\,b^2\,\sqrt{a^3\,b^7}+15\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^7}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{a^3\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}}{16\,b^7}-\frac{3\,a}{8\,b^3}-\frac{5}{4\,b^2}-\frac{3}{8\,a\,b}+\frac{15\,\sqrt{a^3\,b^7}}{16\,a\,b^6}+\frac{15\,\sqrt{a^3\,b^7}}{16\,a^2\,b^5}+\frac{\sqrt{a^3\,b^7}}{16\,a^3\,b^4}}\,8{}\mathrm{i}}{92\,a\,b-\frac{120\,\sqrt{a^3\,b^7}}{b^3}+120\,a^2+6\,b^2+\frac{36\,a^3}{b}+\frac{2\,a^4}{b^2}-\frac{36\,\sqrt{a^3\,b^7}}{a\,b^2}-\frac{2\,\sqrt{a^3\,b^7}}{a^2\,b}-\frac{6\,a^2\,\sqrt{a^3\,b^7}}{b^5}-\frac{92\,a\,\sqrt{a^3\,b^7}}{b^4}}+\frac{b^3\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}}{16\,b^7}-\frac{3\,a}{8\,b^3}-\frac{5}{4\,b^2}-\frac{3}{8\,a\,b}+\frac{15\,\sqrt{a^3\,b^7}}{16\,a\,b^6}+\frac{15\,\sqrt{a^3\,b^7}}{16\,a^2\,b^5}+\frac{\sqrt{a^3\,b^7}}{16\,a^3\,b^4}}\,8{}\mathrm{i}}{92\,a\,b-\frac{120\,\sqrt{a^3\,b^7}}{b^3}+120\,a^2+6\,b^2+\frac{36\,a^3}{b}+\frac{2\,a^4}{b^2}-\frac{36\,\sqrt{a^3\,b^7}}{a\,b^2}-\frac{2\,\sqrt{a^3\,b^7}}{a^2\,b}-\frac{6\,a^2\,\sqrt{a^3\,b^7}}{b^5}-\frac{92\,a\,\sqrt{a^3\,b^7}}{b^4}}+\frac{a\,b^2\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}}{16\,b^7}-\frac{3\,a}{8\,b^3}-\frac{5}{4\,b^2}-\frac{3}{8\,a\,b}+\frac{15\,\sqrt{a^3\,b^7}}{16\,a\,b^6}+\frac{15\,\sqrt{a^3\,b^7}}{16\,a^2\,b^5}+\frac{\sqrt{a^3\,b^7}}{16\,a^3\,b^4}}\,120{}\mathrm{i}}{92\,a\,b-\frac{120\,\sqrt{a^3\,b^7}}{b^3}+120\,a^2+6\,b^2+\frac{36\,a^3}{b}+\frac{2\,a^4}{b^2}-\frac{36\,\sqrt{a^3\,b^7}}{a\,b^2}-\frac{2\,\sqrt{a^3\,b^7}}{a^2\,b}-\frac{6\,a^2\,\sqrt{a^3\,b^7}}{b^5}-\frac{92\,a\,\sqrt{a^3\,b^7}}{b^4}}+\frac{a^2\,b\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^7}}{16\,b^7}-\frac{3\,a}{8\,b^3}-\frac{5}{4\,b^2}-\frac{3}{8\,a\,b}+\frac{15\,\sqrt{a^3\,b^7}}{16\,a\,b^6}+\frac{15\,\sqrt{a^3\,b^7}}{16\,a^2\,b^5}+\frac{\sqrt{a^3\,b^7}}{16\,a^3\,b^4}}\,120{}\mathrm{i}}{92\,a\,b-\frac{120\,\sqrt{a^3\,b^7}}{b^3}+120\,a^2+6\,b^2+\frac{36\,a^3}{b}+\frac{2\,a^4}{b^2}-\frac{36\,\sqrt{a^3\,b^7}}{a\,b^2}-\frac{2\,\sqrt{a^3\,b^7}}{a^2\,b}-\frac{6\,a^2\,\sqrt{a^3\,b^7}}{b^5}-\frac{92\,a\,\sqrt{a^3\,b^7}}{b^4}}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-6\,a^2\,b^6-20\,a^3\,b^5-6\,a^4\,b^4+15\,a\,b^2\,\sqrt{a^3\,b^7}+15\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^7}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan((a^3*sin(c + d*x)*(- (a^3*b^7)^(1/2)/(16*b^7) - (3*a)/(8*b^3) - 5/(4*b^2) - 3/(8*a*b) - (15*(a^3*b^7)^(1/2))/(16*a*b^6) - (15*(a^3*b^7)^(1/2))/(16*a^2*b^5) - (a^3*b^7)^(1/2)/(16*a^3*b^4))^(1/2)*8i)/(92*a*b + (120*(a^3*b^7)^(1/2))/b^3 + 120*a^2 + 6*b^2 + (36*a^3)/b + (2*a^4)/b^2 + (36*(a^3*b^7)^(1/2))/(a*b^2) + (2*(a^3*b^7)^(1/2))/(a^2*b) + (6*a^2*(a^3*b^7)^(1/2))/b^5 + (92*a*(a^3*b^7)^(1/2))/b^4) + (b^3*sin(c + d*x)*(- (a^3*b^7)^(1/2)/(16*b^7) - (3*a)/(8*b^3) - 5/(4*b^2) - 3/(8*a*b) - (15*(a^3*b^7)^(1/2))/(16*a*b^6) - (15*(a^3*b^7)^(1/2))/(16*a^2*b^5) - (a^3*b^7)^(1/2)/(16*a^3*b^4))^(1/2)*8i)/(92*a*b + (120*(a^3*b^7)^(1/2))/b^3 + 120*a^2 + 6*b^2 + (36*a^3)/b + (2*a^4)/b^2 + (36*(a^3*b^7)^(1/2))/(a*b^2) + (2*(a^3*b^7)^(1/2))/(a^2*b) + (6*a^2*(a^3*b^7)^(1/2))/b^5 + (92*a*(a^3*b^7)^(1/2))/b^4) + (a*b^2*sin(c + d*x)*(- (a^3*b^7)^(1/2)/(16*b^7) - (3*a)/(8*b^3) - 5/(4*b^2) - 3/(8*a*b) - (15*(a^3*b^7)^(1/2))/(16*a*b^6) - (15*(a^3*b^7)^(1/2))/(16*a^2*b^5) - (a^3*b^7)^(1/2)/(16*a^3*b^4))^(1/2)*120i)/(92*a*b + (120*(a^3*b^7)^(1/2))/b^3 + 120*a^2 + 6*b^2 + (36*a^3)/b + (2*a^4)/b^2 + (36*(a^3*b^7)^(1/2))/(a*b^2) + (2*(a^3*b^7)^(1/2))/(a^2*b) + (6*a^2*(a^3*b^7)^(1/2))/b^5 + (92*a*(a^3*b^7)^(1/2))/b^4) + (a^2*b*sin(c + d*x)*(- (a^3*b^7)^(1/2)/(16*b^7) - (3*a)/(8*b^3) - 5/(4*b^2) - 3/(8*a*b) - (15*(a^3*b^7)^(1/2))/(16*a*b^6) - (15*(a^3*b^7)^(1/2))/(16*a^2*b^5) - (a^3*b^7)^(1/2)/(16*a^3*b^4))^(1/2)*120i)/(92*a*b + (120*(a^3*b^7)^(1/2))/b^3 + 120*a^2 + 6*b^2 + (36*a^3)/b + (2*a^4)/b^2 + (36*(a^3*b^7)^(1/2))/(a*b^2) + (2*(a^3*b^7)^(1/2))/(a^2*b) + (6*a^2*(a^3*b^7)^(1/2))/b^5 + (92*a*(a^3*b^7)^(1/2))/b^4))*(-(a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 6*a^2*b^6 + 20*a^3*b^5 + 6*a^4*b^4 + 15*a*b^2*(a^3*b^7)^(1/2) + 15*a^2*b*(a^3*b^7)^(1/2))/(16*a^3*b^7))^(1/2)*2i)/d - (3*sin(c + d*x))/(b*d) + (atan((a^3*sin(c + d*x)*((a^3*b^7)^(1/2)/(16*b^7) - (3*a)/(8*b^3) - 5/(4*b^2) - 3/(8*a*b) + (15*(a^3*b^7)^(1/2))/(16*a*b^6) + (15*(a^3*b^7)^(1/2))/(16*a^2*b^5) + (a^3*b^7)^(1/2)/(16*a^3*b^4))^(1/2)*8i)/(92*a*b - (120*(a^3*b^7)^(1/2))/b^3 + 120*a^2 + 6*b^2 + (36*a^3)/b + (2*a^4)/b^2 - (36*(a^3*b^7)^(1/2))/(a*b^2) - (2*(a^3*b^7)^(1/2))/(a^2*b) - (6*a^2*(a^3*b^7)^(1/2))/b^5 - (92*a*(a^3*b^7)^(1/2))/b^4) + (b^3*sin(c + d*x)*((a^3*b^7)^(1/2)/(16*b^7) - (3*a)/(8*b^3) - 5/(4*b^2) - 3/(8*a*b) + (15*(a^3*b^7)^(1/2))/(16*a*b^6) + (15*(a^3*b^7)^(1/2))/(16*a^2*b^5) + (a^3*b^7)^(1/2)/(16*a^3*b^4))^(1/2)*8i)/(92*a*b - (120*(a^3*b^7)^(1/2))/b^3 + 120*a^2 + 6*b^2 + (36*a^3)/b + (2*a^4)/b^2 - (36*(a^3*b^7)^(1/2))/(a*b^2) - (2*(a^3*b^7)^(1/2))/(a^2*b) - (6*a^2*(a^3*b^7)^(1/2))/b^5 - (92*a*(a^3*b^7)^(1/2))/b^4) + (a*b^2*sin(c + d*x)*((a^3*b^7)^(1/2)/(16*b^7) - (3*a)/(8*b^3) - 5/(4*b^2) - 3/(8*a*b) + (15*(a^3*b^7)^(1/2))/(16*a*b^6) + (15*(a^3*b^7)^(1/2))/(16*a^2*b^5) + (a^3*b^7)^(1/2)/(16*a^3*b^4))^(1/2)*120i)/(92*a*b - (120*(a^3*b^7)^(1/2))/b^3 + 120*a^2 + 6*b^2 + (36*a^3)/b + (2*a^4)/b^2 - (36*(a^3*b^7)^(1/2))/(a*b^2) - (2*(a^3*b^7)^(1/2))/(a^2*b) - (6*a^2*(a^3*b^7)^(1/2))/b^5 - (92*a*(a^3*b^7)^(1/2))/b^4) + (a^2*b*sin(c + d*x)*((a^3*b^7)^(1/2)/(16*b^7) - (3*a)/(8*b^3) - 5/(4*b^2) - 3/(8*a*b) + (15*(a^3*b^7)^(1/2))/(16*a*b^6) + (15*(a^3*b^7)^(1/2))/(16*a^2*b^5) + (a^3*b^7)^(1/2)/(16*a^3*b^4))^(1/2)*120i)/(92*a*b - (120*(a^3*b^7)^(1/2))/b^3 + 120*a^2 + 6*b^2 + (36*a^3)/b + (2*a^4)/b^2 - (36*(a^3*b^7)^(1/2))/(a*b^2) - (2*(a^3*b^7)^(1/2))/(a^2*b) - (6*a^2*(a^3*b^7)^(1/2))/b^5 - (92*a*(a^3*b^7)^(1/2))/b^4))*((a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 6*a^2*b^6 - 20*a^3*b^5 - 6*a^4*b^4 + 15*a*b^2*(a^3*b^7)^(1/2) + 15*a^2*b*(a^3*b^7)^(1/2))/(16*a^3*b^7))^(1/2)*2i)/d + sin(c + d*x)^3/(3*b*d)","B"
405,1,1097,113,15.783546,"\text{Not used}","int(cos(c + d*x)^5/(a - b*sin(c + d*x)^4),x)","\frac{2\,\mathrm{atanh}\left(\frac{8\,b^3\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^5}}{16\,a\,b^5}-\frac{1}{4\,a\,b}-\frac{1}{4\,b^2}+\frac{3\,\sqrt{a^3\,b^5}}{8\,a^2\,b^4}+\frac{\sqrt{a^3\,b^5}}{16\,a^3\,b^3}}}{\frac{2\,\sqrt{a^3\,b^5}}{a^2}-24\,a\,b+\frac{14\,\sqrt{a^3\,b^5}}{b^2}-4\,a^2-4\,b^2+\frac{14\,\sqrt{a^3\,b^5}}{a\,b}+\frac{2\,a\,\sqrt{a^3\,b^5}}{b^3}}+\frac{48\,a\,b^2\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^5}}{16\,a\,b^5}-\frac{1}{4\,a\,b}-\frac{1}{4\,b^2}+\frac{3\,\sqrt{a^3\,b^5}}{8\,a^2\,b^4}+\frac{\sqrt{a^3\,b^5}}{16\,a^3\,b^3}}}{\frac{2\,\sqrt{a^3\,b^5}}{a^2}-24\,a\,b+\frac{14\,\sqrt{a^3\,b^5}}{b^2}-4\,a^2-4\,b^2+\frac{14\,\sqrt{a^3\,b^5}}{a\,b}+\frac{2\,a\,\sqrt{a^3\,b^5}}{b^3}}+\frac{8\,a^2\,b\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^5}}{16\,a\,b^5}-\frac{1}{4\,a\,b}-\frac{1}{4\,b^2}+\frac{3\,\sqrt{a^3\,b^5}}{8\,a^2\,b^4}+\frac{\sqrt{a^3\,b^5}}{16\,a^3\,b^3}}}{\frac{2\,\sqrt{a^3\,b^5}}{a^2}-24\,a\,b+\frac{14\,\sqrt{a^3\,b^5}}{b^2}-4\,a^2-4\,b^2+\frac{14\,\sqrt{a^3\,b^5}}{a\,b}+\frac{2\,a\,\sqrt{a^3\,b^5}}{b^3}}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-4\,a^2\,b^4-4\,a^3\,b^3+6\,a\,b\,\sqrt{a^3\,b^5}}{16\,a^3\,b^5}}}{d}-\frac{2\,\mathrm{atanh}\left(\frac{8\,b^3\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{1}{4\,b^2}-\frac{1}{4\,a\,b}-\frac{\sqrt{a^3\,b^5}}{16\,a\,b^5}-\frac{3\,\sqrt{a^3\,b^5}}{8\,a^2\,b^4}-\frac{\sqrt{a^3\,b^5}}{16\,a^3\,b^3}}}{24\,a\,b+\frac{2\,\sqrt{a^3\,b^5}}{a^2}+\frac{14\,\sqrt{a^3\,b^5}}{b^2}+4\,a^2+4\,b^2+\frac{14\,\sqrt{a^3\,b^5}}{a\,b}+\frac{2\,a\,\sqrt{a^3\,b^5}}{b^3}}+\frac{48\,a\,b^2\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{1}{4\,b^2}-\frac{1}{4\,a\,b}-\frac{\sqrt{a^3\,b^5}}{16\,a\,b^5}-\frac{3\,\sqrt{a^3\,b^5}}{8\,a^2\,b^4}-\frac{\sqrt{a^3\,b^5}}{16\,a^3\,b^3}}}{24\,a\,b+\frac{2\,\sqrt{a^3\,b^5}}{a^2}+\frac{14\,\sqrt{a^3\,b^5}}{b^2}+4\,a^2+4\,b^2+\frac{14\,\sqrt{a^3\,b^5}}{a\,b}+\frac{2\,a\,\sqrt{a^3\,b^5}}{b^3}}+\frac{8\,a^2\,b\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{1}{4\,b^2}-\frac{1}{4\,a\,b}-\frac{\sqrt{a^3\,b^5}}{16\,a\,b^5}-\frac{3\,\sqrt{a^3\,b^5}}{8\,a^2\,b^4}-\frac{\sqrt{a^3\,b^5}}{16\,a^3\,b^3}}}{24\,a\,b+\frac{2\,\sqrt{a^3\,b^5}}{a^2}+\frac{14\,\sqrt{a^3\,b^5}}{b^2}+4\,a^2+4\,b^2+\frac{14\,\sqrt{a^3\,b^5}}{a\,b}+\frac{2\,a\,\sqrt{a^3\,b^5}}{b^3}}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+4\,a^2\,b^4+4\,a^3\,b^3+6\,a\,b\,\sqrt{a^3\,b^5}}{16\,a^3\,b^5}}}{d}-\frac{\sin\left(c+d\,x\right)}{b\,d}","Not used",1,"(2*atanh((8*b^3*sin(c + d*x)*((a^3*b^5)^(1/2)/(16*a*b^5) - 1/(4*a*b) - 1/(4*b^2) + (3*(a^3*b^5)^(1/2))/(8*a^2*b^4) + (a^3*b^5)^(1/2)/(16*a^3*b^3))^(1/2))/((2*(a^3*b^5)^(1/2))/a^2 - 24*a*b + (14*(a^3*b^5)^(1/2))/b^2 - 4*a^2 - 4*b^2 + (14*(a^3*b^5)^(1/2))/(a*b) + (2*a*(a^3*b^5)^(1/2))/b^3) + (48*a*b^2*sin(c + d*x)*((a^3*b^5)^(1/2)/(16*a*b^5) - 1/(4*a*b) - 1/(4*b^2) + (3*(a^3*b^5)^(1/2))/(8*a^2*b^4) + (a^3*b^5)^(1/2)/(16*a^3*b^3))^(1/2))/((2*(a^3*b^5)^(1/2))/a^2 - 24*a*b + (14*(a^3*b^5)^(1/2))/b^2 - 4*a^2 - 4*b^2 + (14*(a^3*b^5)^(1/2))/(a*b) + (2*a*(a^3*b^5)^(1/2))/b^3) + (8*a^2*b*sin(c + d*x)*((a^3*b^5)^(1/2)/(16*a*b^5) - 1/(4*a*b) - 1/(4*b^2) + (3*(a^3*b^5)^(1/2))/(8*a^2*b^4) + (a^3*b^5)^(1/2)/(16*a^3*b^3))^(1/2))/((2*(a^3*b^5)^(1/2))/a^2 - 24*a*b + (14*(a^3*b^5)^(1/2))/b^2 - 4*a^2 - 4*b^2 + (14*(a^3*b^5)^(1/2))/(a*b) + (2*a*(a^3*b^5)^(1/2))/b^3))*((a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 4*a^2*b^4 - 4*a^3*b^3 + 6*a*b*(a^3*b^5)^(1/2))/(16*a^3*b^5))^(1/2))/d - (2*atanh((8*b^3*sin(c + d*x)*(- 1/(4*b^2) - 1/(4*a*b) - (a^3*b^5)^(1/2)/(16*a*b^5) - (3*(a^3*b^5)^(1/2))/(8*a^2*b^4) - (a^3*b^5)^(1/2)/(16*a^3*b^3))^(1/2))/(24*a*b + (2*(a^3*b^5)^(1/2))/a^2 + (14*(a^3*b^5)^(1/2))/b^2 + 4*a^2 + 4*b^2 + (14*(a^3*b^5)^(1/2))/(a*b) + (2*a*(a^3*b^5)^(1/2))/b^3) + (48*a*b^2*sin(c + d*x)*(- 1/(4*b^2) - 1/(4*a*b) - (a^3*b^5)^(1/2)/(16*a*b^5) - (3*(a^3*b^5)^(1/2))/(8*a^2*b^4) - (a^3*b^5)^(1/2)/(16*a^3*b^3))^(1/2))/(24*a*b + (2*(a^3*b^5)^(1/2))/a^2 + (14*(a^3*b^5)^(1/2))/b^2 + 4*a^2 + 4*b^2 + (14*(a^3*b^5)^(1/2))/(a*b) + (2*a*(a^3*b^5)^(1/2))/b^3) + (8*a^2*b*sin(c + d*x)*(- 1/(4*b^2) - 1/(4*a*b) - (a^3*b^5)^(1/2)/(16*a*b^5) - (3*(a^3*b^5)^(1/2))/(8*a^2*b^4) - (a^3*b^5)^(1/2)/(16*a^3*b^3))^(1/2))/(24*a*b + (2*(a^3*b^5)^(1/2))/a^2 + (14*(a^3*b^5)^(1/2))/b^2 + 4*a^2 + 4*b^2 + (14*(a^3*b^5)^(1/2))/(a*b) + (2*a*(a^3*b^5)^(1/2))/b^3))*(-(a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 4*a^2*b^4 + 4*a^3*b^3 + 6*a*b*(a^3*b^5)^(1/2))/(16*a^3*b^5))^(1/2))/d - sin(c + d*x)/(b*d)","B"
406,1,489,95,15.811157,"\text{Not used}","int(cos(c + d*x)^3/(a - b*sin(c + d*x)^4),x)","-\frac{2\,\mathrm{atanh}\left(\frac{8\,b^3\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{1}{8\,a\,b}-\frac{\sqrt{a^3\,b^3}}{16\,a^2\,b^3}-\frac{\sqrt{a^3\,b^3}}{16\,a^3\,b^2}}}{2\,a\,b+\frac{2\,\sqrt{a^3\,b^3}}{a}+2\,b^2+\frac{2\,b\,\sqrt{a^3\,b^3}}{a^2}}+\frac{8\,a\,b^2\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{1}{8\,a\,b}-\frac{\sqrt{a^3\,b^3}}{16\,a^2\,b^3}-\frac{\sqrt{a^3\,b^3}}{16\,a^3\,b^2}}}{2\,a\,b+\frac{2\,\sqrt{a^3\,b^3}}{a}+2\,b^2+\frac{2\,b\,\sqrt{a^3\,b^3}}{a^2}}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+2\,a^2\,b^2}{16\,a^3\,b^3}}}{d}-\frac{2\,\mathrm{atanh}\left(\frac{8\,b^3\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}}{16\,a^2\,b^3}-\frac{1}{8\,a\,b}+\frac{\sqrt{a^3\,b^3}}{16\,a^3\,b^2}}}{2\,a\,b-\frac{2\,\sqrt{a^3\,b^3}}{a}+2\,b^2-\frac{2\,b\,\sqrt{a^3\,b^3}}{a^2}}+\frac{8\,a\,b^2\,\sin\left(c+d\,x\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}}{16\,a^2\,b^3}-\frac{1}{8\,a\,b}+\frac{\sqrt{a^3\,b^3}}{16\,a^3\,b^2}}}{2\,a\,b-\frac{2\,\sqrt{a^3\,b^3}}{a}+2\,b^2-\frac{2\,b\,\sqrt{a^3\,b^3}}{a^2}}\right)\,\sqrt{\frac{a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-2\,a^2\,b^2}{16\,a^3\,b^3}}}{d}","Not used",1,"- (2*atanh((8*b^3*sin(c + d*x)*(- 1/(8*a*b) - (a^3*b^3)^(1/2)/(16*a^2*b^3) - (a^3*b^3)^(1/2)/(16*a^3*b^2))^(1/2))/(2*a*b + (2*(a^3*b^3)^(1/2))/a + 2*b^2 + (2*b*(a^3*b^3)^(1/2))/a^2) + (8*a*b^2*sin(c + d*x)*(- 1/(8*a*b) - (a^3*b^3)^(1/2)/(16*a^2*b^3) - (a^3*b^3)^(1/2)/(16*a^3*b^2))^(1/2))/(2*a*b + (2*(a^3*b^3)^(1/2))/a + 2*b^2 + (2*b*(a^3*b^3)^(1/2))/a^2))*(-(a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + 2*a^2*b^2)/(16*a^3*b^3))^(1/2))/d - (2*atanh((8*b^3*sin(c + d*x)*((a^3*b^3)^(1/2)/(16*a^2*b^3) - 1/(8*a*b) + (a^3*b^3)^(1/2)/(16*a^3*b^2))^(1/2))/(2*a*b - (2*(a^3*b^3)^(1/2))/a + 2*b^2 - (2*b*(a^3*b^3)^(1/2))/a^2) + (8*a*b^2*sin(c + d*x)*((a^3*b^3)^(1/2)/(16*a^2*b^3) - 1/(8*a*b) + (a^3*b^3)^(1/2)/(16*a^3*b^2))^(1/2))/(2*a*b - (2*(a^3*b^3)^(1/2))/a + 2*b^2 - (2*b*(a^3*b^3)^(1/2))/a^2))*((a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - 2*a^2*b^2)/(16*a^3*b^3))^(1/2))/d","B"
407,1,40,71,0.105424,"\text{Not used}","int(cos(c + d*x)/(a - b*sin(c + d*x)^4),x)","\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sin\left(c+d\,x\right)}{a^{1/4}}\right)+\mathrm{atanh}\left(\frac{b^{1/4}\,\sin\left(c+d\,x\right)}{a^{1/4}}\right)}{2\,a^{3/4}\,b^{1/4}\,d}","Not used",1,"(atan((b^(1/4)*sin(c + d*x))/a^(1/4)) + atanh((b^(1/4)*sin(c + d*x))/a^(1/4)))/(2*a^(3/4)*b^(1/4)*d)","B"
408,1,3891,117,17.906093,"\text{Not used}","int(1/(cos(c + d*x)*(a - b*sin(c + d*x)^4)),x)","-\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(64\,a\,b^7+128\,a^2\,b^6-448\,a^3\,b^5+256\,a^4\,b^4+\sin\left(c+d\,x\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)\right)-\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-20\,a\,b^5+4\,b^6\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-6\,b^5\,\sin\left(c+d\,x\right)\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(64\,a\,b^7+128\,a^2\,b^6-448\,a^3\,b^5+256\,a^4\,b^4-\sin\left(c+d\,x\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)\right)+\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-20\,a\,b^5+4\,b^6\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}+6\,b^5\,\sin\left(c+d\,x\right)\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(64\,a\,b^7+128\,a^2\,b^6-448\,a^3\,b^5+256\,a^4\,b^4+\sin\left(c+d\,x\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)\right)-\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-20\,a\,b^5+4\,b^6\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-6\,b^5\,\sin\left(c+d\,x\right)\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}+\left(\left(\left(\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(64\,a\,b^7+128\,a^2\,b^6-448\,a^3\,b^5+256\,a^4\,b^4-\sin\left(c+d\,x\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)\right)+\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-20\,a\,b^5+4\,b^6\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}+6\,b^5\,\sin\left(c+d\,x\right)\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}}\right)\,\sqrt{-\frac{a\,\sqrt{a^3\,b}-2\,a^2\,b+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(64\,a\,b^7+128\,a^2\,b^6-448\,a^3\,b^5+256\,a^4\,b^4+\sin\left(c+d\,x\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)\right)-\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-20\,a\,b^5+4\,b^6\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-6\,b^5\,\sin\left(c+d\,x\right)\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(64\,a\,b^7+128\,a^2\,b^6-448\,a^3\,b^5+256\,a^4\,b^4-\sin\left(c+d\,x\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)\right)+\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-20\,a\,b^5+4\,b^6\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}+6\,b^5\,\sin\left(c+d\,x\right)\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(64\,a\,b^7+128\,a^2\,b^6-448\,a^3\,b^5+256\,a^4\,b^4+\sin\left(c+d\,x\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)\right)-\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-20\,a\,b^5+4\,b^6\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-6\,b^5\,\sin\left(c+d\,x\right)\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}+\left(\left(\left(\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(64\,a\,b^7+128\,a^2\,b^6-448\,a^3\,b^5+256\,a^4\,b^4-\sin\left(c+d\,x\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)\right)+\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}-20\,a\,b^5+4\,b^6\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}+6\,b^5\,\sin\left(c+d\,x\right)\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}}\right)\,\sqrt{\frac{2\,a^2\,b+a\,\sqrt{a^3\,b}+b\,\sqrt{a^3\,b}}{16\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\frac{b^5\,\sin\left(c+d\,x\right)\,3{}\mathrm{i}+\frac{\left(\frac{\frac{32\,a\,b^7+64\,a^2\,b^6-224\,a^3\,b^5+128\,a^4\,b^4-\frac{\sin\left(c+d\,x\right)\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)}{4\,\left(a-b\right)}}{2\,\left(a-b\right)}+\frac{\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)}{2}}{2\,\left(a-b\right)}-10\,a\,b^5+2\,b^6\right)\,1{}\mathrm{i}}{2\,\left(a-b\right)}}{a-b}+\frac{b^5\,\sin\left(c+d\,x\right)\,3{}\mathrm{i}-\frac{\left(\frac{\frac{32\,a\,b^7+64\,a^2\,b^6-224\,a^3\,b^5+128\,a^4\,b^4+\frac{\sin\left(c+d\,x\right)\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)}{4\,\left(a-b\right)}}{2\,\left(a-b\right)}-\frac{\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)}{2}}{2\,\left(a-b\right)}-10\,a\,b^5+2\,b^6\right)\,1{}\mathrm{i}}{2\,\left(a-b\right)}}{a-b}}{\frac{3\,b^5\,\sin\left(c+d\,x\right)+\frac{\frac{\frac{32\,a\,b^7+64\,a^2\,b^6-224\,a^3\,b^5+128\,a^4\,b^4-\frac{\sin\left(c+d\,x\right)\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)}{4\,\left(a-b\right)}}{2\,\left(a-b\right)}+\frac{\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)}{2}}{2\,\left(a-b\right)}-10\,a\,b^5+2\,b^6}{2\,\left(a-b\right)}}{a-b}-\frac{3\,b^5\,\sin\left(c+d\,x\right)-\frac{\frac{\frac{32\,a\,b^7+64\,a^2\,b^6-224\,a^3\,b^5+128\,a^4\,b^4+\frac{\sin\left(c+d\,x\right)\,\left(512\,a^5\,b^4-512\,a^4\,b^5-512\,a^3\,b^6+512\,a^2\,b^7\right)}{4\,\left(a-b\right)}}{2\,\left(a-b\right)}-\frac{\sin\left(c+d\,x\right)\,\left(240\,a^2\,b^5+32\,a\,b^6-16\,b^7\right)}{2}}{2\,\left(a-b\right)}-10\,a\,b^5+2\,b^6}{2\,\left(a-b\right)}}{a-b}}\right)\,1{}\mathrm{i}}{d\,\left(a-b\right)}","Not used",1,"(atan(((b^5*sin(c + d*x)*3i + ((((32*a*b^7 + 64*a^2*b^6 - 224*a^3*b^5 + 128*a^4*b^4 - (sin(c + d*x)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4))/(4*(a - b)))/(2*(a - b)) + (sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))/2)/(2*(a - b)) - 10*a*b^5 + 2*b^6)*1i)/(2*(a - b)))/(a - b) + (b^5*sin(c + d*x)*3i - ((((32*a*b^7 + 64*a^2*b^6 - 224*a^3*b^5 + 128*a^4*b^4 + (sin(c + d*x)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4))/(4*(a - b)))/(2*(a - b)) - (sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))/2)/(2*(a - b)) - 10*a*b^5 + 2*b^6)*1i)/(2*(a - b)))/(a - b))/((3*b^5*sin(c + d*x) + (((32*a*b^7 + 64*a^2*b^6 - 224*a^3*b^5 + 128*a^4*b^4 - (sin(c + d*x)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4))/(4*(a - b)))/(2*(a - b)) + (sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))/2)/(2*(a - b)) - 10*a*b^5 + 2*b^6)/(2*(a - b)))/(a - b) - (3*b^5*sin(c + d*x) - (((32*a*b^7 + 64*a^2*b^6 - 224*a^3*b^5 + 128*a^4*b^4 + (sin(c + d*x)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4))/(4*(a - b)))/(2*(a - b)) - (sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))/2)/(2*(a - b)) - 10*a*b^5 + 2*b^6)/(2*(a - b)))/(a - b)))*1i)/(d*(a - b)) - (atan(((((((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(64*a*b^7 + 128*a^2*b^6 - 448*a^3*b^5 + 256*a^4*b^4 + sin(c + d*x)*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4)) - sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 20*a*b^5 + 4*b^6)*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 6*b^5*sin(c + d*x))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*1i - (((((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(64*a*b^7 + 128*a^2*b^6 - 448*a^3*b^5 + 256*a^4*b^4 - sin(c + d*x)*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4)) + sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 20*a*b^5 + 4*b^6)*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) + 6*b^5*sin(c + d*x))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*1i)/((((((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(64*a*b^7 + 128*a^2*b^6 - 448*a^3*b^5 + 256*a^4*b^4 + sin(c + d*x)*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4)) - sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 20*a*b^5 + 4*b^6)*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 6*b^5*sin(c + d*x))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) + (((((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(64*a*b^7 + 128*a^2*b^6 - 448*a^3*b^5 + 256*a^4*b^4 - sin(c + d*x)*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4)) + sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 20*a*b^5 + 4*b^6)*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) + 6*b^5*sin(c + d*x))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)))*((2*a^2*b + a*(a^3*b)^(1/2) + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*2i)/d - (atan((((((-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(64*a*b^7 + 128*a^2*b^6 - 448*a^3*b^5 + 256*a^4*b^4 + sin(c + d*x)*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4)) - sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 20*a*b^5 + 4*b^6)*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 6*b^5*sin(c + d*x))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*1i - ((((-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(64*a*b^7 + 128*a^2*b^6 - 448*a^3*b^5 + 256*a^4*b^4 - sin(c + d*x)*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4)) + sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 20*a*b^5 + 4*b^6)*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) + 6*b^5*sin(c + d*x))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*1i)/(((((-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(64*a*b^7 + 128*a^2*b^6 - 448*a^3*b^5 + 256*a^4*b^4 + sin(c + d*x)*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4)) - sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 20*a*b^5 + 4*b^6)*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 6*b^5*sin(c + d*x))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) + ((((-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(64*a*b^7 + 128*a^2*b^6 - 448*a^3*b^5 + 256*a^4*b^4 - sin(c + d*x)*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*(512*a^2*b^7 - 512*a^3*b^6 - 512*a^4*b^5 + 512*a^5*b^4)) + sin(c + d*x)*(32*a*b^6 - 16*b^7 + 240*a^2*b^5))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) - 20*a*b^5 + 4*b^6)*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2) + 6*b^5*sin(c + d*x))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)))*(-(a*(a^3*b)^(1/2) - 2*a^2*b + b*(a^3*b)^(1/2))/(16*(a^5 - 2*a^4*b + a^3*b^2)))^(1/2)*2i)/d","B"
409,1,7758,175,19.191622,"\text{Not used}","int(1/(cos(c + d*x)^3*(a - b*sin(c + d*x)^4)),x)","\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{b}{{\left(a-b\right)}^2}-\frac{1}{4\,\left(a-b\right)}\right)}{d}+\frac{\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2\,\left(a-b\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-5\,b\right)}{4\,d\,{\left(a-b\right)}^2}+\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{256\,a^8\,b^4-2176\,a^7\,b^5+6912\,a^6\,b^6-10880\,a^5\,b^7+8960\,a^4\,b^8-3456\,a^3\,b^9+256\,a^2\,b^{10}+128\,a\,b^{11}}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}-\frac{\sin\left(c+d\,x\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,\left(512\,a^9\,b^4-2560\,a^8\,b^5+4608\,a^7\,b^6-2560\,a^6\,b^7-2560\,a^5\,b^8+4608\,a^4\,b^9-2560\,a^3\,b^{10}+512\,a^2\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(32\,a^6\,b^5-144\,a^5\,b^6+1264\,a^4\,b^7-2208\,a^3\,b^8+1024\,a^2\,b^9+48\,a\,b^{10}-16\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{8\,a^5\,b^5+96\,a^4\,b^6-784\,a^3\,b^7+480\,a^2\,b^8+200\,a\,b^9}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(a^3\,b^6-7\,a^2\,b^7+11\,a\,b^8+27\,b^9\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{256\,a^8\,b^4-2176\,a^7\,b^5+6912\,a^6\,b^6-10880\,a^5\,b^7+8960\,a^4\,b^8-3456\,a^3\,b^9+256\,a^2\,b^{10}+128\,a\,b^{11}}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}+\frac{\sin\left(c+d\,x\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,\left(512\,a^9\,b^4-2560\,a^8\,b^5+4608\,a^7\,b^6-2560\,a^6\,b^7-2560\,a^5\,b^8+4608\,a^4\,b^9-2560\,a^3\,b^{10}+512\,a^2\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(32\,a^6\,b^5-144\,a^5\,b^6+1264\,a^4\,b^7-2208\,a^3\,b^8+1024\,a^2\,b^9+48\,a\,b^{10}-16\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{8\,a^5\,b^5+96\,a^4\,b^6-784\,a^3\,b^7+480\,a^2\,b^8+200\,a\,b^9}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(a^3\,b^6-7\,a^2\,b^7+11\,a\,b^8+27\,b^9\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{256\,a^8\,b^4-2176\,a^7\,b^5+6912\,a^6\,b^6-10880\,a^5\,b^7+8960\,a^4\,b^8-3456\,a^3\,b^9+256\,a^2\,b^{10}+128\,a\,b^{11}}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}-\frac{\sin\left(c+d\,x\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,\left(512\,a^9\,b^4-2560\,a^8\,b^5+4608\,a^7\,b^6-2560\,a^6\,b^7-2560\,a^5\,b^8+4608\,a^4\,b^9-2560\,a^3\,b^{10}+512\,a^2\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(32\,a^6\,b^5-144\,a^5\,b^6+1264\,a^4\,b^7-2208\,a^3\,b^8+1024\,a^2\,b^9+48\,a\,b^{10}-16\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{8\,a^5\,b^5+96\,a^4\,b^6-784\,a^3\,b^7+480\,a^2\,b^8+200\,a\,b^9}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(a^3\,b^6-7\,a^2\,b^7+11\,a\,b^8+27\,b^9\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\left(\left(\left(\left(\frac{256\,a^8\,b^4-2176\,a^7\,b^5+6912\,a^6\,b^6-10880\,a^5\,b^7+8960\,a^4\,b^8-3456\,a^3\,b^9+256\,a^2\,b^{10}+128\,a\,b^{11}}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}+\frac{\sin\left(c+d\,x\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,\left(512\,a^9\,b^4-2560\,a^8\,b^5+4608\,a^7\,b^6-2560\,a^6\,b^7-2560\,a^5\,b^8+4608\,a^4\,b^9-2560\,a^3\,b^{10}+512\,a^2\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(32\,a^6\,b^5-144\,a^5\,b^6+1264\,a^4\,b^7-2208\,a^3\,b^8+1024\,a^2\,b^9+48\,a\,b^{10}-16\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{8\,a^5\,b^5+96\,a^4\,b^6-784\,a^3\,b^7+480\,a^2\,b^8+200\,a\,b^9}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(a^3\,b^6-7\,a^2\,b^7+11\,a\,b^8+27\,b^9\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{a\,b^7-5\,b^8}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}}\right)\,\sqrt{-\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}-4\,a^2\,b^3-4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{256\,a^8\,b^4-2176\,a^7\,b^5+6912\,a^6\,b^6-10880\,a^5\,b^7+8960\,a^4\,b^8-3456\,a^3\,b^9+256\,a^2\,b^{10}+128\,a\,b^{11}}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}-\frac{\sin\left(c+d\,x\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,\left(512\,a^9\,b^4-2560\,a^8\,b^5+4608\,a^7\,b^6-2560\,a^6\,b^7-2560\,a^5\,b^8+4608\,a^4\,b^9-2560\,a^3\,b^{10}+512\,a^2\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(32\,a^6\,b^5-144\,a^5\,b^6+1264\,a^4\,b^7-2208\,a^3\,b^8+1024\,a^2\,b^9+48\,a\,b^{10}-16\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{8\,a^5\,b^5+96\,a^4\,b^6-784\,a^3\,b^7+480\,a^2\,b^8+200\,a\,b^9}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(a^3\,b^6-7\,a^2\,b^7+11\,a\,b^8+27\,b^9\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{256\,a^8\,b^4-2176\,a^7\,b^5+6912\,a^6\,b^6-10880\,a^5\,b^7+8960\,a^4\,b^8-3456\,a^3\,b^9+256\,a^2\,b^{10}+128\,a\,b^{11}}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}+\frac{\sin\left(c+d\,x\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,\left(512\,a^9\,b^4-2560\,a^8\,b^5+4608\,a^7\,b^6-2560\,a^6\,b^7-2560\,a^5\,b^8+4608\,a^4\,b^9-2560\,a^3\,b^{10}+512\,a^2\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(32\,a^6\,b^5-144\,a^5\,b^6+1264\,a^4\,b^7-2208\,a^3\,b^8+1024\,a^2\,b^9+48\,a\,b^{10}-16\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{8\,a^5\,b^5+96\,a^4\,b^6-784\,a^3\,b^7+480\,a^2\,b^8+200\,a\,b^9}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(a^3\,b^6-7\,a^2\,b^7+11\,a\,b^8+27\,b^9\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{256\,a^8\,b^4-2176\,a^7\,b^5+6912\,a^6\,b^6-10880\,a^5\,b^7+8960\,a^4\,b^8-3456\,a^3\,b^9+256\,a^2\,b^{10}+128\,a\,b^{11}}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}-\frac{\sin\left(c+d\,x\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,\left(512\,a^9\,b^4-2560\,a^8\,b^5+4608\,a^7\,b^6-2560\,a^6\,b^7-2560\,a^5\,b^8+4608\,a^4\,b^9-2560\,a^3\,b^{10}+512\,a^2\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(32\,a^6\,b^5-144\,a^5\,b^6+1264\,a^4\,b^7-2208\,a^3\,b^8+1024\,a^2\,b^9+48\,a\,b^{10}-16\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{8\,a^5\,b^5+96\,a^4\,b^6-784\,a^3\,b^7+480\,a^2\,b^8+200\,a\,b^9}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(a^3\,b^6-7\,a^2\,b^7+11\,a\,b^8+27\,b^9\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}+\left(\left(\left(\left(\frac{256\,a^8\,b^4-2176\,a^7\,b^5+6912\,a^6\,b^6-10880\,a^5\,b^7+8960\,a^4\,b^8-3456\,a^3\,b^9+256\,a^2\,b^{10}+128\,a\,b^{11}}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}+\frac{\sin\left(c+d\,x\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,\left(512\,a^9\,b^4-2560\,a^8\,b^5+4608\,a^7\,b^6-2560\,a^6\,b^7-2560\,a^5\,b^8+4608\,a^4\,b^9-2560\,a^3\,b^{10}+512\,a^2\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(32\,a^6\,b^5-144\,a^5\,b^6+1264\,a^4\,b^7-2208\,a^3\,b^8+1024\,a^2\,b^9+48\,a\,b^{10}-16\,b^{11}\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{8\,a^5\,b^5+96\,a^4\,b^6-784\,a^3\,b^7+480\,a^2\,b^8+200\,a\,b^9}{2\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(a^3\,b^6-7\,a^2\,b^7+11\,a\,b^8+27\,b^9\right)}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}-\frac{a\,b^7-5\,b^8}{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}}\right)\,\sqrt{\frac{a^2\,\sqrt{a^3\,b^3}+b^2\,\sqrt{a^3\,b^3}+4\,a^2\,b^3+4\,a^3\,b^2+6\,a\,b\,\sqrt{a^3\,b^3}}{16\,\left(a^7-4\,a^6\,b+6\,a^5\,b^2-4\,a^4\,b^3+a^3\,b^4\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((((((128*a*b^11 + 256*a^2*b^10 - 3456*a^3*b^9 + 8960*a^4*b^8 - 10880*a^5*b^7 + 6912*a^6*b^6 - 2176*a^7*b^5 + 256*a^8*b^4)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)) - (sin(c + d*x)*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*(512*a^2*b^11 - 2560*a^3*b^10 + 4608*a^4*b^9 - 2560*a^5*b^8 - 2560*a^6*b^7 + 4608*a^7*b^6 - 2560*a^8*b^5 + 512*a^9*b^4))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (sin(c + d*x)*(48*a*b^10 - 16*b^11 + 1024*a^2*b^9 - 2208*a^3*b^8 + 1264*a^4*b^7 - 144*a^5*b^6 + 32*a^6*b^5))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (200*a*b^9 + 480*a^2*b^8 - 784*a^3*b^7 + 96*a^4*b^6 + 8*a^5*b^5)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (sin(c + d*x)*(11*a*b^8 + 27*b^9 - 7*a^2*b^7 + a^3*b^6))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*1i - (((((128*a*b^11 + 256*a^2*b^10 - 3456*a^3*b^9 + 8960*a^4*b^8 - 10880*a^5*b^7 + 6912*a^6*b^6 - 2176*a^7*b^5 + 256*a^8*b^4)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)) + (sin(c + d*x)*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*(512*a^2*b^11 - 2560*a^3*b^10 + 4608*a^4*b^9 - 2560*a^5*b^8 - 2560*a^6*b^7 + 4608*a^7*b^6 - 2560*a^8*b^5 + 512*a^9*b^4))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (sin(c + d*x)*(48*a*b^10 - 16*b^11 + 1024*a^2*b^9 - 2208*a^3*b^8 + 1264*a^4*b^7 - 144*a^5*b^6 + 32*a^6*b^5))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (200*a*b^9 + 480*a^2*b^8 - 784*a^3*b^7 + 96*a^4*b^6 + 8*a^5*b^5)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (sin(c + d*x)*(11*a*b^8 + 27*b^9 - 7*a^2*b^7 + a^3*b^6))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*1i)/((((((128*a*b^11 + 256*a^2*b^10 - 3456*a^3*b^9 + 8960*a^4*b^8 - 10880*a^5*b^7 + 6912*a^6*b^6 - 2176*a^7*b^5 + 256*a^8*b^4)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)) - (sin(c + d*x)*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*(512*a^2*b^11 - 2560*a^3*b^10 + 4608*a^4*b^9 - 2560*a^5*b^8 - 2560*a^6*b^7 + 4608*a^7*b^6 - 2560*a^8*b^5 + 512*a^9*b^4))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (sin(c + d*x)*(48*a*b^10 - 16*b^11 + 1024*a^2*b^9 - 2208*a^3*b^8 + 1264*a^4*b^7 - 144*a^5*b^6 + 32*a^6*b^5))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (200*a*b^9 + 480*a^2*b^8 - 784*a^3*b^7 + 96*a^4*b^6 + 8*a^5*b^5)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (sin(c + d*x)*(11*a*b^8 + 27*b^9 - 7*a^2*b^7 + a^3*b^6))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (((((128*a*b^11 + 256*a^2*b^10 - 3456*a^3*b^9 + 8960*a^4*b^8 - 10880*a^5*b^7 + 6912*a^6*b^6 - 2176*a^7*b^5 + 256*a^8*b^4)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)) + (sin(c + d*x)*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*(512*a^2*b^11 - 2560*a^3*b^10 + 4608*a^4*b^9 - 2560*a^5*b^8 - 2560*a^6*b^7 + 4608*a^7*b^6 - 2560*a^8*b^5 + 512*a^9*b^4))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (sin(c + d*x)*(48*a*b^10 - 16*b^11 + 1024*a^2*b^9 - 2208*a^3*b^8 + 1264*a^4*b^7 - 144*a^5*b^6 + 32*a^6*b^5))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (200*a*b^9 + 480*a^2*b^8 - 784*a^3*b^7 + 96*a^4*b^6 + 8*a^5*b^5)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (sin(c + d*x)*(11*a*b^8 + 27*b^9 - 7*a^2*b^7 + a^3*b^6))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (a*b^7 - 5*b^8)/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*(-(a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) - 4*a^2*b^3 - 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*2i)/d + (atan(((((((128*a*b^11 + 256*a^2*b^10 - 3456*a^3*b^9 + 8960*a^4*b^8 - 10880*a^5*b^7 + 6912*a^6*b^6 - 2176*a^7*b^5 + 256*a^8*b^4)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)) - (sin(c + d*x)*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*(512*a^2*b^11 - 2560*a^3*b^10 + 4608*a^4*b^9 - 2560*a^5*b^8 - 2560*a^6*b^7 + 4608*a^7*b^6 - 2560*a^8*b^5 + 512*a^9*b^4))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (sin(c + d*x)*(48*a*b^10 - 16*b^11 + 1024*a^2*b^9 - 2208*a^3*b^8 + 1264*a^4*b^7 - 144*a^5*b^6 + 32*a^6*b^5))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (200*a*b^9 + 480*a^2*b^8 - 784*a^3*b^7 + 96*a^4*b^6 + 8*a^5*b^5)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (sin(c + d*x)*(11*a*b^8 + 27*b^9 - 7*a^2*b^7 + a^3*b^6))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*1i - (((((128*a*b^11 + 256*a^2*b^10 - 3456*a^3*b^9 + 8960*a^4*b^8 - 10880*a^5*b^7 + 6912*a^6*b^6 - 2176*a^7*b^5 + 256*a^8*b^4)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)) + (sin(c + d*x)*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*(512*a^2*b^11 - 2560*a^3*b^10 + 4608*a^4*b^9 - 2560*a^5*b^8 - 2560*a^6*b^7 + 4608*a^7*b^6 - 2560*a^8*b^5 + 512*a^9*b^4))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (sin(c + d*x)*(48*a*b^10 - 16*b^11 + 1024*a^2*b^9 - 2208*a^3*b^8 + 1264*a^4*b^7 - 144*a^5*b^6 + 32*a^6*b^5))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (200*a*b^9 + 480*a^2*b^8 - 784*a^3*b^7 + 96*a^4*b^6 + 8*a^5*b^5)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (sin(c + d*x)*(11*a*b^8 + 27*b^9 - 7*a^2*b^7 + a^3*b^6))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*1i)/((((((128*a*b^11 + 256*a^2*b^10 - 3456*a^3*b^9 + 8960*a^4*b^8 - 10880*a^5*b^7 + 6912*a^6*b^6 - 2176*a^7*b^5 + 256*a^8*b^4)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)) - (sin(c + d*x)*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*(512*a^2*b^11 - 2560*a^3*b^10 + 4608*a^4*b^9 - 2560*a^5*b^8 - 2560*a^6*b^7 + 4608*a^7*b^6 - 2560*a^8*b^5 + 512*a^9*b^4))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (sin(c + d*x)*(48*a*b^10 - 16*b^11 + 1024*a^2*b^9 - 2208*a^3*b^8 + 1264*a^4*b^7 - 144*a^5*b^6 + 32*a^6*b^5))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (200*a*b^9 + 480*a^2*b^8 - 784*a^3*b^7 + 96*a^4*b^6 + 8*a^5*b^5)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (sin(c + d*x)*(11*a*b^8 + 27*b^9 - 7*a^2*b^7 + a^3*b^6))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) + (((((128*a*b^11 + 256*a^2*b^10 - 3456*a^3*b^9 + 8960*a^4*b^8 - 10880*a^5*b^7 + 6912*a^6*b^6 - 2176*a^7*b^5 + 256*a^8*b^4)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)) + (sin(c + d*x)*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*(512*a^2*b^11 - 2560*a^3*b^10 + 4608*a^4*b^9 - 2560*a^5*b^8 - 2560*a^6*b^7 + 4608*a^7*b^6 - 2560*a^8*b^5 + 512*a^9*b^4))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (sin(c + d*x)*(48*a*b^10 - 16*b^11 + 1024*a^2*b^9 - 2208*a^3*b^8 + 1264*a^4*b^7 - 144*a^5*b^6 + 32*a^6*b^5))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (200*a*b^9 + 480*a^2*b^8 - 784*a^3*b^7 + 96*a^4*b^6 + 8*a^5*b^5)/(2*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (sin(c + d*x)*(11*a*b^8 + 27*b^9 - 7*a^2*b^7 + a^3*b^6))/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2) - (a*b^7 - 5*b^8)/(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)))*((a^2*(a^3*b^3)^(1/2) + b^2*(a^3*b^3)^(1/2) + 4*a^2*b^3 + 4*a^3*b^2 + 6*a*b*(a^3*b^3)^(1/2))/(16*(a^7 - 4*a^6*b + a^3*b^4 - 4*a^4*b^3 + 6*a^5*b^2)))^(1/2)*2i)/d + (log(sin(c + d*x) - 1)*(b/(a - b)^2 - 1/(4*(a - b))))/d + sin(c + d*x)/(2*d*cos(c + d*x)^2*(a - b)) + (log(sin(c + d*x) + 1)*(a - 5*b))/(4*d*(a - b)^2)","B"
410,1,12217,249,20.571670,"\text{Not used}","int(1/(cos(c + d*x)^5*(a - b*sin(c + d*x)^4)),x)","\frac{\frac{\sin\left(c+d\,x\right)\,\left(5\,a-13\,b\right)}{8\,\left(a^2-2\,a\,b+b^2\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(3\,a-11\,b\right)}{8\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left({\cos\left(c+d\,x\right)}^2+{\sin\left(c+d\,x\right)}^4-{\sin\left(c+d\,x\right)}^2\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{2\,b^2}{{\left(a-b\right)}^3}+\frac{3}{16\,\left(a-b\right)}\right)}{d}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(3\,a^2-6\,a\,b+35\,b^2\right)}{16\,d\,{\left(a-b\right)}^3}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-720\,a^8\,b^6+6768\,a^7\,b^7-13712\,a^6\,b^8+28848\,a^5\,b^9+116624\,a^4\,b^{10}-275888\,a^3\,b^{11}+119760\,a^2\,b^{12}+18064\,a\,b^{13}+256\,b^{14}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\left(\left(\frac{6144\,a^{12}\,b^4-55296\,a^{11}\,b^5+266240\,a^{10}\,b^6-872448\,a^9\,b^7+2002944\,a^8\,b^8-3182592\,a^7\,b^9+3440640\,a^6\,b^{10}-2457600\,a^5\,b^{11}+1087488\,a^4\,b^{12}-251904\,a^3\,b^{13}+12288\,a^2\,b^{14}+4096\,a\,b^{15}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\frac{\sin\left(c+d\,x\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,\left(8192\,a^{13}\,b^4-73728\,a^{12}\,b^5+286720\,a^{11}\,b^6-614400\,a^{10}\,b^7+737280\,a^9\,b^8-344064\,a^8\,b^9-344064\,a^7\,b^{10}+737280\,a^6\,b^{11}-614400\,a^5\,b^{12}+286720\,a^4\,b^{13}-73728\,a^3\,b^{14}+8192\,a^2\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(-288\,a^{10}\,b^5+2304\,a^9\,b^6-20096\,a^8\,b^7+57088\,a^7\,b^8-111296\,a^6\,b^9+212736\,a^5\,b^{10}-280960\,a^4\,b^{11}+190720\,a^3\,b^{12}-50464\,a^2\,b^{13}+256\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(9\,a^6\,b^7+18\,a^5\,b^8+71\,a^4\,b^9+892\,a^3\,b^{10}-857\,a^2\,b^{11}+6802\,a\,b^{12}+1257\,b^{13}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-720\,a^8\,b^6+6768\,a^7\,b^7-13712\,a^6\,b^8+28848\,a^5\,b^9+116624\,a^4\,b^{10}-275888\,a^3\,b^{11}+119760\,a^2\,b^{12}+18064\,a\,b^{13}+256\,b^{14}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\left(\left(\frac{6144\,a^{12}\,b^4-55296\,a^{11}\,b^5+266240\,a^{10}\,b^6-872448\,a^9\,b^7+2002944\,a^8\,b^8-3182592\,a^7\,b^9+3440640\,a^6\,b^{10}-2457600\,a^5\,b^{11}+1087488\,a^4\,b^{12}-251904\,a^3\,b^{13}+12288\,a^2\,b^{14}+4096\,a\,b^{15}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}+\frac{\sin\left(c+d\,x\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,\left(8192\,a^{13}\,b^4-73728\,a^{12}\,b^5+286720\,a^{11}\,b^6-614400\,a^{10}\,b^7+737280\,a^9\,b^8-344064\,a^8\,b^9-344064\,a^7\,b^{10}+737280\,a^6\,b^{11}-614400\,a^5\,b^{12}+286720\,a^4\,b^{13}-73728\,a^3\,b^{14}+8192\,a^2\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(-288\,a^{10}\,b^5+2304\,a^9\,b^6-20096\,a^8\,b^7+57088\,a^7\,b^8-111296\,a^6\,b^9+212736\,a^5\,b^{10}-280960\,a^4\,b^{11}+190720\,a^3\,b^{12}-50464\,a^2\,b^{13}+256\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(9\,a^6\,b^7+18\,a^5\,b^8+71\,a^4\,b^9+892\,a^3\,b^{10}-857\,a^2\,b^{11}+6802\,a\,b^{12}+1257\,b^{13}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-720\,a^8\,b^6+6768\,a^7\,b^7-13712\,a^6\,b^8+28848\,a^5\,b^9+116624\,a^4\,b^{10}-275888\,a^3\,b^{11}+119760\,a^2\,b^{12}+18064\,a\,b^{13}+256\,b^{14}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\left(\left(\frac{6144\,a^{12}\,b^4-55296\,a^{11}\,b^5+266240\,a^{10}\,b^6-872448\,a^9\,b^7+2002944\,a^8\,b^8-3182592\,a^7\,b^9+3440640\,a^6\,b^{10}-2457600\,a^5\,b^{11}+1087488\,a^4\,b^{12}-251904\,a^3\,b^{13}+12288\,a^2\,b^{14}+4096\,a\,b^{15}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\frac{\sin\left(c+d\,x\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,\left(8192\,a^{13}\,b^4-73728\,a^{12}\,b^5+286720\,a^{11}\,b^6-614400\,a^{10}\,b^7+737280\,a^9\,b^8-344064\,a^8\,b^9-344064\,a^7\,b^{10}+737280\,a^6\,b^{11}-614400\,a^5\,b^{12}+286720\,a^4\,b^{13}-73728\,a^3\,b^{14}+8192\,a^2\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(-288\,a^{10}\,b^5+2304\,a^9\,b^6-20096\,a^8\,b^7+57088\,a^7\,b^8-111296\,a^6\,b^9+212736\,a^5\,b^{10}-280960\,a^4\,b^{11}+190720\,a^3\,b^{12}-50464\,a^2\,b^{13}+256\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(9\,a^6\,b^7+18\,a^5\,b^8+71\,a^4\,b^9+892\,a^3\,b^{10}-857\,a^2\,b^{11}+6802\,a\,b^{12}+1257\,b^{13}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\left(\left(\frac{-720\,a^8\,b^6+6768\,a^7\,b^7-13712\,a^6\,b^8+28848\,a^5\,b^9+116624\,a^4\,b^{10}-275888\,a^3\,b^{11}+119760\,a^2\,b^{12}+18064\,a\,b^{13}+256\,b^{14}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\left(\left(\frac{6144\,a^{12}\,b^4-55296\,a^{11}\,b^5+266240\,a^{10}\,b^6-872448\,a^9\,b^7+2002944\,a^8\,b^8-3182592\,a^7\,b^9+3440640\,a^6\,b^{10}-2457600\,a^5\,b^{11}+1087488\,a^4\,b^{12}-251904\,a^3\,b^{13}+12288\,a^2\,b^{14}+4096\,a\,b^{15}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}+\frac{\sin\left(c+d\,x\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,\left(8192\,a^{13}\,b^4-73728\,a^{12}\,b^5+286720\,a^{11}\,b^6-614400\,a^{10}\,b^7+737280\,a^9\,b^8-344064\,a^8\,b^9-344064\,a^7\,b^{10}+737280\,a^6\,b^{11}-614400\,a^5\,b^{12}+286720\,a^4\,b^{13}-73728\,a^3\,b^{14}+8192\,a^2\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(-288\,a^{10}\,b^5+2304\,a^9\,b^6-20096\,a^8\,b^7+57088\,a^7\,b^8-111296\,a^6\,b^9+212736\,a^5\,b^{10}-280960\,a^4\,b^{11}+190720\,a^3\,b^{12}-50464\,a^2\,b^{13}+256\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(9\,a^6\,b^7+18\,a^5\,b^8+71\,a^4\,b^9+892\,a^3\,b^{10}-857\,a^2\,b^{11}+6802\,a\,b^{12}+1257\,b^{13}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{9\,a^4\,b^8-60\,a^3\,b^9+318\,a^2\,b^{10}-748\,a\,b^{11}+1505\,b^{12}}{32\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}}\right)\,\sqrt{-\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}-6\,a^2\,b^5-20\,a^3\,b^4-6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-720\,a^8\,b^6+6768\,a^7\,b^7-13712\,a^6\,b^8+28848\,a^5\,b^9+116624\,a^4\,b^{10}-275888\,a^3\,b^{11}+119760\,a^2\,b^{12}+18064\,a\,b^{13}+256\,b^{14}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\left(\left(\frac{6144\,a^{12}\,b^4-55296\,a^{11}\,b^5+266240\,a^{10}\,b^6-872448\,a^9\,b^7+2002944\,a^8\,b^8-3182592\,a^7\,b^9+3440640\,a^6\,b^{10}-2457600\,a^5\,b^{11}+1087488\,a^4\,b^{12}-251904\,a^3\,b^{13}+12288\,a^2\,b^{14}+4096\,a\,b^{15}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\frac{\sin\left(c+d\,x\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,\left(8192\,a^{13}\,b^4-73728\,a^{12}\,b^5+286720\,a^{11}\,b^6-614400\,a^{10}\,b^7+737280\,a^9\,b^8-344064\,a^8\,b^9-344064\,a^7\,b^{10}+737280\,a^6\,b^{11}-614400\,a^5\,b^{12}+286720\,a^4\,b^{13}-73728\,a^3\,b^{14}+8192\,a^2\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(-288\,a^{10}\,b^5+2304\,a^9\,b^6-20096\,a^8\,b^7+57088\,a^7\,b^8-111296\,a^6\,b^9+212736\,a^5\,b^{10}-280960\,a^4\,b^{11}+190720\,a^3\,b^{12}-50464\,a^2\,b^{13}+256\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(9\,a^6\,b^7+18\,a^5\,b^8+71\,a^4\,b^9+892\,a^3\,b^{10}-857\,a^2\,b^{11}+6802\,a\,b^{12}+1257\,b^{13}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-720\,a^8\,b^6+6768\,a^7\,b^7-13712\,a^6\,b^8+28848\,a^5\,b^9+116624\,a^4\,b^{10}-275888\,a^3\,b^{11}+119760\,a^2\,b^{12}+18064\,a\,b^{13}+256\,b^{14}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\left(\left(\frac{6144\,a^{12}\,b^4-55296\,a^{11}\,b^5+266240\,a^{10}\,b^6-872448\,a^9\,b^7+2002944\,a^8\,b^8-3182592\,a^7\,b^9+3440640\,a^6\,b^{10}-2457600\,a^5\,b^{11}+1087488\,a^4\,b^{12}-251904\,a^3\,b^{13}+12288\,a^2\,b^{14}+4096\,a\,b^{15}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}+\frac{\sin\left(c+d\,x\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,\left(8192\,a^{13}\,b^4-73728\,a^{12}\,b^5+286720\,a^{11}\,b^6-614400\,a^{10}\,b^7+737280\,a^9\,b^8-344064\,a^8\,b^9-344064\,a^7\,b^{10}+737280\,a^6\,b^{11}-614400\,a^5\,b^{12}+286720\,a^4\,b^{13}-73728\,a^3\,b^{14}+8192\,a^2\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(-288\,a^{10}\,b^5+2304\,a^9\,b^6-20096\,a^8\,b^7+57088\,a^7\,b^8-111296\,a^6\,b^9+212736\,a^5\,b^{10}-280960\,a^4\,b^{11}+190720\,a^3\,b^{12}-50464\,a^2\,b^{13}+256\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(9\,a^6\,b^7+18\,a^5\,b^8+71\,a^4\,b^9+892\,a^3\,b^{10}-857\,a^2\,b^{11}+6802\,a\,b^{12}+1257\,b^{13}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-720\,a^8\,b^6+6768\,a^7\,b^7-13712\,a^6\,b^8+28848\,a^5\,b^9+116624\,a^4\,b^{10}-275888\,a^3\,b^{11}+119760\,a^2\,b^{12}+18064\,a\,b^{13}+256\,b^{14}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\left(\left(\frac{6144\,a^{12}\,b^4-55296\,a^{11}\,b^5+266240\,a^{10}\,b^6-872448\,a^9\,b^7+2002944\,a^8\,b^8-3182592\,a^7\,b^9+3440640\,a^6\,b^{10}-2457600\,a^5\,b^{11}+1087488\,a^4\,b^{12}-251904\,a^3\,b^{13}+12288\,a^2\,b^{14}+4096\,a\,b^{15}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\frac{\sin\left(c+d\,x\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,\left(8192\,a^{13}\,b^4-73728\,a^{12}\,b^5+286720\,a^{11}\,b^6-614400\,a^{10}\,b^7+737280\,a^9\,b^8-344064\,a^8\,b^9-344064\,a^7\,b^{10}+737280\,a^6\,b^{11}-614400\,a^5\,b^{12}+286720\,a^4\,b^{13}-73728\,a^3\,b^{14}+8192\,a^2\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(-288\,a^{10}\,b^5+2304\,a^9\,b^6-20096\,a^8\,b^7+57088\,a^7\,b^8-111296\,a^6\,b^9+212736\,a^5\,b^{10}-280960\,a^4\,b^{11}+190720\,a^3\,b^{12}-50464\,a^2\,b^{13}+256\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{\sin\left(c+d\,x\right)\,\left(9\,a^6\,b^7+18\,a^5\,b^8+71\,a^4\,b^9+892\,a^3\,b^{10}-857\,a^2\,b^{11}+6802\,a\,b^{12}+1257\,b^{13}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\left(\left(\frac{-720\,a^8\,b^6+6768\,a^7\,b^7-13712\,a^6\,b^8+28848\,a^5\,b^9+116624\,a^4\,b^{10}-275888\,a^3\,b^{11}+119760\,a^2\,b^{12}+18064\,a\,b^{13}+256\,b^{14}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}-\left(\left(\frac{6144\,a^{12}\,b^4-55296\,a^{11}\,b^5+266240\,a^{10}\,b^6-872448\,a^9\,b^7+2002944\,a^8\,b^8-3182592\,a^7\,b^9+3440640\,a^6\,b^{10}-2457600\,a^5\,b^{11}+1087488\,a^4\,b^{12}-251904\,a^3\,b^{13}+12288\,a^2\,b^{14}+4096\,a\,b^{15}}{64\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}+\frac{\sin\left(c+d\,x\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,\left(8192\,a^{13}\,b^4-73728\,a^{12}\,b^5+286720\,a^{11}\,b^6-614400\,a^{10}\,b^7+737280\,a^9\,b^8-344064\,a^8\,b^9-344064\,a^7\,b^{10}+737280\,a^6\,b^{11}-614400\,a^5\,b^{12}+286720\,a^4\,b^{13}-73728\,a^3\,b^{14}+8192\,a^2\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(-288\,a^{10}\,b^5+2304\,a^9\,b^6-20096\,a^8\,b^7+57088\,a^7\,b^8-111296\,a^6\,b^9+212736\,a^5\,b^{10}-280960\,a^4\,b^{11}+190720\,a^3\,b^{12}-50464\,a^2\,b^{13}+256\,b^{15}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}+\frac{\sin\left(c+d\,x\right)\,\left(9\,a^6\,b^7+18\,a^5\,b^8+71\,a^4\,b^9+892\,a^3\,b^{10}-857\,a^2\,b^{11}+6802\,a\,b^{12}+1257\,b^{13}\right)}{16\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}-\frac{9\,a^4\,b^8-60\,a^3\,b^9+318\,a^2\,b^{10}-748\,a\,b^{11}+1505\,b^{12}}{32\,\left(a^8-8\,a^7\,b+28\,a^6\,b^2-56\,a^5\,b^3+70\,a^4\,b^4-56\,a^3\,b^5+28\,a^2\,b^6-8\,a\,b^7+b^8\right)}}\right)\,\sqrt{\frac{a^3\,\sqrt{a^3\,b^5}+b^3\,\sqrt{a^3\,b^5}+6\,a^2\,b^5+20\,a^3\,b^4+6\,a^4\,b^3+15\,a\,b^2\,\sqrt{a^3\,b^5}+15\,a^2\,b\,\sqrt{a^3\,b^5}}{16\,\left(a^9-6\,a^8\,b+15\,a^7\,b^2-20\,a^6\,b^3+15\,a^5\,b^4-6\,a^4\,b^5+a^3\,b^6\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((((18064*a*b^13 + 256*b^14 + 119760*a^2*b^12 - 275888*a^3*b^11 + 116624*a^4*b^10 + 28848*a^5*b^9 - 13712*a^6*b^8 + 6768*a^7*b^7 - 720*a^8*b^6)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (((4096*a*b^15 + 12288*a^2*b^14 - 251904*a^3*b^13 + 1087488*a^4*b^12 - 2457600*a^5*b^11 + 3440640*a^6*b^10 - 3182592*a^7*b^9 + 2002944*a^8*b^8 - 872448*a^9*b^7 + 266240*a^10*b^6 - 55296*a^11*b^5 + 6144*a^12*b^4)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (sin(c + d*x)*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*(8192*a^2*b^15 - 73728*a^3*b^14 + 286720*a^4*b^13 - 614400*a^5*b^12 + 737280*a^6*b^11 - 344064*a^7*b^10 - 344064*a^8*b^9 + 737280*a^9*b^8 - 614400*a^10*b^7 + 286720*a^11*b^6 - 73728*a^12*b^5 + 8192*a^13*b^4))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (sin(c + d*x)*(256*b^15 - 50464*a^2*b^13 + 190720*a^3*b^12 - 280960*a^4*b^11 + 212736*a^5*b^10 - 111296*a^6*b^9 + 57088*a^7*b^8 - 20096*a^8*b^7 + 2304*a^9*b^6 - 288*a^10*b^5))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (sin(c + d*x)*(6802*a*b^12 + 1257*b^13 - 857*a^2*b^11 + 892*a^3*b^10 + 71*a^4*b^9 + 18*a^5*b^8 + 9*a^6*b^7))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*1i - (((18064*a*b^13 + 256*b^14 + 119760*a^2*b^12 - 275888*a^3*b^11 + 116624*a^4*b^10 + 28848*a^5*b^9 - 13712*a^6*b^8 + 6768*a^7*b^7 - 720*a^8*b^6)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (((4096*a*b^15 + 12288*a^2*b^14 - 251904*a^3*b^13 + 1087488*a^4*b^12 - 2457600*a^5*b^11 + 3440640*a^6*b^10 - 3182592*a^7*b^9 + 2002944*a^8*b^8 - 872448*a^9*b^7 + 266240*a^10*b^6 - 55296*a^11*b^5 + 6144*a^12*b^4)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) + (sin(c + d*x)*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*(8192*a^2*b^15 - 73728*a^3*b^14 + 286720*a^4*b^13 - 614400*a^5*b^12 + 737280*a^6*b^11 - 344064*a^7*b^10 - 344064*a^8*b^9 + 737280*a^9*b^8 - 614400*a^10*b^7 + 286720*a^11*b^6 - 73728*a^12*b^5 + 8192*a^13*b^4))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (sin(c + d*x)*(256*b^15 - 50464*a^2*b^13 + 190720*a^3*b^12 - 280960*a^4*b^11 + 212736*a^5*b^10 - 111296*a^6*b^9 + 57088*a^7*b^8 - 20096*a^8*b^7 + 2304*a^9*b^6 - 288*a^10*b^5))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (sin(c + d*x)*(6802*a*b^12 + 1257*b^13 - 857*a^2*b^11 + 892*a^3*b^10 + 71*a^4*b^9 + 18*a^5*b^8 + 9*a^6*b^7))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*1i)/((((18064*a*b^13 + 256*b^14 + 119760*a^2*b^12 - 275888*a^3*b^11 + 116624*a^4*b^10 + 28848*a^5*b^9 - 13712*a^6*b^8 + 6768*a^7*b^7 - 720*a^8*b^6)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (((4096*a*b^15 + 12288*a^2*b^14 - 251904*a^3*b^13 + 1087488*a^4*b^12 - 2457600*a^5*b^11 + 3440640*a^6*b^10 - 3182592*a^7*b^9 + 2002944*a^8*b^8 - 872448*a^9*b^7 + 266240*a^10*b^6 - 55296*a^11*b^5 + 6144*a^12*b^4)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (sin(c + d*x)*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*(8192*a^2*b^15 - 73728*a^3*b^14 + 286720*a^4*b^13 - 614400*a^5*b^12 + 737280*a^6*b^11 - 344064*a^7*b^10 - 344064*a^8*b^9 + 737280*a^9*b^8 - 614400*a^10*b^7 + 286720*a^11*b^6 - 73728*a^12*b^5 + 8192*a^13*b^4))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (sin(c + d*x)*(256*b^15 - 50464*a^2*b^13 + 190720*a^3*b^12 - 280960*a^4*b^11 + 212736*a^5*b^10 - 111296*a^6*b^9 + 57088*a^7*b^8 - 20096*a^8*b^7 + 2304*a^9*b^6 - 288*a^10*b^5))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (sin(c + d*x)*(6802*a*b^12 + 1257*b^13 - 857*a^2*b^11 + 892*a^3*b^10 + 71*a^4*b^9 + 18*a^5*b^8 + 9*a^6*b^7))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (((18064*a*b^13 + 256*b^14 + 119760*a^2*b^12 - 275888*a^3*b^11 + 116624*a^4*b^10 + 28848*a^5*b^9 - 13712*a^6*b^8 + 6768*a^7*b^7 - 720*a^8*b^6)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (((4096*a*b^15 + 12288*a^2*b^14 - 251904*a^3*b^13 + 1087488*a^4*b^12 - 2457600*a^5*b^11 + 3440640*a^6*b^10 - 3182592*a^7*b^9 + 2002944*a^8*b^8 - 872448*a^9*b^7 + 266240*a^10*b^6 - 55296*a^11*b^5 + 6144*a^12*b^4)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) + (sin(c + d*x)*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*(8192*a^2*b^15 - 73728*a^3*b^14 + 286720*a^4*b^13 - 614400*a^5*b^12 + 737280*a^6*b^11 - 344064*a^7*b^10 - 344064*a^8*b^9 + 737280*a^9*b^8 - 614400*a^10*b^7 + 286720*a^11*b^6 - 73728*a^12*b^5 + 8192*a^13*b^4))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (sin(c + d*x)*(256*b^15 - 50464*a^2*b^13 + 190720*a^3*b^12 - 280960*a^4*b^11 + 212736*a^5*b^10 - 111296*a^6*b^9 + 57088*a^7*b^8 - 20096*a^8*b^7 + 2304*a^9*b^6 - 288*a^10*b^5))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (sin(c + d*x)*(6802*a*b^12 + 1257*b^13 - 857*a^2*b^11 + 892*a^3*b^10 + 71*a^4*b^9 + 18*a^5*b^8 + 9*a^6*b^7))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (1505*b^12 - 748*a*b^11 + 318*a^2*b^10 - 60*a^3*b^9 + 9*a^4*b^8)/(32*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2))))*(-(a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) - 6*a^2*b^5 - 20*a^3*b^4 - 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*2i)/d - (log(sin(c + d*x) - 1)*((2*b^2)/(a - b)^3 + 3/(16*(a - b))))/d + (atan(((((18064*a*b^13 + 256*b^14 + 119760*a^2*b^12 - 275888*a^3*b^11 + 116624*a^4*b^10 + 28848*a^5*b^9 - 13712*a^6*b^8 + 6768*a^7*b^7 - 720*a^8*b^6)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (((4096*a*b^15 + 12288*a^2*b^14 - 251904*a^3*b^13 + 1087488*a^4*b^12 - 2457600*a^5*b^11 + 3440640*a^6*b^10 - 3182592*a^7*b^9 + 2002944*a^8*b^8 - 872448*a^9*b^7 + 266240*a^10*b^6 - 55296*a^11*b^5 + 6144*a^12*b^4)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (sin(c + d*x)*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*(8192*a^2*b^15 - 73728*a^3*b^14 + 286720*a^4*b^13 - 614400*a^5*b^12 + 737280*a^6*b^11 - 344064*a^7*b^10 - 344064*a^8*b^9 + 737280*a^9*b^8 - 614400*a^10*b^7 + 286720*a^11*b^6 - 73728*a^12*b^5 + 8192*a^13*b^4))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (sin(c + d*x)*(256*b^15 - 50464*a^2*b^13 + 190720*a^3*b^12 - 280960*a^4*b^11 + 212736*a^5*b^10 - 111296*a^6*b^9 + 57088*a^7*b^8 - 20096*a^8*b^7 + 2304*a^9*b^6 - 288*a^10*b^5))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (sin(c + d*x)*(6802*a*b^12 + 1257*b^13 - 857*a^2*b^11 + 892*a^3*b^10 + 71*a^4*b^9 + 18*a^5*b^8 + 9*a^6*b^7))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*1i - (((18064*a*b^13 + 256*b^14 + 119760*a^2*b^12 - 275888*a^3*b^11 + 116624*a^4*b^10 + 28848*a^5*b^9 - 13712*a^6*b^8 + 6768*a^7*b^7 - 720*a^8*b^6)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (((4096*a*b^15 + 12288*a^2*b^14 - 251904*a^3*b^13 + 1087488*a^4*b^12 - 2457600*a^5*b^11 + 3440640*a^6*b^10 - 3182592*a^7*b^9 + 2002944*a^8*b^8 - 872448*a^9*b^7 + 266240*a^10*b^6 - 55296*a^11*b^5 + 6144*a^12*b^4)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) + (sin(c + d*x)*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*(8192*a^2*b^15 - 73728*a^3*b^14 + 286720*a^4*b^13 - 614400*a^5*b^12 + 737280*a^6*b^11 - 344064*a^7*b^10 - 344064*a^8*b^9 + 737280*a^9*b^8 - 614400*a^10*b^7 + 286720*a^11*b^6 - 73728*a^12*b^5 + 8192*a^13*b^4))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (sin(c + d*x)*(256*b^15 - 50464*a^2*b^13 + 190720*a^3*b^12 - 280960*a^4*b^11 + 212736*a^5*b^10 - 111296*a^6*b^9 + 57088*a^7*b^8 - 20096*a^8*b^7 + 2304*a^9*b^6 - 288*a^10*b^5))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (sin(c + d*x)*(6802*a*b^12 + 1257*b^13 - 857*a^2*b^11 + 892*a^3*b^10 + 71*a^4*b^9 + 18*a^5*b^8 + 9*a^6*b^7))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*1i)/((((18064*a*b^13 + 256*b^14 + 119760*a^2*b^12 - 275888*a^3*b^11 + 116624*a^4*b^10 + 28848*a^5*b^9 - 13712*a^6*b^8 + 6768*a^7*b^7 - 720*a^8*b^6)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (((4096*a*b^15 + 12288*a^2*b^14 - 251904*a^3*b^13 + 1087488*a^4*b^12 - 2457600*a^5*b^11 + 3440640*a^6*b^10 - 3182592*a^7*b^9 + 2002944*a^8*b^8 - 872448*a^9*b^7 + 266240*a^10*b^6 - 55296*a^11*b^5 + 6144*a^12*b^4)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (sin(c + d*x)*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*(8192*a^2*b^15 - 73728*a^3*b^14 + 286720*a^4*b^13 - 614400*a^5*b^12 + 737280*a^6*b^11 - 344064*a^7*b^10 - 344064*a^8*b^9 + 737280*a^9*b^8 - 614400*a^10*b^7 + 286720*a^11*b^6 - 73728*a^12*b^5 + 8192*a^13*b^4))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (sin(c + d*x)*(256*b^15 - 50464*a^2*b^13 + 190720*a^3*b^12 - 280960*a^4*b^11 + 212736*a^5*b^10 - 111296*a^6*b^9 + 57088*a^7*b^8 - 20096*a^8*b^7 + 2304*a^9*b^6 - 288*a^10*b^5))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (sin(c + d*x)*(6802*a*b^12 + 1257*b^13 - 857*a^2*b^11 + 892*a^3*b^10 + 71*a^4*b^9 + 18*a^5*b^8 + 9*a^6*b^7))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (((18064*a*b^13 + 256*b^14 + 119760*a^2*b^12 - 275888*a^3*b^11 + 116624*a^4*b^10 + 28848*a^5*b^9 - 13712*a^6*b^8 + 6768*a^7*b^7 - 720*a^8*b^6)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) - (((4096*a*b^15 + 12288*a^2*b^14 - 251904*a^3*b^13 + 1087488*a^4*b^12 - 2457600*a^5*b^11 + 3440640*a^6*b^10 - 3182592*a^7*b^9 + 2002944*a^8*b^8 - 872448*a^9*b^7 + 266240*a^10*b^6 - 55296*a^11*b^5 + 6144*a^12*b^4)/(64*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)) + (sin(c + d*x)*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*(8192*a^2*b^15 - 73728*a^3*b^14 + 286720*a^4*b^13 - 614400*a^5*b^12 + 737280*a^6*b^11 - 344064*a^7*b^10 - 344064*a^8*b^9 + 737280*a^9*b^8 - 614400*a^10*b^7 + 286720*a^11*b^6 - 73728*a^12*b^5 + 8192*a^13*b^4))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (sin(c + d*x)*(256*b^15 - 50464*a^2*b^13 + 190720*a^3*b^12 - 280960*a^4*b^11 + 212736*a^5*b^10 - 111296*a^6*b^9 + 57088*a^7*b^8 - 20096*a^8*b^7 + 2304*a^9*b^6 - 288*a^10*b^5))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) + (sin(c + d*x)*(6802*a*b^12 + 1257*b^13 - 857*a^2*b^11 + 892*a^3*b^10 + 71*a^4*b^9 + 18*a^5*b^8 + 9*a^6*b^7))/(16*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2)))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2) - (1505*b^12 - 748*a*b^11 + 318*a^2*b^10 - 60*a^3*b^9 + 9*a^4*b^8)/(32*(a^8 - 8*a^7*b - 8*a*b^7 + b^8 + 28*a^2*b^6 - 56*a^3*b^5 + 70*a^4*b^4 - 56*a^5*b^3 + 28*a^6*b^2))))*((a^3*(a^3*b^5)^(1/2) + b^3*(a^3*b^5)^(1/2) + 6*a^2*b^5 + 20*a^3*b^4 + 6*a^4*b^3 + 15*a*b^2*(a^3*b^5)^(1/2) + 15*a^2*b*(a^3*b^5)^(1/2))/(16*(a^9 - 6*a^8*b + a^3*b^6 - 6*a^4*b^5 + 15*a^5*b^4 - 20*a^6*b^3 + 15*a^7*b^2)))^(1/2)*2i)/d + ((sin(c + d*x)*(5*a - 13*b))/(8*(a^2 - 2*a*b + b^2)) - (sin(c + d*x)^3*(3*a - 11*b))/(8*(a^2 - 2*a*b + b^2)))/(d*(cos(c + d*x)^2 - sin(c + d*x)^2 + sin(c + d*x)^4)) + (log(sin(c + d*x) + 1)*(3*a^2 - 6*a*b + 35*b^2))/(16*d*(a - b)^3)","B"
411,1,10319,252,18.798650,"\text{Not used}","int(cos(c + d*x)^10/(a - b*sin(c + d*x)^4),x)","-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-19456\,a^9\,b^5-354048\,a^8\,b^6-246912\,a^7\,b^7+2456376\,a^6\,b^8+550440\,a^5\,b^9-3842640\,a^4\,b^{10}-215472\,a^3\,b^{11}+1591704\,a^2\,b^{12}+78984\,a\,b^{13}+1024\,b^{14}}{128\,b^8}+\left(\left(\frac{-90112\,a^6\,b^{10}+251904\,a^5\,b^{11}-61440\,a^4\,b^{12}-264192\,a^3\,b^{13}+155648\,a^2\,b^{14}+8192\,a\,b^{15}}{128\,b^8}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,1{}\mathrm{i}-\left(\left(\frac{-19456\,a^9\,b^5-354048\,a^8\,b^6-246912\,a^7\,b^7+2456376\,a^6\,b^8+550440\,a^5\,b^9-3842640\,a^4\,b^{10}-215472\,a^3\,b^{11}+1591704\,a^2\,b^{12}+78984\,a\,b^{13}+1024\,b^{14}}{128\,b^8}+\left(\left(\frac{-90112\,a^6\,b^{10}+251904\,a^5\,b^{11}-61440\,a^4\,b^{12}-264192\,a^3\,b^{13}+155648\,a^2\,b^{14}+8192\,a\,b^{15}}{128\,b^8}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,1{}\mathrm{i}}{\left(\left(\frac{-19456\,a^9\,b^5-354048\,a^8\,b^6-246912\,a^7\,b^7+2456376\,a^6\,b^8+550440\,a^5\,b^9-3842640\,a^4\,b^{10}-215472\,a^3\,b^{11}+1591704\,a^2\,b^{12}+78984\,a\,b^{13}+1024\,b^{14}}{128\,b^8}+\left(\left(\frac{-90112\,a^6\,b^{10}+251904\,a^5\,b^{11}-61440\,a^4\,b^{12}-264192\,a^3\,b^{13}+155648\,a^2\,b^{14}+8192\,a\,b^{15}}{128\,b^8}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\left(\left(\frac{-19456\,a^9\,b^5-354048\,a^8\,b^6-246912\,a^7\,b^7+2456376\,a^6\,b^8+550440\,a^5\,b^9-3842640\,a^4\,b^{10}-215472\,a^3\,b^{11}+1591704\,a^2\,b^{12}+78984\,a\,b^{13}+1024\,b^{14}}{128\,b^8}+\left(\left(\frac{-90112\,a^6\,b^{10}+251904\,a^5\,b^{11}-61440\,a^4\,b^{12}-264192\,a^3\,b^{13}+155648\,a^2\,b^{14}+8192\,a\,b^{15}}{128\,b^8}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{576\,a^{12}-312\,a^{11}\,b-9096\,a^{10}\,b^2+12729\,a^9\,b^3+61119\,a^8\,b^4-208908\,a^7\,b^5+203868\,a^6\,b^6+117486\,a^5\,b^7-487854\,a^4\,b^8+535356\,a^3\,b^9-305868\,a^2\,b^{10}+92769\,a\,b^{11}-11865\,b^{12}}{64\,b^8}}\right)\,\sqrt{-\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}+9\,a^2\,b^9+84\,a^3\,b^8+126\,a^4\,b^7+36\,a^5\,b^6+a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-19456\,a^9\,b^5-354048\,a^8\,b^6-246912\,a^7\,b^7+2456376\,a^6\,b^8+550440\,a^5\,b^9-3842640\,a^4\,b^{10}-215472\,a^3\,b^{11}+1591704\,a^2\,b^{12}+78984\,a\,b^{13}+1024\,b^{14}}{128\,b^8}+\left(\left(\frac{-90112\,a^6\,b^{10}+251904\,a^5\,b^{11}-61440\,a^4\,b^{12}-264192\,a^3\,b^{13}+155648\,a^2\,b^{14}+8192\,a\,b^{15}}{128\,b^8}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,1{}\mathrm{i}-\left(\left(\frac{-19456\,a^9\,b^5-354048\,a^8\,b^6-246912\,a^7\,b^7+2456376\,a^6\,b^8+550440\,a^5\,b^9-3842640\,a^4\,b^{10}-215472\,a^3\,b^{11}+1591704\,a^2\,b^{12}+78984\,a\,b^{13}+1024\,b^{14}}{128\,b^8}+\left(\left(\frac{-90112\,a^6\,b^{10}+251904\,a^5\,b^{11}-61440\,a^4\,b^{12}-264192\,a^3\,b^{13}+155648\,a^2\,b^{14}+8192\,a\,b^{15}}{128\,b^8}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,1{}\mathrm{i}}{\left(\left(\frac{-19456\,a^9\,b^5-354048\,a^8\,b^6-246912\,a^7\,b^7+2456376\,a^6\,b^8+550440\,a^5\,b^9-3842640\,a^4\,b^{10}-215472\,a^3\,b^{11}+1591704\,a^2\,b^{12}+78984\,a\,b^{13}+1024\,b^{14}}{128\,b^8}+\left(\left(\frac{-90112\,a^6\,b^{10}+251904\,a^5\,b^{11}-61440\,a^4\,b^{12}-264192\,a^3\,b^{13}+155648\,a^2\,b^{14}+8192\,a\,b^{15}}{128\,b^8}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\left(\left(\frac{-19456\,a^9\,b^5-354048\,a^8\,b^6-246912\,a^7\,b^7+2456376\,a^6\,b^8+550440\,a^5\,b^9-3842640\,a^4\,b^{10}-215472\,a^3\,b^{11}+1591704\,a^2\,b^{12}+78984\,a\,b^{13}+1024\,b^{14}}{128\,b^8}+\left(\left(\frac{-90112\,a^6\,b^{10}+251904\,a^5\,b^{11}-61440\,a^4\,b^{12}-264192\,a^3\,b^{13}+155648\,a^2\,b^{14}+8192\,a\,b^{15}}{128\,b^8}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}-\frac{576\,a^{12}-312\,a^{11}\,b-9096\,a^{10}\,b^2+12729\,a^9\,b^3+61119\,a^8\,b^4-208908\,a^7\,b^5+203868\,a^6\,b^6+117486\,a^5\,b^7-487854\,a^4\,b^8+535356\,a^3\,b^9-305868\,a^2\,b^{10}+92769\,a\,b^{11}-11865\,b^{12}}{64\,b^8}}\right)\,\sqrt{\frac{9\,a^4\,\sqrt{a^3\,b^{11}}+b^4\,\sqrt{a^3\,b^{11}}-9\,a^2\,b^9-84\,a^3\,b^8-126\,a^4\,b^7-36\,a^5\,b^6-a^6\,b^5+126\,a^2\,b^2\,\sqrt{a^3\,b^{11}}+36\,a\,b^3\,\sqrt{a^3\,b^{11}}+84\,a^3\,b\,\sqrt{a^3\,b^{11}}}{16\,a^3\,b^{10}}}\,2{}\mathrm{i}}{d}-\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a+55\,b\right)}{16\,b^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(6\,a+35\,b\right)}{6\,b^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(8\,a+41\,b\right)}{16\,b^2}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^6+3\,{\mathrm{tan}\left(c+d\,x\right)}^4+3\,{\mathrm{tan}\left(c+d\,x\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}+\frac{3\,\left(\frac{-152\,a^9\,b^5-2766\,a^8\,b^6-1929\,a^7\,b^7+\frac{307047\,a^6\,b^8}{16}+\frac{68805\,a^5\,b^9}{16}-\frac{240165\,a^4\,b^{10}}{8}-\frac{13467\,a^3\,b^{11}}{8}+\frac{198963\,a^2\,b^{12}}{16}+\frac{9873\,a\,b^{13}}{16}+8\,b^{14}}{b^8}+\frac{3\,\left(\frac{3\,\left(\frac{-704\,a^6\,b^{10}+1968\,a^5\,b^{11}-480\,a^4\,b^{12}-2064\,a^3\,b^{13}+1216\,a^2\,b^{14}+64\,a\,b^{15}}{b^8}-\frac{3\,\mathrm{tan}\left(c+d\,x\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{2048\,b^8}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,3{}\mathrm{i}}{32\,b^2}+\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}-\frac{3\,\left(\frac{-152\,a^9\,b^5-2766\,a^8\,b^6-1929\,a^7\,b^7+\frac{307047\,a^6\,b^8}{16}+\frac{68805\,a^5\,b^9}{16}-\frac{240165\,a^4\,b^{10}}{8}-\frac{13467\,a^3\,b^{11}}{8}+\frac{198963\,a^2\,b^{12}}{16}+\frac{9873\,a\,b^{13}}{16}+8\,b^{14}}{b^8}+\frac{3\,\left(\frac{3\,\left(\frac{-704\,a^6\,b^{10}+1968\,a^5\,b^{11}-480\,a^4\,b^{12}-2064\,a^3\,b^{13}+1216\,a^2\,b^{14}+64\,a\,b^{15}}{b^8}+\frac{3\,\mathrm{tan}\left(c+d\,x\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{2048\,b^8}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,3{}\mathrm{i}}{32\,b^2}}{\frac{9\,a^{12}-\frac{39\,a^{11}\,b}{8}-\frac{1137\,a^{10}\,b^2}{8}+\frac{12729\,a^9\,b^3}{64}+\frac{61119\,a^8\,b^4}{64}-\frac{52227\,a^7\,b^5}{16}+\frac{50967\,a^6\,b^6}{16}+\frac{58743\,a^5\,b^7}{32}-\frac{243927\,a^4\,b^8}{32}+\frac{133839\,a^3\,b^9}{16}-\frac{76467\,a^2\,b^{10}}{16}+\frac{92769\,a\,b^{11}}{64}-\frac{11865\,b^{12}}{64}}{b^8}-\frac{3\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}+\frac{3\,\left(\frac{-152\,a^9\,b^5-2766\,a^8\,b^6-1929\,a^7\,b^7+\frac{307047\,a^6\,b^8}{16}+\frac{68805\,a^5\,b^9}{16}-\frac{240165\,a^4\,b^{10}}{8}-\frac{13467\,a^3\,b^{11}}{8}+\frac{198963\,a^2\,b^{12}}{16}+\frac{9873\,a\,b^{13}}{16}+8\,b^{14}}{b^8}+\frac{3\,\left(\frac{3\,\left(\frac{-704\,a^6\,b^{10}+1968\,a^5\,b^{11}-480\,a^4\,b^{12}-2064\,a^3\,b^{13}+1216\,a^2\,b^{14}+64\,a\,b^{15}}{b^8}-\frac{3\,\mathrm{tan}\left(c+d\,x\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{2048\,b^8}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}+\frac{3\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-128\,a^{11}-3776\,a^{10}\,b-74000\,a^9\,b^2+118095\,a^8\,b^3+261366\,a^7\,b^4-387534\,a^6\,b^5-444642\,a^5\,b^6+780960\,a^4\,b^7+2370\,a^3\,b^8-387826\,a^2\,b^9+123962\,a\,b^{10}+11153\,b^{11}\right)}{64\,b^6}-\frac{3\,\left(\frac{-152\,a^9\,b^5-2766\,a^8\,b^6-1929\,a^7\,b^7+\frac{307047\,a^6\,b^8}{16}+\frac{68805\,a^5\,b^9}{16}-\frac{240165\,a^4\,b^{10}}{8}-\frac{13467\,a^3\,b^{11}}{8}+\frac{198963\,a^2\,b^{12}}{16}+\frac{9873\,a\,b^{13}}{16}+8\,b^{14}}{b^8}+\frac{3\,\left(\frac{3\,\left(\frac{-704\,a^6\,b^{10}+1968\,a^5\,b^{11}-480\,a^4\,b^{12}-2064\,a^3\,b^{13}+1216\,a^2\,b^{14}+64\,a\,b^{15}}{b^8}+\frac{3\,\mathrm{tan}\left(c+d\,x\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(49152\,a^5\,b^{10}-49152\,a^4\,b^{11}-49152\,a^3\,b^{12}+49152\,a^2\,b^{13}\right)}{2048\,b^8}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(5120\,a^8\,b^5+232448\,a^7\,b^6+498944\,a^6\,b^7-469488\,a^5\,b^8-919536\,a^4\,b^9+46512\,a^3\,b^{10}+617264\,a^2\,b^{11}-10240\,a\,b^{12}-1024\,b^{13}\right)}{64\,b^6}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{32\,b^2}}\right)\,\left(a\,24{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,3{}\mathrm{i}}{16\,b^2\,d}","Not used",1,"(atan(((((tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6) + (3*(((9873*a*b^13)/16 + 8*b^14 + (198963*a^2*b^12)/16 - (13467*a^3*b^11)/8 - (240165*a^4*b^10)/8 + (68805*a^5*b^9)/16 + (307047*a^6*b^8)/16 - 1929*a^7*b^7 - 2766*a^8*b^6 - 152*a^9*b^5)/b^8 + (3*((3*((64*a*b^15 + 1216*a^2*b^14 - 2064*a^3*b^13 - 480*a^4*b^12 + 1968*a^5*b^11 - 704*a^6*b^10)/b^8 - (3*tan(c + d*x)*(a*24i + b*35i)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(2048*b^8))*(a*24i + b*35i))/(32*b^2) - (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*(a*24i + b*35i))/(32*b^2))*(a*24i + b*35i))/(32*b^2))*(a*24i + b*35i)*3i)/(32*b^2) + (((tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6) - (3*(((9873*a*b^13)/16 + 8*b^14 + (198963*a^2*b^12)/16 - (13467*a^3*b^11)/8 - (240165*a^4*b^10)/8 + (68805*a^5*b^9)/16 + (307047*a^6*b^8)/16 - 1929*a^7*b^7 - 2766*a^8*b^6 - 152*a^9*b^5)/b^8 + (3*((3*((64*a*b^15 + 1216*a^2*b^14 - 2064*a^3*b^13 - 480*a^4*b^12 + 1968*a^5*b^11 - 704*a^6*b^10)/b^8 + (3*tan(c + d*x)*(a*24i + b*35i)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(2048*b^8))*(a*24i + b*35i))/(32*b^2) + (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*(a*24i + b*35i))/(32*b^2))*(a*24i + b*35i))/(32*b^2))*(a*24i + b*35i)*3i)/(32*b^2))/(((92769*a*b^11)/64 - (39*a^11*b)/8 + 9*a^12 - (11865*b^12)/64 - (76467*a^2*b^10)/16 + (133839*a^3*b^9)/16 - (243927*a^4*b^8)/32 + (58743*a^5*b^7)/32 + (50967*a^6*b^6)/16 - (52227*a^7*b^5)/16 + (61119*a^8*b^4)/64 + (12729*a^9*b^3)/64 - (1137*a^10*b^2)/8)/b^8 - (3*((tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6) + (3*(((9873*a*b^13)/16 + 8*b^14 + (198963*a^2*b^12)/16 - (13467*a^3*b^11)/8 - (240165*a^4*b^10)/8 + (68805*a^5*b^9)/16 + (307047*a^6*b^8)/16 - 1929*a^7*b^7 - 2766*a^8*b^6 - 152*a^9*b^5)/b^8 + (3*((3*((64*a*b^15 + 1216*a^2*b^14 - 2064*a^3*b^13 - 480*a^4*b^12 + 1968*a^5*b^11 - 704*a^6*b^10)/b^8 - (3*tan(c + d*x)*(a*24i + b*35i)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(2048*b^8))*(a*24i + b*35i))/(32*b^2) - (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*(a*24i + b*35i))/(32*b^2))*(a*24i + b*35i))/(32*b^2))*(a*24i + b*35i))/(32*b^2) + (3*((tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6) - (3*(((9873*a*b^13)/16 + 8*b^14 + (198963*a^2*b^12)/16 - (13467*a^3*b^11)/8 - (240165*a^4*b^10)/8 + (68805*a^5*b^9)/16 + (307047*a^6*b^8)/16 - 1929*a^7*b^7 - 2766*a^8*b^6 - 152*a^9*b^5)/b^8 + (3*((3*((64*a*b^15 + 1216*a^2*b^14 - 2064*a^3*b^13 - 480*a^4*b^12 + 1968*a^5*b^11 - 704*a^6*b^10)/b^8 + (3*tan(c + d*x)*(a*24i + b*35i)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(2048*b^8))*(a*24i + b*35i))/(32*b^2) + (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*(a*24i + b*35i))/(32*b^2))*(a*24i + b*35i))/(32*b^2))*(a*24i + b*35i))/(32*b^2)))*(a*24i + b*35i)*3i)/(16*b^2*d) - (atan(((((78984*a*b^13 + 1024*b^14 + 1591704*a^2*b^12 - 215472*a^3*b^11 - 3842640*a^4*b^10 + 550440*a^5*b^9 + 2456376*a^6*b^8 - 246912*a^7*b^7 - 354048*a^8*b^6 - 19456*a^9*b^5)/(128*b^8) + (((8192*a*b^15 + 155648*a^2*b^14 - 264192*a^3*b^13 - 61440*a^4*b^12 + 251904*a^5*b^11 - 90112*a^6*b^10)/(128*b^8) - (tan(c + d*x)*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*1i - (((78984*a*b^13 + 1024*b^14 + 1591704*a^2*b^12 - 215472*a^3*b^11 - 3842640*a^4*b^10 + 550440*a^5*b^9 + 2456376*a^6*b^8 - 246912*a^7*b^7 - 354048*a^8*b^6 - 19456*a^9*b^5)/(128*b^8) + (((8192*a*b^15 + 155648*a^2*b^14 - 264192*a^3*b^13 - 61440*a^4*b^12 + 251904*a^5*b^11 - 90112*a^6*b^10)/(128*b^8) + (tan(c + d*x)*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*1i)/((((78984*a*b^13 + 1024*b^14 + 1591704*a^2*b^12 - 215472*a^3*b^11 - 3842640*a^4*b^10 + 550440*a^5*b^9 + 2456376*a^6*b^8 - 246912*a^7*b^7 - 354048*a^8*b^6 - 19456*a^9*b^5)/(128*b^8) + (((8192*a*b^15 + 155648*a^2*b^14 - 264192*a^3*b^13 - 61440*a^4*b^12 + 251904*a^5*b^11 - 90112*a^6*b^10)/(128*b^8) - (tan(c + d*x)*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (((78984*a*b^13 + 1024*b^14 + 1591704*a^2*b^12 - 215472*a^3*b^11 - 3842640*a^4*b^10 + 550440*a^5*b^9 + 2456376*a^6*b^8 - 246912*a^7*b^7 - 354048*a^8*b^6 - 19456*a^9*b^5)/(128*b^8) + (((8192*a*b^15 + 155648*a^2*b^14 - 264192*a^3*b^13 - 61440*a^4*b^12 + 251904*a^5*b^11 - 90112*a^6*b^10)/(128*b^8) + (tan(c + d*x)*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (92769*a*b^11 - 312*a^11*b + 576*a^12 - 11865*b^12 - 305868*a^2*b^10 + 535356*a^3*b^9 - 487854*a^4*b^8 + 117486*a^5*b^7 + 203868*a^6*b^6 - 208908*a^7*b^5 + 61119*a^8*b^4 + 12729*a^9*b^3 - 9096*a^10*b^2)/(64*b^8)))*((9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) - 9*a^2*b^9 - 84*a^3*b^8 - 126*a^4*b^7 - 36*a^5*b^6 - a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*2i)/d - ((tan(c + d*x)*(8*a + 55*b))/(16*b^2) + (tan(c + d*x)^3*(6*a + 35*b))/(6*b^2) + (tan(c + d*x)^5*(8*a + 41*b))/(16*b^2))/(d*(3*tan(c + d*x)^2 + 3*tan(c + d*x)^4 + tan(c + d*x)^6 + 1)) - (atan(((((78984*a*b^13 + 1024*b^14 + 1591704*a^2*b^12 - 215472*a^3*b^11 - 3842640*a^4*b^10 + 550440*a^5*b^9 + 2456376*a^6*b^8 - 246912*a^7*b^7 - 354048*a^8*b^6 - 19456*a^9*b^5)/(128*b^8) + (((8192*a*b^15 + 155648*a^2*b^14 - 264192*a^3*b^13 - 61440*a^4*b^12 + 251904*a^5*b^11 - 90112*a^6*b^10)/(128*b^8) - (tan(c + d*x)*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*1i - (((78984*a*b^13 + 1024*b^14 + 1591704*a^2*b^12 - 215472*a^3*b^11 - 3842640*a^4*b^10 + 550440*a^5*b^9 + 2456376*a^6*b^8 - 246912*a^7*b^7 - 354048*a^8*b^6 - 19456*a^9*b^5)/(128*b^8) + (((8192*a*b^15 + 155648*a^2*b^14 - 264192*a^3*b^13 - 61440*a^4*b^12 + 251904*a^5*b^11 - 90112*a^6*b^10)/(128*b^8) + (tan(c + d*x)*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*1i)/((((78984*a*b^13 + 1024*b^14 + 1591704*a^2*b^12 - 215472*a^3*b^11 - 3842640*a^4*b^10 + 550440*a^5*b^9 + 2456376*a^6*b^8 - 246912*a^7*b^7 - 354048*a^8*b^6 - 19456*a^9*b^5)/(128*b^8) + (((8192*a*b^15 + 155648*a^2*b^14 - 264192*a^3*b^13 - 61440*a^4*b^12 + 251904*a^5*b^11 - 90112*a^6*b^10)/(128*b^8) - (tan(c + d*x)*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (((78984*a*b^13 + 1024*b^14 + 1591704*a^2*b^12 - 215472*a^3*b^11 - 3842640*a^4*b^10 + 550440*a^5*b^9 + 2456376*a^6*b^8 - 246912*a^7*b^7 - 354048*a^8*b^6 - 19456*a^9*b^5)/(128*b^8) + (((8192*a*b^15 + 155648*a^2*b^14 - 264192*a^3*b^13 - 61440*a^4*b^12 + 251904*a^5*b^11 - 90112*a^6*b^10)/(128*b^8) + (tan(c + d*x)*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*(49152*a^2*b^13 - 49152*a^3*b^12 - 49152*a^4*b^11 + 49152*a^5*b^10))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) + (tan(c + d*x)*(617264*a^2*b^11 - 1024*b^13 - 10240*a*b^12 + 46512*a^3*b^10 - 919536*a^4*b^9 - 469488*a^5*b^8 + 498944*a^6*b^7 + 232448*a^7*b^6 + 5120*a^8*b^5))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (tan(c + d*x)*(123962*a*b^10 - 3776*a^10*b - 128*a^11 + 11153*b^11 - 387826*a^2*b^9 + 2370*a^3*b^8 + 780960*a^4*b^7 - 444642*a^5*b^6 - 387534*a^6*b^5 + 261366*a^7*b^4 + 118095*a^8*b^3 - 74000*a^9*b^2))/(64*b^6))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2) - (92769*a*b^11 - 312*a^11*b + 576*a^12 - 11865*b^12 - 305868*a^2*b^10 + 535356*a^3*b^9 - 487854*a^4*b^8 + 117486*a^5*b^7 + 203868*a^6*b^6 - 208908*a^7*b^5 + 61119*a^8*b^4 + 12729*a^9*b^3 - 9096*a^10*b^2)/(64*b^8)))*(-(9*a^4*(a^3*b^11)^(1/2) + b^4*(a^3*b^11)^(1/2) + 9*a^2*b^9 + 84*a^3*b^8 + 126*a^4*b^7 + 36*a^5*b^6 + a^6*b^5 + 126*a^2*b^2*(a^3*b^11)^(1/2) + 36*a*b^3*(a^3*b^11)^(1/2) + 84*a^3*b*(a^3*b^11)^(1/2))/(16*a^3*b^10))^(1/2)*2i)/d","B"
412,1,8773,186,17.463094,"\text{Not used}","int(cos(c + d*x)^8/(a - b*sin(c + d*x)^4),x)","-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{768\,a^8\,b^3+27648\,a^7\,b^4+29040\,a^6\,b^5-240464\,a^5\,b^6+35296\,a^4\,b^7+373728\,a^3\,b^8-208208\,a^2\,b^9-17552\,a\,b^{10}-256\,b^{11}}{64\,b^5}-\left(\left(\frac{-12288\,a^6\,b^7+14336\,a^5\,b^8+69632\,a^4\,b^9-129024\,a^3\,b^{10}+53248\,a^2\,b^{11}+4096\,a\,b^{12}}{64\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,1{}\mathrm{i}-\left(\left(\frac{768\,a^8\,b^3+27648\,a^7\,b^4+29040\,a^6\,b^5-240464\,a^5\,b^6+35296\,a^4\,b^7+373728\,a^3\,b^8-208208\,a^2\,b^9-17552\,a\,b^{10}-256\,b^{11}}{64\,b^5}-\left(\left(\frac{-12288\,a^6\,b^7+14336\,a^5\,b^8+69632\,a^4\,b^9-129024\,a^3\,b^{10}+53248\,a^2\,b^{11}+4096\,a\,b^{12}}{64\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,1{}\mathrm{i}}{\frac{-344\,a^9+1247\,a^8\,b+2408\,a^7\,b^2-22876\,a^6\,b^3+60200\,a^5\,b^4-86086\,a^4\,b^5+74648\,a^3\,b^6-39388\,a^2\,b^7+11696\,a\,b^8-1505\,b^9}{32\,b^5}+\left(\left(\frac{768\,a^8\,b^3+27648\,a^7\,b^4+29040\,a^6\,b^5-240464\,a^5\,b^6+35296\,a^4\,b^7+373728\,a^3\,b^8-208208\,a^2\,b^9-17552\,a\,b^{10}-256\,b^{11}}{64\,b^5}-\left(\left(\frac{-12288\,a^6\,b^7+14336\,a^5\,b^8+69632\,a^4\,b^9-129024\,a^3\,b^{10}+53248\,a^2\,b^{11}+4096\,a\,b^{12}}{64\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\left(\left(\frac{768\,a^8\,b^3+27648\,a^7\,b^4+29040\,a^6\,b^5-240464\,a^5\,b^6+35296\,a^4\,b^7+373728\,a^3\,b^8-208208\,a^2\,b^9-17552\,a\,b^{10}-256\,b^{11}}{64\,b^5}-\left(\left(\frac{-12288\,a^6\,b^7+14336\,a^5\,b^8+69632\,a^4\,b^9-129024\,a^3\,b^{10}+53248\,a^2\,b^{11}+4096\,a\,b^{12}}{64\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}+7\,a^2\,b^7+35\,a^3\,b^6+21\,a^4\,b^5+a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,2{}\mathrm{i}}{d}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{768\,a^8\,b^3+27648\,a^7\,b^4+29040\,a^6\,b^5-240464\,a^5\,b^6+35296\,a^4\,b^7+373728\,a^3\,b^8-208208\,a^2\,b^9-17552\,a\,b^{10}-256\,b^{11}}{64\,b^5}-\left(\left(\frac{-12288\,a^6\,b^7+14336\,a^5\,b^8+69632\,a^4\,b^9-129024\,a^3\,b^{10}+53248\,a^2\,b^{11}+4096\,a\,b^{12}}{64\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,1{}\mathrm{i}-\left(\left(\frac{768\,a^8\,b^3+27648\,a^7\,b^4+29040\,a^6\,b^5-240464\,a^5\,b^6+35296\,a^4\,b^7+373728\,a^3\,b^8-208208\,a^2\,b^9-17552\,a\,b^{10}-256\,b^{11}}{64\,b^5}-\left(\left(\frac{-12288\,a^6\,b^7+14336\,a^5\,b^8+69632\,a^4\,b^9-129024\,a^3\,b^{10}+53248\,a^2\,b^{11}+4096\,a\,b^{12}}{64\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,1{}\mathrm{i}}{\frac{-344\,a^9+1247\,a^8\,b+2408\,a^7\,b^2-22876\,a^6\,b^3+60200\,a^5\,b^4-86086\,a^4\,b^5+74648\,a^3\,b^6-39388\,a^2\,b^7+11696\,a\,b^8-1505\,b^9}{32\,b^5}+\left(\left(\frac{768\,a^8\,b^3+27648\,a^7\,b^4+29040\,a^6\,b^5-240464\,a^5\,b^6+35296\,a^4\,b^7+373728\,a^3\,b^8-208208\,a^2\,b^9-17552\,a\,b^{10}-256\,b^{11}}{64\,b^5}-\left(\left(\frac{-12288\,a^6\,b^7+14336\,a^5\,b^8+69632\,a^4\,b^9-129024\,a^3\,b^{10}+53248\,a^2\,b^{11}+4096\,a\,b^{12}}{64\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}+\left(\left(\frac{768\,a^8\,b^3+27648\,a^7\,b^4+29040\,a^6\,b^5-240464\,a^5\,b^6+35296\,a^4\,b^7+373728\,a^3\,b^8-208208\,a^2\,b^9-17552\,a\,b^{10}-256\,b^{11}}{64\,b^5}-\left(\left(\frac{-12288\,a^6\,b^7+14336\,a^5\,b^8+69632\,a^4\,b^9-129024\,a^3\,b^{10}+53248\,a^2\,b^{11}+4096\,a\,b^{12}}{64\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^9}+b^3\,\sqrt{a^3\,b^9}-7\,a^2\,b^7-35\,a^3\,b^6-21\,a^4\,b^5-a^5\,b^4+21\,a\,b^2\,\sqrt{a^3\,b^9}+35\,a^2\,b\,\sqrt{a^3\,b^9}}{16\,a^3\,b^8}}\,2{}\mathrm{i}}{d}-\frac{\frac{13\,\mathrm{tan}\left(c+d\,x\right)}{8\,b}+\frac{11\,{\mathrm{tan}\left(c+d\,x\right)}^3}{8\,b}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4+2\,{\mathrm{tan}\left(c+d\,x\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(\frac{\left(\frac{12\,a^8\,b^3+432\,a^7\,b^4+\frac{1815\,a^6\,b^5}{4}-\frac{15029\,a^5\,b^6}{4}+\frac{1103\,a^4\,b^7}{2}+\frac{11679\,a^3\,b^8}{2}-\frac{13013\,a^2\,b^9}{4}-\frac{1097\,a\,b^{10}}{4}-4\,b^{11}}{b^5}-\frac{\left(\frac{\left(\frac{-192\,a^6\,b^7+224\,a^5\,b^8+1088\,a^4\,b^9-2016\,a^3\,b^{10}+832\,a^2\,b^{11}+64\,a\,b^{12}}{b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{256\,b^6}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,1{}\mathrm{i}}{16\,b^2}-\frac{\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(\frac{\left(\frac{12\,a^8\,b^3+432\,a^7\,b^4+\frac{1815\,a^6\,b^5}{4}-\frac{15029\,a^5\,b^6}{4}+\frac{1103\,a^4\,b^7}{2}+\frac{11679\,a^3\,b^8}{2}-\frac{13013\,a^2\,b^9}{4}-\frac{1097\,a\,b^{10}}{4}-4\,b^{11}}{b^5}-\frac{\left(\frac{\left(\frac{-192\,a^6\,b^7+224\,a^5\,b^8+1088\,a^4\,b^9-2016\,a^3\,b^{10}+832\,a^2\,b^{11}+64\,a\,b^{12}}{b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{256\,b^6}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)\,1{}\mathrm{i}}{16\,b^2}}{\frac{-\frac{43\,a^9}{4}+\frac{1247\,a^8\,b}{32}+\frac{301\,a^7\,b^2}{4}-\frac{5719\,a^6\,b^3}{8}+\frac{7525\,a^5\,b^4}{4}-\frac{43043\,a^4\,b^5}{16}+\frac{9331\,a^3\,b^6}{4}-\frac{9847\,a^2\,b^7}{8}+\frac{731\,a\,b^8}{2}-\frac{1505\,b^9}{32}}{b^5}+\frac{\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(\frac{\left(\frac{12\,a^8\,b^3+432\,a^7\,b^4+\frac{1815\,a^6\,b^5}{4}-\frac{15029\,a^5\,b^6}{4}+\frac{1103\,a^4\,b^7}{2}+\frac{11679\,a^3\,b^8}{2}-\frac{13013\,a^2\,b^9}{4}-\frac{1097\,a\,b^{10}}{4}-4\,b^{11}}{b^5}-\frac{\left(\frac{\left(\frac{-192\,a^6\,b^7+224\,a^5\,b^8+1088\,a^4\,b^9-2016\,a^3\,b^{10}+832\,a^2\,b^{11}+64\,a\,b^{12}}{b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{256\,b^6}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)}{16\,b^2}+\frac{\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(\frac{\left(\frac{12\,a^8\,b^3+432\,a^7\,b^4+\frac{1815\,a^6\,b^5}{4}-\frac{15029\,a^5\,b^6}{4}+\frac{1103\,a^4\,b^7}{2}+\frac{11679\,a^3\,b^8}{2}-\frac{13013\,a^2\,b^9}{4}-\frac{1097\,a\,b^{10}}{4}-4\,b^{11}}{b^5}-\frac{\left(\frac{\left(\frac{-192\,a^6\,b^7+224\,a^5\,b^8+1088\,a^4\,b^9-2016\,a^3\,b^{10}+832\,a^2\,b^{11}+64\,a\,b^{12}}{b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,\left(12288\,a^5\,b^8-12288\,a^4\,b^9-12288\,a^3\,b^{10}+12288\,a^2\,b^{11}\right)}{256\,b^6}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2304\,a^7\,b^4-29696\,a^6\,b^5-12432\,a^5\,b^6+53616\,a^4\,b^7+61136\,a^3\,b^8-70832\,a^2\,b^9+256\,a\,b^{10}+256\,b^{11}\right)}{16\,b^4}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)}{16\,b^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(96\,a^9+336\,a^8\,b+1721\,a^7\,b^2-9223\,a^6\,b^3+3077\,a^5\,b^4+27109\,a^4\,b^5-41861\,a^3\,b^6+21499\,a^2\,b^7-1497\,a\,b^8-1257\,b^9\right)}{16\,b^4}\right)}{16\,b^2}}\right)\,\left(a\,8{}\mathrm{i}+b\,35{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^2\,d}","Not used",1,"- (atan(((((373728*a^3*b^8 - 256*b^11 - 208208*a^2*b^9 - 17552*a*b^10 + 35296*a^4*b^7 - 240464*a^5*b^6 + 29040*a^6*b^5 + 27648*a^7*b^4 + 768*a^8*b^3)/(64*b^5) - (((4096*a*b^12 + 53248*a^2*b^11 - 129024*a^3*b^10 + 69632*a^4*b^9 + 14336*a^5*b^8 - 12288*a^6*b^7)/(64*b^5) - (tan(c + d*x)*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*1i - (((373728*a^3*b^8 - 256*b^11 - 208208*a^2*b^9 - 17552*a*b^10 + 35296*a^4*b^7 - 240464*a^5*b^6 + 29040*a^6*b^5 + 27648*a^7*b^4 + 768*a^8*b^3)/(64*b^5) - (((4096*a*b^12 + 53248*a^2*b^11 - 129024*a^3*b^10 + 69632*a^4*b^9 + 14336*a^5*b^8 - 12288*a^6*b^7)/(64*b^5) + (tan(c + d*x)*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) - (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) - (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*1i)/((11696*a*b^8 + 1247*a^8*b - 344*a^9 - 1505*b^9 - 39388*a^2*b^7 + 74648*a^3*b^6 - 86086*a^4*b^5 + 60200*a^5*b^4 - 22876*a^6*b^3 + 2408*a^7*b^2)/(32*b^5) + (((373728*a^3*b^8 - 256*b^11 - 208208*a^2*b^9 - 17552*a*b^10 + 35296*a^4*b^7 - 240464*a^5*b^6 + 29040*a^6*b^5 + 27648*a^7*b^4 + 768*a^8*b^3)/(64*b^5) - (((4096*a*b^12 + 53248*a^2*b^11 - 129024*a^3*b^10 + 69632*a^4*b^9 + 14336*a^5*b^8 - 12288*a^6*b^7)/(64*b^5) - (tan(c + d*x)*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (((373728*a^3*b^8 - 256*b^11 - 208208*a^2*b^9 - 17552*a*b^10 + 35296*a^4*b^7 - 240464*a^5*b^6 + 29040*a^6*b^5 + 27648*a^7*b^4 + 768*a^8*b^3)/(64*b^5) - (((4096*a*b^12 + 53248*a^2*b^11 - 129024*a^3*b^10 + 69632*a^4*b^9 + 14336*a^5*b^8 - 12288*a^6*b^7)/(64*b^5) + (tan(c + d*x)*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) - (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) - (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)))*(-(7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) + 7*a^2*b^7 + 35*a^3*b^6 + 21*a^4*b^5 + a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*2i)/d - (atan(((((373728*a^3*b^8 - 256*b^11 - 208208*a^2*b^9 - 17552*a*b^10 + 35296*a^4*b^7 - 240464*a^5*b^6 + 29040*a^6*b^5 + 27648*a^7*b^4 + 768*a^8*b^3)/(64*b^5) - (((4096*a*b^12 + 53248*a^2*b^11 - 129024*a^3*b^10 + 69632*a^4*b^9 + 14336*a^5*b^8 - 12288*a^6*b^7)/(64*b^5) - (tan(c + d*x)*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*1i - (((373728*a^3*b^8 - 256*b^11 - 208208*a^2*b^9 - 17552*a*b^10 + 35296*a^4*b^7 - 240464*a^5*b^6 + 29040*a^6*b^5 + 27648*a^7*b^4 + 768*a^8*b^3)/(64*b^5) - (((4096*a*b^12 + 53248*a^2*b^11 - 129024*a^3*b^10 + 69632*a^4*b^9 + 14336*a^5*b^8 - 12288*a^6*b^7)/(64*b^5) + (tan(c + d*x)*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) - (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) - (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*1i)/((11696*a*b^8 + 1247*a^8*b - 344*a^9 - 1505*b^9 - 39388*a^2*b^7 + 74648*a^3*b^6 - 86086*a^4*b^5 + 60200*a^5*b^4 - 22876*a^6*b^3 + 2408*a^7*b^2)/(32*b^5) + (((373728*a^3*b^8 - 256*b^11 - 208208*a^2*b^9 - 17552*a*b^10 + 35296*a^4*b^7 - 240464*a^5*b^6 + 29040*a^6*b^5 + 27648*a^7*b^4 + 768*a^8*b^3)/(64*b^5) - (((4096*a*b^12 + 53248*a^2*b^11 - 129024*a^3*b^10 + 69632*a^4*b^9 + 14336*a^5*b^8 - 12288*a^6*b^7)/(64*b^5) - (tan(c + d*x)*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) + (((373728*a^3*b^8 - 256*b^11 - 208208*a^2*b^9 - 17552*a*b^10 + 35296*a^4*b^7 - 240464*a^5*b^6 + 29040*a^6*b^5 + 27648*a^7*b^4 + 768*a^8*b^3)/(64*b^5) - (((4096*a*b^12 + 53248*a^2*b^11 - 129024*a^3*b^10 + 69632*a^4*b^9 + 14336*a^5*b^8 - 12288*a^6*b^7)/(64*b^5) + (tan(c + d*x)*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) - (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2) - (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)))*((7*a^3*(a^3*b^9)^(1/2) + b^3*(a^3*b^9)^(1/2) - 7*a^2*b^7 - 35*a^3*b^6 - 21*a^4*b^5 - a^5*b^4 + 21*a*b^2*(a^3*b^9)^(1/2) + 35*a^2*b*(a^3*b^9)^(1/2))/(16*a^3*b^8))^(1/2)*2i)/d - ((13*tan(c + d*x))/(8*b) + (11*tan(c + d*x)^3)/(8*b))/(d*(2*tan(c + d*x)^2 + tan(c + d*x)^4 + 1)) - (atan((((a*8i + b*35i)*(((((11679*a^3*b^8)/2 - 4*b^11 - (13013*a^2*b^9)/4 - (1097*a*b^10)/4 + (1103*a^4*b^7)/2 - (15029*a^5*b^6)/4 + (1815*a^6*b^5)/4 + 432*a^7*b^4 + 12*a^8*b^3)/b^5 - (((((64*a*b^12 + 832*a^2*b^11 - 2016*a^3*b^10 + 1088*a^4*b^9 + 224*a^5*b^8 - 192*a^6*b^7)/b^5 - (tan(c + d*x)*(a*8i + b*35i)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(256*b^6))*(a*8i + b*35i))/(16*b^2) + (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*(a*8i + b*35i))/(16*b^2))*(a*8i + b*35i))/(16*b^2) + (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*1i)/(16*b^2) - ((a*8i + b*35i)*(((((11679*a^3*b^8)/2 - 4*b^11 - (13013*a^2*b^9)/4 - (1097*a*b^10)/4 + (1103*a^4*b^7)/2 - (15029*a^5*b^6)/4 + (1815*a^6*b^5)/4 + 432*a^7*b^4 + 12*a^8*b^3)/b^5 - (((((64*a*b^12 + 832*a^2*b^11 - 2016*a^3*b^10 + 1088*a^4*b^9 + 224*a^5*b^8 - 192*a^6*b^7)/b^5 + (tan(c + d*x)*(a*8i + b*35i)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(256*b^6))*(a*8i + b*35i))/(16*b^2) - (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*(a*8i + b*35i))/(16*b^2))*(a*8i + b*35i))/(16*b^2) - (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4))*1i)/(16*b^2))/(((731*a*b^8)/2 + (1247*a^8*b)/32 - (43*a^9)/4 - (1505*b^9)/32 - (9847*a^2*b^7)/8 + (9331*a^3*b^6)/4 - (43043*a^4*b^5)/16 + (7525*a^5*b^4)/4 - (5719*a^6*b^3)/8 + (301*a^7*b^2)/4)/b^5 + ((a*8i + b*35i)*(((((11679*a^3*b^8)/2 - 4*b^11 - (13013*a^2*b^9)/4 - (1097*a*b^10)/4 + (1103*a^4*b^7)/2 - (15029*a^5*b^6)/4 + (1815*a^6*b^5)/4 + 432*a^7*b^4 + 12*a^8*b^3)/b^5 - (((((64*a*b^12 + 832*a^2*b^11 - 2016*a^3*b^10 + 1088*a^4*b^9 + 224*a^5*b^8 - 192*a^6*b^7)/b^5 - (tan(c + d*x)*(a*8i + b*35i)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(256*b^6))*(a*8i + b*35i))/(16*b^2) + (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*(a*8i + b*35i))/(16*b^2))*(a*8i + b*35i))/(16*b^2) + (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4)))/(16*b^2) + ((a*8i + b*35i)*(((((11679*a^3*b^8)/2 - 4*b^11 - (13013*a^2*b^9)/4 - (1097*a*b^10)/4 + (1103*a^4*b^7)/2 - (15029*a^5*b^6)/4 + (1815*a^6*b^5)/4 + 432*a^7*b^4 + 12*a^8*b^3)/b^5 - (((((64*a*b^12 + 832*a^2*b^11 - 2016*a^3*b^10 + 1088*a^4*b^9 + 224*a^5*b^8 - 192*a^6*b^7)/b^5 + (tan(c + d*x)*(a*8i + b*35i)*(12288*a^2*b^11 - 12288*a^3*b^10 - 12288*a^4*b^9 + 12288*a^5*b^8))/(256*b^6))*(a*8i + b*35i))/(16*b^2) - (tan(c + d*x)*(256*a*b^10 + 256*b^11 - 70832*a^2*b^9 + 61136*a^3*b^8 + 53616*a^4*b^7 - 12432*a^5*b^6 - 29696*a^6*b^5 - 2304*a^7*b^4))/(16*b^4))*(a*8i + b*35i))/(16*b^2))*(a*8i + b*35i))/(16*b^2) - (tan(c + d*x)*(336*a^8*b - 1497*a*b^8 + 96*a^9 - 1257*b^9 + 21499*a^2*b^7 - 41861*a^3*b^6 + 27109*a^4*b^5 + 3077*a^5*b^4 - 9223*a^6*b^3 + 1721*a^7*b^2))/(16*b^4)))/(16*b^2)))*(a*8i + b*35i)*1i)/(8*b^2*d)","B"
413,1,3088,155,18.041791,"\text{Not used}","int(cos(c + d*x)^6/(a - b*sin(c + d*x)^4),x)","-\frac{\sin\left(2\,c+2\,d\,x\right)}{4\,b\,d}-\frac{5\,\mathrm{atan}\left(\frac{\sin\left(c+d\,x\right)}{\cos\left(c+d\,x\right)}\right)}{2\,b\,d}+\frac{\mathrm{atan}\left(\frac{-a^3\,b^9\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,108{}\mathrm{i}+a^4\,b^8\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,240{}\mathrm{i}-a^5\,b^7\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,80{}\mathrm{i}-a^6\,b^6\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,120{}\mathrm{i}+a^7\,b^5\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,60{}\mathrm{i}+a^8\,b^4\,\sin\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,8{}\mathrm{i}-a^3\,b^{11}\,\sin\left(c+d\,x\right)\,{\left(-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,64{}\mathrm{i}+a^4\,b^{10}\,\sin\left(c+d\,x\right)\,{\left(-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,128{}\mathrm{i}+a^5\,b^9\,\sin\left(c+d\,x\right)\,{\left(-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,6080{}\mathrm{i}+a^6\,b^8\,\sin\left(c+d\,x\right)\,{\left(-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,4032{}\mathrm{i}+a^7\,b^7\,\sin\left(c+d\,x\right)\,{\left(-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,320{}\mathrm{i}+a^5\,b^{11}\,\sin\left(c+d\,x\right)\,{\left(-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{5/2}\,3072{}\mathrm{i}+a^6\,b^{10}\,\sin\left(c+d\,x\right)\,{\left(-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{5/2}\,3072{}\mathrm{i}}{55\,a^2\,b^9\,\cos\left(c+d\,x\right)+540\,a^3\,b^8\,\cos\left(c+d\,x\right)+1035\,a^4\,b^7\,\cos\left(c+d\,x\right)+45\,a^5\,b^6\,\cos\left(c+d\,x\right)+a^6\,b^5\,\cos\left(c+d\,x\right)+110\,a^7\,b^4\,\cos\left(c+d\,x\right)+5\,a^8\,b^3\,\cos\left(c+d\,x\right)+50\,a^6\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}+10\,b^6\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}+a\,b^{10}\,\cos\left(c+d\,x\right)+195\,a\,b^5\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}+75\,a^5\,b\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}+1002\,a^2\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}+490\,a^3\,b^3\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}-30\,a^4\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}+5\,a^2\,b^5+10\,a^3\,b^4+a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{-a^3\,b^9\,\sin\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,108{}\mathrm{i}+a^4\,b^8\,\sin\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,240{}\mathrm{i}-a^5\,b^7\,\sin\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,80{}\mathrm{i}-a^6\,b^6\,\sin\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,120{}\mathrm{i}+a^7\,b^5\,\sin\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,60{}\mathrm{i}+a^8\,b^4\,\sin\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,8{}\mathrm{i}-a^3\,b^{11}\,\sin\left(c+d\,x\right)\,{\left(\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,64{}\mathrm{i}+a^4\,b^{10}\,\sin\left(c+d\,x\right)\,{\left(\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,128{}\mathrm{i}+a^5\,b^9\,\sin\left(c+d\,x\right)\,{\left(\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,6080{}\mathrm{i}+a^6\,b^8\,\sin\left(c+d\,x\right)\,{\left(\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,4032{}\mathrm{i}+a^7\,b^7\,\sin\left(c+d\,x\right)\,{\left(\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{3/2}\,320{}\mathrm{i}+a^5\,b^{11}\,\sin\left(c+d\,x\right)\,{\left(\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{5/2}\,3072{}\mathrm{i}+a^6\,b^{10}\,\sin\left(c+d\,x\right)\,{\left(\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}\right)}^{5/2}\,3072{}\mathrm{i}}{55\,a^2\,b^9\,\cos\left(c+d\,x\right)+540\,a^3\,b^8\,\cos\left(c+d\,x\right)+1035\,a^4\,b^7\,\cos\left(c+d\,x\right)+45\,a^5\,b^6\,\cos\left(c+d\,x\right)+a^6\,b^5\,\cos\left(c+d\,x\right)+110\,a^7\,b^4\,\cos\left(c+d\,x\right)+5\,a^8\,b^3\,\cos\left(c+d\,x\right)-50\,a^6\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}-10\,b^6\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}+a\,b^{10}\,\cos\left(c+d\,x\right)-195\,a\,b^5\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}-75\,a^5\,b\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}-1002\,a^2\,b^4\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}-490\,a^3\,b^3\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}+30\,a^4\,b^2\,\cos\left(c+d\,x\right)\,\sqrt{a^3\,b^7}}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^7}+b^2\,\sqrt{a^3\,b^7}-5\,a^2\,b^5-10\,a^3\,b^4-a^4\,b^3+10\,a\,b\,\sqrt{a^3\,b^7}}{16\,a^3\,b^6}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan((a^4*b^8*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*240i - a^3*b^9*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*108i - a^5*b^7*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*80i - a^6*b^6*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*120i + a^7*b^5*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*60i + a^8*b^4*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*8i - a^3*b^11*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*64i + a^4*b^10*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*128i + a^5*b^9*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*6080i + a^6*b^8*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*4032i + a^7*b^7*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*320i + a^5*b^11*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(5/2)*3072i + a^6*b^10*sin(c + d*x)*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(5/2)*3072i)/(55*a^2*b^9*cos(c + d*x) + 540*a^3*b^8*cos(c + d*x) + 1035*a^4*b^7*cos(c + d*x) + 45*a^5*b^6*cos(c + d*x) + a^6*b^5*cos(c + d*x) + 110*a^7*b^4*cos(c + d*x) + 5*a^8*b^3*cos(c + d*x) + 50*a^6*cos(c + d*x)*(a^3*b^7)^(1/2) + 10*b^6*cos(c + d*x)*(a^3*b^7)^(1/2) + a*b^10*cos(c + d*x) + 195*a*b^5*cos(c + d*x)*(a^3*b^7)^(1/2) + 75*a^5*b*cos(c + d*x)*(a^3*b^7)^(1/2) + 1002*a^2*b^4*cos(c + d*x)*(a^3*b^7)^(1/2) + 490*a^3*b^3*cos(c + d*x)*(a^3*b^7)^(1/2) - 30*a^4*b^2*cos(c + d*x)*(a^3*b^7)^(1/2)))*(-(5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) + 5*a^2*b^5 + 10*a^3*b^4 + a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*2i)/d + (atan((a^4*b^8*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*240i - a^3*b^9*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*108i - a^5*b^7*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*80i - a^6*b^6*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*120i + a^7*b^5*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*60i + a^8*b^4*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*8i - a^3*b^11*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*64i + a^4*b^10*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*128i + a^5*b^9*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*6080i + a^6*b^8*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*4032i + a^7*b^7*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(3/2)*320i + a^5*b^11*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(5/2)*3072i + a^6*b^10*sin(c + d*x)*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(5/2)*3072i)/(55*a^2*b^9*cos(c + d*x) + 540*a^3*b^8*cos(c + d*x) + 1035*a^4*b^7*cos(c + d*x) + 45*a^5*b^6*cos(c + d*x) + a^6*b^5*cos(c + d*x) + 110*a^7*b^4*cos(c + d*x) + 5*a^8*b^3*cos(c + d*x) - 50*a^6*cos(c + d*x)*(a^3*b^7)^(1/2) - 10*b^6*cos(c + d*x)*(a^3*b^7)^(1/2) + a*b^10*cos(c + d*x) - 195*a*b^5*cos(c + d*x)*(a^3*b^7)^(1/2) - 75*a^5*b*cos(c + d*x)*(a^3*b^7)^(1/2) - 1002*a^2*b^4*cos(c + d*x)*(a^3*b^7)^(1/2) - 490*a^3*b^3*cos(c + d*x)*(a^3*b^7)^(1/2) + 30*a^4*b^2*cos(c + d*x)*(a^3*b^7)^(1/2)))*((5*a^2*(a^3*b^7)^(1/2) + b^2*(a^3*b^7)^(1/2) - 5*a^2*b^5 - 10*a^3*b^4 - a^4*b^3 + 10*a*b*(a^3*b^7)^(1/2))/(16*a^3*b^6))^(1/2)*2i)/d - sin(2*c + 2*d*x)/(4*b*d) - (5*atan(sin(c + d*x)/cos(c + d*x)))/(2*b*d)","B"
414,1,4299,127,16.400374,"\text{Not used}","int(cos(c + d*x)^4/(a - b*sin(c + d*x)^4),x)","\frac{\mathrm{atan}\left(\frac{90\,a^4\,\mathrm{tan}\left(c+d\,x\right)}{10\,a\,b^3+132\,a^3\,b-90\,a^4-2\,b^4-68\,a^2\,b^2+\frac{18\,a^5}{b}}-\frac{18\,a^5\,\mathrm{tan}\left(c+d\,x\right)}{18\,a^5-90\,a^4\,b+132\,a^3\,b^2-68\,a^2\,b^3+10\,a\,b^4-2\,b^5}+\frac{2\,b^4\,\mathrm{tan}\left(c+d\,x\right)}{10\,a\,b^3+132\,a^3\,b-90\,a^4-2\,b^4-68\,a^2\,b^2+\frac{18\,a^5}{b}}+\frac{68\,a^2\,b^2\,\mathrm{tan}\left(c+d\,x\right)}{10\,a\,b^3+132\,a^3\,b-90\,a^4-2\,b^4-68\,a^2\,b^2+\frac{18\,a^5}{b}}-\frac{10\,a\,b^3\,\mathrm{tan}\left(c+d\,x\right)}{10\,a\,b^3+132\,a^3\,b-90\,a^4-2\,b^4-68\,a^2\,b^2+\frac{18\,a^5}{b}}-\frac{132\,a^3\,b\,\mathrm{tan}\left(c+d\,x\right)}{10\,a\,b^3+132\,a^3\,b-90\,a^4-2\,b^4-68\,a^2\,b^2+\frac{18\,a^5}{b}}\right)}{b\,d}+\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5-30\,a^4\,b+60\,a^3\,b^2-60\,a^2\,b^3+30\,a\,b^4-6\,b^5\right)+\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(36\,a\,b^5-12\,a^5\,b-4\,b^6+\left(\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(64\,a\,b^7+256\,a^2\,b^6-896\,a^3\,b^5+768\,a^4\,b^4-192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+48\,a^4\,b^3-480\,a^3\,b^4+224\,a^2\,b^5+80\,a\,b^6-16\,b^7\right)\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}-72\,a^2\,b^4+40\,a^3\,b^3+12\,a^4\,b^2\right)\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,1{}\mathrm{i}+\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5-30\,a^4\,b+60\,a^3\,b^2-60\,a^2\,b^3+30\,a\,b^4-6\,b^5\right)-\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(36\,a\,b^5-12\,a^5\,b-4\,b^6+\left(\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(64\,a\,b^7+256\,a^2\,b^6-896\,a^3\,b^5+768\,a^4\,b^4-192\,a^5\,b^3-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+48\,a^4\,b^3-480\,a^3\,b^4+224\,a^2\,b^5+80\,a\,b^6-16\,b^7\right)\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}-72\,a^2\,b^4+40\,a^3\,b^3+12\,a^4\,b^2\right)\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5-30\,a^4\,b+60\,a^3\,b^2-60\,a^2\,b^3+30\,a\,b^4-6\,b^5\right)+\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(36\,a\,b^5-12\,a^5\,b-4\,b^6+\left(\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(64\,a\,b^7+256\,a^2\,b^6-896\,a^3\,b^5+768\,a^4\,b^4-192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+48\,a^4\,b^3-480\,a^3\,b^4+224\,a^2\,b^5+80\,a\,b^6-16\,b^7\right)\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}-72\,a^2\,b^4+40\,a^3\,b^3+12\,a^4\,b^2\right)\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}-\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5-30\,a^4\,b+60\,a^3\,b^2-60\,a^2\,b^3+30\,a\,b^4-6\,b^5\right)-\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(36\,a\,b^5-12\,a^5\,b-4\,b^6+\left(\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(64\,a\,b^7+256\,a^2\,b^6-896\,a^3\,b^5+768\,a^4\,b^4-192\,a^5\,b^3-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+48\,a^4\,b^3-480\,a^3\,b^4+224\,a^2\,b^5+80\,a\,b^6-16\,b^7\right)\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}-72\,a^2\,b^4+40\,a^3\,b^3+12\,a^4\,b^2\right)\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}+3\,a^2\,b^3+a^3\,b^2}{16\,a^3\,b^4}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5-30\,a^4\,b+60\,a^3\,b^2-60\,a^2\,b^3+30\,a\,b^4-6\,b^5\right)+\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(36\,a\,b^5-12\,a^5\,b-4\,b^6+\left(\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(64\,a\,b^7+256\,a^2\,b^6-896\,a^3\,b^5+768\,a^4\,b^4-192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+48\,a^4\,b^3-480\,a^3\,b^4+224\,a^2\,b^5+80\,a\,b^6-16\,b^7\right)\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}-72\,a^2\,b^4+40\,a^3\,b^3+12\,a^4\,b^2\right)\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,1{}\mathrm{i}+\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5-30\,a^4\,b+60\,a^3\,b^2-60\,a^2\,b^3+30\,a\,b^4-6\,b^5\right)-\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(36\,a\,b^5-12\,a^5\,b-4\,b^6+\left(\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(64\,a\,b^7+256\,a^2\,b^6-896\,a^3\,b^5+768\,a^4\,b^4-192\,a^5\,b^3-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+48\,a^4\,b^3-480\,a^3\,b^4+224\,a^2\,b^5+80\,a\,b^6-16\,b^7\right)\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}-72\,a^2\,b^4+40\,a^3\,b^3+12\,a^4\,b^2\right)\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5-30\,a^4\,b+60\,a^3\,b^2-60\,a^2\,b^3+30\,a\,b^4-6\,b^5\right)+\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(36\,a\,b^5-12\,a^5\,b-4\,b^6+\left(\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(64\,a\,b^7+256\,a^2\,b^6-896\,a^3\,b^5+768\,a^4\,b^4-192\,a^5\,b^3+\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)+\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+48\,a^4\,b^3-480\,a^3\,b^4+224\,a^2\,b^5+80\,a\,b^6-16\,b^7\right)\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}-72\,a^2\,b^4+40\,a^3\,b^3+12\,a^4\,b^2\right)\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}-\left(\mathrm{tan}\left(c+d\,x\right)\,\left(6\,a^5-30\,a^4\,b+60\,a^3\,b^2-60\,a^2\,b^3+30\,a\,b^4-6\,b^5\right)-\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(36\,a\,b^5-12\,a^5\,b-4\,b^6+\left(\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(64\,a\,b^7+256\,a^2\,b^6-896\,a^3\,b^5+768\,a^4\,b^4-192\,a^5\,b^3-\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,\left(768\,a^5\,b^4-768\,a^4\,b^5-768\,a^3\,b^6+768\,a^2\,b^7\right)\right)-\mathrm{tan}\left(c+d\,x\right)\,\left(144\,a^5\,b^2+48\,a^4\,b^3-480\,a^3\,b^4+224\,a^2\,b^5+80\,a\,b^6-16\,b^7\right)\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}-72\,a^2\,b^4+40\,a^3\,b^3+12\,a^4\,b^2\right)\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^5}+b\,\sqrt{a^3\,b^5}-3\,a^2\,b^3-a^3\,b^2}{16\,a^3\,b^4}}\,2{}\mathrm{i}}{d}","Not used",1,"atan((90*a^4*tan(c + d*x))/(10*a*b^3 + 132*a^3*b - 90*a^4 - 2*b^4 - 68*a^2*b^2 + (18*a^5)/b) - (18*a^5*tan(c + d*x))/(10*a*b^4 - 90*a^4*b + 18*a^5 - 2*b^5 - 68*a^2*b^3 + 132*a^3*b^2) + (2*b^4*tan(c + d*x))/(10*a*b^3 + 132*a^3*b - 90*a^4 - 2*b^4 - 68*a^2*b^2 + (18*a^5)/b) + (68*a^2*b^2*tan(c + d*x))/(10*a*b^3 + 132*a^3*b - 90*a^4 - 2*b^4 - 68*a^2*b^2 + (18*a^5)/b) - (10*a*b^3*tan(c + d*x))/(10*a*b^3 + 132*a^3*b - 90*a^4 - 2*b^4 - 68*a^2*b^2 + (18*a^5)/b) - (132*a^3*b*tan(c + d*x))/(10*a*b^3 + 132*a^3*b - 90*a^4 - 2*b^4 - 68*a^2*b^2 + (18*a^5)/b))/(b*d) + (atan(((tan(c + d*x)*(30*a*b^4 - 30*a^4*b + 6*a^5 - 6*b^5 - 60*a^2*b^3 + 60*a^3*b^2) + (-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(36*a*b^5 - 12*a^5*b - 4*b^6 + ((-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(64*a*b^7 + 256*a^2*b^6 - 896*a^3*b^5 + 768*a^4*b^4 - 192*a^5*b^3 + tan(c + d*x)*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) + tan(c + d*x)*(80*a*b^6 - 16*b^7 + 224*a^2*b^5 - 480*a^3*b^4 + 48*a^4*b^3 + 144*a^5*b^2))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2) - 72*a^2*b^4 + 40*a^3*b^3 + 12*a^4*b^2))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*1i + (tan(c + d*x)*(30*a*b^4 - 30*a^4*b + 6*a^5 - 6*b^5 - 60*a^2*b^3 + 60*a^3*b^2) - (-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(36*a*b^5 - 12*a^5*b - 4*b^6 + ((-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(64*a*b^7 + 256*a^2*b^6 - 896*a^3*b^5 + 768*a^4*b^4 - 192*a^5*b^3 - tan(c + d*x)*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) - tan(c + d*x)*(80*a*b^6 - 16*b^7 + 224*a^2*b^5 - 480*a^3*b^4 + 48*a^4*b^3 + 144*a^5*b^2))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2) - 72*a^2*b^4 + 40*a^3*b^3 + 12*a^4*b^2))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*1i)/((tan(c + d*x)*(30*a*b^4 - 30*a^4*b + 6*a^5 - 6*b^5 - 60*a^2*b^3 + 60*a^3*b^2) + (-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(36*a*b^5 - 12*a^5*b - 4*b^6 + ((-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(64*a*b^7 + 256*a^2*b^6 - 896*a^3*b^5 + 768*a^4*b^4 - 192*a^5*b^3 + tan(c + d*x)*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) + tan(c + d*x)*(80*a*b^6 - 16*b^7 + 224*a^2*b^5 - 480*a^3*b^4 + 48*a^4*b^3 + 144*a^5*b^2))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2) - 72*a^2*b^4 + 40*a^3*b^3 + 12*a^4*b^2))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2) - (tan(c + d*x)*(30*a*b^4 - 30*a^4*b + 6*a^5 - 6*b^5 - 60*a^2*b^3 + 60*a^3*b^2) - (-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(36*a*b^5 - 12*a^5*b - 4*b^6 + ((-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(64*a*b^7 + 256*a^2*b^6 - 896*a^3*b^5 + 768*a^4*b^4 - 192*a^5*b^3 - tan(c + d*x)*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) - tan(c + d*x)*(80*a*b^6 - 16*b^7 + 224*a^2*b^5 - 480*a^3*b^4 + 48*a^4*b^3 + 144*a^5*b^2))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2) - 72*a^2*b^4 + 40*a^3*b^3 + 12*a^4*b^2))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)))*(-(3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) + 3*a^2*b^3 + a^3*b^2)/(16*a^3*b^4))^(1/2)*2i)/d + (atan(((tan(c + d*x)*(30*a*b^4 - 30*a^4*b + 6*a^5 - 6*b^5 - 60*a^2*b^3 + 60*a^3*b^2) + ((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(36*a*b^5 - 12*a^5*b - 4*b^6 + (((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(64*a*b^7 + 256*a^2*b^6 - 896*a^3*b^5 + 768*a^4*b^4 - 192*a^5*b^3 + tan(c + d*x)*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) + tan(c + d*x)*(80*a*b^6 - 16*b^7 + 224*a^2*b^5 - 480*a^3*b^4 + 48*a^4*b^3 + 144*a^5*b^2))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2) - 72*a^2*b^4 + 40*a^3*b^3 + 12*a^4*b^2))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*1i + (tan(c + d*x)*(30*a*b^4 - 30*a^4*b + 6*a^5 - 6*b^5 - 60*a^2*b^3 + 60*a^3*b^2) - ((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(36*a*b^5 - 12*a^5*b - 4*b^6 + (((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(64*a*b^7 + 256*a^2*b^6 - 896*a^3*b^5 + 768*a^4*b^4 - 192*a^5*b^3 - tan(c + d*x)*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) - tan(c + d*x)*(80*a*b^6 - 16*b^7 + 224*a^2*b^5 - 480*a^3*b^4 + 48*a^4*b^3 + 144*a^5*b^2))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2) - 72*a^2*b^4 + 40*a^3*b^3 + 12*a^4*b^2))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*1i)/((tan(c + d*x)*(30*a*b^4 - 30*a^4*b + 6*a^5 - 6*b^5 - 60*a^2*b^3 + 60*a^3*b^2) + ((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(36*a*b^5 - 12*a^5*b - 4*b^6 + (((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(64*a*b^7 + 256*a^2*b^6 - 896*a^3*b^5 + 768*a^4*b^4 - 192*a^5*b^3 + tan(c + d*x)*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) + tan(c + d*x)*(80*a*b^6 - 16*b^7 + 224*a^2*b^5 - 480*a^3*b^4 + 48*a^4*b^3 + 144*a^5*b^2))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2) - 72*a^2*b^4 + 40*a^3*b^3 + 12*a^4*b^2))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2) - (tan(c + d*x)*(30*a*b^4 - 30*a^4*b + 6*a^5 - 6*b^5 - 60*a^2*b^3 + 60*a^3*b^2) - ((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(36*a*b^5 - 12*a^5*b - 4*b^6 + (((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(64*a*b^7 + 256*a^2*b^6 - 896*a^3*b^5 + 768*a^4*b^4 - 192*a^5*b^3 - tan(c + d*x)*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*(768*a^2*b^7 - 768*a^3*b^6 - 768*a^4*b^5 + 768*a^5*b^4)) - tan(c + d*x)*(80*a*b^6 - 16*b^7 + 224*a^2*b^5 - 480*a^3*b^4 + 48*a^4*b^3 + 144*a^5*b^2))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2) - 72*a^2*b^4 + 40*a^3*b^3 + 12*a^4*b^2))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)))*((3*a*(a^3*b^5)^(1/2) + b*(a^3*b^5)^(1/2) - 3*a^2*b^3 - a^3*b^2)/(16*a^3*b^4))^(1/2)*2i)/d","B"
415,1,1409,125,15.661067,"\text{Not used}","int(cos(c + d*x)^2/(a - b*sin(c + d*x)^4),x)","\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)+\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\,\left(16\,a\,b^3+16\,a^3\,b-32\,a^2\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\right)\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\,1{}\mathrm{i}+\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)-\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\,\left(16\,a\,b^3+16\,a^3\,b-32\,a^2\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\right)\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)+\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\,\left(16\,a\,b^3+16\,a^3\,b-32\,a^2\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\right)\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}-\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)-\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\,\left(16\,a\,b^3+16\,a^3\,b-32\,a^2\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\right)\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}}\right)\,\sqrt{-\frac{\sqrt{a^3\,b^3}+a^2\,b}{16\,a^3\,b^2}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)+\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\,\left(16\,a\,b^3+16\,a^3\,b-32\,a^2\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\right)\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\,1{}\mathrm{i}+\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)-\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\,\left(16\,a\,b^3+16\,a^3\,b-32\,a^2\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\right)\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)+\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\,\left(16\,a\,b^3+16\,a^3\,b-32\,a^2\,b^2+\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\right)\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}-\left(\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)-\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\,\left(16\,a\,b^3+16\,a^3\,b-32\,a^2\,b^2-\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\right)\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}}\right)\,\sqrt{\frac{\sqrt{a^3\,b^3}-a^2\,b}{16\,a^3\,b^2}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((tan(c + d*x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3) + (-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)*(16*a*b^3 + 16*a^3*b - 32*a^2*b^2 + tan(c + d*x)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2)*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)))*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)*1i + (tan(c + d*x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3) - (-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)*(16*a*b^3 + 16*a^3*b - 32*a^2*b^2 - tan(c + d*x)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2)*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)))*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)*1i)/((tan(c + d*x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3) + (-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)*(16*a*b^3 + 16*a^3*b - 32*a^2*b^2 + tan(c + d*x)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2)*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)))*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2) - (tan(c + d*x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3) - (-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)*(16*a*b^3 + 16*a^3*b - 32*a^2*b^2 - tan(c + d*x)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2)*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)))*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)))*(-((a^3*b^3)^(1/2) + a^2*b)/(16*a^3*b^2))^(1/2)*2i)/d + (atan(((tan(c + d*x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3) + (((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)*(16*a*b^3 + 16*a^3*b - 32*a^2*b^2 + tan(c + d*x)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2)*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)))*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)*1i + (tan(c + d*x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3) - (((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)*(16*a*b^3 + 16*a^3*b - 32*a^2*b^2 - tan(c + d*x)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2)*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)))*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)*1i)/((tan(c + d*x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3) + (((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)*(16*a*b^3 + 16*a^3*b - 32*a^2*b^2 + tan(c + d*x)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2)*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)))*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2) - (tan(c + d*x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3) - (((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)*(16*a*b^3 + 16*a^3*b - 32*a^2*b^2 - tan(c + d*x)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2)*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)))*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)))*(((a^3*b^3)^(1/2) - a^2*b)/(16*a^3*b^2))^(1/2)*2i)/d","B"
416,1,2832,142,16.940475,"\text{Not used}","int(1/(cos(c + d*x)^2*(a - b*sin(c + d*x)^4)),x)","\frac{\mathrm{tan}\left(c+d\,x\right)}{d\,\left(a-b\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{2\,\left(8\,a^3\,b^2-16\,a^2\,b^3+8\,a\,b^4\right)}{a-b}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,\left(16\,a^5\,b-48\,a^4\,b^2+48\,a^3\,b^3-16\,a^2\,b^4\right)}{a-b}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,b^2+6\,a\,b^3+b^4\right)}{a-b}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{2\,\left(8\,a^3\,b^2-16\,a^2\,b^3+8\,a\,b^4\right)}{a-b}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,\left(16\,a^5\,b-48\,a^4\,b^2+48\,a^3\,b^3-16\,a^2\,b^4\right)}{a-b}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,b^2+6\,a\,b^3+b^4\right)}{a-b}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{2\,\left(8\,a^3\,b^2-16\,a^2\,b^3+8\,a\,b^4\right)}{a-b}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,\left(16\,a^5\,b-48\,a^4\,b^2+48\,a^3\,b^3-16\,a^2\,b^4\right)}{a-b}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,b^2+6\,a\,b^3+b^4\right)}{a-b}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}-\frac{4\,b^3}{a-b}+\left(\left(\frac{2\,\left(8\,a^3\,b^2-16\,a^2\,b^3+8\,a\,b^4\right)}{a-b}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,\left(16\,a^5\,b-48\,a^4\,b^2+48\,a^3\,b^3-16\,a^2\,b^4\right)}{a-b}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,b^2+6\,a\,b^3+b^4\right)}{a-b}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}}\right)\,\sqrt{\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}+a^3\,b+3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{2\,\left(8\,a^3\,b^2-16\,a^2\,b^3+8\,a\,b^4\right)}{a-b}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,\left(16\,a^5\,b-48\,a^4\,b^2+48\,a^3\,b^3-16\,a^2\,b^4\right)}{a-b}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,b^2+6\,a\,b^3+b^4\right)}{a-b}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{2\,\left(8\,a^3\,b^2-16\,a^2\,b^3+8\,a\,b^4\right)}{a-b}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,\left(16\,a^5\,b-48\,a^4\,b^2+48\,a^3\,b^3-16\,a^2\,b^4\right)}{a-b}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,b^2+6\,a\,b^3+b^4\right)}{a-b}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{2\,\left(8\,a^3\,b^2-16\,a^2\,b^3+8\,a\,b^4\right)}{a-b}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,\left(16\,a^5\,b-48\,a^4\,b^2+48\,a^3\,b^3-16\,a^2\,b^4\right)}{a-b}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,b^2+6\,a\,b^3+b^4\right)}{a-b}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}-\frac{4\,b^3}{a-b}+\left(\left(\frac{2\,\left(8\,a^3\,b^2-16\,a^2\,b^3+8\,a\,b^4\right)}{a-b}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,\left(16\,a^5\,b-48\,a^4\,b^2+48\,a^3\,b^3-16\,a^2\,b^4\right)}{a-b}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^2\,b^2+6\,a\,b^3+b^4\right)}{a-b}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}}\right)\,\sqrt{-\frac{3\,a\,\sqrt{a^3\,b^3}+b\,\sqrt{a^3\,b^3}-a^3\,b-3\,a^2\,b^2}{16\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"tan(c + d*x)/(d*(a - b)) + (atan(((((2*(8*a*b^4 - 16*a^2*b^3 + 8*a^3*b^2))/(a - b) - (4*tan(c + d*x)*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*(16*a^5*b - 16*a^2*b^4 + 48*a^3*b^3 - 48*a^4*b^2))/(a - b))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) - (4*tan(c + d*x)*(6*a*b^3 + b^4 + a^2*b^2))/(a - b))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*1i - (((2*(8*a*b^4 - 16*a^2*b^3 + 8*a^3*b^2))/(a - b) + (4*tan(c + d*x)*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*(16*a^5*b - 16*a^2*b^4 + 48*a^3*b^3 - 48*a^4*b^2))/(a - b))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) + (4*tan(c + d*x)*(6*a*b^3 + b^4 + a^2*b^2))/(a - b))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*1i)/((((2*(8*a*b^4 - 16*a^2*b^3 + 8*a^3*b^2))/(a - b) - (4*tan(c + d*x)*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*(16*a^5*b - 16*a^2*b^4 + 48*a^3*b^3 - 48*a^4*b^2))/(a - b))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) - (4*tan(c + d*x)*(6*a*b^3 + b^4 + a^2*b^2))/(a - b))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) - (4*b^3)/(a - b) + (((2*(8*a*b^4 - 16*a^2*b^3 + 8*a^3*b^2))/(a - b) + (4*tan(c + d*x)*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*(16*a^5*b - 16*a^2*b^4 + 48*a^3*b^3 - 48*a^4*b^2))/(a - b))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) + (4*tan(c + d*x)*(6*a*b^3 + b^4 + a^2*b^2))/(a - b))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)))*((3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) + a^3*b + 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*2i)/d + (atan(((((2*(8*a*b^4 - 16*a^2*b^3 + 8*a^3*b^2))/(a - b) - (4*tan(c + d*x)*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*(16*a^5*b - 16*a^2*b^4 + 48*a^3*b^3 - 48*a^4*b^2))/(a - b))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) - (4*tan(c + d*x)*(6*a*b^3 + b^4 + a^2*b^2))/(a - b))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*1i - (((2*(8*a*b^4 - 16*a^2*b^3 + 8*a^3*b^2))/(a - b) + (4*tan(c + d*x)*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*(16*a^5*b - 16*a^2*b^4 + 48*a^3*b^3 - 48*a^4*b^2))/(a - b))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) + (4*tan(c + d*x)*(6*a*b^3 + b^4 + a^2*b^2))/(a - b))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*1i)/((((2*(8*a*b^4 - 16*a^2*b^3 + 8*a^3*b^2))/(a - b) - (4*tan(c + d*x)*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*(16*a^5*b - 16*a^2*b^4 + 48*a^3*b^3 - 48*a^4*b^2))/(a - b))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) - (4*tan(c + d*x)*(6*a*b^3 + b^4 + a^2*b^2))/(a - b))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) - (4*b^3)/(a - b) + (((2*(8*a*b^4 - 16*a^2*b^3 + 8*a^3*b^2))/(a - b) + (4*tan(c + d*x)*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*(16*a^5*b - 16*a^2*b^4 + 48*a^3*b^3 - 48*a^4*b^2))/(a - b))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2) + (4*tan(c + d*x)*(6*a*b^3 + b^4 + a^2*b^2))/(a - b))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)))*(-(3*a*(a^3*b^3)^(1/2) + b*(a^3*b^3)^(1/2) - a^3*b - 3*a^2*b^2)/(16*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)))^(1/2)*2i)/d","B"
417,1,4664,161,17.738532,"\text{Not used}","int(1/(cos(c + d*x)^4*(a - b*sin(c + d*x)^4)),x)","\frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{3\,d\,\left(a-b\right)}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(\frac{2\,a}{{\left(a-b\right)}^2}-\frac{3}{a-b}\right)}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-16\,a^5\,b^2+32\,a^4\,b^3-32\,a^2\,b^5+16\,a\,b^6}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,\left(16\,a^7\,b-80\,a^6\,b^2+160\,a^5\,b^3-160\,a^4\,b^4+80\,a^3\,b^5-16\,a^2\,b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,b^3+15\,a^2\,b^4+15\,a\,b^5+b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-16\,a^5\,b^2+32\,a^4\,b^3-32\,a^2\,b^5+16\,a\,b^6}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,\left(16\,a^7\,b-80\,a^6\,b^2+160\,a^5\,b^3-160\,a^4\,b^4+80\,a^3\,b^5-16\,a^2\,b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,b^3+15\,a^2\,b^4+15\,a\,b^5+b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-16\,a^5\,b^2+32\,a^4\,b^3-32\,a^2\,b^5+16\,a\,b^6}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,\left(16\,a^7\,b-80\,a^6\,b^2+160\,a^5\,b^3-160\,a^4\,b^4+80\,a^3\,b^5-16\,a^2\,b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,b^3+15\,a^2\,b^4+15\,a\,b^5+b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}-\frac{2\,\left(3\,b^5+a\,b^4\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}+\left(\left(\frac{-16\,a^5\,b^2+32\,a^4\,b^3-32\,a^2\,b^5+16\,a\,b^6}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,\left(16\,a^7\,b-80\,a^6\,b^2+160\,a^5\,b^3-160\,a^4\,b^4+80\,a^3\,b^5-16\,a^2\,b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,b^3+15\,a^2\,b^4+15\,a\,b^5+b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}}\right)\,\sqrt{\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}+5\,a^2\,b^4+10\,a^3\,b^3+a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{-16\,a^5\,b^2+32\,a^4\,b^3-32\,a^2\,b^5+16\,a\,b^6}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,\left(16\,a^7\,b-80\,a^6\,b^2+160\,a^5\,b^3-160\,a^4\,b^4+80\,a^3\,b^5-16\,a^2\,b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,b^3+15\,a^2\,b^4+15\,a\,b^5+b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-16\,a^5\,b^2+32\,a^4\,b^3-32\,a^2\,b^5+16\,a\,b^6}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,\left(16\,a^7\,b-80\,a^6\,b^2+160\,a^5\,b^3-160\,a^4\,b^4+80\,a^3\,b^5-16\,a^2\,b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,b^3+15\,a^2\,b^4+15\,a\,b^5+b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-16\,a^5\,b^2+32\,a^4\,b^3-32\,a^2\,b^5+16\,a\,b^6}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,\left(16\,a^7\,b-80\,a^6\,b^2+160\,a^5\,b^3-160\,a^4\,b^4+80\,a^3\,b^5-16\,a^2\,b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,b^3+15\,a^2\,b^4+15\,a\,b^5+b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}-\frac{2\,\left(3\,b^5+a\,b^4\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}+\left(\left(\frac{-16\,a^5\,b^2+32\,a^4\,b^3-32\,a^2\,b^5+16\,a\,b^6}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,\left(16\,a^7\,b-80\,a^6\,b^2+160\,a^5\,b^3-160\,a^4\,b^4+80\,a^3\,b^5-16\,a^2\,b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^3\,b^3+15\,a^2\,b^4+15\,a\,b^5+b^6\right)}{a^3-3\,a^2\,b+3\,a\,b^2-b^3}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}}\right)\,\sqrt{-\frac{5\,a^2\,\sqrt{a^3\,b^5}+b^2\,\sqrt{a^3\,b^5}-5\,a^2\,b^4-10\,a^3\,b^3-a^4\,b^2+10\,a\,b\,\sqrt{a^3\,b^5}}{16\,\left(-a^8+5\,a^7\,b-10\,a^6\,b^2+10\,a^5\,b^3-5\,a^4\,b^4+a^3\,b^5\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"tan(c + d*x)^3/(3*d*(a - b)) - (tan(c + d*x)*((2*a)/(a - b)^2 - 3/(a - b)))/d + (atan(((((16*a*b^6 - 32*a^2*b^5 + 32*a^4*b^3 - 16*a^5*b^2)/(3*a*b^2 - 3*a^2*b + a^3 - b^3) - (4*tan(c + d*x)*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*(16*a^7*b - 16*a^2*b^6 + 80*a^3*b^5 - 160*a^4*b^4 + 160*a^5*b^3 - 80*a^6*b^2))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) - (4*tan(c + d*x)*(15*a*b^5 + b^6 + 15*a^2*b^4 + a^3*b^3))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*1i - (((16*a*b^6 - 32*a^2*b^5 + 32*a^4*b^3 - 16*a^5*b^2)/(3*a*b^2 - 3*a^2*b + a^3 - b^3) + (4*tan(c + d*x)*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*(16*a^7*b - 16*a^2*b^6 + 80*a^3*b^5 - 160*a^4*b^4 + 160*a^5*b^3 - 80*a^6*b^2))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) + (4*tan(c + d*x)*(15*a*b^5 + b^6 + 15*a^2*b^4 + a^3*b^3))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*1i)/((((16*a*b^6 - 32*a^2*b^5 + 32*a^4*b^3 - 16*a^5*b^2)/(3*a*b^2 - 3*a^2*b + a^3 - b^3) - (4*tan(c + d*x)*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*(16*a^7*b - 16*a^2*b^6 + 80*a^3*b^5 - 160*a^4*b^4 + 160*a^5*b^3 - 80*a^6*b^2))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) - (4*tan(c + d*x)*(15*a*b^5 + b^6 + 15*a^2*b^4 + a^3*b^3))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) - (2*(a*b^4 + 3*b^5))/(3*a*b^2 - 3*a^2*b + a^3 - b^3) + (((16*a*b^6 - 32*a^2*b^5 + 32*a^4*b^3 - 16*a^5*b^2)/(3*a*b^2 - 3*a^2*b + a^3 - b^3) + (4*tan(c + d*x)*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*(16*a^7*b - 16*a^2*b^6 + 80*a^3*b^5 - 160*a^4*b^4 + 160*a^5*b^3 - 80*a^6*b^2))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) + (4*tan(c + d*x)*(15*a*b^5 + b^6 + 15*a^2*b^4 + a^3*b^3))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)))*((5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) + 5*a^2*b^4 + 10*a^3*b^3 + a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*2i)/d + (atan(((((16*a*b^6 - 32*a^2*b^5 + 32*a^4*b^3 - 16*a^5*b^2)/(3*a*b^2 - 3*a^2*b + a^3 - b^3) - (4*tan(c + d*x)*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*(16*a^7*b - 16*a^2*b^6 + 80*a^3*b^5 - 160*a^4*b^4 + 160*a^5*b^3 - 80*a^6*b^2))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) - (4*tan(c + d*x)*(15*a*b^5 + b^6 + 15*a^2*b^4 + a^3*b^3))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*1i - (((16*a*b^6 - 32*a^2*b^5 + 32*a^4*b^3 - 16*a^5*b^2)/(3*a*b^2 - 3*a^2*b + a^3 - b^3) + (4*tan(c + d*x)*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*(16*a^7*b - 16*a^2*b^6 + 80*a^3*b^5 - 160*a^4*b^4 + 160*a^5*b^3 - 80*a^6*b^2))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) + (4*tan(c + d*x)*(15*a*b^5 + b^6 + 15*a^2*b^4 + a^3*b^3))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*1i)/((((16*a*b^6 - 32*a^2*b^5 + 32*a^4*b^3 - 16*a^5*b^2)/(3*a*b^2 - 3*a^2*b + a^3 - b^3) - (4*tan(c + d*x)*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*(16*a^7*b - 16*a^2*b^6 + 80*a^3*b^5 - 160*a^4*b^4 + 160*a^5*b^3 - 80*a^6*b^2))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) - (4*tan(c + d*x)*(15*a*b^5 + b^6 + 15*a^2*b^4 + a^3*b^3))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) - (2*(a*b^4 + 3*b^5))/(3*a*b^2 - 3*a^2*b + a^3 - b^3) + (((16*a*b^6 - 32*a^2*b^5 + 32*a^4*b^3 - 16*a^5*b^2)/(3*a*b^2 - 3*a^2*b + a^3 - b^3) + (4*tan(c + d*x)*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*(16*a^7*b - 16*a^2*b^6 + 80*a^3*b^5 - 160*a^4*b^4 + 160*a^5*b^3 - 80*a^6*b^2))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2) + (4*tan(c + d*x)*(15*a*b^5 + b^6 + 15*a^2*b^4 + a^3*b^3))/(3*a*b^2 - 3*a^2*b + a^3 - b^3))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)))*(-(5*a^2*(a^3*b^5)^(1/2) + b^2*(a^3*b^5)^(1/2) - 5*a^2*b^4 - 10*a^3*b^3 - a^4*b^2 + 10*a*b*(a^3*b^5)^(1/2))/(16*(5*a^7*b - a^8 + a^3*b^5 - 5*a^4*b^4 + 10*a^5*b^3 - 10*a^6*b^2)))^(1/2)*2i)/d","B"
418,1,6534,204,18.225685,"\text{Not used}","int(1/(cos(c + d*x)^6*(a - b*sin(c + d*x)^4)),x)","\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(\frac{6}{a-b}-\frac{a}{{\left(a-b\right)}^2}+\frac{2\,a\,\left(\frac{2\,a}{{\left(a-b\right)}^2}-\frac{4}{a-b}\right)}{a-b}\right)}{d}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(\frac{2\,a}{3\,{\left(a-b\right)}^2}-\frac{4}{3\,\left(a-b\right)}\right)}{d}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^5}{5\,d\,\left(a-b\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{4\,\left(12\,a^6\,b^3-44\,a^5\,b^4+56\,a^4\,b^5-24\,a^3\,b^6-4\,a^2\,b^7+4\,a\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,\left(16\,a^9\,b-112\,a^8\,b^2+336\,a^7\,b^3-560\,a^6\,b^4+560\,a^5\,b^5-336\,a^4\,b^6+112\,a^3\,b^7-16\,a^2\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4\,b^4+28\,a^3\,b^5+70\,a^2\,b^6+28\,a\,b^7+b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,1{}\mathrm{i}-\left(\left(\frac{4\,\left(12\,a^6\,b^3-44\,a^5\,b^4+56\,a^4\,b^5-24\,a^3\,b^6-4\,a^2\,b^7+4\,a\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,\left(16\,a^9\,b-112\,a^8\,b^2+336\,a^7\,b^3-560\,a^6\,b^4+560\,a^5\,b^5-336\,a^4\,b^6+112\,a^3\,b^7-16\,a^2\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4\,b^4+28\,a^3\,b^5+70\,a^2\,b^6+28\,a\,b^7+b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{4\,\left(12\,a^6\,b^3-44\,a^5\,b^4+56\,a^4\,b^5-24\,a^3\,b^6-4\,a^2\,b^7+4\,a\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,\left(16\,a^9\,b-112\,a^8\,b^2+336\,a^7\,b^3-560\,a^6\,b^4+560\,a^5\,b^5-336\,a^4\,b^6+112\,a^3\,b^7-16\,a^2\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4\,b^4+28\,a^3\,b^5+70\,a^2\,b^6+28\,a\,b^7+b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}+\left(\left(\frac{4\,\left(12\,a^6\,b^3-44\,a^5\,b^4+56\,a^4\,b^5-24\,a^3\,b^6-4\,a^2\,b^7+4\,a\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,\left(16\,a^9\,b-112\,a^8\,b^2+336\,a^7\,b^3-560\,a^6\,b^4+560\,a^5\,b^5-336\,a^4\,b^6+112\,a^3\,b^7-16\,a^2\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4\,b^4+28\,a^3\,b^5+70\,a^2\,b^6+28\,a\,b^7+b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}-\frac{8\,\left(b^7+a\,b^6\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}}\right)\,\sqrt{\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}+7\,a^2\,b^6+35\,a^3\,b^5+21\,a^4\,b^4+a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,2{}\mathrm{i}}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{4\,\left(12\,a^6\,b^3-44\,a^5\,b^4+56\,a^4\,b^5-24\,a^3\,b^6-4\,a^2\,b^7+4\,a\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,\left(16\,a^9\,b-112\,a^8\,b^2+336\,a^7\,b^3-560\,a^6\,b^4+560\,a^5\,b^5-336\,a^4\,b^6+112\,a^3\,b^7-16\,a^2\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4\,b^4+28\,a^3\,b^5+70\,a^2\,b^6+28\,a\,b^7+b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,1{}\mathrm{i}-\left(\left(\frac{4\,\left(12\,a^6\,b^3-44\,a^5\,b^4+56\,a^4\,b^5-24\,a^3\,b^6-4\,a^2\,b^7+4\,a\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,\left(16\,a^9\,b-112\,a^8\,b^2+336\,a^7\,b^3-560\,a^6\,b^4+560\,a^5\,b^5-336\,a^4\,b^6+112\,a^3\,b^7-16\,a^2\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4\,b^4+28\,a^3\,b^5+70\,a^2\,b^6+28\,a\,b^7+b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{4\,\left(12\,a^6\,b^3-44\,a^5\,b^4+56\,a^4\,b^5-24\,a^3\,b^6-4\,a^2\,b^7+4\,a\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,\left(16\,a^9\,b-112\,a^8\,b^2+336\,a^7\,b^3-560\,a^6\,b^4+560\,a^5\,b^5-336\,a^4\,b^6+112\,a^3\,b^7-16\,a^2\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}-\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4\,b^4+28\,a^3\,b^5+70\,a^2\,b^6+28\,a\,b^7+b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}+\left(\left(\frac{4\,\left(12\,a^6\,b^3-44\,a^5\,b^4+56\,a^4\,b^5-24\,a^3\,b^6-4\,a^2\,b^7+4\,a\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,\left(16\,a^9\,b-112\,a^8\,b^2+336\,a^7\,b^3-560\,a^6\,b^4+560\,a^5\,b^5-336\,a^4\,b^6+112\,a^3\,b^7-16\,a^2\,b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}+\frac{4\,\mathrm{tan}\left(c+d\,x\right)\,\left(a^4\,b^4+28\,a^3\,b^5+70\,a^2\,b^6+28\,a\,b^7+b^8\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}-\frac{8\,\left(b^7+a\,b^6\right)}{a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5}}\right)\,\sqrt{-\frac{7\,a^3\,\sqrt{a^3\,b^7}+b^3\,\sqrt{a^3\,b^7}-7\,a^2\,b^6-35\,a^3\,b^5-21\,a^4\,b^4-a^5\,b^3+21\,a\,b^2\,\sqrt{a^3\,b^7}+35\,a^2\,b\,\sqrt{a^3\,b^7}}{16\,\left(-a^{10}+7\,a^9\,b-21\,a^8\,b^2+35\,a^7\,b^3-35\,a^6\,b^4+21\,a^5\,b^5-7\,a^4\,b^6+a^3\,b^7\right)}}\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((((4*(4*a*b^8 - 4*a^2*b^7 - 24*a^3*b^6 + 56*a^4*b^5 - 44*a^5*b^4 + 12*a^6*b^3))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2) - (4*tan(c + d*x)*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*(16*a^9*b - 16*a^2*b^8 + 112*a^3*b^7 - 336*a^4*b^6 + 560*a^5*b^5 - 560*a^6*b^4 + 336*a^7*b^3 - 112*a^8*b^2))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) - (4*tan(c + d*x)*(28*a*b^7 + b^8 + 70*a^2*b^6 + 28*a^3*b^5 + a^4*b^4))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*1i - (((4*(4*a*b^8 - 4*a^2*b^7 - 24*a^3*b^6 + 56*a^4*b^5 - 44*a^5*b^4 + 12*a^6*b^3))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2) + (4*tan(c + d*x)*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*(16*a^9*b - 16*a^2*b^8 + 112*a^3*b^7 - 336*a^4*b^6 + 560*a^5*b^5 - 560*a^6*b^4 + 336*a^7*b^3 - 112*a^8*b^2))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) + (4*tan(c + d*x)*(28*a*b^7 + b^8 + 70*a^2*b^6 + 28*a^3*b^5 + a^4*b^4))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*1i)/((((4*(4*a*b^8 - 4*a^2*b^7 - 24*a^3*b^6 + 56*a^4*b^5 - 44*a^5*b^4 + 12*a^6*b^3))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2) - (4*tan(c + d*x)*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*(16*a^9*b - 16*a^2*b^8 + 112*a^3*b^7 - 336*a^4*b^6 + 560*a^5*b^5 - 560*a^6*b^4 + 336*a^7*b^3 - 112*a^8*b^2))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) - (4*tan(c + d*x)*(28*a*b^7 + b^8 + 70*a^2*b^6 + 28*a^3*b^5 + a^4*b^4))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) + (((4*(4*a*b^8 - 4*a^2*b^7 - 24*a^3*b^6 + 56*a^4*b^5 - 44*a^5*b^4 + 12*a^6*b^3))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2) + (4*tan(c + d*x)*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*(16*a^9*b - 16*a^2*b^8 + 112*a^3*b^7 - 336*a^4*b^6 + 560*a^5*b^5 - 560*a^6*b^4 + 336*a^7*b^3 - 112*a^8*b^2))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) + (4*tan(c + d*x)*(28*a*b^7 + b^8 + 70*a^2*b^6 + 28*a^3*b^5 + a^4*b^4))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) - (8*(a*b^6 + b^7))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2)))*((7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) + 7*a^2*b^6 + 35*a^3*b^5 + 21*a^4*b^4 + a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*2i)/d + (atan(((((4*(4*a*b^8 - 4*a^2*b^7 - 24*a^3*b^6 + 56*a^4*b^5 - 44*a^5*b^4 + 12*a^6*b^3))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2) - (4*tan(c + d*x)*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*(16*a^9*b - 16*a^2*b^8 + 112*a^3*b^7 - 336*a^4*b^6 + 560*a^5*b^5 - 560*a^6*b^4 + 336*a^7*b^3 - 112*a^8*b^2))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) - (4*tan(c + d*x)*(28*a*b^7 + b^8 + 70*a^2*b^6 + 28*a^3*b^5 + a^4*b^4))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*1i - (((4*(4*a*b^8 - 4*a^2*b^7 - 24*a^3*b^6 + 56*a^4*b^5 - 44*a^5*b^4 + 12*a^6*b^3))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2) + (4*tan(c + d*x)*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*(16*a^9*b - 16*a^2*b^8 + 112*a^3*b^7 - 336*a^4*b^6 + 560*a^5*b^5 - 560*a^6*b^4 + 336*a^7*b^3 - 112*a^8*b^2))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) + (4*tan(c + d*x)*(28*a*b^7 + b^8 + 70*a^2*b^6 + 28*a^3*b^5 + a^4*b^4))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*1i)/((((4*(4*a*b^8 - 4*a^2*b^7 - 24*a^3*b^6 + 56*a^4*b^5 - 44*a^5*b^4 + 12*a^6*b^3))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2) - (4*tan(c + d*x)*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*(16*a^9*b - 16*a^2*b^8 + 112*a^3*b^7 - 336*a^4*b^6 + 560*a^5*b^5 - 560*a^6*b^4 + 336*a^7*b^3 - 112*a^8*b^2))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) - (4*tan(c + d*x)*(28*a*b^7 + b^8 + 70*a^2*b^6 + 28*a^3*b^5 + a^4*b^4))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) + (((4*(4*a*b^8 - 4*a^2*b^7 - 24*a^3*b^6 + 56*a^4*b^5 - 44*a^5*b^4 + 12*a^6*b^3))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2) + (4*tan(c + d*x)*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*(16*a^9*b - 16*a^2*b^8 + 112*a^3*b^7 - 336*a^4*b^6 + 560*a^5*b^5 - 560*a^6*b^4 + 336*a^7*b^3 - 112*a^8*b^2))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) + (4*tan(c + d*x)*(28*a*b^7 + b^8 + 70*a^2*b^6 + 28*a^3*b^5 + a^4*b^4))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2) - (8*(a*b^6 + b^7))/(5*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2)))*(-(7*a^3*(a^3*b^7)^(1/2) + b^3*(a^3*b^7)^(1/2) - 7*a^2*b^6 - 35*a^3*b^5 - 21*a^4*b^4 - a^5*b^3 + 21*a*b^2*(a^3*b^7)^(1/2) + 35*a^2*b*(a^3*b^7)^(1/2))/(16*(7*a^9*b - a^10 + a^3*b^7 - 7*a^4*b^6 + 21*a^5*b^5 - 35*a^6*b^4 + 35*a^7*b^3 - 21*a^8*b^2)))^(1/2)*2i)/d - (tan(c + d*x)^3*((2*a)/(3*(a - b)^2) - 4/(3*(a - b))))/d + (tan(c + d*x)*(6/(a - b) - a/(a - b)^2 + (2*a*((2*a)/(a - b)^2 - 4/(a - b)))/(a - b)))/d + tan(c + d*x)^5/(5*d*(a - b))","B"
419,0,-1,26,0.000000,"\text{Not used}","int(cos(e + f*x)^m*(a + b*sin(e + f*x)^4)^p,x)","\int {\cos\left(e+f\,x\right)}^m\,{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int(cos(e + f*x)^m*(a + b*sin(e + f*x)^4)^p, x)","F"
420,0,-1,197,0.000000,"\text{Not used}","int(cos(e + f*x)^5*(a + b*sin(e + f*x)^4)^p,x)","\int {\cos\left(e+f\,x\right)}^5\,{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p \,d x","Not used",1,"int(cos(e + f*x)^5*(a + b*sin(e + f*x)^4)^p, x)","F"
421,0,-1,140,0.000000,"\text{Not used}","int(cos(e + f*x)^3*(a + b*sin(e + f*x)^4)^p,x)","\int {\cos\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p \,d x","Not used",1,"int(cos(e + f*x)^3*(a + b*sin(e + f*x)^4)^p, x)","F"
422,1,64,67,15.618568,"\text{Not used}","int(cos(e + f*x)*(a + b*sin(e + f*x)^4)^p,x)","\frac{\sin\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{4},-p;\ \frac{5}{4};\ -\frac{b\,{\sin\left(e+f\,x\right)}^4}{a}\right)}{f\,{\left(\frac{b\,{\sin\left(e+f\,x\right)}^4}{a}+1\right)}^p}","Not used",1,"(sin(e + f*x)*(a + b*sin(e + f*x)^4)^p*hypergeom([1/4, -p], 5/4, -(b*sin(e + f*x)^4)/a))/(f*((b*sin(e + f*x)^4)/a + 1)^p)","B"
423,0,-1,158,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^4)^p/cos(e + f*x),x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p}{\cos\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x)^4)^p/cos(e + f*x), x)","F"
424,0,-1,239,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^4)^p/cos(e + f*x)^3,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p}{{\cos\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(e + f*x)^4)^p/cos(e + f*x)^3, x)","F"
425,0,-1,26,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(a + b*sin(e + f*x)^4)^p,x)","\int {\cos\left(e+f\,x\right)}^4\,{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int(cos(e + f*x)^4*(a + b*sin(e + f*x)^4)^p, x)","F"
426,0,-1,26,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x)^4)^p,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int(cos(e + f*x)^2*(a + b*sin(e + f*x)^4)^p, x)","F"
427,0,-1,17,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^4)^p,x)","\int {\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int((a + b*sin(e + f*x)^4)^p, x)","F"
428,0,-1,26,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^4)^p/cos(e + f*x)^2,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p}{{\cos\left(e+f\,x\right)}^2} \,d x","Not used",0,"int((a + b*sin(e + f*x)^4)^p/cos(e + f*x)^2, x)","F"
429,0,-1,26,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^4)^p/cos(e + f*x)^4,x)","\int \frac{{\left(b\,{\sin\left(e+f\,x\right)}^4+a\right)}^p}{{\cos\left(e+f\,x\right)}^4} \,d x","Not used",0,"int((a + b*sin(e + f*x)^4)^p/cos(e + f*x)^4, x)","F"
430,0,-1,26,0.000000,"\text{Not used}","int(cos(e + f*x)^m*(a + b*sin(e + f*x)^n)^p,x)","\int {\cos\left(e+f\,x\right)}^m\,{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p \,d x","Not used",0,"int(cos(e + f*x)^m*(a + b*sin(e + f*x)^n)^p, x)","F"
431,0,-1,226,0.000000,"\text{Not used}","int(cos(e + f*x)^5*(a + b*sin(e + f*x)^n)^p,x)","\int {\cos\left(e+f\,x\right)}^5\,{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p \,d x","Not used",1,"int(cos(e + f*x)^5*(a + b*sin(e + f*x)^n)^p, x)","F"
432,0,-1,148,0.000000,"\text{Not used}","int(cos(e + f*x)^3*(a + b*sin(e + f*x)^n)^p,x)","\int {\cos\left(e+f\,x\right)}^3\,{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p \,d x","Not used",1,"int(cos(e + f*x)^3*(a + b*sin(e + f*x)^n)^p, x)","F"
433,1,70,69,15.906124,"\text{Not used}","int(cos(e + f*x)*(a + b*sin(e + f*x)^n)^p,x)","\frac{\sin\left(e+f\,x\right)\,{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{n},-p;\ \frac{1}{n}+1;\ -\frac{b\,{\sin\left(e+f\,x\right)}^n}{a}\right)}{f\,{\left(\frac{b\,{\sin\left(e+f\,x\right)}^n}{a}+1\right)}^p}","Not used",1,"(sin(e + f*x)*(a + b*sin(e + f*x)^n)^p*hypergeom([1/n, -p], 1/n + 1, -(b*sin(e + f*x)^n)/a))/(f*((b*sin(e + f*x)^n)/a + 1)^p)","B"
434,0,-1,24,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^n)^p/cos(e + f*x),x)","\int \frac{{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p}{\cos\left(e+f\,x\right)} \,d x","Not used",0,"int((a + b*sin(e + f*x)^n)^p/cos(e + f*x), x)","F"
435,0,-1,26,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^n)^p/cos(e + f*x)^3,x)","\int \frac{{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p}{{\cos\left(e+f\,x\right)}^3} \,d x","Not used",0,"int((a + b*sin(e + f*x)^n)^p/cos(e + f*x)^3, x)","F"
436,0,-1,26,0.000000,"\text{Not used}","int(cos(e + f*x)^4*(a + b*sin(e + f*x)^n)^p,x)","\int {\cos\left(e+f\,x\right)}^4\,{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p \,d x","Not used",0,"int(cos(e + f*x)^4*(a + b*sin(e + f*x)^n)^p, x)","F"
437,0,-1,26,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b*sin(e + f*x)^n)^p,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p \,d x","Not used",0,"int(cos(e + f*x)^2*(a + b*sin(e + f*x)^n)^p, x)","F"
438,0,-1,17,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^n)^p,x)","\int {\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p \,d x","Not used",0,"int((a + b*sin(e + f*x)^n)^p, x)","F"
439,0,-1,26,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^n)^p/cos(e + f*x)^2,x)","\int \frac{{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p}{{\cos\left(e+f\,x\right)}^2} \,d x","Not used",0,"int((a + b*sin(e + f*x)^n)^p/cos(e + f*x)^2, x)","F"
440,0,-1,26,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^n)^p/cos(e + f*x)^4,x)","\int \frac{{\left(a+b\,{\sin\left(e+f\,x\right)}^n\right)}^p}{{\cos\left(e+f\,x\right)}^4} \,d x","Not used",0,"int((a + b*sin(e + f*x)^n)^p/cos(e + f*x)^4, x)","F"
441,1,115,128,14.339960,"\text{Not used}","int(tan(c + d*x)^7/(a + b*sin(c + d*x)^2),x)","\frac{{\mathrm{tan}\left(c+d\,x\right)}^6}{6\,d\,\left(a+b\right)}+\frac{a^2\,{\mathrm{tan}\left(c+d\,x\right)}^2}{2\,d\,{\left(a+b\right)}^3}-\frac{a^3\,\ln\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}{d\,\left(2\,a^4+8\,a^3\,b+12\,a^2\,b^2+8\,a\,b^3+2\,b^4\right)}-\frac{a\,{\mathrm{tan}\left(c+d\,x\right)}^4}{4\,d\,{\left(a+b\right)}^2}","Not used",1,"tan(c + d*x)^6/(6*d*(a + b)) + (a^2*tan(c + d*x)^2)/(2*d*(a + b)^3) - (a^3*log(a + tan(c + d*x)^2*(a + b)))/(d*(8*a*b^3 + 8*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2)) - (a*tan(c + d*x)^4)/(4*d*(a + b)^2)","B"
442,1,90,94,14.353300,"\text{Not used}","int(tan(c + d*x)^5/(a + b*sin(c + d*x)^2),x)","\frac{a^2\,\left(\frac{\ln\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}{2}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2}{2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4}{4}\right)+\frac{b^2\,{\mathrm{tan}\left(c+d\,x\right)}^4}{4}-a\,b\,\left(\frac{{\mathrm{tan}\left(c+d\,x\right)}^2}{2}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^4}{2}\right)}{d\,{\left(a+b\right)}^3}","Not used",1,"(a^2*(log(a + tan(c + d*x)^2*(a + b))/2 - tan(c + d*x)^2/2 + tan(c + d*x)^4/4) + (b^2*tan(c + d*x)^4)/4 - a*b*(tan(c + d*x)^2/2 - tan(c + d*x)^4/2))/(d*(a + b)^3)","B"
443,1,52,64,14.281736,"\text{Not used}","int(tan(c + d*x)^3/(a + b*sin(c + d*x)^2),x)","-\frac{a\,\left(\frac{\ln\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}{2}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2}{2}\right)-\frac{b\,{\mathrm{tan}\left(c+d\,x\right)}^2}{2}}{d\,{\left(a+b\right)}^2}","Not used",1,"-(a*(log(a + tan(c + d*x)^2*(a + b))/2 - tan(c + d*x)^2/2) - (b*tan(c + d*x)^2)/2)/(d*(a + b)^2)","B"
444,1,28,43,14.506055,"\text{Not used}","int(tan(c + d*x)/(a + b*sin(c + d*x)^2),x)","\frac{\ln\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)}{d\,\left(2\,a+2\,b\right)}","Not used",1,"log(a + tan(c + d*x)^2*(a + b))/(d*(2*a + 2*b))","B"
445,1,41,38,14.429550,"\text{Not used}","int(cot(c + d*x)/(a + b*sin(c + d*x)^2),x)","-\frac{\ln\left(a+a\,{\mathrm{tan}\left(c+d\,x\right)}^2+b\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)-2\,\ln\left(\mathrm{tan}\left(c+d\,x\right)\right)}{2\,a\,d}","Not used",1,"-(log(a + a*tan(c + d*x)^2 + b*tan(c + d*x)^2) - 2*log(tan(c + d*x)))/(2*a*d)","B"
446,1,69,63,14.457117,"\text{Not used}","int(cot(c + d*x)^3/(a + b*sin(c + d*x)^2),x)","\frac{\ln\left(a+a\,{\mathrm{tan}\left(c+d\,x\right)}^2+b\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)\,\left(a+b\right)}{2\,a^2\,d}-\frac{{\mathrm{cot}\left(c+d\,x\right)}^2}{2\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(c+d\,x\right)\right)\,\left(a+b\right)}{a^2\,d}","Not used",1,"(log(a + a*tan(c + d*x)^2 + b*tan(c + d*x)^2)*(a + b))/(2*a^2*d) - cot(c + d*x)^2/(2*a*d) - (log(tan(c + d*x))*(a + b))/(a^2*d)","B"
447,1,103,89,14.504428,"\text{Not used}","int(cot(c + d*x)^5/(a + b*sin(c + d*x)^2),x)","\frac{\ln\left(\mathrm{tan}\left(c+d\,x\right)\right)\,\left(a^2+2\,a\,b+b^2\right)}{a^3\,d}-\frac{\ln\left(a+a\,{\mathrm{tan}\left(c+d\,x\right)}^2+b\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)\,\left(a^2+2\,a\,b+b^2\right)}{2\,a^3\,d}-\frac{\frac{1}{4\,a}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(a+b\right)}{2\,a^2}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^4}","Not used",1,"(log(tan(c + d*x))*(2*a*b + a^2 + b^2))/(a^3*d) - (log(a + a*tan(c + d*x)^2 + b*tan(c + d*x)^2)*(2*a*b + a^2 + b^2))/(2*a^3*d) - (1/(4*a) - (tan(c + d*x)^2*(a + b))/(2*a^2))/(d*tan(c + d*x)^4)","B"
448,1,138,121,15.350634,"\text{Not used}","int(cot(c + d*x)^7/(a + b*sin(c + d*x)^2),x)","\frac{\ln\left(a+a\,{\mathrm{tan}\left(c+d\,x\right)}^2+b\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}{2\,a^4\,d}-\frac{\frac{1}{6\,a}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(a+b\right)}{4\,a^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,{\left(a+b\right)}^2}{2\,a^3}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^6}-\frac{\ln\left(\mathrm{tan}\left(c+d\,x\right)\right)\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}{a^4\,d}","Not used",1,"(log(a + a*tan(c + d*x)^2 + b*tan(c + d*x)^2)*(3*a*b^2 + 3*a^2*b + a^3 + b^3))/(2*a^4*d) - (1/(6*a) - (tan(c + d*x)^2*(a + b))/(4*a^2) + (tan(c + d*x)^4*(a + b)^2)/(2*a^3))/(d*tan(c + d*x)^6) - (log(tan(c + d*x))*(3*a*b^2 + 3*a^2*b + a^3 + b^3))/(a^4*d)","B"
449,1,141,120,14.780008,"\text{Not used}","int(tan(c + d*x)^8/(a + b*sin(c + d*x)^2),x)","\frac{{\mathrm{tan}\left(c+d\,x\right)}^7}{7\,d\,\left(a+b\right)}+\frac{a^2\,{\mathrm{tan}\left(c+d\,x\right)}^3}{3\,d\,{\left(a+b\right)}^3}+\frac{a^{7/2}\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)\,\left(a^4+4\,a^3\,b+6\,a^2\,b^2+4\,a\,b^3+b^4\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{9/2}}\right)}{d\,{\left(a+b\right)}^{9/2}}-\frac{a\,{\mathrm{tan}\left(c+d\,x\right)}^5}{5\,d\,{\left(a+b\right)}^2}-\frac{a^3\,\mathrm{tan}\left(c+d\,x\right)}{d\,{\left(a+b\right)}^4}","Not used",1,"tan(c + d*x)^7/(7*d*(a + b)) + (a^2*tan(c + d*x)^3)/(3*d*(a + b)^3) + (a^(7/2)*atan((tan(c + d*x)*(2*a + 2*b)*(4*a*b^3 + 4*a^3*b + a^4 + b^4 + 6*a^2*b^2))/(2*a^(1/2)*(a + b)^(9/2))))/(d*(a + b)^(9/2)) - (a*tan(c + d*x)^5)/(5*d*(a + b)^2) - (a^3*tan(c + d*x))/(d*(a + b)^4)","B"
450,1,112,97,15.110342,"\text{Not used}","int(tan(c + d*x)^6/(a + b*sin(c + d*x)^2),x)","\frac{{\mathrm{tan}\left(c+d\,x\right)}^5}{5\,d\,\left(a+b\right)}-\frac{a^{5/2}\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{7/2}}\right)}{d\,{\left(a+b\right)}^{7/2}}-\frac{a\,{\mathrm{tan}\left(c+d\,x\right)}^3}{3\,d\,{\left(a+b\right)}^2}+\frac{a^2\,\mathrm{tan}\left(c+d\,x\right)}{d\,{\left(a+b\right)}^3}","Not used",1,"tan(c + d*x)^5/(5*d*(a + b)) - (a^(5/2)*atan((tan(c + d*x)*(2*a + 2*b)*(3*a*b^2 + 3*a^2*b + a^3 + b^3))/(2*a^(1/2)*(a + b)^(7/2))))/(d*(a + b)^(7/2)) - (a*tan(c + d*x)^3)/(3*d*(a + b)^2) + (a^2*tan(c + d*x))/(d*(a + b)^3)","B"
451,1,83,74,15.183552,"\text{Not used}","int(tan(c + d*x)^4/(a + b*sin(c + d*x)^2),x)","\frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{3\,d\,\left(a+b\right)}-\frac{a\,\mathrm{tan}\left(c+d\,x\right)}{d\,{\left(a+b\right)}^2}+\frac{a^{3/2}\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)\,\left(a^2+2\,a\,b+b^2\right)}{2\,\sqrt{a}\,{\left(a+b\right)}^{5/2}}\right)}{d\,{\left(a+b\right)}^{5/2}}","Not used",1,"tan(c + d*x)^3/(3*d*(a + b)) - (a*tan(c + d*x))/(d*(a + b)^2) + (a^(3/2)*atan((tan(c + d*x)*(2*a + 2*b)*(2*a*b + a^2 + b^2))/(2*a^(1/2)*(a + b)^(5/2))))/(d*(a + b)^(5/2))","B"
452,1,53,53,14.922040,"\text{Not used}","int(tan(c + d*x)^2/(a + b*sin(c + d*x)^2),x)","\frac{\mathrm{tan}\left(c+d\,x\right)}{d\,\left(a+b\right)}-\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+2\,b\right)}{2\,\sqrt{a}\,\sqrt{a+b}}\right)}{d\,{\left(a+b\right)}^{3/2}}","Not used",1,"tan(c + d*x)/(d*(a + b)) - (a^(1/2)*atan((tan(c + d*x)*(2*a + 2*b))/(2*a^(1/2)*(a + b)^(1/2))))/(d*(a + b)^(3/2))","B"
453,1,44,52,14.714502,"\text{Not used}","int(cot(c + d*x)^2/(a + b*sin(c + d*x)^2),x)","-\frac{\mathrm{cot}\left(c+d\,x\right)}{a\,d}-\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{a+b}}{\sqrt{a}}\right)\,\sqrt{a+b}}{a^{3/2}\,d}","Not used",1,"- cot(c + d*x)/(a*d) - (atan((tan(c + d*x)*(a + b)^(1/2))/a^(1/2))*(a + b)^(1/2))/(a^(3/2)*d)","B"
454,1,64,71,15.090300,"\text{Not used}","int(cot(c + d*x)^4/(a + b*sin(c + d*x)^2),x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{a+b}}{\sqrt{a}}\right)\,{\left(a+b\right)}^{3/2}}{a^{5/2}\,d}-\frac{\frac{1}{3\,a}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(a+b\right)}{a^2}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^3}","Not used",1,"(atan((tan(c + d*x)*(a + b)^(1/2))/a^(1/2))*(a + b)^(3/2))/(a^(5/2)*d) - (1/(3*a) - (tan(c + d*x)^2*(a + b))/a^2)/(d*tan(c + d*x)^3)","B"
455,1,82,96,16.149728,"\text{Not used}","int(cot(c + d*x)^6/(a + b*sin(c + d*x)^2),x)","-\frac{\frac{1}{5\,a}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(a+b\right)}{3\,a^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,{\left(a+b\right)}^2}{a^3}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^5}-\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{a+b}}{\sqrt{a}}\right)\,{\left(a+b\right)}^{5/2}}{a^{7/2}\,d}","Not used",1,"- (1/(5*a) - (tan(c + d*x)^2*(a + b))/(3*a^2) + (tan(c + d*x)^4*(a + b)^2)/a^3)/(d*tan(c + d*x)^5) - (atan((tan(c + d*x)*(a + b)^(1/2))/a^(1/2))*(a + b)^(5/2))/(a^(7/2)*d)","B"
456,1,100,117,18.907927,"\text{Not used}","int(cot(c + d*x)^8/(a + b*sin(c + d*x)^2),x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{a+b}}{\sqrt{a}}\right)\,{\left(a+b\right)}^{7/2}}{a^{9/2}\,d}-\frac{\frac{1}{7\,a}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(a+b\right)}{5\,a^2}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^4\,{\left(a+b\right)}^2}{3\,a^3}-\frac{{\mathrm{tan}\left(c+d\,x\right)}^6\,{\left(a+b\right)}^3}{a^4}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^7}","Not used",1,"(atan((tan(c + d*x)*(a + b)^(1/2))/a^(1/2))*(a + b)^(7/2))/(a^(9/2)*d) - (1/(7*a) - (tan(c + d*x)^2*(a + b))/(5*a^2) + (tan(c + d*x)^4*(a + b)^2)/(3*a^3) - (tan(c + d*x)^6*(a + b)^3)/a^4)/(d*tan(c + d*x)^7)","B"
457,1,326,64,19.711478,"\text{Not used}","int(tan(e + f*x)^5*(a - a*sin(e + f*x)^2)^(1/2),x)","-\frac{\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{f}-\frac{8\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{f\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{16\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{3\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{16\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{3\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"(16*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(3*f*(exp(e*2i + f*x*2i) + 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (8*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(f*(exp(e*2i + f*x*2i) + 1)*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)/f - (16*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(3*f*(exp(e*2i + f*x*2i) + 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
458,1,69,38,0.716443,"\text{Not used}","int(tan(e + f*x)^3*(a - a*sin(e + f*x)^2)^(1/2),x)","\frac{\sqrt{2}\,\sqrt{a\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}\,\left(8\,\cos\left(2\,e+2\,f\,x\right)+\cos\left(4\,e+4\,f\,x\right)+7\right)}{2\,f\,\left(4\,\cos\left(2\,e+2\,f\,x\right)+\cos\left(4\,e+4\,f\,x\right)+3\right)}","Not used",1,"(2^(1/2)*(a*(cos(2*e + 2*f*x) + 1))^(1/2)*(8*cos(2*e + 2*f*x) + cos(4*e + 4*f*x) + 7))/(2*f*(4*cos(2*e + 2*f*x) + cos(4*e + 4*f*x) + 3))","B"
459,1,20,19,15.251938,"\text{Not used}","int(tan(e + f*x)*(a - a*sin(e + f*x)^2)^(1/2),x)","-\frac{\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2}}{f}","Not used",1,"-(a - a*sin(e + f*x)^2)^(1/2)/f","B"
460,0,-1,50,0.000000,"\text{Not used}","int(cot(e + f*x)*(a - a*sin(e + f*x)^2)^(1/2),x)","\int \mathrm{cot}\left(e+f\,x\right)\,\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int(cot(e + f*x)*(a - a*sin(e + f*x)^2)^(1/2), x)","F"
461,0,-1,87,0.000000,"\text{Not used}","int(cot(e + f*x)^3*(a - a*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^3\,\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int(cot(e + f*x)^3*(a - a*sin(e + f*x)^2)^(1/2), x)","F"
462,0,-1,120,0.000000,"\text{Not used}","int(tan(e + f*x)^6*(a - a*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^6\,\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int(tan(e + f*x)^6*(a - a*sin(e + f*x)^2)^(1/2), x)","F"
463,0,-1,91,0.000000,"\text{Not used}","int(tan(e + f*x)^4*(a - a*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^4\,\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int(tan(e + f*x)^4*(a - a*sin(e + f*x)^2)^(1/2), x)","F"
464,0,-1,57,0.000000,"\text{Not used}","int(tan(e + f*x)^2*(a - a*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^2\,\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int(tan(e + f*x)^2*(a - a*sin(e + f*x)^2)^(1/2), x)","F"
465,1,88,57,18.528923,"\text{Not used}","int(cot(e + f*x)^2*(a - a*sin(e + f*x)^2)^(1/2),x)","\frac{\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,\left(-{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,6{}\mathrm{i}+{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}+1{}\mathrm{i}\right)}{f\,\left({\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-1\right)}","Not used",1,"((a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*(exp(e*4i + f*x*4i)*1i - exp(e*2i + f*x*2i)*6i + 1i))/(f*(exp(e*4i + f*x*4i) - 1))","B"
466,1,364,91,18.418030,"\text{Not used}","int(cot(e + f*x)^4*(a - a*sin(e + f*x)^2)^(1/2),x)","\frac{\left(\frac{1{}\mathrm{i}}{f}-\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}}{f}\right)\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,8{}\mathrm{i}}{f\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,16{}\mathrm{i}}{3\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,16{}\mathrm{i}}{3\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"((1i/f - (exp(e*2i + f*x*2i)*1i)/f)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(exp(e*2i + f*x*2i) + 1) + (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*8i)/(f*(exp(e*2i + f*x*2i) - 1)*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*16i)/(3*f*(exp(e*2i + f*x*2i) - 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*16i)/(3*f*(exp(e*2i + f*x*2i) - 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
467,1,555,124,26.642844,"\text{Not used}","int(cot(e + f*x)^6*(a - a*sin(e + f*x)^2)^(1/2),x)","-\frac{\left(\frac{1{}\mathrm{i}}{f}-\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}}{f}\right)\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,12{}\mathrm{i}}{f\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,16{}\mathrm{i}}{f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,144{}\mathrm{i}}{5\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,128{}\mathrm{i}}{5\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^4\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,64{}\mathrm{i}}{5\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^5\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"- ((1i/f - (exp(e*2i + f*x*2i)*1i)/f)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(exp(e*2i + f*x*2i) + 1) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*12i)/(f*(exp(e*2i + f*x*2i) - 1)*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*16i)/(f*(exp(e*2i + f*x*2i) - 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*144i)/(5*f*(exp(e*2i + f*x*2i) - 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*128i)/(5*f*(exp(e*2i + f*x*2i) - 1)^4*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*64i)/(5*f*(exp(e*2i + f*x*2i) - 1)^5*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
468,1,486,65,23.609963,"\text{Not used}","int(tan(e + f*x)^5/(a - a*sin(e + f*x)^2)^(1/2),x)","\frac{4\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{a\,f\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{32\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{3\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{352\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{15\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{128\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{5\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^4\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{64\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{5\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^5\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"(4*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(a*f*(exp(e*2i + f*x*2i) + 1)*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (32*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(3*a*f*(exp(e*2i + f*x*2i) + 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (352*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(15*a*f*(exp(e*2i + f*x*2i) + 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (128*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(5*a*f*(exp(e*2i + f*x*2i) + 1)^4*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (64*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(5*a*f*(exp(e*2i + f*x*2i) + 1)^5*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
469,1,100,42,19.496581,"\text{Not used}","int(tan(e + f*x)^3/(a - a*sin(e + f*x)^2)^(1/2),x)","-\frac{4\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,\left(2\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+3\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}+3\right)}{3\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^4}","Not used",1,"-(4*exp(e*2i + f*x*2i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*(2*exp(e*2i + f*x*2i) + 3*exp(e*4i + f*x*4i) + 3))/(3*a*f*(exp(e*2i + f*x*2i) + 1)^4)","B"
470,1,61,18,0.390078,"\text{Not used}","int(tan(e + f*x)/(a - a*sin(e + f*x)^2)^(1/2),x)","\frac{2\,\sqrt{2}\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)\,\sqrt{a\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}}{a\,f\,\left(4\,\cos\left(2\,e+2\,f\,x\right)+\cos\left(4\,e+4\,f\,x\right)+3\right)}","Not used",1,"(2*2^(1/2)*(cos(2*e + 2*f*x) + 1)*(a*(cos(2*e + 2*f*x) + 1))^(1/2))/(a*f*(4*cos(2*e + 2*f*x) + cos(4*e + 4*f*x) + 3))","B"
471,0,-1,31,0.000000,"\text{Not used}","int(cot(e + f*x)/(a - a*sin(e + f*x)^2)^(1/2),x)","\int \frac{\mathrm{cot}\left(e+f\,x\right)}{\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2}} \,d x","Not used",1,"int(cot(e + f*x)/(a - a*sin(e + f*x)^2)^(1/2), x)","F"
472,0,-1,66,0.000000,"\text{Not used}","int(cot(e + f*x)^3/(a - a*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^3}{\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2}} \,d x","Not used",1,"int(cot(e + f*x)^3/(a - a*sin(e + f*x)^2)^(1/2), x)","F"
473,0,-1,91,0.000000,"\text{Not used}","int(tan(e + f*x)^4/(a - a*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^4}{\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2}} \,d x","Not used",1,"int(tan(e + f*x)^4/(a - a*sin(e + f*x)^2)^(1/2), x)","F"
474,0,-1,62,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a - a*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{\sqrt{a-a\,{\sin\left(e+f\,x\right)}^2}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a - a*sin(e + f*x)^2)^(1/2), x)","F"
475,1,37,25,15.062943,"\text{Not used}","int(cot(e + f*x)^2/(a - a*sin(e + f*x)^2)^(1/2),x)","-\frac{\sqrt{2\,a\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}}{a\,f\,\sin\left(2\,e+2\,f\,x\right)}","Not used",1,"-(2*a*(cos(2*e + 2*f*x) + 1))^(1/2)/(a*f*sin(2*e + 2*f*x))","B"
476,1,118,60,19.187339,"\text{Not used}","int(cot(e + f*x)^4/(a - a*sin(e + f*x)^2)^(1/2),x)","\frac{4\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,\left(-{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,2{}\mathrm{i}+{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,3{}\mathrm{i}+3{}\mathrm{i}\right)}{3\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^3\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"(4*exp(e*2i + f*x*2i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*(exp(e*4i + f*x*4i)*3i - exp(e*2i + f*x*2i)*2i + 3i))/(3*a*f*(exp(e*2i + f*x*2i) - 1)^3*(exp(e*2i + f*x*2i) + 1))","B"
477,1,491,96,22.469594,"\text{Not used}","int(cot(e + f*x)^6/(a - a*sin(e + f*x)^2)^(1/2),x)","-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,4{}\mathrm{i}}{a\,f\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,32{}\mathrm{i}}{3\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,352{}\mathrm{i}}{15\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,128{}\mathrm{i}}{5\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^4\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,64{}\mathrm{i}}{5\,a\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^5\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"- (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*4i)/(a*f*(exp(e*2i + f*x*2i) - 1)*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*32i)/(3*a*f*(exp(e*2i + f*x*2i) - 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*352i)/(15*a*f*(exp(e*2i + f*x*2i) - 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*128i)/(5*a*f*(exp(e*2i + f*x*2i) - 1)^4*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*64i)/(5*a*f*(exp(e*2i + f*x*2i) - 1)^5*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
478,1,583,68,33.909211,"\text{Not used}","int(tan(e + f*x)^5/(a - a*sin(e + f*x)^2)^(3/2),x)","\frac{16\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{3\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{464\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{15\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{3072\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{35\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^4\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{4736\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{35\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^5\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{768\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{7\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^6\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{256\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{7\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^7\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"(16*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(3*a^2*f*(exp(e*2i + f*x*2i) + 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (464*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(15*a^2*f*(exp(e*2i + f*x*2i) + 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (3072*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(35*a^2*f*(exp(e*2i + f*x*2i) + 1)^4*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (4736*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(35*a^2*f*(exp(e*2i + f*x*2i) + 1)^5*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (768*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(7*a^2*f*(exp(e*2i + f*x*2i) + 1)^6*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (256*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(7*a^2*f*(exp(e*2i + f*x*2i) + 1)^7*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
479,1,389,44,20.209049,"\text{Not used}","int(tan(e + f*x)^3/(a - a*sin(e + f*x)^2)^(3/2),x)","-\frac{16\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{3\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{272\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{15\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{128\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{5\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^4\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{64\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{5\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^5\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"(272*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(15*a^2*f*(exp(e*2i + f*x*2i) + 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (16*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(3*a^2*f*(exp(e*2i + f*x*2i) + 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (128*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(5*a^2*f*(exp(e*2i + f*x*2i) + 1)^4*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (64*exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(5*a^2*f*(exp(e*2i + f*x*2i) + 1)^5*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
480,1,72,21,18.310252,"\text{Not used}","int(tan(e + f*x)/(a - a*sin(e + f*x)^2)^(3/2),x)","\frac{16\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}}{3\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}^4}","Not used",1,"(16*exp(e*4i + f*x*4i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2))/(3*a^2*f*(exp(e*2i + f*x*2i) + 1)^4)","B"
481,0,-1,53,0.000000,"\text{Not used}","int(cot(e + f*x)/(a - a*sin(e + f*x)^2)^(3/2),x)","\int \frac{\mathrm{cot}\left(e+f\,x\right)}{{\left(a-a\,{\sin\left(e+f\,x\right)}^2\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)/(a - a*sin(e + f*x)^2)^(3/2), x)","F"
482,0,-1,66,0.000000,"\text{Not used}","int(cot(e + f*x)^3/(a - a*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^3}{{\left(a-a\,{\sin\left(e+f\,x\right)}^2\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)^3/(a - a*sin(e + f*x)^2)^(3/2), x)","F"
483,0,-1,106,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a - a*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{{\left(a-a\,{\sin\left(e+f\,x\right)}^2\right)}^{3/2}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a - a*sin(e + f*x)^2)^(3/2), x)","F"
484,0,-1,63,0.000000,"\text{Not used}","int(cot(e + f*x)^2/(a - a*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^2}{{\left(a-a\,{\sin\left(e+f\,x\right)}^2\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)^2/(a - a*sin(e + f*x)^2)^(3/2), x)","F"
485,1,88,38,18.686740,"\text{Not used}","int(cot(e + f*x)^4/(a - a*sin(e + f*x)^2)^(3/2),x)","\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,16{}\mathrm{i}}{3\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^3\,\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"(exp(e*4i + f*x*4i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*16i)/(3*a^2*f*(exp(e*2i + f*x*2i) - 1)^3*(exp(e*2i + f*x*2i) + 1))","B"
486,1,393,77,20.606387,"\text{Not used}","int(cot(e + f*x)^6/(a - a*sin(e + f*x)^2)^(3/2),x)","-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,16{}\mathrm{i}}{3\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,272{}\mathrm{i}}{15\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,128{}\mathrm{i}}{5\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^4\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,64{}\mathrm{i}}{5\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^5\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"- (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*16i)/(3*a^2*f*(exp(e*2i + f*x*2i) - 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*272i)/(15*a^2*f*(exp(e*2i + f*x*2i) - 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*128i)/(5*a^2*f*(exp(e*2i + f*x*2i) - 1)^4*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) - (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*64i)/(5*a^2*f*(exp(e*2i + f*x*2i) - 1)^5*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
487,1,589,115,33.013682,"\text{Not used}","int(cot(e + f*x)^8/(a - a*sin(e + f*x)^2)^(3/2),x)","\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,16{}\mathrm{i}}{3\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^2\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,464{}\mathrm{i}}{15\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^3\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,3072{}\mathrm{i}}{35\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^4\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,4736{}\mathrm{i}}{35\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^5\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,768{}\mathrm{i}}{7\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^6\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a-a\,{\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}^2}\,256{}\mathrm{i}}{7\,a^2\,f\,{\left({\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}-1\right)}^7\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\right)}","Not used",1,"(exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*16i)/(3*a^2*f*(exp(e*2i + f*x*2i) - 1)^2*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*464i)/(15*a^2*f*(exp(e*2i + f*x*2i) - 1)^3*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*3072i)/(35*a^2*f*(exp(e*2i + f*x*2i) - 1)^4*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*4736i)/(35*a^2*f*(exp(e*2i + f*x*2i) - 1)^5*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*768i)/(7*a^2*f*(exp(e*2i + f*x*2i) - 1)^6*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i))) + (exp(e*3i + f*x*3i)*(a - a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2)^2)^(1/2)*256i)/(7*a^2*f*(exp(e*2i + f*x*2i) - 1)^7*(exp(e*1i + f*x*1i) + exp(e*3i + f*x*3i)))","B"
488,0,-1,177,0.000000,"\text{Not used}","int(tan(e + f*x)^5*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^5\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(tan(e + f*x)^5*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
489,0,-1,118,0.000000,"\text{Not used}","int(tan(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^3\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(tan(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
490,0,-1,58,0.000000,"\text{Not used}","int(tan(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2),x)","\int \mathrm{tan}\left(e+f\,x\right)\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(tan(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
491,0,-1,54,0.000000,"\text{Not used}","int(cot(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2),x)","\int \mathrm{cot}\left(e+f\,x\right)\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(cot(e + f*x)*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
492,0,-1,110,0.000000,"\text{Not used}","int(cot(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^3\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(cot(e + f*x)^3*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
493,0,-1,165,0.000000,"\text{Not used}","int(cot(e + f*x)^5*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^5\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(cot(e + f*x)^5*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
494,0,-1,234,0.000000,"\text{Not used}","int(tan(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^4\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(tan(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
495,0,-1,171,0.000000,"\text{Not used}","int(tan(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^2\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(tan(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
496,0,-1,51,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(1/2),x)","\left\{\begin{array}{cl} \frac{\sqrt{a}\,\mathrm{E}\left(e+f\,x\middle|-\frac{b}{a}\right)}{f} & \text{\ if\ \ }0<a\\ \int \sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x & \text{\ if\ \ }\neg 0<a \end{array}\right.","Not used",1,"piecewise(0 < a, (a^(1/2)*ellipticE(e + f*x, -b/a))/f, ~0 < a, int((a + b*sin(e + f*x)^2)^(1/2), x))","F"
497,0,-1,174,0.000000,"\text{Not used}","int(cot(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^2\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(cot(e + f*x)^2*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
498,0,-1,232,0.000000,"\text{Not used}","int(cot(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^4\,\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a} \,d x","Not used",1,"int(cot(e + f*x)^4*(a + b*sin(e + f*x)^2)^(1/2), x)","F"
499,0,-1,220,0.000000,"\text{Not used}","int(tan(e + f*x)^5*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^5\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(tan(e + f*x)^5*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
500,0,-1,148,0.000000,"\text{Not used}","int(tan(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(tan(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
501,0,-1,84,0.000000,"\text{Not used}","int(tan(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2),x)","\int \mathrm{tan}\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(tan(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
502,0,-1,78,0.000000,"\text{Not used}","int(cot(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2),x)","\int \mathrm{cot}\left(e+f\,x\right)\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cot(e + f*x)*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
503,0,-1,140,0.000000,"\text{Not used}","int(cot(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^3\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cot(e + f*x)^3*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
504,0,-1,208,0.000000,"\text{Not used}","int(cot(e + f*x)^5*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^5\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cot(e + f*x)^5*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
505,0,-1,275,0.000000,"\text{Not used}","int(tan(e + f*x)^4*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^4\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(tan(e + f*x)^4*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
506,0,-1,222,0.000000,"\text{Not used}","int(tan(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(tan(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
507,0,-1,154,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)^(3/2),x)","\int {\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)^(3/2), x)","F"
508,0,-1,223,0.000000,"\text{Not used}","int(cot(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^2\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cot(e + f*x)^2*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
509,0,-1,276,0.000000,"\text{Not used}","int(cot(e + f*x)^4*(a + b*sin(e + f*x)^2)^(3/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^4\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cot(e + f*x)^4*(a + b*sin(e + f*x)^2)^(3/2), x)","F"
510,0,-1,134,0.000000,"\text{Not used}","int(tan(e + f*x)^5/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^5}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(tan(e + f*x)^5/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
511,0,-1,81,0.000000,"\text{Not used}","int(tan(e + f*x)^3/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^3}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(tan(e + f*x)^3/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
512,0,-1,36,0.000000,"\text{Not used}","int(tan(e + f*x)/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{\mathrm{tan}\left(e+f\,x\right)}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(tan(e + f*x)/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
513,0,-1,33,0.000000,"\text{Not used}","int(cot(e + f*x)/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{\mathrm{cot}\left(e+f\,x\right)}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(cot(e + f*x)/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
514,0,-1,75,0.000000,"\text{Not used}","int(cot(e + f*x)^3/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^3}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(cot(e + f*x)^3/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
515,0,-1,126,0.000000,"\text{Not used}","int(cot(e + f*x)^5/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^5}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(cot(e + f*x)^5/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
516,0,-1,246,0.000000,"\text{Not used}","int(tan(e + f*x)^4/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^4}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(tan(e + f*x)^4/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
517,0,-1,109,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
518,0,-1,51,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{1}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
519,0,-1,106,0.000000,"\text{Not used}","int(cot(e + f*x)^2/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^2}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(cot(e + f*x)^2/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
520,0,-1,240,0.000000,"\text{Not used}","int(cot(e + f*x)^4/(a + b*sin(e + f*x)^2)^(1/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^4}{\sqrt{b\,{\sin\left(e+f\,x\right)}^2+a}} \,d x","Not used",1,"int(cot(e + f*x)^4/(a + b*sin(e + f*x)^2)^(1/2), x)","F"
521,0,-1,177,0.000000,"\text{Not used}","int(tan(e + f*x)^5/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^5}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(tan(e + f*x)^5/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
522,0,-1,118,0.000000,"\text{Not used}","int(tan(e + f*x)^3/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^3}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(tan(e + f*x)^3/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
523,0,-1,63,0.000000,"\text{Not used}","int(tan(e + f*x)/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{\mathrm{tan}\left(e+f\,x\right)}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(tan(e + f*x)/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
524,0,-1,57,0.000000,"\text{Not used}","int(cot(e + f*x)/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{\mathrm{cot}\left(e+f\,x\right)}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
525,0,-1,110,0.000000,"\text{Not used}","int(cot(e + f*x)^3/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^3}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)^3/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
526,-1,-1,167,0.000000,"\text{Not used}","int(cot(e + f*x)^5/(a + b*sin(e + f*x)^2)^(3/2),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
527,0,-1,292,0.000000,"\text{Not used}","int(tan(e + f*x)^4/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^4}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(tan(e + f*x)^4/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
528,0,-1,224,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
529,0,-1,101,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{1}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
530,0,-1,209,0.000000,"\text{Not used}","int(cot(e + f*x)^2/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^2}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)^2/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
531,0,-1,297,0.000000,"\text{Not used}","int(cot(e + f*x)^4/(a + b*sin(e + f*x)^2)^(3/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^4}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)^4/(a + b*sin(e + f*x)^2)^(3/2), x)","F"
532,-1,-1,218,0.000000,"\text{Not used}","int(tan(e + f*x)^5/(a + b*sin(e + f*x)^2)^(5/2),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
533,0,-1,153,0.000000,"\text{Not used}","int(tan(e + f*x)^3/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^3}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(tan(e + f*x)^3/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
534,0,-1,91,0.000000,"\text{Not used}","int(tan(e + f*x)/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{\mathrm{tan}\left(e+f\,x\right)}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(tan(e + f*x)/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
535,0,-1,83,0.000000,"\text{Not used}","int(cot(e + f*x)/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{\mathrm{cot}\left(e+f\,x\right)}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cot(e + f*x)/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
536,0,-1,143,0.000000,"\text{Not used}","int(cot(e + f*x)^3/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^3}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cot(e + f*x)^3/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
537,-1,-1,208,0.000000,"\text{Not used}","int(cot(e + f*x)^5/(a + b*sin(e + f*x)^2)^(5/2),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
538,0,-1,348,0.000000,"\text{Not used}","int(tan(e + f*x)^4/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^4}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(tan(e + f*x)^4/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
539,0,-1,292,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
540,0,-1,223,0.000000,"\text{Not used}","int(1/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{1}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
541,0,-1,287,0.000000,"\text{Not used}","int(cot(e + f*x)^2/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^2}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cot(e + f*x)^2/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
542,0,-1,348,0.000000,"\text{Not used}","int(cot(e + f*x)^4/(a + b*sin(e + f*x)^2)^(5/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^4}{{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cot(e + f*x)^4/(a + b*sin(e + f*x)^2)^(5/2), x)","F"
543,0,-1,120,0.000000,"\text{Not used}","int((d*tan(e + f*x))^m*(a + b*sin(e + f*x)^2)^p,x)","\int {\left(d\,\mathrm{tan}\left(e+f\,x\right)\right)}^m\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int((d*tan(e + f*x))^m*(a + b*sin(e + f*x)^2)^p, x)","F"
544,0,-1,102,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + b*sin(c + d*x)^2)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^3\,{\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(tan(c + d*x)^3*(a + b*sin(c + d*x)^2)^p, x)","F"
545,0,-1,59,0.000000,"\text{Not used}","int(tan(c + d*x)*(a + b*sin(c + d*x)^2)^p,x)","\int \mathrm{tan}\left(c+d\,x\right)\,{\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(tan(c + d*x)*(a + b*sin(c + d*x)^2)^p, x)","F"
546,0,-1,54,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + b*sin(c + d*x)^2)^p,x)","\int \mathrm{cot}\left(c+d\,x\right)\,{\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(cot(c + d*x)*(a + b*sin(c + d*x)^2)^p, x)","F"
547,0,-1,95,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + b*sin(c + d*x)^2)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^3\,{\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(cot(c + d*x)^3*(a + b*sin(c + d*x)^2)^p, x)","F"
548,0,-1,101,0.000000,"\text{Not used}","int(tan(c + d*x)^4*(a + b*sin(c + d*x)^2)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^4\,{\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(tan(c + d*x)^4*(a + b*sin(c + d*x)^2)^p, x)","F"
549,0,-1,101,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + b*sin(c + d*x)^2)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^2\,{\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(tan(c + d*x)^2*(a + b*sin(c + d*x)^2)^p, x)","F"
550,0,-1,97,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + b*sin(c + d*x)^2)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^2\,{\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(cot(c + d*x)^2*(a + b*sin(c + d*x)^2)^p, x)","F"
551,0,-1,101,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x)^2)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,{\left(b\,{\sin\left(c+d\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int(cot(c + d*x)^4*(a + b*sin(c + d*x)^2)^p, x)","F"
552,1,2003,153,17.542349,"\text{Not used}","int(cot(x)^3/(a + b*sin(x)^3),x)","\left(\sum _{k=1}^3\ln\left(-\frac{\left(64\,b^7\,\mathrm{tan}\left(\frac{x}{2}\right)+32\,a\,b^6-44\,a^3\,b^4+15\,a^5\,b^2-\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,b^8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,1024-84\,a^2\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)+26\,a^4\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)+48\,a\,b^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a^2\,b^6\,16+\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a^4\,b^4\,328-\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a^6\,b^2\,165-70\,a^3\,b^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+25\,a^5\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^3\,b^6\,48-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^5\,b^4\,915+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^7\,b^2\,630+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^3\,a^6\,b^4\,873-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^3\,a^8\,b^2\,810+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^4\,a^7\,b^4\,864-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^4\,a^9\,b^2\,405-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^5\,a^8\,b^4\,1296+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^5\,a^{10}\,b^2\,1215-\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a\,b^7\,\mathrm{tan}\left(\frac{x}{2}\right)\,608-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^3\,b^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,8880+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^5\,b^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,5067+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^7\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,1050+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^3\,a^4\,b^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,27648-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^3\,a^6\,b^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,15543-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^3\,a^8\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,1350-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^4\,a^5\,b^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,27648+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^4\,a^7\,b^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,10800-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^4\,a^9\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,675+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^5\,a^8\,b^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,9072+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^5\,a^{10}\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,2025+\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a^3\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,1566-\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a^5\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,610+\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a^2\,b^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,1760-\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a^4\,b^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,260-\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\,a^6\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,275+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^2\,b^7\,\mathrm{tan}\left(\frac{x}{2}\right)\,1536-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^4\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,9870+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^2\,a^6\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,5238+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^3\,a^5\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,31968-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^3\,a^7\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,21150-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^4\,a^6\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,57888+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^4\,a^8\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,40824+{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^5\,a^7\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,41472-{\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)}^5\,a^9\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,30456\right)\,256}{a^3}\right)\,\mathrm{root}\left(27\,a^5\,e^3-27\,a^4\,e^2+9\,a^3\,e-a^2+b^2,e,k\right)\right)-\frac{1}{8\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}","Not used",1,"symsum(log(-(256*(64*b^7*tan(x/2) + 32*a*b^6 - 44*a^3*b^4 + 15*a^5*b^2 - 1024*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*b^8*tan(x/2)^2 - 84*a^2*b^5*tan(x/2) + 26*a^4*b^3*tan(x/2) + 48*a*b^6*tan(x/2)^2 - 16*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a^2*b^6 + 328*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a^4*b^4 - 165*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a^6*b^2 - 70*a^3*b^4*tan(x/2)^2 + 25*a^5*b^2*tan(x/2)^2 - 48*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^3*b^6 - 915*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^5*b^4 + 630*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^7*b^2 + 873*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^3*a^6*b^4 - 810*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^3*a^8*b^2 + 864*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^4*a^7*b^4 - 405*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^4*a^9*b^2 - 1296*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^5*a^8*b^4 + 1215*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^5*a^10*b^2 - 608*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a*b^7*tan(x/2) - 8880*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^3*b^6*tan(x/2)^2 + 5067*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^5*b^4*tan(x/2)^2 + 1050*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^7*b^2*tan(x/2)^2 + 27648*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^3*a^4*b^6*tan(x/2)^2 - 15543*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^3*a^6*b^4*tan(x/2)^2 - 1350*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^3*a^8*b^2*tan(x/2)^2 - 27648*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^4*a^5*b^6*tan(x/2)^2 + 10800*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^4*a^7*b^4*tan(x/2)^2 - 675*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^4*a^9*b^2*tan(x/2)^2 + 9072*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^5*a^8*b^4*tan(x/2)^2 + 2025*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^5*a^10*b^2*tan(x/2)^2 + 1566*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a^3*b^5*tan(x/2) - 610*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a^5*b^3*tan(x/2) + 1760*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a^2*b^6*tan(x/2)^2 - 260*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a^4*b^4*tan(x/2)^2 - 275*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)*a^6*b^2*tan(x/2)^2 + 1536*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^2*b^7*tan(x/2) - 9870*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^4*b^5*tan(x/2) + 5238*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^2*a^6*b^3*tan(x/2) + 31968*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^3*a^5*b^5*tan(x/2) - 21150*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^3*a^7*b^3*tan(x/2) - 57888*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^4*a^6*b^5*tan(x/2) + 40824*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^4*a^8*b^3*tan(x/2) + 41472*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^5*a^7*b^5*tan(x/2) - 30456*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k)^5*a^9*b^3*tan(x/2)))/a^3)*root(27*a^5*e^3 - 27*a^4*e^2 + 9*a^3*e - a^2 + b^2, e, k), k, 1, 3) - 1/(8*a*tan(x/2)^2) - tan(x/2)^2/(8*a) - log(tan(x/2))/a","B"
553,0,-1,45,0.000000,"\text{Not used}","int(cot(x)*(a + b*sin(x)^3)^(1/2),x)","\int \mathrm{cot}\left(x\right)\,\sqrt{b\,{\sin\left(x\right)}^3+a} \,d x","Not used",1,"int(cot(x)*(a + b*sin(x)^3)^(1/2), x)","F"
554,0,-1,28,0.000000,"\text{Not used}","int(cot(x)/(a + b*sin(x)^3)^(1/2),x)","\int \frac{\mathrm{cot}\left(x\right)}{\sqrt{b\,{\sin\left(x\right)}^3+a}} \,d x","Not used",1,"int(cot(x)/(a + b*sin(x)^3)^(1/2), x)","F"
555,0,-1,59,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + b*sin(c + d*x)^4)^(1/2),x)","\int \mathrm{cot}\left(c+d\,x\right)\,\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a} \,d x","Not used",1,"int(cot(c + d*x)*(a + b*sin(c + d*x)^4)^(1/2), x)","F"
556,0,-1,89,0.000000,"\text{Not used}","int(tan(c + d*x)^3/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(tan(c + d*x)^3/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
557,0,-1,51,0.000000,"\text{Not used}","int(tan(c + d*x)/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{\mathrm{tan}\left(c+d\,x\right)}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(tan(c + d*x)/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
558,0,-1,35,0.000000,"\text{Not used}","int(cot(c + d*x)/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{\mathrm{cot}\left(c+d\,x\right)}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(cot(c + d*x)/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
559,0,-1,70,0.000000,"\text{Not used}","int(cot(c + d*x)^3/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^3}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(cot(c + d*x)^3/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
560,0,-1,108,0.000000,"\text{Not used}","int(cot(c + d*x)^5/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^5}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(cot(c + d*x)^5/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
561,0,-1,411,0.000000,"\text{Not used}","int(tan(c + d*x)^2/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^2}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(tan(c + d*x)^2/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
562,0,-1,162,0.000000,"\text{Not used}","int(1/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{1}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(1/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
563,0,-1,477,0.000000,"\text{Not used}","int(cot(c + d*x)^2/(a + b*sin(c + d*x)^4)^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^2}{\sqrt{b\,{\sin\left(c+d\,x\right)}^4+a}} \,d x","Not used",1,"int(cot(c + d*x)^2/(a + b*sin(c + d*x)^4)^(1/2), x)","F"
564,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^m*(a + b*sin(c + d*x)^4)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^m\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int(tan(c + d*x)^m*(a + b*sin(c + d*x)^4)^p, x)","F"
565,0,-1,279,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + b*sin(c + d*x)^4)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^3\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",1,"int(tan(c + d*x)^3*(a + b*sin(c + d*x)^4)^p, x)","F"
566,0,-1,141,0.000000,"\text{Not used}","int(tan(c + d*x)*(a + b*sin(c + d*x)^4)^p,x)","\int \mathrm{tan}\left(c+d\,x\right)\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",1,"int(tan(c + d*x)*(a + b*sin(c + d*x)^4)^p, x)","F"
567,0,-1,54,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + b*sin(c + d*x)^4)^p,x)","\int \mathrm{cot}\left(c+d\,x\right)\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",1,"int(cot(c + d*x)*(a + b*sin(c + d*x)^4)^p, x)","F"
568,0,-1,127,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + b*sin(c + d*x)^4)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^3\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",1,"int(cot(c + d*x)^3*(a + b*sin(c + d*x)^4)^p, x)","F"
569,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^4*(a + b*sin(c + d*x)^4)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^4\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int(tan(c + d*x)^4*(a + b*sin(c + d*x)^4)^p, x)","F"
570,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + b*sin(c + d*x)^4)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^2\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int(tan(c + d*x)^2*(a + b*sin(c + d*x)^4)^p, x)","F"
571,0,-1,17,0.000000,"\text{Not used}","int((a + b*sin(c + d*x)^4)^p,x)","\int {\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int((a + b*sin(c + d*x)^4)^p, x)","F"
572,0,-1,26,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + b*sin(c + d*x)^4)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^2\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int(cot(c + d*x)^2*(a + b*sin(c + d*x)^4)^p, x)","F"
573,0,-1,26,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x)^4)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,{\left(b\,{\sin\left(c+d\,x\right)}^4+a\right)}^p \,d x","Not used",0,"int(cot(c + d*x)^4*(a + b*sin(c + d*x)^4)^p, x)","F"
574,0,-1,306,0.000000,"\text{Not used}","int(tan(c + d*x)^m*(a + b*sin(c + d*x)^n)^3,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^m\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^3 \,d x","Not used",1,"int(tan(c + d*x)^m*(a + b*sin(c + d*x)^n)^3, x)","F"
575,0,-1,215,0.000000,"\text{Not used}","int(tan(c + d*x)^m*(a + b*sin(c + d*x)^n)^2,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^m\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^2 \,d x","Not used",1,"int(tan(c + d*x)^m*(a + b*sin(c + d*x)^n)^2, x)","F"
576,0,-1,124,0.000000,"\text{Not used}","int(tan(c + d*x)^m*(a + b*sin(c + d*x)^n),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^m\,\left(a+b\,{\sin\left(c+d\,x\right)}^n\right) \,d x","Not used",1,"int(tan(c + d*x)^m*(a + b*sin(c + d*x)^n), x)","F"
577,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^m/(a + b*sin(c + d*x)^n),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^m}{a+b\,{\sin\left(c+d\,x\right)}^n} \,d x","Not used",0,"int(tan(c + d*x)^m/(a + b*sin(c + d*x)^n), x)","F"
578,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^m/(a + b*sin(c + d*x)^n)^2,x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^m}{{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^2} \,d x","Not used",0,"int(tan(c + d*x)^m/(a + b*sin(c + d*x)^n)^2, x)","F"
579,0,-1,47,0.000000,"\text{Not used}","int(cot(x)*(a + b*sin(x)^n)^(1/2),x)","\int \mathrm{cot}\left(x\right)\,\sqrt{a+b\,{\sin\left(x\right)}^n} \,d x","Not used",1,"int(cot(x)*(a + b*sin(x)^n)^(1/2), x)","F"
580,0,-1,29,0.000000,"\text{Not used}","int(cot(x)/(a + b*sin(x)^n)^(1/2),x)","\int \frac{\mathrm{cot}\left(x\right)}{\sqrt{a+b\,{\sin\left(x\right)}^n}} \,d x","Not used",1,"int(cot(x)/(a + b*sin(x)^n)^(1/2), x)","F"
581,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^m*(a + b*sin(c + d*x)^n)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^m\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",0,"int(tan(c + d*x)^m*(a + b*sin(c + d*x)^n)^p, x)","F"
582,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + b*sin(c + d*x)^n)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^3\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",0,"int(tan(c + d*x)^3*(a + b*sin(c + d*x)^n)^p, x)","F"
583,0,-1,24,0.000000,"\text{Not used}","int(tan(c + d*x)*(a + b*sin(c + d*x)^n)^p,x)","\int \mathrm{tan}\left(c+d\,x\right)\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",0,"int(tan(c + d*x)*(a + b*sin(c + d*x)^n)^p, x)","F"
584,0,-1,55,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + b*sin(c + d*x)^n)^p,x)","\int \mathrm{cot}\left(c+d\,x\right)\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",1,"int(cot(c + d*x)*(a + b*sin(c + d*x)^n)^p, x)","F"
585,0,-1,136,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + b*sin(c + d*x)^n)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^3\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",1,"int(cot(c + d*x)^3*(a + b*sin(c + d*x)^n)^p, x)","F"
586,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^4*(a + b*sin(c + d*x)^n)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^4\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",0,"int(tan(c + d*x)^4*(a + b*sin(c + d*x)^n)^p, x)","F"
587,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + b*sin(c + d*x)^n)^p,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^2\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",0,"int(tan(c + d*x)^2*(a + b*sin(c + d*x)^n)^p, x)","F"
588,0,-1,17,0.000000,"\text{Not used}","int((a + b*sin(c + d*x)^n)^p,x)","\int {\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",0,"int((a + b*sin(c + d*x)^n)^p, x)","F"
589,0,-1,26,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + b*sin(c + d*x)^n)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^2\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",0,"int(cot(c + d*x)^2*(a + b*sin(c + d*x)^n)^p, x)","F"
590,0,-1,26,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x)^n)^p,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,{\left(a+b\,{\sin\left(c+d\,x\right)}^n\right)}^p \,d x","Not used",0,"int(cot(c + d*x)^4*(a + b*sin(c + d*x)^n)^p, x)","F"
591,0,-1,107,0.000000,"\text{Not used}","int((a + b*sin(e + f*x)^2)/((g*cos(e + f*x))^(5/2)*(d*sin(e + f*x))^(1/2)),x)","\int \frac{b\,{\sin\left(e+f\,x\right)}^2+a}{{\left(g\,\cos\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x)^2)/((g*cos(e + f*x))^(5/2)*(d*sin(e + f*x))^(1/2)), x)","F"
592,0,-1,137,0.000000,"\text{Not used}","int((c*cos(e + f*x))^m*(d*sin(e + f*x))^n*(a + b*sin(e + f*x)^2)^p,x)","\int {\left(c\,\cos\left(e+f\,x\right)\right)}^m\,{\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(b\,{\sin\left(e+f\,x\right)}^2+a\right)}^p \,d x","Not used",1,"int((c*cos(e + f*x))^m*(d*sin(e + f*x))^n*(a + b*sin(e + f*x)^2)^p, x)","F"
593,0,-1,79,0.000000,"\text{Not used}","int((a + (c*cos(e + f*x) + b*sin(e + f*x))^2)^(1/2),x)","\int \sqrt{a+{\left(c\,\cos\left(e+f\,x\right)+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((a + (c*cos(e + f*x) + b*sin(e + f*x))^2)^(1/2), x)","F"
594,0,-1,79,0.000000,"\text{Not used}","int(1/(a + (c*cos(e + f*x) + b*sin(e + f*x))^2)^(1/2),x)","\int \frac{1}{\sqrt{a+{\left(c\,\cos\left(e+f\,x\right)+b\,\sin\left(e+f\,x\right)\right)}^2}} \,d x","Not used",1,"int(1/(a + (c*cos(e + f*x) + b*sin(e + f*x))^2)^(1/2), x)","F"